Detecting and Classifying Low Probability of Intercept Radar

Detecting and Classifying Low Probability of Intercept Radar Second Edition DISCLAIMER OF WARRANTY The technical desc...

Author: Philip E. Pace

115 downloads 1556 Views 30MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!

Report copyright / DMCA form

DOWNLOAD PDF

Detecting and Classifying Low Probability of Intercept Radar Second Edition

DISCLAIMER OF WARRANTY The technical descriptions, procedures, and computer programs in this book have been developed with the greatest of care and they have been useful to the author in a broad range of applications; however, they are provided as is, without warranty of any kind. Artech House, Inc. and the author and editors of the book titled Detecting and Classifying Low Probability of Intercept Radar, Second Edition make no warranties, expressed or implied, that the equations, programs, and procedures in this book or its associated software are free of error, or are consistent with any particular standard of merchantability, or will meet your requirements for any particular application. They should not be relied upon for solving a problem whose incorrect solution could result in injury to a person or loss of property. Any use of the programs or procedures in such a manner is at the user’s own risk. The editors, author, and publisher disclaim all liability for direct, incidental, or consequent damages resulting from use of the programs or procedures in this book or the associated software.

For a listing of recent titles in the Artech House Radar Library, turn to the back of this book.

Detecting and Classifying Low Probability of Intercept Radar Second Edition

Phillip E. Pace

Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress.

British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library.

ISBN-13 978-1-59693-234-0

Cover design by Igor Valdman

© 2009 ARTECH HOUSE 685 Canton Street Norwood, MA 02062 All rights reserved. Printed and bound in the United States of America. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All terms mentioned in this book that are known to be trademarks or service marks have been appropriately capitalized. Artech House cannot attest to the accuracy of this information. Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark.

10 9 8 7 6 5 4 3 2 1

Disclaimer: This eBook does not include the ancillary media that was packaged with the original printed version of the book.

To my wife, Ann Marie Pace, and to our children, Amanda, Zachary, and Molly

Contents Foreword

xix

Preface

xxi

Acknowledgments

xxix

PART I: FUNDAMENTALS OF LPI RADAR DESIGN 1

To See and Not Be Seen 1.1 The Requirement for LPI . . . . . . . . . . . . . . . 1.2 Characteristics of LPI Radar . . . . . . . . . . . . . 1.2.1 Antenna Considerations . . . . . . . . . . . . 1.2.2 Achieving Ultra-Low Side Lobes . . . . . . . 1.2.3 Antenna Scan Patterns for Search Processing 1.2.4 Advanced Multifunction RF Concept . . . . . 1.2.5 Transmitter Considerations . . . . . . . . . . 1.2.6 Power Management . . . . . . . . . . . . . . 1.2.7 Carrier Frequency Considerations . . . . . . . 1.3 Pulse Compression—The Key to LPI Radar . . . . . 1.4 Radar Detection Range . . . . . . . . . . . . . . . . 1.5 Interception Range . . . . . . . . . . . . . . . . . . . 1.6 Comparing Radar Range and Interception Range . . 1.7 The Pilot LPI Radar . . . . . . . . . . . . . . . . . . 1.8 Concluding Remarks . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . . . . .

2 LPI Technology and Applications 2.1 Altimeters . . . . . . . . . . . . . 2.1.1 Introduction . . . . . . . 2.1.2 Fielded LPI Altimeters . 2.2 Landing Systems . . . . . . . . . 2.2.1 Introduction . . . . . . .

vii

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

1

. . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . .

3 3 5 5 7 10 13 14 16 17 18 24 27 29 31 36 37 39

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

41 41 41 42 45 45

viii

Detecting and Classifying LPI Radar

2.3

2.4

2.5

3

2.2.2 Fielded LPI Landing Systems . . . . . . Surveillance and Fire Control Radar . . . . . . 2.3.1 Battlefield Awareness . . . . . . . . . . 2.3.2 LPI Ground-Based Systems . . . . . . . 2.3.3 LPI Airborne Systems . . . . . . . . . . Antiship Capable Missile and Torpedo Seekers 2.4.1 A Significant Threat to Surface Navies . 2.4.2 Fielded LPI Seeker Systems . . . . . . . Summary of LPI Radar Systems . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . .

Ambiguity Analysis of LPI Waveforms 3.1 The Ambiguity Function . . . . . . . . . . . . 3.2 Periodic Autocorrelation Function . . . . . . 3.3 Periodic Ambiguity Function . . . . . . . . . 3.3.1 Periodicity of the PAF . . . . . . . . . 3.3.2 Peak and Integrated Side Lobe Levels 3.4 Frank Phase Modulation Example . . . . . . 3.4.1 Transmitted Waveform . . . . . . . . . 3.4.2 Simulation Results . . . . . . . . . . . 3.5 Reducing the Doppler Side Lobes . . . . . . . References . . . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

46 48 48 48 56 58 58 58 62 64 65

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

67 68 68 69 70 70 71 71 72 75 78 78

. . . . . . . . .

. . . . . . . . .

81 81 83 86 86 89 91 94 95 96

. . . . . . . .

. . . . . . . .

97 100 101 104 105 107 108 110

4 FMCW Radar 4.1 Advantages of FMCW . . . . . . . . . . . . . . . . . . . . 4.2 Single Antenna LPI Radar for Target Detection . . . . . . 4.3 Transmitted Waveform Design . . . . . . . . . . . . . . . 4.3.1 Triangular Waveform . . . . . . . . . . . . . . . . . 4.3.2 Waveform Spectrum . . . . . . . . . . . . . . . . . 4.3.3 Generating Linear FM Waveforms . . . . . . . . . 4.4 Receiver-Transmitter Isolation . . . . . . . . . . . . . . . 4.4.1 Transmission Line Basics . . . . . . . . . . . . . . 4.4.2 Single Antenna Isolation Using a Circulator . . . . 4.4.3 Single Antenna Isolation Using a Reflected Power Canceler . . . . . . . . . . . . . . . . . . . . . . . . 4.5 The Received Signal . . . . . . . . . . . . . . . . . . . . . 4.6 LPI Search Mode Processing . . . . . . . . . . . . . . . . 4.7 Track Mode Processing Techniques . . . . . . . . . . . . . 4.8 Eﬀect of Sweep Nonlinearities . . . . . . . . . . . . . . . . 4.9 Moving Target Indication Filtering . . . . . . . . . . . . . 4.10 Matched Receiver Response . . . . . . . . . . . . . . . . . 4.11 Mismatched Receiver Response . . . . . . . . . . . . . . .

Table of Contents

ix

4.12 PANDORA FMCW Radar . . . . . . . 4.13 Electronic Attack Considerations . . . . 4.14 Technology Trends for FMCW Emitters References . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

113 115 115 119 122

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

125 125 126 128 133 134 139 148 152 152 157 163 163 165 169 169 179 182 182 183

6 Frequency Shift Keying Techniques 6.1 Advantages of the FSK Radar . . . . . . . . . . . . . 6.2 Description of the FSK CW Signal . . . . . . . . . . 6.3 Range Computation in FSK Radar . . . . . . . . . . 6.4 Costas Codes . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Characteristics of a Costas Array or Sequence 6.4.2 Computing the Diﬀerence Triangle . . . . . . 6.4.3 Deriving the Costas Sequence PAF . . . . . . 6.4.4 Welch Construction of Costas Arrays . . . . . 6.5 Hybrid FSK/PSK Technique . . . . . . . . . . . . . 6.5.1 Description of the FSK/PSK Signal . . . . . 6.6 Matched FSK/PSK Signaling . . . . . . . . . . . . . 6.7 Concluding Remarks . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

187 187 189 189 191 191 192 192 193 195 195 199 201 205 206

5 Phase Shift Keying Techniques 5.1 Introduction . . . . . . . . . . . 5.2 The Transmitted Signal . . . . 5.3 Binary Phase Codes . . . . . . 5.4 Polyphase Codes . . . . . . . . 5.5 Polyphase Barker Codes . . . . 5.6 Frank Code . . . . . . . . . . . 5.7 P1 Code . . . . . . . . . . . . . 5.8 P2 Code . . . . . . . . . . . . . 5.9 P3 Code . . . . . . . . . . . . . 5.10 P4 Code . . . . . . . . . . . . . 5.11 Polytime Codes . . . . . . . . . 5.11.1 T1(n) Code . . . . . . . 5.11.2 T2(n) Code . . . . . . . 5.11.3 T3(n) Code . . . . . . . 5.11.4 T4(n) Code . . . . . . . 5.12 Omnidirectional LPI Radar . . 5.13 Summary . . . . . . . . . . . . References . . . . . . . . . . . . Problems . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

x

Detecting and Classifying LPI Radar

7 Noise Techniques 7.1 Historical Perspective . . . . . . . . . . 7.2 Ultrawideband Considerations . . . . . . 7.3 Principles of Random Noise Radars . . . 7.4 Narayanan Random Noise Radar Design 7.4.1 Operating Characteristics . . . . 7.4.2 Model of RNR Transmitter . . . 7.4.3 Periodic Ambiguity Results . . . 7.5 Random Noise Plus FMCW Radar . . . 7.5.1 RNFR Spectrum . . . . . . . . . 7.5.2 Model of RNFR Transmitter . . 7.5.3 Periodic Ambiguity Results . . . 7.6 Random Noise FMCW Plus Sine . . . . 7.6.1 Model of RNFSR Transmitter . . 7.6.2 Periodic Ambiguity Results . . . 7.7 Random Binary Phase Modulation . . . 7.7.1 Model of RBPC Transmitter . . 7.7.2 Periodic Ambiguity Results . . . 7.8 Millimeter Wave Noise Radar . . . . . . 7.9 Correlation Receiver Techniques . . . . 7.9.1 Ideal Correlation . . . . . . . . . 7.9.2 Digital-Analog Correlation . . . 7.9.3 Fully Digital Correlation . . . . . 7.9.4 Acousto-Optic Correlation . . . . 7.10 Concluding Remarks . . . . . . . . . . . References . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . .

207 207 210 212 215 216 219 219 222 223 225 225 227 229 230 234 236 236 238 238 239 239 241 242 243 244 247

8 Over-the-Horizon Radar 8.1 Two Types of OTHR . . . . . . . . . . . . . . . . . 8.2 Sky Wave OTHR . . . . . . . . . . . . . . . . . . . 8.2.1 Characteristics of the Ionosphere . . . . . . 8.2.2 Example of F2-Layer Propagation . . . . . 8.2.3 Doppler Clutter Spectrum . . . . . . . . . . 8.2.4 Example Sky Wave OTHR System . . . . . 8.2.5 Sky Wave Processing . . . . . . . . . . . . . 8.3 Sky Wave LPI Waveform Considerations . . . . . . 8.3.1 Phase Modulation Techniques . . . . . . . . 8.3.2 Costas Frequency Hopping . . . . . . . . . 8.3.3 Reducing the CIT . . . . . . . . . . . . . . 8.3.4 Multiple Waveform Repetition Frequencies 8.3.5 Out-of-Band Emission Suppression . . . . . 8.4 Sky Wave Maximum Detection Range . . . . . . . 8.5 Sky Wave Footprint Prediction . . . . . . . . . . .

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .

249 249 252 253 259 259 261 261 265 265 266 266 266 270 271 274

. . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . .

Table of Contents 8.6

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

276 281 282 282 287 288 295 295 299

9 Case Study: Antiship LPI Missile Seeker 9.1 History of ASCM Seeker Technology . . . . . . . . . 9.2 The Future for ASCM Technology . . . . . . . . . . 9.3 Detecting the Threat . . . . . . . . . . . . . . . . . . 9.4 ASCM Target Scenario . . . . . . . . . . . . . . . . . 9.4.1 Low RCS Targets . . . . . . . . . . . . . . . . 9.4.2 Sea Clutter Model . . . . . . . . . . . . . . . 9.4.3 Linear FMCW Emitter Power Management 9.4.4 Target-to-Clutter Ratio . . . . . . . . . . . . 9.5 ASCM Ship Target Model . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

301 301 302 305 306 306 308 310 312 315 315 316

8.7

8.8 8.9

Surface Wave OTHR . . . . . . . . . . . . . . 8.6.1 Example Surface Wave OTHR System Surface Wave LPI Waveform Considerations . 8.7.1 FMICW Characteristics . . . . . . . . 8.7.2 FMICW Ambiguity Space . . . . . . . Surface Wave Maximum Detection Range . . Concluding Remarks . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . .

xi . . . . . . . . .

. . . . . . . . .

. . . . . . . . .

10 Network-Centric Warfare and Netted LPI Radar Systems 319 10.1 Network-Centric Warfare . . . . . . . . . . . . . . . . . . . . 319 10.1.1 NCW Requirements . . . . . . . . . . . . . . . . . . . 322 10.1.2 Situational Awareness . . . . . . . . . . . . . . . . . . 323 10.1.3 Maneuverability . . . . . . . . . . . . . . . . . . . . . 323 10.1.4 Decision Speed and Operational Tempo . . . . . . . . 324 10.1.5 Agility . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 10.1.6 Lethality . . . . . . . . . . . . . . . . . . . . . . . . . 326 10.2 Metrics for Information Grid Analysis . . . . . . . . . . . . . 326 10.2.1 Generalized Connectivity Measure . . . . . . . . . . . 326 10.2.2 Reference Connectivity Measure . . . . . . . . . . . . 328 10.2.3 Network Reach . . . . . . . . . . . . . . . . . . . . . . 329 10.2.4 Suppression Example . . . . . . . . . . . . . . . . . . 331 10.2.5 Extended Generalized Connectivity Measure . . . . . 333 10.2.6 Entropy and Network Richness . . . . . . . . . . . . . 333 10.2.7 Maximum Operation Tempo . . . . . . . . . . . . . . 336 10.3 Electronic Attack . . . . . . . . . . . . . . . . . . . . . . . . . 337 10.4 Information Network Analysis Using LPIsimNet . . . . . . . . 338 10.5 Netted LPI Radar Systems . . . . . . . . . . . . . . . . . . . 342 10.5.1 Advantages of the Netted LPI Radar Systems . . . . . 346 10.5.2 Netted LPI Radar Sensitivity . . . . . . . . . . . . . . 348

xii

Detecting and Classifying LPI Radar 10.5.3 Signal Model . . . . . . . . . . . . . . . . . . . . . . . 10.5.4 Netted Radar Electronic Attack . . . . . . . . . . . . 10.6 Netted Radar Analysis Using LPIsimNet . . . . . . . . . . . . 10.6.1 Monostatic LPI Emitter and the SNR Contour Chart 10.6.2 Three Netted LPI Emitters . . . . . . . . . . . . . . . 10.6.3 Two Netted LPI Emitters with Jammer . . . . . . . . 10.7 Orthogonal Waveforms for Netted Radar . . . . . . . . . . . . 10.7.1 Orthogonal Polyphase Codes . . . . . . . . . . . . . . 10.7.2 Addressing Doppler Shift Degradation . . . . . . . . . 10.7.3 Orthogonal Frequency Hopping Sequences . . . . . . . 10.7.4 Noise Waveforms . . . . . . . . . . . . . . . . . . . . 10.8 Netted Over-the-Horizon Radar Systems . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

PART II: INTERCEPT RECEIVER STRATEGIES AND SIGNAL PROCESSING

349 352 353 353 354 358 358 362 365 370 374 377 378 380 385

11 Strategies for Intercepting LPI Radar Signals 11.1 EW Intercept Receiver Techniques . . . . . . . . . . 11.1.1 Traditional Approach . . . . . . . . . . . . . 11.1.2 The Look-Through Problem . . . . . . . . . . 11.1.3 Modern Network-Centric Concepts Arriving . 11.2 Detecting the LPI Radar with UAVs . . . . . . . . . 11.3 Noncooperative Intercept Receivers . . . . . . . . . 11.3.1 Comparison of Classic Receiver Architectures for Detecting LPI Waveforms . . . . . . . . . 11.3.2 Digital EW Receivers . . . . . . . . . . . . . 11.3.3 Direct RF Sampling . . . . . . . . . . . . . . 11.4 Demodulation of the LPI Waveform . . . . . . . . . 11.5 EW Receiver Challenges . . . . . . . . . . . . . . . . 11.6 Concluding Remarks . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

387 387 387 388 389 391 392

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

392 396 398 400 400 402 403

12 Wigner-Ville Distribution Analysis of LPI Radar Waveforms 12.1 Wigner-Ville Distribution . . . . . . . . . . . . . . . 12.1.1 Continuous WVD . . . . . . . . . . . . . . . 12.1.2 Example Calculation: Real Input Signal . . . 12.1.3 Example Calculation: Complex Input Signal 12.1.4 Two-Tone Input Signal Results . . . . . . . . 12.2 FMCW Analysis . . . . . . . . . . . . . . . . . . . . 12.3 BPSK Analysis . . . . . . . . . . . . . . . . . . . . . 12.4 Polyphase Code Analysis . . . . . . . . . . . . . . .

. . . . . . . .

. . . . . . . .

. . . . . . . .

. . . . . . . .

. . . . . . . .

405 406 406 409 411 414 419 421 426

Table of Contents 12.5 12.6 12.7 12.8

Polytime Code Analysis . . . Distinguishing Between Phase FSK and FSK/PSK Analysis Summary . . . . . . . . . . . References . . . . . . . . . . . Problems . . . . . . . . . . .

. . . . Codes . . . . . . . . . . . . . . . .

xiii . . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

429 431 438 438 442 444

13 Choi-Williams Distribution Analysis of LPI Radar Waveforms 13.1 Mathematical Development . . . . . . . . . . . . . . 13.2 LPI Signal Analysis . . . . . . . . . . . . . . . . . . 13.2.1 FMCW Analysis . . . . . . . . . . . . . . . . 13.2.2 BPSK Analysis . . . . . . . . . . . . . . . . . 13.2.3 Polyphase Code Analysis . . . . . . . . . . . 13.2.4 Polytime Code Analysis . . . . . . . . . . . . 13.2.5 FSK and FSK/PSK Analysis . . . . . . . . . 13.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

445 446 448 449 449 455 455 458 458 464 464

14 LPI Radar Analysis Using Quadrature Mirror Filtering 14.1 Time-Frequency Wavelet Decomposition . . . . . . . . . . 14.1.1 Basis Functions . . . . . . . . . . . . . . . . . . . . 14.1.2 Short-Time Fourier Transform Decomposition . . . 14.1.3 Wavelets and the Wavelet Transform . . . . . . . . 14.1.4 Wavelet Filters . . . . . . . . . . . . . . . . . . . . 14.2 Discrete Two-Channel Quadrature Mirror Filter Bank . . 14.3 Tree Structure to Filter the Lowpass Component . . . . . 14.4 Tree Structure to Filter the Highpass Component . . . . . 14.5 QMFB Tree Receiver . . . . . . . . . . . . . . . . . . . . . 14.6 Example Calculations . . . . . . . . . . . . . . . . . . . . 14.6.1 Complex Single-Tone Signal . . . . . . . . . . . . . 14.6.2 Complex Two-Tone Signal . . . . . . . . . . . . . . 14.7 FMCW Analysis . . . . . . . . . . . . . . . . . . . . . . . 14.8 BPSK Analysis . . . . . . . . . . . . . . . . . . . . . . . . 14.9 Polyphase Code Analysis . . . . . . . . . . . . . . . . . . 14.10 Polytime Code Analysis . . . . . . . . . . . . . . . . . . . 14.11 Costas Frequency Hopping Analysis . . . . . . . . . . . . 14.12 FSK/PSK Signal Analysis . . . . . . . . . . . . . . . . . 14.13 Noise Waveform Analysis . . . . . . . . . . . . . . . . . . 14.14 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . .

467 468 468 469 469 472 474 476 477 478 482 482 485 487 489 494 495 499 499 499 506 509 510

xiv

Detecting and Classifying LPI Radar

15 Cyclostationary Spectral Analysis for Detection of LPI Radar Parameters 15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 15.1.1 Cyclic Autocorrelation . . . . . . . . . . . . . . . . 15.1.2 Spectral Correlation Density . . . . . . . . . . . . 15.2 Spectral Correlation Density Estimation . . . . . . . . . . 15.3 Discrete Time Cyclostationary Algorithms . . . . . . . . . 15.3.1 The Time-Smoothing FFT Accumulation Method 15.3.2 Direct Frequency-Smoothing Method . . . . . . . . 15.4 Test Signals . . . . . . . . . . . . . . . . . . . . . . . . . . 15.5 BPSK Analysis . . . . . . . . . . . . . . . . . . . . . . . . 15.6 FMCW Analysis . . . . . . . . . . . . . . . . . . . . . . . 15.7 Polyphase Code Analysis . . . . . . . . . . . . . . . . . . 15.8 Polytime Code Analysis . . . . . . . . . . . . . . . . . . . 15.9 Costas Frequency Hopping Results . . . . . . . . . . . . . 15.10 Random Noise Analysis . . . . . . . . . . . . . . . . . . . 15.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . .

513 513 514 515 516 520 520 522 525 528 531 535 540 540 543 545 547 548

16 Antiradiation Missiles 16.1 Suppression of Enemy Air Defense . . . . . . . . . 16.1.1 The Beginning of SEAD . . . . . . . . . . . 16.1.2 Early ARM Developments . . . . . . . . . . 16.1.3 Vietnam . . . . . . . . . . . . . . . . . . . . 16.1.4 Post Vietnam . . . . . . . . . . . . . . . . . 16.1.5 Miniature Air-Launched Decoys . . . . . . . 16.2 Antiradiation Missile Seeker Design . . . . . . . . . 16.2.1 Antenna Design . . . . . . . . . . . . . . . . 16.2.2 Receiver and Signal Processing . . . . . . . 16.2.3 Dual-Mode Design . . . . . . . . . . . . . . 16.2.4 Signal Processing . . . . . . . . . . . . . . . 16.2.5 Future ARMs–Addressing the LPI Emitter 16.3 ARM Performance Metrics . . . . . . . . . . . . . 16.4 Former Soviet Union and Warsaw Pact Allies . . . 16.4.1 AA-10 Alamo . . . . . . . . . . . . . . . . . 16.4.2 AS-4 Kitchen . . . . . . . . . . . . . . . . . 16.4.3 AS-5 Kelt . . . . . . . . . . . . . . . . . . . 16.4.4 AS-6 Kingfish . . . . . . . . . . . . . . . . . 16.4.5 AS-9 Kyle . . . . . . . . . . . . . . . . . . . 16.4.6 AS-11 Kilter . . . . . . . . . . . . . . . . . 16.4.7 Kh-27 . . . . . . . . . . . . . . . . . . . . . 16.4.8 AS-12 Kegler . . . . . . . . . . . . . . . . . 16.4.9 AS-16 Kickback . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

551 551 553 554 555 556 558 559 559 566 567 571 572 577 578 578 579 580 581 582 584 585 585 587

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

Table of Contents 16.4.10 AS-17 Krypton . . . . . . . . . . . 16.5 United States . . . . . . . . . . . . . . . . 16.5.1 Shrike . . . . . . . . . . . . . . . . 16.5.2 Standard ARM . . . . . . . . . . . 16.5.3 HARM . . . . . . . . . . . . . . . 16.5.4 AARGM . . . . . . . . . . . . . . 16.5.5 Aﬀordable Reactive Strike Missile 16.5.6 Sidearm . . . . . . . . . . . . . . . 16.5.7 Rolling Airframe Missile . . . . . . 16.5.8 Army UAVs . . . . . . . . . . . . . 16.6 France . . . . . . . . . . . . . . . . . . . . 16.7 United Kingdom . . . . . . . . . . . . . . 16.8 Taiwan . . . . . . . . . . . . . . . . . . . . 16.9 Germany . . . . . . . . . . . . . . . . . . 16.10 Israel . . . . . . . . . . . . . . . . . . . . 16.10.1 Harpy . . . . . . . . . . . . . . . . 16.10.2 STAR-1 . . . . . . . . . . . . . . . 16.11 China . . . . . . . . . . . . . . . . . . . . 16.12 Anti-ARM Techniques . . . . . . . . . . . 16.12.1 Decoys . . . . . . . . . . . . . . . 16.12.2 Gazetchik . . . . . . . . . . . . . 16.12.3 AN/TLQ-32 ARM-D Decoy . . . References . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . .

xv . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

17 Autonomous Classification of LPI Radar Modulations 17.1 Classification Using Time-Frequency Imaging . . . . . . 17.2 Classification Authority and Automation . . . . . . . . . 17.2.1 Human-Computer Interface Considerations . . . 17.2.2 Automation and the Human Operator . . . . . . 17.2.3 Autonomous Modulation Classification . . . . . . 17.3 Nonlinear Classification Networks . . . . . . . . . . . . . 17.3.1 Single Perceptron Networks . . . . . . . . . . . . 17.3.2 Multilayer Perceptron Networks . . . . . . . . . 17.3.3 Radial Basis Function . . . . . . . . . . . . . . . 17.4 Feature Extraction Signal Processing . . . . . . . . . . . 17.4.1 Marginal Frequency Adaptive Binarization . . . 17.4.2 Classification Results with Multilayer Perceptron 17.4.3 Classification Results with Radial Basis Function Network . . . . . . . . . . . . . . . . . . . . . . . 17.4.4 Discussion of Classification Results . . . . . . . . 17.5 Modified Feature Extraction Signal Processing . . . . . 17.5.1 Lowpass Filtering for Cropping Consistency . . . 17.5.2 Calculating the Marginal Frequency Distribution

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

587 589 589 591 591 592 593 593 594 595 596 597 598 600 601 601 603 604 606 607 610 611 612 616

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

619 620 621 621 622 623 624 625 629 632 634 634 638

. . . . .

. . . . .

. . . . .

642 647 648 648 651

xvi

Detecting and Classifying LPI Radar 17.5.3 Principal Components Analysis . . . . . . . . . . . . . 17.5.4 Classification Using Modified Feature Extraction . . . 17.5.5 Classification Results with the Multilayer Perceptron . 17.5.6 Classification Results with the Radial Basis Function . 17.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18 Autonomous Extraction of Modulation Parameters 18.1 Emitter Clustering . . . . . . . . . . . . . . . . . . . . . . . . 18.2 Polyphase Parameters Using Wigner-Ville Distribution–Radon Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.2.1 Time-Frequency Algorithm Description . . . . . . . . 18.2.2 Testing the Algorithm . . . . . . . . . . . . . . . . . . 18.3 Polyphase Parameters from Quadrature Mirror Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . 18.3.1 Wavelet Decomposition Algorithm Description . . . . 18.3.2 Testing the Algorithm . . . . . . . . . . . . . . . . . . 18.4 FMCW Parameters from Cyclostationary Bifrequency Plane . 18.4.1 Cyclostationary Algorithm Description . . . . . . . . . 18.4.2 Testing the Algorithm . . . . . . . . . . . . . . . . . . 18.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

656 660 667 674 682 682 685 687 687 688 689 694 695 695 699 699 700 703 705 705 705

APPENDIXES A Low Probability of Intercept Toolbox 709 A.1 Introduction to the LPIT . . . . . . . . . . . . . . . . . . . . 709 A.2 Naming Convention and Example . . . . . . . . . . . . . . . . 710 B Generating PAF Plots Using the LPIT Files

713

C Primitive Roots and Costas Sequences 715 C.1 Primes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715 C.2 Complete and Reduced Residue Systems . . . . . . . . . . . . 716 C.3 Primitive Roots . . . . . . . . . . . . . . . . . . . . . . . . . . 717 D LPIsimNet 721 D.1 Overview of LPIsimNet Architecture . . . . . . . . . . . . . . 721 D.1.1 Loading the Default Sensor Network . . . . . . . . . . 722 D.1.2 Building a Scenario File and Running the Simulation . 722 D.2 Setting the Node Properties . . . . . . . . . . . . . . . . . . . 726 D.3 Viewing the Simulation Results . . . . . . . . . . . . . . . . . 728

Table of Contents

xvii

D.4 Adding a Moving Jammer to the Scenario . . . . . . . . . . . D.5 Netted Radar with a Jammer . . . . . . . . . . . . . . . . . .

731 733

E PWVD for FMCW with ∆F = 500 Hz

741

F PWVD for Frank Code with T = 64 ms

745

G PWVD Results for P1, G.1 P1 Code Analysis . . G.2 P2 Code Analysis . . G.3 P3 Code Analysis . . G.4 P4 Code Analysis . .

P2, P3, and P4 Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

H PWVD Results for Polytime Codes T2, H.1 T2(2) Polytime Code . . . . . . . . . . . H.2 T3(2) Polytime Code . . . . . . . . . . . H.3 T4(2) Polytime Code . . . . . . . . . . . I

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

749 749 749 752 752

T3, and T4 759 . . . . . . . . . . . . 759 . . . . . . . . . . . . 763 . . . . . . . . . . . . 763

QMFB Results for FMCW with ∆F = 500 Hz

771

J QMFB Results for 11-Bit BPSK

773

K QMFB Results for Frank Signal with Nc = 16

777

L QMFB L.1 P1 L.2 P2 L.3 P3 L.4 P4

Results Analysis Analysis Analysis Analysis

for P1, . . . . . . . . . . . . . . . . . . . .

P2, P3, . . . . . . . . . . . . . . . . . . . .

and . . . . . . . . . . . .

P4 . . . . . . . . . . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

781 781 782 782 788

M QMFB Results for T2, T3, and T4

797

N Cyclostationary Processing Results with FMCW, ∆F = 500 Hz

805

O Cyclostationary Processing Results with Frank Signal, Nc = 16

809

P Cyclostationary Processing Results and P4 P.1 P1 Code Analysis . . . . . . . . . . P.2 P2 Code Analysis . . . . . . . . . . P.3 P3 Code Analysis . . . . . . . . . . P.4 P4 Code Analysis . . . . . . . . . .

for P1, P2, P3, . . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

813 813 816 816 816

xviii

Detecting and Classifying LPI Radar

Q Cyclostationary Processing Results Polytime Codes Q.1 Polytime T2(2) Code Analysis . . Q.2 Polytime T3(2) Code Analysis . . Q.3 Polytime T4(2) Code Analysis . .

for T2, T3, and T4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

821 821 821 823

List of Symbols

829

Glossary

841

About the Author

847

Index

849

Foreword

In the foreword of Detecting and Classifying Low Probability of Intercept Radar, 1st Edition, I noted that there is considerable interest in radars that can “see and not be seen,” commonly called low probability of intercept or “LPI” radars. If anything, interest has grown in the intervening years and this new book on the subject is both timely and welcome. The problem of LPI radar design is diﬃcult to solve for long range radars because the signal available to the listener is reduced by the square of the distance from transmitter to listening receiver, whereas signal available to the radar receiver decreases in proportion to the fourth power of the distance between the radar and its target. Phillip E. Pace has included the many facets of LPI radar from his earlier work and has added valuable insights in nearly every area. He has also added much that is entirely new to this volume, including topics of noise radar and network centric warfare and radar netting. He also considers the interception problem and has added material on use of the Choi-Williams distribution, as well as chapters on autonomous extraction and recognition architectures. This coverage of both the radar and interception problems in one volume provides a valuable reference work for this important technical field. As radar interception techniques evolved over the past half-century, the generally high signal strength available to the intercept receiver led to intercept receivers which detect each radar “pulse” using threshold detection and then estimate parameters such as carrier frequency, angle of arrival, pulse duration, time of arrival, polarization, and other single pulse parameters. These form pulse descriptor words and are further sorted, “deinterleaved” and analyzed to discern PRI patterns. This approach to signal interception and threat recognition requires a high probability of detection for each individual xix

xx

Detecting and Classifying LPI Radar

pulse. Antiradiation missiles and other approaches to suppression of enemy air defenses makes reduction of peak power a matter of radar survivability. This in turn forces a reexamination of the single pulse detection approach for signal interception as well as a reexamination of the use of high peak power transmissions for performing radar functions. Whether you are interested in techniques used in the design of LPI radar or in techniques which may be useful for countering such LPI designs, this book provides a good starting point for rethinking both the radar problem and the interception problem.

Richard G. Wiley, Ph.D. Vice President-Chief Scientist of Research Associates of Syracuse, Inc. East Syracuse, New York December, 2008

Preface Introduction

The second edition of Detecting and Classifying Low Probability of Intercept Radar is designed to meet the needs of electrical engineering, physics, and systems engineering students at the senior undergraduate and beginning graduate levels and especially those of practicing engineers. A low probability of intercept (LPI) radar course must present, as they say, both sides of the story. Whereas radar proper has little appeal and seems even less pointed to most of these students, the subject becomes highly significant to them when it is presented along with the digital intercept receiver and signal processing techniques for counter-LPI. My experiences as a student, engineer, and teacher have led to the thought that a successful text for this study must present both the radar design characteristics as well as the noncooperative detection strategies and algorithms. In doing so, the course provides an interesting opportunity to study the various trade-oﬀs that are involved not only in intercept receiver architectures but also in the design of LPI waveform modulations. This book has grown out of research and teaching in the field of networkcentric radar electronic warfare, signal processing, and wideband digital receiver technologies at the Naval Postgraduate School. Even though the first edition of this book was published barely four years ago, based on the helpful reviews published in the IEEE Aerospace and Electronic Systems Magazine and the feedback from the many students in industry and universities, it became evident that a new edition was needed to incorporate the suggested topics and changes to the contents. LPI radar systems are seeing unprecedented levels of growth. In many countries, new milestones are being established for streamlined acquisition of these emitters for all types of applications. On the other hand, the recent xxi

xxii

Detecting and Classifying LPI Radar

advances in LPI radar technology have pushed the door open for the design of extremely sensitive intercept receivers and high-speed signal processors for autonomous LPI emitter detection, classification, and counter-LPI operations.

What’s New LPI radar techniques added to this second edition include; random noise radar waveforms, their periodic ambiguity characteristics, and the diﬀerent types of correlation receivers used (Chapter 7); sky wave and surface wave overthe-horizon radar systems and their move away from the traditional waveforms to the incorporation of new LPI modulations (Chapter 8); netted LPI radar sensors and orthogonal polyphase modulations, network-centric warfare principles, frequency hopping waveforms, and information network analysis (Chapter 10). New intercept receiver strategies and signal processing algorithms supplied in the second edition include; the Choi-Williams time-frequency analysis of LPI waveforms (Chapter 13); antiradiation missiles and the new seeker designs for detecting LPI emitters (Chapter 16); autonomous feature extraction and classification algorithms for identifying the intercepted modulation (Chapter 17); and autonomous modulation parameter extraction signal processing (Chapter 18). A distinguishing feature of this book is investigating the LPI techniques that go beyond the use of a single emitter and use a network to integrate several distributed sensors to provide additional aspects of the target. Employing a sensor network can unfold new capabilities in many important applications. Secondly, this book examines extending the detection and classification algorithms to execute autonomously, independent of any human interpretation to the extent desired. Executing these modulation decisions autonomously can draw these techniques closer to providing the intercept receiver the real-time response capability needed for fast, reactive counter-LPI.

Course Structure The book is written to serve not only as a textbook, but also as a reference for the practicing radar and digital intercept receiver design engineer. The layout was intended to be applicable to many diﬀerent course structures including, a one-semester (two quarters) course of study in low probability of intercept radar systems design (Part I) and the noncooperative detection and classification of these types of emitters (Part II). The book is especially appropriate for 2-, 3-, and 4-day short courses. For the prerequisites, it is assumed that the student has at least senior-level academic experience in engineering and

Preface

xxiii

mathematics, and has the ability to write and run computer programs. A course in radar and a course in signal processing would provide a very useful background.

Overview of the Book As with the first edition, this book is divided into two parts with the main objective in Part I being the unified presentation of the fundamental design principles of LPI radar. This includes a thorough treatment of the numerous types of wideband modulations that can be used to reduce the probability of a noncooperative intercept receiver’s ability to extract the waveform parameters (which may easily lead to an eﬀective jammer response). The main objective in Part II is to present the intercept receiver time-frequency and bifrequency signal processing techniques that can extract the wideband waveform parameters. Autonomous classification and parameter extraction algorithms are also an objective such that a real-time jammer response can be developed–just what we did not want to happen in Part I! In summary, a balanced coverage is provided of both LPI radar and waveform design concepts (Part I) and the signal processing techniques for LPI waveform detection and characterization for counter-LPI (Part II). Each chapter ends with exercises that are an essential part of any course using the text. A key feature of this book is the extensive use of MATLAB. The CD accompanying this book contains many programs that should be used for the problem exercises in order to further the understanding of the concepts, and also to generate new and useful results that are of special interest to the reader. The exercises are often used to complete the reader’s understanding of a concept or to present diﬀerent applications of ideas in the text. A distinguishing feature of this book is that it includes many graphical illustrations of the results, especially in Part II. It is hoped that this will lead to a better understanding of the underlying principles of waveform design and will provide a clearer visualization of how the waveform parameters can be extracted. As they say, “a picture is worth a thousand words.” Identification of the waveform parameters is the first step to the development of autonomous classification and parameter extraction algorithms. The text contains suﬃcient mathematical detail to enable the average undergraduate electrical engineering and physics student to follow, without too much diﬃculty, the flow of analysis and design. A certain amount of analytical detail, rigor, and thoroughness allows many of the topics to be investigated further with the aid of many references. A brief overview of each chapter is given below.

xxiv

Detecting and Classifying LPI Radar

PART I: Fundamentals of LPI Radar Design In Chapter 1, an introduction to LPI radar is presented which provides the reasons for the LPI requirement that include advanced intercept receivers and the threat of antiradiation missiles. The characteristics of LPI radar that distinguish them from conventional radar are also presented, as well as the LPI radar architectures emphasizing continuous waveform (CW) radar. The detection range of the LPI radar is examined and the advantage of the LPI radar is quantified in terms of the intercept range and processing gain. To illustrate the analysis, several examples using the Pilot LPI radar are presented. In Chapter 2, an updated and comprehensive review of the applications that utilize LPI radar technology is presented. Applications include altimeters, surveillance, navigation, and landing radar for unmanned aerial vehicles (UAVs). Also discussed are the tactical multimode airborne radar, antiship capable missile (ASCM) seekers, and torpedo seekers. In Chapter 3, the ambiguity analysis of LPI waveforms is introduced in order to quantify their delay-Doppler properties. The concepts are used throughout Part I to examine the various waveforms being studied. The mathematical tools include the autocorrelation function (ACF), the periodic autocorrelation function (PACF), and the periodic ambiguity function (PAF). The eﬀect of weighting functions on the PAF is also discussed. The low probability of intercept toolbox (LPIT) is a collection of MATLAB routines that enable the student to quickly design all of the LPI waveforms. The LPIT is introduced in Appendix A. Appendix B discusses the download of MATLAB code from N. Levanon’s Web site in order to compute the ACF, PACF, and PAF. Chapter 4 investigates the characteristics of frequency modulation CW (FMCW) LPI radar. A detailed architecture is analyzed. Mathematical formulations of the transmitted waveform and the received signal are developed, and there is an analysis of the receiver-transmitter isolation problems being overcome (single antenna systems). The search mode signal processing is described, including the details of the system components (e.g., filter bandwidths, analog-to-digital converter speeds, and so forth). Track mode processing techniques are also presented. Nonlinearities in the frequency sweep waveform are addressed, and the PAF of the FMCW is analyzed. As an example of an FMCW LPI radar, details of the Parallel Array for Numerous Diﬀerent Operational Research Activities (PANDORA) are presented. Finally, the technology trends and latest developments in FMCW emitters are presented.

Preface

xxv

In Chapter 5, phase shift keying (PSK) LPI radar is discussed. Details on polyphase Barker sequences, Frank code, P1, P2, P3, and P4 codes are presented, and their spectral and ambiguity properties investigated. Also presented are polytime codes T1(n), T2(n), T3(n), and T4(n). As an example of a phase coding LPI radar, the details of the Omnidirectional LPI radar are presented. Chapter 6 discusses frequency shift keying (FSK) radar waveform design. The design of Costas codes is presented. By combining Costas coding with PSK, an additional advantage is obtained for the LPI radar. Tailoring the FSK/PSK waveform to the power spectral density of a particular target of interest can improve detection probabilities by transmitting (randomly) at those frequencies where the target resonates the most. This concept is also presented and examples of the waveform are given. In Chapter 7, random noise radar concepts are introduced. Four types are presented including random noise, random noise plus FMCW, random noise FMCW plus sine, and random binary phase code modulation. The ambiguity analysis of the waveforms is discussed and the correlation receiver techniques used in the radar receiver are examined including an acousto-optic approach. In Chapter 8, over-the-horizon radar concepts are discussed emphasizing the new movement away from the traditional FMCW waveforms to the more LPI type waveforms. Ionospheric eﬀects are presented and both surface wave and sky wave emitter concepts are investigated. The maximum detection range is also quantified for both types of emitters. In Chapter 9, the design of LPI seekers for antiship capable missiles is discussed. The design of a modern 9.3-GHz homodyne triangular-FMCW emitter for detection of low radar cross section (RCS) ships is described. To predict target detection capability, clutter and target models are developed as the emitter is flown at 300 m/s in a scenario that starts at a range of 15 nmi from the target. To evaluate the feasibility of detecting low RCS ships at the horizon, a low RCS ship design is examined. Each sea state (0-4) is characterized by using a second-order polynomial that describes the normalized mean sea backscatter coeﬃcient as a function of the grazing angle. The emitter transmit power is adapted in time to measure the target characteristics (power management). The emitter transmit power level is consistent with the RCS and range to the target, while keeping a target-to-clutter power ratio at 20 dB. For detection analysis, 50, 100, and 500 m2 RCS values are considered. In Chapter 10, the concept of network-centric warfare is introduced and the use of a sensor network is analyzed. Performance of the information grid is quantified. Netted radar concepts are introduced and minimum input minimum output techniques are reviewed. Sensor network and netted radar performance are examined including their capabilities under electronic attack using the MATLAB program LPIsimNet. The use of orthogonal polyphase modulations and orthogonal frequency hopping waveforms is also discussed.

xxvi

Detecting and Classifying LPI Radar

PART II: Intercept Receiver Strategies and Signal Processing To begin Part II, Chapter 11 takes a look at (noncooperative) digital intercept receiver strategies. The trend today is toward the all-digital receiver with the analog-to-digital conversion taking place directly at the antenna (direct conversion). Network-centric and swarm intercept strategies are discussed. The trade-oﬀs of various receiver architectures is presented and a new digital analog-to-information receiver is discussed. Problems that intercept receivers must deal with are presented as well as future trends in intercept receiver architectures. For the remaining chapters, it is assumed that the sampled signal is available within bulk memory of the receiver, and used as input to the signal processor. Chapter 12 examines the Wigner-Ville distribution (WD) time-frequency analysis technique, including an eﬃcient kernel transformation that helps speed up the computation time. Two small examples are carried through (real input signal and complex input signal) to demonstrate the WD timefrequency calculation. A two-tone input signal is analyzed to further the understanding of the WD output and to demonstrate the presence of the cross term. Although not an LPI waveform, the binary PSK (BPSK) signal is analyzed first for various signal-to-noise ratios (SNRs), so that the WD results can be verified and compared to other phase coding techniques. Extraction of the signal parameters such as code period, subcode period, number of phase codes, carrier frequency, and signal bandwidth is developed. The LPI waveforms developed in Part I are analyzed. These include the FMCW technique and the phase coding techniques: Frank, P1, P2, P3, and P4. The advanced phase coding techniques where the subcode width is not uniform throughout the code period are examined next. These include the T1(n) through T4(n). Using the WD, it is shown that the numerous LPI signals can be distinguished and the signal parameters can be extracted, even for moderately low SNR. The frequency coding techniques are examined last and include Costas sequences (FSK), Costas sequences with phase modulation (FSK/PSK), and the target matched FSK/PSK signals. In Chapter 13, the Choi-Williams distribution is presented. Using an exponential kernel and the same transformation as outlined for the Wigner-Ville distribution, the amplitude of the cross terms is significantly reduced making the identification of the modulation parameters easier. The LPI modulations are calculated using the Choi-Williams to quantify the amplitude reduction of the cross terms and to compare the results with those shown in Chapter 12. LPI modulations examined include FMCW, BPSK and polyphase modulations. Also examined are polytime, FSK, and FSK/PSK modulations.

Preface

xxvii

Chapter 14 investigates the use of quadrature mirror filter banks (QMFBs) for the extraction of LPI radar waveform parameters. The introduction of time-frequency wavelets and the wavelet transform are presented first, followed by the development of the discrete two-channel quadrature mirror filter bank. This leads to a discussion on filtering the lowpass component and the highpass component, and the arrangement of the filters into a tree structure. The QMFB tree is then considered, and the results for a complex single-tone signal are shown as an example of the time-frequency output. A complex two-tone signal is then considered, followed by the QMFB analysis of the LPI signals. This investigation then examines the LPI waveforms and parallels the analysis carried out in Chapters 12 and 13, so a direct comparison of the methods can be made. The fundamentals of cyclostationary signal processing are presented in Chapter 15. Discrete time algorithms are presented to generate the spectral correlation density and include the time-smoothing fast Fourier transform (FFT) accumulation method and the direct frequency smoothing method. A single-tone test frequency is used to illustrate the cyclostationary results on the bifrequency plane for both methods. The extraction of the waveform parameters on the bifrequency plane provides some significant advantages when compared to the time-frequency methods discussed in Chapters 12—14. Chapter 16 introduces the concept of suppression of integrated defense systems using antiradiation missiles (ARMs). The ARM seeker and signal processing are detailed and the algorithms used to address the LPI threat are introduced. Performance metrics are examined and the important ARMs of the world are presented. Anti-ARM techniques are also reviewed. Chapter 17 examines the task of autonomously classifying the types of signal modulation using time-frequency imaging and detection. Classification authority and the human computer interface considerations are emphasized. Feature extraction algorithms are presented and nonlinear neural network classification architectures are introduced. Classification results using the LPI emitter modulations discussed in Part I are presented. Chapter 18 introduces the algorithms that can be used to autonomously extract the modulation parameters from the time-frequency and bifrequency results. The concept of emitter clustering is presented and the extraction of polyphase modulation parameters from a WD-Radon transform algorithm is discussed. Extraction of the polyphase modulation parameters from the QMFB are also discussed. An algorithm for extracting FMCW parameters from the cyclostationary bifrequency plane is presented. Results are shown to illustrate the performance of the techniques.

xxviii

Detecting and Classifying LPI Radar

Final Message Every attempt has been made to ensure the accuracy of all materials in this book, including the many MATLAB programs contained on the CD. I would, however, appreciate readers bringing to my attention any errors that may appear. I have been extremely gratified by the tremendous success of this text. The many improvements and additions in the second edition have been made possible by the feedback and suggestions of a large number of instructors and students at many companies and universities. Finally, on a personal note, it continues to be very encouraging to learn that many people working with or having to learn about detecting and classifying LPI radar systems have found the first edition useful. It is still my hope that this second edition, with its new chapters and additional software, will be of value not only to new readers, but will also be worthwhile to those who have already read the first edition.

Acknowledgments

This book would not have been possible without the help, encouragement, and support received during its preparation. First, I thank God for giving me the strength and endurance to complete this work. I would also like to thank my family Ann, Amanda, Zachary, and Molly. I could not have completed this enormous task without their support, patience, sacrifice, and understanding for the many hours of neglect during the completion of the first and second editions of this book and it is to them to whom this book is dedicated. I would also like to thank the following people who were invaluable in reviewing the first edition of this work. Foremost, I would like to thank Dr. David K. Barton, ANRO Engineering Inc., and Dr. Richard G. Wiley, Research Associates of Syracuse, Inc., for taking the time to oﬀer numerous helpful suggestions that improved the quality of the manuscript. Many thanks also go to Professor Nadav Levanon, Tel Aviv University, for working with me tirelessly on the ambiguity analysis, and to Professor Herschel H. Loomis Jr., Naval Postgraduate School, for helpful discussions in cyclostationary signal processing. I am also grateful to Professor David Styer, University of Cincinnati, for sharing his insights into the world of number theory. Reviewers for various portions of this second edition include Dr. Carlo Kopp, defense analyst and consulting engineer, Air Power Australia for his insights into antiradiation weapons, Dr. Ram Narayanan, Penn State University for his help with noise radar concepts, Dr. Jeﬀrey B. Knorr, Naval Postgraduate School, for his many years of experience in the HF world, and again Dr. David Barton, and Dr. Richard Wiley. I would also like to thank graduate students Fernando Taboada, Antonio Lima, Jen Gau, Pedro Jarpa,

xxix

xxx

Detecting and Classifying LPI Radar

Siew-Yam Yeo, and Christer Persson, Taylan Gulum, You-Chen, Bin-Yi Liu, You-Quan Chen, Teresa and Gary Upperman, Patrick Kistner, Eugene R. Heuschel III, Micael Grahn, Jason Phillips, Pick Guan Hui, and Sharon Ai Lin Tan for their eﬀort in helping develop the software tools, and the many graduate students who have contributed their valuable time to understanding the results in the text. I am also very grateful to the staﬀ of Artech House, especially Mark Walsh, senior acquisitions editor, for his interest, support, and cooperation of this second edition; Barbara Lovenvirth, developmental editor, for helping me along; Erin Donahue, production editor, for the production of the book; and Igor Valdman, for managing the production of the cover. It has been a satisfying but sometimes overwhelming task. Phillip E. Pace Naval Postgraduate School Monterey, CA [email protected]

PART I: FUNDAMENTALS OF LPI RADAR DESIGN

Chapter 1

To See and Not Be Seen This chapter addresses the questions: What is a low probability of intercept radar, and why is this capability needed? After answering these basic questions, the radar design characteristics that make these type of sensors diﬀerent are presented. The radar range equation is used to quantify the detection performance of an LPI radar design. The range at which an intercept receiver can detect the LPI radar emission is also addressed. The Pilot radar is used to illustrate a complete design, and its performance is also examined.

1.1

The Requirement for LPI

Many users of radar today are specifying a low probability of intercept (LPI) and low probability of identification (LPID) as an important tactical requirement. As of 2008, the ANSI/IEEE Standard 686: Radar Terms and Definitions, does not address this type of radar. The term LPI is that property of a radar that, because of its low power, wide bandwidth, frequency variability, or other design attributes, makes it diﬃcult for it to be detected by means of a passive intercept receiver. An LPID radar is an LPI radar with a waveform that makes it diﬃcult for an intercept receiver to correctly identify the parameters and radar type. More formal definitions for LPI and LPID are oﬀered below: Definition 1.1 A low probability of intercept (LPI) radar is defined as a radar that uses a special emitted waveform intended to prevent a noncooperative intercept receiver from intercepting and detecting its emission. 3

4

Detecting and Classifying LPI Radar

Definition 1.2 Low probability of identification (LPID) radar is defined as a radar that uses a special emitted waveform intended to prevent a noncooperative intercept receiver from intercepting and detecting its emission but if intercepted, makes identification of the emitted waveform modulation and its parameters diﬃcult. According to the definitions 1.1 and 1.2 above, an LPID radar is an LPI radar but and LPI radar is not necessarily an LPID radar. It follows that the LPI and LPID radar attempts detection of targets at longer ranges than the intercept receiver can accomplish detection/jamming of the radar [1—3]. It is important to note that defining a radar to be LPI and/or LPID necessarily involves the definition of the corresponding intercept receiver. That is, the success of an LPI radar is measured by how hard it is for the intercept receiver to detect/intercept the radar emissions. The LPI requirement is in response to the increase in capability of modern intercept receivers to detect and locate a radar emitter [4]. One thing is for certain. For every improvement in LPI radar, improvements in intercept receiver design can be expected (which is why this book addresses both areas). In applications such as altimeters, tactical airborne targeting, surveillance, and navigation, the interception of the radar transmission can quickly lead to electronic attack (or jamming) if the parameters of the emitter can be determined. Due to the wideband nature of these pulse compression waveforms, however, this is typically a diﬃcult task. The LPI requirement is also in response to the ever-present threat of being destroyed by precision guided munitions and antiradiation missiles (ARMs). ARMs are designed to home in on active, ground-based, airborne or shipboard radars, and disable them by destroying their antenna systems and/or killing or wounding their operator crews [4]. ARMs are typically used for suppression of enemy air defense (SEAD). The intercept receiver on board the aircraft (or the ARM system itself) locates the victim radar. The victim radar is then designated to the ARM if the parameters of the intercepted signal are correct. In Chapter 16, a thorough treatment of the ARM threat and the new signal processing techniques to counter the LPI emitter are presented. The denial of signal intercept protects the emitters from most of these types of threats and is the objective of using a low probability of intercept waveform. Since LPI radar tries to use signals that are diﬃcult to intercept and/or identify, they have diﬀerent design characteristics compared to conventional radar systems. These characteristics are discussed below.

To See and Not Be Seen

1.2

5

Characteristics of LPI Radar

Many combined features help the LPI radar prevent its detection by modern intercept receivers. These features are centered on the antenna (antenna pattern and scan patterns) and the transmitter (radiated waveform).

1.2.1

Antenna Considerations

The antenna is the interface, or connecting link, between some guiding system and (usually) free space. Its function is to either radiate electromagnetic energy (the transmitter feeds the guiding system) or receive electromagnetic energy (the guiding system feeds a receiving system). The antenna pattern is the electric field radiated as a function of the angle measured from boresight (center of the beam). The various parts of a radiation pattern are referred to as lobes that may be subclassified into main, side, and back lobes [5]. The main lobe is defined as the lobe containing the direction of maximum radiation. The side lobe is a radiation lobe in any direction other than the intended lobe. A back lobe refers to a lobe that occupies the hemisphere in a direction opposite to that of the main lobe. The side lobe level is usually expressed as a ratio of the power density in the lobe in question to that of the main lobe. That is, the side lobe level is amplitude of the side lobe normalized to the main beam peak. The highest side lobe is usually that lobe closest to the main beam. It is also convenient to use the side lobe ratio (SLR) which is the inverse of the side lobe level. The radiation intensity of an antenna is the power per unit solid angle. The power gain of an antenna’s main lobe is defined as 4π times the ratio of the radiation intensity in the maximum direction to the net power accepted by the antenna from the transmitter. The power gain can be estimated closely using Kraus’s approximation [5] G=η

4π θa θe

(1.1)

where θa is the half-power beamwidth in the azimuth plane, θe is the halfpower beamwidth in the elevation plane (in radians), and η is the antenna aperture eﬃciency Prad (1.2) η= Pin or the ratio of the radiated power of the antenna to the total input power. The half-power beamwidth is the angle between two directions in which the radiation intensity is one-half the maximum value of the beam. The gain of the antenna can also be approximated using the physical aperture area A as G≈

4πηA λ2

6

Detecting and Classifying LPI Radar

For any antenna aperture, the antenna radiation pattern is obtained by taking the Fourier transform of the field distribution across the aperture; for example, in a rectangular aperture θa , θe =

0.88λ da , de

(1.3)

where da is the aperture dimension in the azimuth plane and de is the aperture dimension in the elevation plane (same dimensions as λ). There are two types of antenna beams that can be used. These are the pencil beam and the fan beam. The pencil beam antenna pattern has a beamwidth in the horizontal plane that is approximately equal to the beamwidth in the vertical plane (θe ≈ θa ). The beamwidth for a radar pencil beam is generally only a few degrees, since a small angular resolution is usually desired. From (1.3), the resolution depends on the aperture size as well as the wavelength of operation. For the fan beam pattern, one angular dimension is smaller than the other (usually θa < θe to maintain good angular resolution in azimuth). The bandwidth of the antenna is defined as the range of frequencies for which the performance of the antenna conforms to a specific standard. It is usually specified as a range of frequencies about the center frequency of radiation. The polarization of a radiated waveform is that property of the wave that describes the time-varying direction and relative magnitude of the electric field vector (the curve traced by the instantaneous electric field vector). Polarization of the radiation can be linear, circular, or elliptical. Polarization modulation can also reduce the probability of intercept. A phased array is an array antenna whose beam direction or radiation pattern is controlled primarily by the relative phases of the excitation coefficients of the radiating elements. A single multifunction phased array radar system can perform surveillance, fire control, communications, and electronic warfare without requiring separate radars and antennas for these functions. Phased arrays generally have bandwidths less than 10% and are steered by using passive phase shifters that are controlled over electrical paths (usually by digital signals). More advanced phased arrays are being developed where the transmit and receive modules employ photonic switching (at optical frequencies), allowing high accuracy pointing and instantaneous beam positioning. They also allow multiple pulse compression modulation signals to be scanned over large angles. An example of a recent pioneering development is shown in Figure 1.1. This figure shows the phased array used in the F-22 multimode fire control radar [6]. The F-22’s AN/APG-77 electronically scanned array antenna is composed of several thousand transmit/receive modules, circulators, radiators, and manifolds assembled into subarrays and then integrated into a complete array. The baseline design used thousands of hand-soldered flex circuit interconnects to make the numerous radio frequency, digital, and direct current connections between the components and manifolds that make

To See and Not Be Seen

7

Figure 1.1: Phased array antenna for the F-22 multimode radar [6]. up the subarray. The phased array aids the APG-77 with the capability to transmit an LPI waveform. More of these types of systems are discussed in Chapter 2.

1.2.2

Achieving Ultra-Low Side Lobes

The fields radiated from a linear array are a superposition (sum) of the fields radiated by each element in the presence of the other elements. Each element has an excitation parameter (current for a dipole, voltage for a slot, and mode voltage for a multiple-mode element) [7]. The excitation of each element in the aperture has a diﬀerent amplitude and phase and is known as the aperture distribution. The far-field radiation pattern is the discrete Fourier transform of the array excitation. The array pattern can be written as F (u) =

Ne 3

An ej2π(n−1)u

(1.4)

n=1

where An are the excitation coeﬃcients of the array which has Ne elements and d (1.5) u = (sin θ − sin θ0 ) λ and θ represents the angle from broadside, d the element spacing, and u the array variable. The main lobe peak is at θ0 . Using w = ej2πu

(1.6)

8

Detecting and Classifying LPI Radar

(1.4) can be written as F (u) =

Ne 3

An wn−1

(1.7)

n=1

If the aperture excitation is uniform (An = 1), it can be shown that [7] F (u) =

sin Ne πu jπ(Ne −1)u e Ne sin πu

(1.8)

In this case the radiation intensity has a (sin x/x)2 pattern. The field strength voltage pattern has a sin x/x pattern with a highest side lobe level of −13 dB. The LPI antenna must have a transmit radiation pattern with very low side lobes. The low side lobes in the transmit pattern reduce the possibility of an intercept receiver detecting the radio frequency (RF) emissions from the side lobe structures of the antenna pattern. The important general rules for developing low side lobe antennas are [7]: • Symmetric amplitude distributions give lower side lobes. • F (u) should be an entire function of u. • A distribution with a pedestal produces a far-out side lobe envelope of 1/u. • A distribution going linearly to zero at the ends produces a far-out side lobe envelope of 1/u2 . • A distribution that is nonzero at the ends (pedestal) is more eﬃcient. • Zeros should be real (located on the unit circle). • Far-out zeros should be separated by unity (in u). By applying a tapered (apodized) excitation from the center to the ends of the antenna, the side lobe level can be lowered below −13 dB. A level of −20 dB is normally acceptable, but with LPI radar, ultra-low side lobes are required (−45 dB). Table 1.1 shows three excitation tapers (cosine, triangular, and parabolic) for a rectangular array of length d, and the resulting antenna performance [8]. A circular array has similar numbers. Note that as the side lobe level goes down (SLR gets larger), the beamwidth gets larger and the antenna gain decreases. Another significant aperture excitation is the Taylor distribution developed by T. T. Taylor in 1960 [9, 10]. Taylor realized that to produce a linear aperture distribution with a side lobe envelope approximating a 1/u falloﬀ, the uniform amplitude sin x/x pattern could be used as a starting point by realizing that the height of each side lobe is controlled by the spacing between

To See and Not Be Seen

9

Table 1.1: Aperture Taper Functions and Resulting Characteristics 3-dB Beamwidth Excitation (rad) Cosine G(x) = cosN (πx/2); |x| < 1

Side Lobe Ratio (dB)

Relative Gain

Full Null Position

13.2 23.0 32.0 40.0 48.0

1.000 0.810 0.667 0.575 0.515

1.0λ/d 1.5λ/d 2.0λ/d 2.5λ/d 3.0λ/d

Triangular G(x) = 1 − |x|; |x| ≤ 1 1.28λ/d Parabolic G(x) = 1 − (1 − ∆)x2 ; |x| < 1

26.4

0.75

2.0λ/d

∆ = 1.0 ∆ = 0.8 ∆ = 0.5 ∆=0

13.2 15.8 17.1 20.6

1.00 0.99 0.97 0.83

1.00λ/d 1.06λ/d 1.14λ/d 1.43λ/d

N N N N N

=0 =1 =2 =3 =4

0.88λ/d 1.20λ/d 1.45λ/d 1.66λ/d 1.94λ/d

0.88λ/d 0.92λ/d 0.97λ/d 1.15λ/d

the aperture pattern factor zeros on each side of the side lobe. That is, since the sinc pattern has a 1/u side lobe envelope it is only necessary to modify the close-in zeros to reduce the close-in side lobes. The shifting is accomplished by setting zeros equal to 0 (1.9) u = n2 + B 2 where B is a positive real parameter. The resulting pattern with the zeros shifted can be written as √ sinh π B 2 − u2 √ (1.10) F (u) = π B 2 − u2

for u ≤ B and

√ sin π B 2 − u2 √ F (u) = π B 2 − u2

(1.11)

for u ≥ B and is a modified sinc pattern where the one parameter B controls all of the characteristics (side lobe level, beamwidth, directivity and so forth). Often known as the one-parameter Taylor scheme, the SLR (in decibels) can be expressed as sinh πB + 13.2614 (1.12) SLR = 20 log πB

10

Detecting and Classifying LPI Radar

Table 1.2: Taylor Weighting Characteristics Side Lobe Ratio (dB) 13.26 15 20 25 30 35 40 45 50

B 0 0.3558 0.7386 1.0229 1.2762 1.5136 1.7415 1.9628 2.1793

θ3 (rad) 0.8858λ/d 0.9230λ/d 1.0238λ/d 1.1160λ/d 1.2004λ/d 1.2782λ/d 1.3504λ/d 1.4182λ/d 1.4822λ/d

The SLR for the Taylor weighting as a function of the B parameter, and the 3-dB beamwidth is shown in Table 1.2 as a function of the array length d and the wavelength λ. Tables of circular aperture distributions and the design process for the Taylor scheme are given in [11].

1.2.3

Antenna Scan Patterns for Search Processing

LPI radar systems are often identified by the type of scanning the emitter uses. Scanning is the systematic movement of a radar’s antenna beam in a particular pattern to search or track a target. The two methods of scanning an antenna beam are mechanically and electronically. The antenna can be mechanically scanned by using gimbals to move the entire antenna aperture in any direction. Most often used are the two-dimensional arrays and parabolic reflectors (where instead of moving the reflector, the reflector feed can be nutated to provide the scan coverage needed). The antenna can also be electronically scanned by varying the phase between antenna elements (phased array). The simplest case of a search radar scan is the use of a stationary pencil beam that is fixed in elevation and rotated mechanically at a scan rate of ωr r s−1 to obtain an Ωa = 2π r coverage in azimuth and an Ωe = θe coverage in elevation. If range information is obtained for each beam position in space, this is an example of a one-dimensional (1D) scan pattern. In this case the antenna searches or scans a solid angle field of view or scan volume Ωs = Ωa Ωe = 2πθe sr (steradian). With a total solid angle coverage of the sensor Ωs sr, the number of resolution elements is this value divided by the instantaneous field of view of the antenna or nr =

Ωs θa θe

(1.13)

or 2π/θa . The elevation of the scan can also be changed after each complete

To See and Not Be Seen

11

Figure 1.2: LPI scan patterns: (a) conventional transmit-receive raster, (b) multibeam sector scan, and (c) omnitransmit multibeam receive. rotation. This results in range, azimuth, and elevation information being obtained from the field of view (e.g., a 2D scan pattern). To increase the eﬃciency of this 2D scan pattern, a set of n contiguous fixed pencil beams can be stacked in elevation [12]. The azimuth scan can also be limited as shown in Figure 1.2(a) (azimuth dimension only) and, at the end of the limit, the elevation can be changed for the next azimuth scan (in the opposite direction). This type of transmit-receive pattern is called a raster scan and is used frequently since it provides good coverage both in azimuth and elevation. An example of an LPI radar using this scan pattern is the Signaal’s SMART-L (mechanical scanning implementation) [13, 14]. The SMART-L is discussed further in Chapter 2. The time Tf s required to cover the solid angle of coverage Ωs is called the frame time. For frame time Tf , the dwell time (sometimes known as time-on-target) is Tf s (1.14) τd = nr That is, for τd s, energy is received from any point target at a range RT in

12

Detecting and Classifying LPI Radar

space that is illuminated by the transmitted radiation. The value of the dwell time given by (1.14) is for one pencil beam scanning in azimuth and elevation. If the radar system uses a stacked beam configuration to scan in azimuth and elevation, the on target time will be increased by this factor τd =

nTf nTf θa θe = s nr Ωs

(1.15)

where n is the number of contiguous beams in the stack (usually six to 16 [12]). Note that (1.15) does not include any scanning loss factor such as the time necessary for the mechanically scanning antenna to move from the endof-frame position to the beginning-of-frame position. Accounting for this loss Ls > 1, the dwell time is expressed as τd =

nTf θa θe s Ωs Ls

(1.16)

Phased arrays provide the ability to form multiple beams at diﬀerent frequencies to selectively search diﬀerent portions of the scan volume. In most cases, the transmit scan pattern of the LPI radar is controlled precisely to limit the illumination time to short and infrequent intervals (aperiodic scan cycle). An example of an LPI radar with this capability is described in the next section. By subdividing the scan volume into Nd sections, with every sector simultaneously searched by a diﬀerent stack of beams using a diﬀerent frequency, the dwell time in each beam direction can also be increased by a factor of Nd (see p. 530 in [15]) as nTf θa θe s (1.17) τd = Nd Ωs Ls Figure 1.2(b) shows the multibeam sector scan where the same scan volume Ωs is divided into Nd sectors. For this technique (electronic scanning), each sector has its own transmit-receive beam. Matching the coherent integration time to the dwell time, the power emitted in any one beam direction can be reduced by the factor 1/Nd . To electronically scan a phased array antenna a progressive phase shift is typically used [5]. To maintain a low side lobe level a method based on a pattern search algorithm (PSA) has been recently proposed [16]. Instead of an amplitude taper (such as a Taylor excitation), low side lobe scanning can be achieved using a phase taper. The PSA is a direct search algorithm. By defining a fitness function, the pattern search finds the best group of phase variations to scan the main beam to the desired position while also reducing the peak side lobe level [17]. Figure 1.2(c) shows a nonscanning single-beam transmit, multibeam receive array where enough receive beams are formed to completely fill the scan volume Ωs . This technique requires increased signal processing throughput

To See and Not Be Seen

13

and uses a single beamwidth nonscanning transmit antenna with many simultaneous receive beams. Since no scanning is involved, the dwell time is equal to the frame time (1.18) τd = Tf s One important flexibility with this pattern is that the transmitter does not need to be colocated with the receive array. An example of an LPI radar that uses this technique is the omnidirectional LPI radar (OLPI) [18, 19]. The OLPI is discussed further in Chapter 5. As discussed in Part II (Chapter 11 through Chapter 18) of the text, intercept receivers use a variety of strategies to identify the LPI radar, including angle of arrival, carrier frequency, scan rate, modulation period, bandwidth, and polarization. Randomly altering any of these parameters can therefore provide confusion to the intercept receiver. Scan methodologies can be used to help confuse identification if intercept occurs. For example, a scan technique that attempts to confuse identification might include amplitude modulation of a monopulse array at conical scan frequencies that are not considered threatening. These types of scan methodologies require significant additional processing requirements (and power) that limit the platforms that can carry this type of capability.

1.2.4

Advanced Multifunction RF Concept

A radar that has the capability of forming multiple beams is the advanced multifunction RF concept (AMRFC). The AMRFC is a United States Navy program to investigate the capability to integrate radar (including an LPI navigation radar in the high band 4.5—18.0 GHz), electronic warfare, and communication functions into a common set of wideband, low power level RF apertures, where the functionality is mostly defined by the software [20]. Consequently, the AMRFC reduces the number of topside RF system antenna apertures while increasing the eﬀective functionality (through software), as well as increasing the capability for ship signature control/reduction. The AMRFC divides the frequency band into an optimal number of segments, based on cost and functionality, and then utilizes separate transmit and receive apertures. The separate transmit and receive apertures allow full utilization of the entire time line for the transmitter as well as for the receiver. The transmit array is composed of dynamically allocable subarrays that are sectioned to form multiple simultaneous transmit beams. Since having more than one signal present in a power amplifier is not currently feasible, each transmit subarray is used by one function at a time. However, for the receive array, more than one signal can be present simultaneously in a subarray. The wideband arrays are electronically scanned and use solid state transmit and receive apertures. The use of the contiguous subarray architecture using phase shifters at the element level and true time delays at the subar-

14

Detecting and Classifying LPI Radar

Figure 1.3: High band multifunction transmit array [22]. ray level results in high side lobes, due to subarray dispersion and grating lobe generation [21]. The AMRFC phased arrays achieve side lobe reduction by using an overlapping subarray architecture. Digital beamforming at the subarray level makes it possible to generate multiple cluster beams and achieve pattern control or interference cancelation simultaneously. The overlapping subarray allows the grating lobes to be pushed away from the main lobe and shape the subarray patterns in such a way that all grating lobes are suppressed in the subarray’s low side lobe region. The overlap architecture is further discussed in [21]. Figure 1.3 shows the high-band multifunction transmit array that supports up to four simultaneous transmit beam configurations. Transmit array quadrants may also be combined to form larger apertures [22].

1.2.5

Transmitter Considerations

A conventional radar that uses a coherent pulse train has independent control of both range and Doppler resolution. This type of radar waveform also exhibits a range window that can be inherently free of side lobes. The main drawback of a coherent pulse train waveform is the high peak-to-average power ratio put out by the transmitter. The average power is what determines the detection characteristics of the radar. For high average power, a short pulse (high range resolution) transmitter must have a high peak power, necessitating vacuum tubes and high voltages. The high peak power transmissions can also easily be detected by noncooperative intercept receivers. The duty cycle dc for a pulsed emitter relates the average transmitted power

To See and Not Be Seen

15

Figure 1.4: Comparison of a pulsed radar and a CW radar. Pavg to the peak power Pt as dc =

Pavg Pt

The duty cycle can also be calculated as τR dc = TR

(1.19)

(1.20)

where TR is the pulse repetition interval (time between pulses) and τR is the emitter’s pulse width or duration (in seconds). Typical duty cycles are dc = 0.001 (the average power 0.001 times the peak power) for navigation radar. In modulated CW signals, however, the average-to-peak power ratio is one or 100% duty cycle. This allows a considerably lower transmit power to maintain the same detection performance as the coherent pulse train radar. Also, solid state transmitters can be used that are lighter in weight. A comparison of a coherent pulse train radar and the CW radar is shown in Figure 1.4. The CW radar has a low continuous power compared to the high peak power of the pulse radar but, as will be demonstrated, both can give the same detection performance. On the other hand, the final peak power for a pulsed system may be only a few decibels (dB) higher than that of CW systems having equivalent performance. Consequently, most LPI emitters use continuous wave (CW) signals. A CW (tone) signal is easily detected with a narrowband receiver and cannot resolve targets in range. LPI radars use periodically modulated CW signals resulting in large bandwidths and small resolution cells, and are ideally suited for pulse compression.1 1 The pulse compression concept is being extended here to unpulsed CW waveforms since the techniques are similar and the objectives are the same.

16

Detecting and Classifying LPI Radar

There are many pulse compression modulation techniques available that provide a wideband LPI CW transmit waveform. Any change in the radar’s signature can help confuse an intercept receiver and make intercept diﬃcult. The wide bandwidth makes the interception of the signal more diﬃcult. For the intercept receiver to demodulate the waveform, the particular modulation technique used must be known (which is typically not the case). Pulse compression (wideband) CW modulation techniques include: • Linear, nonlinear frequency modulation (Chapter 4); • Phase modulation (phase shift keying PSK) (Chapter 5); • Frequency hopping (frequency shift keying FSK), Costas arrays (Chapter 6); • Combined phase modulation and frequency hopping (PSK/FSK) (Chapter 6); • Noise modulation (Chapter 7). With the above modulation techniques, the radiated energy is spread over a wide frequency range in a manner that is initially unknown to a hostile receiver. The phase and frequency modulation are not inherently wideband or narrowband. The LPI radar designer chooses the necessary bandwidth in order to get the range resolution properties needed. He then chooses the modulation code necessary to get the ambiguity properties needed. This is where the implementation issues must be addressed. The major goal for the LPI radar designer is to get a 100% duty cycle and still retain the range and velocity performance required. In single antenna systems where leakage from transmitter to receiver can desensitize the target detection capability, an interrupted CW waveform is often used.

1.2.6

Power Management

Another feature of the LPI transmitter is power management (one of the benefits to using a solid-state radar/phased array combination). Of course, the best LPI strategy is to not radiate at all, but the next best strategy is to manage the power that is radiated. Power management is the ability to control the power level emitted by the antenna, and limit the power to the appropriate range/radar cross section detection requirement. The emissions are also limited in time (short dwell time). With the use of wideband pulse compression CW emissions, it is only necessary to transmit a few watts (instead of tens of kilowatts of peak power required by low duty cycle pulsed radars with similar detection performance). The LPI radar operates under low SNR conditions and it is important to recall that the radar’s ability to detect targets depends

To See and Not Be Seen

17

Figure 1.5: Regions of maximum atmospheric absorption in the millimeter wave spectrum from measured data [23] ( c 1999 Artech House, reprinted with permission). not on the waveform characteristics, but on the transmitted energy returned from the target. Many intercept receivers depend on seeing an increase in intercepted power as a closing missile approaches. With power managed seekers, the radar emits only the power required for detection. As the range-to-target is reduced, the intercepted power level decreases and varies directly as a function of R2 . This LPI strategy can then force the intercept receiver into incorrectly placing its priorities for electronic attack. That is, since the intercepted power decreases, the receiver identifies the threat as nonapproaching; therefore no attack should be necessary (unfortunately, a deadly decision). The concept and usefulness of power management is quantified further in Chapter 9.

1.2.7

Carrier Frequency Considerations

Another LPI radar technique is choosing the emitter frequency strategically. The use of a high operating frequency band that is within atmospheric absorption lines makes interception diﬃcult, but also makes the target detection by the radar even more diﬃcult in most cases. The absorption spectrum is shown in Figure 1.5 [23]. Peak absorption occurs at frequencies of 22, 60, 118, 183, and 320 GHz. The RF frequency can be chosen at these frequencies

18

Detecting and Classifying LPI Radar

to maximize the attenuation in order to mask the transmit signal and limit reception by a hostile receiver (atmospheric attenuation shielding). Since the physics of radar detection, however, depends only on the energy placed on the target, LPI radars must still radiate suﬃcient eﬀective radiated power (ERP) to accomplish detection. The loss for the radar due to atmospheric absorption is over its total two-way path (out to the target and back), while the interceptor’s loss is over the one-way path (from the radar to the intercept receiver). Because of the high absorption of the emitter’s energy, this technique is always limited to short range systems. In the case of an intercept receiver on a radar target platform (such as a radar warning receiver), the advantage lies with the interceptor, since there is only one-half the path loss. Another approach to achieving a lower probability of interception is to interleave the LPI radar mode with an infrared sensor (dual mode approach), reducing the amount of time that the RF transmitter is radiating. In summary, the important characteristics of LPI radar include wideband CW emission, low antenna side lobes with infrequent scan modulation, or the use of a broad nonscanning transmitting beam combined with a stationary set of receive beams. Polarization modulation can also be used. The transmitter uses a wideband modulation technique (for the range resolution desired) in combination with power management and a strategic selection of frequency to achieve the desired amount of atmospheric attenuation. That is, the wideband signals are diﬀused in time, appearing in pseudorandom directions at pseudorandom times.

1.3

Pulse Compression—The Key to LPI Radar

The three general types of CW LPI radar architectures are the: (a) frequency modulating radar that includes FMCW and frequency shift keying (hopping), (b) the phase modulating radar that includes polyphase modulation (polyphase shift keying) and polytime modulation, and (c) the radar that is a combination of both (a) and (b). The FMCW radar architecture is now in widespread use. A block diagram of an FMCW radar is shown in Figure 1.6. The radar uses two antennas (one transmit and one receive). The transmitted waveform for the FMCW radar is a linear (or nonlinear) frequency modulated waveform, and can be generated by using a direct digital synthesizer. The received waveform is amplified by a low noise amplifier (LNA) and correlated (or mixed) with the transmit waveform in order to derive the target beat frequencies (homodyne detection). After the analog demodulation is used to generate the intermediate frequency (IF) beat signals, they are digitized with an analog-to-digital converter. The digital signal with input signal-to-noise ratio SNRRi is processed by one or more fast Fourier transform signal processors to derive the range (and possibly Doppler) profile. As shown in Figure 1.6, a certain amount of integration is also commonly used to increase the

To See and Not Be Seen

19

Figure 1.6: Block diagram of an FMCW radar. output signal-to-noise ratio SNRRo . Integration improves SNRRo since the noise energy that accumulates in each range bin varies from one integration period to the next, whereas the target return increases in direct proportion to the integration time. Increasing the integration time can improve SNRRo significantly. After integration, the target detection and tracking function is performed. The radar input SNRRi and output SNRRo are related by the processing gain of the signal processor as P GR =

SNRRo SNRRi

(1.21)

and depends on the time-bandwidth characteristics of the transmit signal modulation as well as any noncoherent integration. The processing gain is also referred to as the pulse compression ratio. A simple empirical formula can also be used for the relationship between SNRRo and the probability of detection Pd , and the probability of false alarm Pf a due to Albersheim is given as [12] (1.22) SNRRo = A + 0.12AB + 1.7B where A = ln

w

0.62 Pf a

W

(1.23)

20

Detecting and Classifying LPI Radar

and B = ln

w

Pd 1 − Pd

W

(1.24)

Here SNRRo is in linear units and not decibels. If the radar uses an FMCW waveform, the processing gain (excluding any noncoherent integration) is the sweep or modulation period, tm , multiplied by the sweep (input) bandwidth, ∆F . That is, P GR = tm ∆F

(1.25)

The modulation period tm in an FMCW radar plays the same role as TR in a pulsed radar and, in either case, both systems normally perform noncoherent integration over as many such intervals as occupy the dwell time of the beam. When noncoherent integration is performed for NI such intervals, √ the processing gain is increased by NI . Also note that although Figure 1.6 shows an analog processing approach, the cross correlation (or homodyne detection) could also be done digitally. Additional details on FMCW LPI radar design are discussed in Chapters 4, 7, 8, and 9. A block diagram of a phase coded radar is shown in Figure 1.7. The phase coded radar can also use a direct digital synthesizer to generate the transmitted waveform. The phase coded radar transmit waveform is generated using various phase modulations and/or frequency modulations. The target return signal is amplified and downconverted using a local oscillator (LO), and digitized with an ADC. The digitized samples are then processed by a digital compressor, which cross correlates the transmitted code with the received signal. For phase modulation of a CW waveform using Nc number of subcodes, the processing gain is the code period, T , multiplied by the transmitted bandwidth, 1/tb , where tb is the subcode period. That is, P GR = T (1/tb ) = (Nc tb )/tb = Nc

(1.26)

In the phase coded radar, the return signal is compressed using digital techniques, and noncoherent integration will also add to this processing gain. Additional details on phase shift keying radar are given in Chapter 5 and an example of the processing gain distribution in a phase coded LPI radar is given in Section 5.12. Note that in the FMCW radar example shown in Figure 1.6, the return signal from the target is compressed using an analog processor. Although Figure 1.6 shows an analog processing approach, the processing could equally well be digital. That is, the distinction between the two is the modulation, not the method of processing or the location of the ADC in the receiver path. For both the frequency modulation and phase modulation LPI radar, the transmitted CW signal is coded with a reference signal to spread the transmitted energy in frequency, to avoid detection and identification by the noncooperative intercept receiver. The reference signal can take the form of either

To See and Not Be Seen

21

Figure 1.7: Block diagram of a phase coding radar. a linear (nonlinear) frequency modulation, a frequency hopping sequence, a phase code sequence, or a combination of these techniques. The FMCW technique has been the most popular implementation, but with the current capabilities of digital processors, phase coding CW waveforms are becoming the standard, since many codes and variations can be employed. Note also that frequency modulated CW signals can be approximated by phase coded signals; a concept also discussed more thoroughly in Chapters 5, 8 and 10. Although the CW signal is continuous, this does not imply that the portion processed by the receiver in order to make a measurement or detect a target is infinitely long. There are physical constraints, such as the illumination time and the size of the receiver’s correlation processor. Fast Fourier transform processors (for frequency modulated waveforms) and finite duration coherent correlation processors (for phase modulation waveforms), as well as combinations of both, are among the most-often-used techniques to derive the target information. The LPI receiver must correlate (or compress) the received signal from the target using the stored reference signal, in order to perform target detection. The correlation receiver is a “matched receiver” if the reference signal is exactly the same duration as the finite duration return signal. Figure 1.8 shows a transmitted waveform (represented as a phase coded signal) of length 1. Also P T , where T is the code period, tb is the subcode period, and P

22

Detecting and Classifying LPI Radar

Figure 1.8: CW transmitted waveform and receiver reference signal [24, 25]. shown is the reference signal of length N T used in the receiver to compress the received signal. Increasing the number of receiver reference waveforms N improves the target detection capabilities by increasing the resolution of the receiver response. The ambiguity analysis in Chapter 3 investigates this concept in more detail. The LPI radar receiver can be modeled as a coherent correlation processor of finite duration N T as shown in Figure 1.9 [27]. The return signal is received by the correlation receiver containing a reference signal which is the conjugate of N periods of the transmitted signal with N < P . The correlation receiver performs a cross correlation between the received signal and a reference signal, whose envelope is the complex conjugate of N periods of the transmitted signal envelope. To do this, the return signal (a binary phase coded signal in this example) is first processed by a filter matched to a rectangular subcode of length tb , followed by a detector that sends forward a one or a zero. The detected output signal is then piped through a tapped delay line where each delay D is tb s. The signal in the tapped delay line is first multiplied by the reference signal. The output of each multiplication is then summed separately for each of the N code periods. The output of the sum block can then be weighted as C1 through CN . With uniform weights, the first stage represents the response of the receiver for a zero-Doppler shift signal (ν = 0), and is identical to the ideal autocorrelation function [26]. The response of the receiver to a Doppler shifted signal ∆ν is obtained from the second stage by first multiplying the output (before addition) from the first stage with q 0 through q MN−1 where q = ej2π∆νtb . In phase coded CW radar systems, return signals with Doppler do not cor-

To See and Not Be Seen

23

Figure 1.9: Doppler matrix correlation receiver matched to N periods of a phase coded signal of length M = 5 including weighting Ci for Doppler side c lobe reduction [26] (s1992 IEEE).

24

Detecting and Classifying LPI Radar

Figure 1.10: LPI radar and intercept receiver configuration. relate perfectly because the Doppler shift changes the phase of the code across its period. This causes imperfect compression. Since the received signal is usually delayed and Doppler shifted, there is a special interest in the response of a matched receiver, such as in Figure 1.9, to its own signal as a function of the two parameters delay and Doppler. To reduce the side lobes, weighting may be factored into the reference signal. If the reference signal is weighted in order to reduce side lobes, the receiver is called a mismatched receiver. In Chapter 3, the ambiguity response of these LPI receivers is discussed, as well as the weighting functions.

1.4

Radar Detection Range

In this section, the maximum detection range for a CW radar is examined. The CW radar has a low continuous power with a 100% duty cycle. The LPI radar and intercept receiver configuration is shown in Figure 1.10. To determine the detection range of a CW radar, we start with the power density at a range R m from an isotropic antenna given as [27] PD =

PCW 4πR2

2

W/m

(1.27)

To See and Not Be Seen

25

where PCW is the average power of the CW transmitter in watts. With a “directive” antenna having a transmit gain Gt along the boresight, the directed power density at a range R from the radar is PCW Gt L1 4πR2

P DD =

2

W/m

(1.28)

The term L1 (< 1) is the one-way atmospheric transmission factor L1 = e−αRk

(1.29)

where Rk is the range or path length in kilometers and α is the one-way extinction coeﬃcient or power attenuation coeﬃcient in nepers per km (Np/km). The one-way attenuation coeﬃcient as a function of frequency is shown in Figure 1.5 in more useful engineering units (dB/km). To convert dB/km into Np/km, multiply the attenuation coeﬃcient in Figure 1.5 by 0.23. The reradiated power density reflected oﬀ a target with radar cross section σT (m2 ) at range RT and appearing back at the radar is w W σT PCW Gt L2 P DDR = W/m2 (1.30) 4πRT2 4πRT2 where RT is the range between the LPI radar and the target. The term L2 (< 1) is the two-way atmospheric transmission factor L2 = e−2αRk

(1.31)

The LPI radar captures the reflected energy with its receive antenna. The received signal power at the radar receiver from the target is w W σT PCW Gt L2 Ae (1.32) PRT = 4πRT2 LRT LRR 4πRT2 where Ae is the eﬀective area of the radar receive antenna and related to the receive antenna gain Gr as Gr λ2 Ae = (1.33) 4π and LRT is the loss between the radar’s transmitter and antenna, and LRR is the loss between the radar’s antenna and receiver. Substituting (1.33) into (1.32) gives the reflected power at the radar receiver as PRT =

PCW Gt Gr λ2 L2 σT (4π)3 RT4 LRT LRR

(1.34)

It is often necessary to know the minimum input signal power at which a receiver can detect and process an incoming target signal. This is called the

26

Detecting and Classifying LPI Radar

receiver’s sensitivity or δR . Substituting the sensitivity for PRT in (1.34), the maximum range at which the LPI radar can detect a target is RR max =

}

PCW Gt Gr λ2 σT L2 (4π)3 (δR )LRT LRR

]1/4

(1.35)

The sensitivity δR is the product of the minimum signal-to-noise ratio required at the input (SNRRi ) times the noise power in the input bandwidth of the receiver. The sensitivity of the radar receiver can be expressed as δR = kT0 FR BRi (SNRRi )

(1.36)

where k = 1.38(10−23 ) joule/K (Boltzmann’s constant), T0 is the standard noise temperature (T0 = 290K), FR is the receiver noise factor, and BRi is the radar receiver’s input bandwidth in Hz, and is usually matched to the particular waveform being transmitted. The maximum detection range can be expressed as RR max

}

PCW Gt Gr λ2 σT L2 = (4π)3 kT0 FR BRi (SNRRi )LRT LRR

]1/4

(1.37)

Also recall that the processing gain of the radar is P GR =

SNRRo SNRRi

(1.38)

and depends on the particular waveform characteristics and integration techniques being used by the LPI radar. Note also that the sensitivity δR can be expressed as a function of the output signal-to-noise SNRRo required for detection and the output bandwidth BRo as δR = kT0 FR BRo (SNRRo )

(1.39)

For example, consider an LPI radar with PCW = 1W, Gt = Gr = 30 dB, fc = 9.375 GHz, FR = 5 dB, and BRi = 1 MHz. If all losses are 0 dB and L2 = 1, Figure 1.11 shows the LPI radar maximum detection range as a function of the required input signal-to-noise ratio SNRRi for σT = 1, 10, and 100 m2 . With an SNRRi = 10 dB, a 1 m2 -target can be detected at a range of 1,450m while a σT = 100 m2 can be detected at a range of 4,500m. This information, however, does not reveal the benefit of the LPI radar. To quantify this, the LPI radar’s maximum target detection range must be compared to the intercept receiver’s maximum interception range.

To See and Not Be Seen

27

Figure 1.11: LPI radar maximum detection range for σT =1, 10, 100 m2 .

1.5

Interception Range

From the configuration shown in Figure 1.10, the signal power available at the intercept receiver from the LPI radar is W w GI λ2 PCW Gt L1 (1.40) PIR = 4πRI2 LRT LIR 4π where RI is the range from the LPI radar to the intercept receiver, and Gt is the gain of the LPI radar’s transmit antenna in the direction of the intercept receiver. Also, GI is the gain of the intercept receiver’s antenna, and LIR represents the losses from the antenna to the receiver. If the intercept receiver detects the radar main lobe, Gt = Gt . If the intercept receiver detects the radar emission from the side lobes, Gt represents the gain of the antenna side lobe in the intercept receiver direction. Replacing the signal power available, PIR , by the intercept receiver’s sensitivity, δI , the maximum interception range of the receiver can be defined as PCW Gt GI L1 λ2 (1.41) RI max = (4π)2 LRT LIR (δI ) where the sensitivity in the intercept receiver is similarly defined as δI = kT0 FI BI (SNRIi )

(1.42)

28

Detecting and Classifying LPI Radar

Figure 1.12: Block diagram of an intercept receiver model showing both the predetection stage and the postdetection stage. where FI is the intercept receiver noise factor, BI is the bandwidth of the intercept receiver, and SNRIi is the SNR at the intercept receiver signal processor input. The maximum interception range can then be expressed as PCW Gt GI L1 λ2 (1.43) RI max = 2 (4π) LRT LIR kT0 FI BI (SNRIi ) Also recall that the intercept receiver processing gain P GI is defined as P GI =

SNRIo SNRIi

(1.44)

Contrary to communication or radar system receiver design where the bandwidth is matched to the known transmitted signal, the intercept receiver does not know the exact nature of the threat signals. Figure 1.12 shows a block diagram of an intercept receiver model showing the predetection stage and the postdetection stage. The three major components include the RF (predetection) amplifier with bandwidth BIR , the detector (e.g., square law), and the postdetection video amplifier with bandwidth BIV . In the intercept receiver design it is most often necessary to match the front-end RF bandwidth BIR to the largest coherent radar bandwidth expected, and to match the video bandwidth BIV to the inverse of the smallest radar coherent integration time expected tI . Exact analysis of intercept receiver bandwidths and sensitivities is complicated. However, since the δI in (1.42) is dependent on the intercept receiver’s overall bandwidth, it is desirable to have an approximate expression for BI that includes the eﬀects of both the predetection and postdetection bandwidths. The approximate expressions have been derived by Klipper [28]. The bandwidth of the intercept receiver for BIR >> BIV (which is typically the case) can be expressed as 0 (1.45) BI = 2BIR BIV

To See and Not Be Seen

29

for a square law detector and BI =

10 2BIR BIV 2

(1.46)

for a linear detector. The time-bandwidth product or processing gain of the intercept receiver often takes the form of [3] P GI = (tI BIR )γ

(1.47)

and depends on the eﬃciency γ. The noncoherent integration eﬃciency is on the order of 0.5 ≤ γ ≤ 0.8 [3]. For example, if an FMCW radar has a modulation bandwidth of ∆F = 55 MHz, and a coherent integration time of tm = 1 ms, the processing gain of the radar is P GR = tm ∆F √= 55,000, whereas the processing gain of the intercept receiver is only P GI = tm ∆F = 234 (γ = 0.5). This is the real origin of the LPI radar. Figure 1.13 shows the maximum interception range of the intercept receiver as a function of the required input SNRIi . This is the maximum range at which the passive intercept receiver can intercept an LPI radar operating at fc = 9.375 GHz with a transmitting antenna gain Gt = 1,000 and transmitter power PCW = 1W. The intercept receiver has an isotropic antenna with gain GI = 1, a noise figure FI = 5 dB, and LRT , LIR = 1. Both a square law and linear detector configuration are considered with BIV = 1 kHz (radar coherent integration time tm = 1 ms). The performance for predetection bandwidths of BIR = 60 MHz and 120 MHz is also compared. Note that the smaller the required predetection RF bandwidth is, the larger the maximum interception range. The use of a square law detector over a linear detector also gives a larger interception range.

1.6

Comparing Radar Range and Interception Range

The radar sensitivity δR (1.36) and intercept receiver sensitivity δI (1.42) can be used to quantify the benefit of the LPI radar. The ratio of the intercept receiver sensitivity to the radar sensitivity is w W kT0 BI FI SNRIi δI (1.48) = δ= δR kT0 BRi FR SNRRi In terms of the processing gains and output signal-to-noise ratios, the ratio of sensitivities can be expressed as w Ww W SNRIo P GR FI BI (1.49) δ= FR BRo SNRRo P GI

30

Detecting and Classifying LPI Radar

Figure 1.13: Intercept receiver with square law and linear detector BIV = 1 kHz, BIR = 60, and 120 MHz, showing maximum interception range for LPI radar with PCW = 1W, Gt = 30 dB, and fc = 9.375 GHz. Also, the sensitivity ratio can be written as a function of the radar and intercept receiver antenna parameters as δ=

4π σT

w

Gt GI L1 Gt Gr L2

W w

2 RR max RI max

W2

(1.50)

and conveniently expresses the sensitivity ratio as a function of the maximum detection ranges. Note that this equation is independent of the radar wavelength (directly) and the radar’s average transmit power. To directly compare the radar detection range and the intercept receiver detection range, we can solve (1.50) for the ratio of the two maximum detection ranges as } w W ]1/2 1 4π Gt GI L1 RI max = RR max RR max δ σT Gt Gr L2

(1.51)

Here the ratio of the radar receiver sensitivity to the intercept receiver sensitivity (δ) is in the denominator. If RI max /RR max < 1, then the radar can be considered a quiet radar. If the ratio RI max /RR max = 1, then the radar cannot be intercepted beyond the range at which it can detect targets. This

To See and Not Be Seen

31

is an important consequence. With RI max /RR max = 1, from (1.51) RR max

]1/2 } p Q σT L2 Gt Gr = δ 4π L1 Gt GI

(1.52)

Note that this is the maximum detection range of the LPI radar without being intercepted by the intercept receiver. This is also the noncooperative receiver’s maximum intercept range. An example is developed next in order to examine this result. To illustrate (1.52), the detection of an LPI radar is considered with both main lobe detection (Gt = Gt = 1,000) and side lobe detection with side lobes Gt = 0.1 (40 dB below main beam). The target RCS σT = 1m2 and we consider that L2 = L1 = 1. The intercept receiver antenna gain GI = 1. Figure 1.14 shows the sensitivity ratio as a function of the maximum detection range for both main lobe intercepts and side lobe intercepts. The figure shows the large diﬀerence in the sensitivity ratio due to the diﬀerence of detecting the radar in the side lobes versus the main lobes. The figure shows that a sensitivity ratio of 60 dB is required for a maximum radar detection range, noncooperative intercept range of ≈ 104 m (intercept receiver intercepting the main lobe). If the intercept receiver is required to intercept the radar in the side lobes at this range, the intercept receiver must decrease the sensitivity ratio from 60 dB to 20 dB. From (1.49), one of the ways this can happen is when the intercept receiver increases its processing gain P GI which is typically diﬃcult to do without sophisticated signal processing techniques (discussed in Part II).

1.7

The Pilot LPI Radar

During 1988, the Philips Research Laboratory developed a “quiet” radar known as Pilot, which was marketed by the then Philips’ subsidiaries PEAB in Sweden and Signaal in the Netherlands. With the sell-oﬀ of Philips’ defense assets, PEAB was taken over by Bofors (subsequently CelsiusTech and now SaabTech), and maintained the name of Pilot for this radar. For its part, Signaal was taken over by the then Thomson-CSF (now Thales), and modified and improved the FMCW Pilot concept and changed the name of the radar to Scout. The Pilot is a well-published example of an FMCW tactical navigation LPI radar [29—33]. It can easily be added on to an existing navigation radar, retaining the original X-band antenna, transceiver, and display system. In a tactical situation, the Pilot can be switched out and the pulsed radar can be switched in when higher signal-to-noise ratios are required. It also has standard video output to simplify integration with standard pulsed navigation radar.

32

Detecting and Classifying LPI Radar

Figure 1.14: LPI radar maximum detection range as a function of the sensitivity ratio δ. The Pilot uses an FMCW 1-kHz sweep repetition frequency with a low noise figure (FR = 5 dB) and very low output power to ensure that it is undetectable by hostile intercept receivers. Other features include a 1,024-point FFT (512 range cells) high range resolution (2.7m to 86m), high reliability, small lightweight designs, and ease of installation. The technical parameters are given in Table 1.3. Note that 1 nautical mile (nmi) = 1.852 km. Figure 1.15 shows the equipment that makes up the Pilot Mk3 version that was developed by Saab Bofors Dynamics AB (formerly CelsiusTech Electronics). The MK3 has an improved LPI performance by combining an FMCW waveform with frequency agility. In this section we use the formulations in previous sections to quantify the Pilot performance. The most important LPI characteristics of the Pilot are that it uses only one low side lobe antenna, transmits a maximum CW power of only 1W, and uses an FMCW waveform with a variable modulation bandwidth ∆F to vary the range resolution. We will return to a detailed discussion of this type of LPI radar modulation in Chapter 4. Below, several examples are shown to illustrate the performance of the radar and compare it with a conventional low pulse repetition frequency (LPRF) navigation radar.

To See and Not Be Seen

Table 1.3: Technical Characteristics of the Pilot Mk3 Antenna

Type: Gain: Side lobes: Beamwidth (3 dB) horizontal: vertical: Rotational speed: Polarization:

Single or dual slotted-waveguide 30 dB < −25 dB < −30 dB 1.2 deg 20 deg 24/48 RPM horizontal

Output power: Frequency: Range selection: Frequency sweep: Sweep repetition frequency:

1 kHz

Receiver

IF bandwidth: Noise figure:

512 kHz 5 dB

Processor Unit

No. of range cells: Range resolution: Range accuracy: Azimuth accuracy: Azimuth resolution:

512 (1,024-point FFT) < 75m at 6 nmi scale < ±25m at 6 nmi scale ±2 degrees 1.4 degrees

Display System

Type: Minimum eﬀective PPI diameter: Resolution: Tracking capacity: Range ring accuracy:

Color

Transmitter

1.0, 0.1, 0.01, or 0.001W (CW) 9.375 GHz (X-band) 24, 12, 6, 3, 1.5, 0.75 nmi 1.7, 3.4, 6.8, 13.75, 27.5, 55 MHz

250 mm 768× 1,024V 40 1.5% of selected scale or 50m, whichever is greater

33

34

Detecting and Classifying LPI Radar

Figure 1.15: Equipment that makes up the Pilot Mk3. Example 1: Sensitivity It is known that the Pilot radar using only PCW = 1W has a maximum detection range of RR max = 28 km for a σT = 100m2 target. Using the system parameter values given in Table 1.3, determine the sensitivity δR of the Pilot receiver. Using (1.35), δR =

PCW Gt Gr λ2 σT L2 4 (4π)3 (RR max )LRT LRR

(1.53)

with Gt = Gr = 1,000, λ = 0.032m, and substitution of the Pilot parameters (assuming that L2 = LRT = LRR = 1) δR = or −130 dBm.

1 ∗ (1,000)2 ∗ (0.032)2 ∗ 100 = 8.4 × 10−17 W (4π)3 ∗ (28,000)4

(1.54)

To See and Not Be Seen

35

Example 2: Required Input SNR Figure 1.6 shows SNRRi is located at the output of the ADC (input to the signal processor). Since the Pilot radar uses down conversion processing to translate the received signal frequency to IF, BRi = 512 kHz which corresponds to the Pilot’s IF bandwidth in Table 1.3. To determine the input signal-to-noise ratio SNRRi we know from (1.36) δR = kT0 FR BRi (SNRRi )

(1.55)

Using FR = 100.5 , kT0 = 4 × 10−21 , and BRi = 512 kHz, SNRRi =

δR = 0.013 kT0 FR BRi

(1.56)

or −19 dB. Example 3: Processing Gain, Output SNR For the maximum modulation bandwidth ∆F = 55 MHz, we can calculate the processing gain P GR and the output SNRRo . The processing gain for a single sweep can be calculated from (1.25) as P GR = tm ∆F = 55,000

(1.57)

The corresponding output SNR is then SNRRo = P GR (SNRRi ) = 715

(1.58)

or 28 dB. The addition of noncoherent integration of more than one modulation period within the signal processor can increase the processing gain and the SNRRo . Example 4: Comparison with Conventional Pulsed Radar If the emitter is a conventional low pulse repetition frequency (PRF) navigation radar with a peak power of Pt = 10 kW, pulse width of τ = 1 μs, and FR = 5 dB, neglecting losses, (a) determine the maximum detection range for a σT = 100m2 target if the minimum required receiver input signal-to-noise ratio SNRRi = −1.7 dB and (b) for the intercept system above (δI = −80 dBmi), determine the maximum intercept range (main lobe intercepts). For (a), we can use (1.37) with PCW replaced by the peak power Pt = 10 kW and

36

Detecting and Classifying LPI Radar

Table 1.4: Pilot Detection and Intercept Range Calculations Radar Detection Range (km) Radar Output Power Pilot Mk2 1W 0.1 W 10 mW 1 mW LPRF Radar 10 kW

Intercept Range (km) Intercept Intercept Intercept δI δI δI −40 dBmi −60 dBmi −80 dBmi

100 m2 target

1 m2 target

28 16 9.0 5.0

8.8 5.0 2.8 1.5

0.25 0 0 0

2.5 0.8 0.25 0

2.5 8.0 2.5 0.8

49.6

15.7

25

254

2.546

BRi = 1(106 ) = 1/τ .2 Rconv or Rconv =

}

}

Pt Gt Gr λ2 σT L2 = (4π)3 kT0 FR BRi (SNRRi )

]1/4

104 ∗ (1, 000)2 ∗ (0.032)2 ∗ 100 (4π)3 ∗ 4(10−21 ) ∗ 100.5 ∗ 1(106 ) ∗ 0.67

(1.59) ]1/4

(1.60)

or Rconv = 49.6 km. For (b), the maximum intercept range can be determined from (1.41) as ]1/2 } Pt Gt GI L1 λ2 (1.61) RI max = (4π)2 δI LRT LIR or ]1/2 } 10, 000 ∗ 1(103 ) ∗ (1) ∗ (0.032)2 RI max = (1.62) (4π)2 ∗ 10−11.0

or RI max = 2,546 km. A summary of the above results and other additional calculations are shown in Table 1.4. Note that we use dBmi to represent dB in mW with reference to a system containing an isotropic antenna GI = 1.

1.8

Concluding Remarks

LPI modulation techniques include frequency modulation such as FMCW and frequency shift keying. Also used are phase modulations such as the polyphase 2 A pulsed radar receiver usually has an input bandwidth that is matched to the transmitted pulse width τ at either the null-to-null bandwidth (BRi = 2/τ ) or the 3-dB bandwidth (BRi = 1/τ ).

To See and Not Be Seen

37

codes Frank, P1, P2, P3, P4, and polytime codes T1, T2, T3, and T4. There are several trade-oﬀs in the design of LPI emitters. The LPI modulations are not inherently wideband (or narrowband). The radar designer chooses the emitter bandwidth to achieve the range resolution properties needed. He also chooses the particular code to get the ambiguity (delay Doppler frequency) code properties needed. Implementation issues must also be addressed (such as digital versus analog). The major question is how to get a 100% duty factor and still get the desired range and velocity performance needed to perform the mission. A larger processing gain can be obtained by wideband coding of the transmitted waveform with a modulation that is known only to itself. What is important is if the coding degrades the sensitivity of the intercept receiver relative to the radar receiver. The coding may or may not have an eﬀect on the sensitivity ratio δ. For example, if the intercept receiver is a simple crystal video receiver, then the wideband coding has no eﬀect on the intercept receiver’s sensitivity. That is, the value of coding in LPI has to do with the eﬀect imposed on the interceptor—not on the radar if it uses a matched filter. The intercept receiver bandwidth BI is typically larger than the radar’s coherent bandwidth in order to maximize the detection of the unknown signals and perform well against large time-bandwidth signals. Also, the intercept receiver’s noncoherent integration time should match the radar’s coherent integration time. The design of the modern intercept receiver, however, is a complicated issue due to the combined capability of an electronic support (ES) receiver, radar warning receiver (RWR), and electronic intelligence (ELINT) receiver in a single system, and many architectures are possible. These issues are addressed in further detail in Part II.

References [1] Wiley, R. G., Electronic Intelligence: The Interception of Radar Signals, Artech House, Dedham, MA, 1985. [2] Schleher, D. C., “Low probability of intercept radar,” Record of the IEEE International Radar Conference, pp. 346—349, 1985. [3] Schrick, G., and Wiley, R. G., “Interception of LPI radar signals,” Record of the IEEE International Radar Conference, Arlington, VA, pp. 108—111, May 7—10, 1990. [4] Ruﬀe, L. I., and Stott, G. F., “LPI considerations for surveillance radars,” Proc. of the International Conference on Radar, Brighton, U.K., pp. 200— 202, 1992. [5] Balanis, C. A., Antenna Theory Analysis and Design, Harper and Row, Publishers, New York, 1982. [6] http://www.f22fighter.com/radar.htm and http://www.globalsecurity.org/military/systems/aircraft/f-22-avionics.htm (APG-77).

38

Detecting and Classifying LPI Radar [7] Rudge, A. W., Milne, K., Olver, A. D., and Knight, P., The Handbook of Antenna Design, Vol. 2, IET, 1983. [8] Forrest, J. R., “Antenna design tradeoﬀs examined,” Microwave Systems News, Vol. 13, No. 12, pp. 237-243, Nov. 1983. [9] Taylor, T. T., “Design of circular apertures for narrow beamwidth and low sidelobes,” IRE Trans. on Antennas and Propagation, AP-8, pp. 17—22, 1960.

[10] Hansen, R. C., “Tables of Taylor distributions for circular aperture antennas,” IRE Trans. on Antennas and Progagation, pp. 23—26, Jan. 1960. [11] Hansen, R. C., “A one parameter circular aperture distribution with narrow beamwidth and low sidelobes,” IEEE Trans. on Antennas and Propagation, pp. 477—480, July, 1976. [12] Skolnik, M. I., Introduction to Radar Systems, 3rd Edition, McGraw-Hill, Boston, MA, 2001. [13] http://www.naval-technology.com/contractors/weapon control/thales5/ (SMART-L). [14] Pietrasinski, J. F., Brenner, T. W., and Lesnik, C. J., “Selected tendencies of modern radars and radar systems development,” 12th International Conference on Microwaves and Radar, MIKON ’98, Krakow, Poland, Vol. 1, pp. 133—137, May 20-22, 1998. [15] Stimson, G. W., Introduction to Airborne Radar, 2nd Edition, Scitech Publishing Inc., Mendham, NJ, 1998. [16] Ebadi, S., Forouraghi, K., and Sattarzadef, S. A., “Optimum low sidelobe level phased array antenna design using pattern search algorithms,” IEEE International Symposium on Antennas and Propagation, pp. 770—773, Vol. 1B, Washington DC, 2005. [17] Ebadi, S., Forouraghi, K., “Pattern scanning in low sidelobe phased array antennas using pattern search algorithms,” Proceedings of the 4th European Radar Conference, pp. 347—349, 2007. [18] Wirth, W. D., “Long term coherent integration for a floodlight radar,” Record of the IEEE International Radar Conference, pp. 698—703, 1995. [19] Wirth, W. D., Radar Techniques Using Array Antennas, IEE Radar, Sonar, Navigation, and Avionics Series 10, 2001. [20] Hughes, P. K., and Choe, J. Y., “Overview of advanced multifunction RF system (AMRFS),” Proc. of the IEEE International Conference on Phased Array Systems and Technology, pp. 21—24, 2000. [21] Ching-Tai Lin, and Ly, Hung, “Sidelobe reduction through subarray overlapping for wideband arrays,” Proc. of IEEE Radar Conference, pp. 228—233 2001. [22] Tavik, G. C., Hilterbrick, C. L., Evins, J. B., Alter, J. J., Crnkovich, J. G., de Graaf, J. W., Habicht, W., Hrin, G. P., Lessin, S. A., Wu, D. C., and Hagewood, S. M., “The advanced multifunction RF concept,” IEEE Trans. on Microwave Theory and Techniques, Vol. 53, No. 3, pp. 1009—1020, March 2005.

To See and Not Be Seen

39

[23] Klein, L. A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Inc., Norwood, MA, 1997. [24] Levanon, N., and Freedman, A. “Periodic ambiguity function of CW signals with perfect periodic autocorrelation,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 28, No. 2, pp. 387—395, April 1992. [25] Levanon, N., and Getz, B., “Weight eﬀects on the periodic ambiguity function,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 31, No. 1, pp. 182—193, July 1994. [26] Levanon, N., “CW alternatives to the coherent pulse train—signals and processors,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 28, No. 2, pp. 387—395, April 1992. [27] Nathanson, F.E., Radar Design Principles, 2nd Ed., McGraw-Hill, New York, 1991. [28] Klipper, H. “Sensitivity of crystal video receivers with RF preamplification,” Microwave Journal pp. 85—92, Aug. 1965. [29] Beasley, P. D. L., and Stove, A. G., “Pilot-an example of advanced FMCW techniques,” IEE Colloquium on High Time-Bandwidth Product Waveforms in Radar and Sonar, pp. 10/1—10/5, May 1, 1991. [30] Fuller, K. L., “To see and not be seen,” IEE Proc. F Radar, Sonar and, Navigation Signal Processing, Vol. 137, Issue: 1, pp. 1—10, Feb. 1990. [31] Pengelley, R. “Philips’ Pilot, covert naval radar,” International Defense Review, pp. 1177—1178, Sept. 1988. [32] Lok, J. J, “Navigation radars, sensors working overtime,” Jane’s Defence Weekly, pp. 39—40, Oct. 1992. [33] Scott, R., “Covert operations: navies seek discreet radars for surveillance,” Janes International Defence Review, 9 Aug. 2006.

Problems 1. (a) Estimate the beamwidth in azimuth and elevation of a rectangular array 10 cm by 10 cm if the wavelength is 3 cm. (b) Estimate the gain of the antenna if the eﬃciency is 90%. 2. An LPI radar has an active phased array antenna with θa = θe = 3 degrees and a total solid angle of coverage, Ωs = 2.4 sr. (a) If the antenna takes only 0.5s to cover the solid angle of coverage and the transmitted CW signal is a low power phase-coded signal with 11 subcodes and a code period of T = 11 μs (repeats every 11 μs), how many code periods would be integrated in a correlation receiver? (b) If noncoherent integration is performed over the entire dwell time, what is the processing gain of the radar?

40

Detecting and Classifying LPI Radar 3. (a) Write a MATLAB program to determine the detection range for both a Pilot LPI radar and a conventional 10kW pulsed emitter (as a function of the transmitter power, antenna parameters, wavelength, and target radar cross section), using the values for the Pilot radar. (b) Compare your output results with those in Table 1.4. (c) To verify the ES intercept range, include in your MATLAB program, a calculation of the intercept range for a δI = −40, −60, −80 dBmi and a high performance intercept receiver −110 dBmi. 4. A CW LPI radar has an average transmit power of PCW = 0.1W, LRT = LRR = 1, and an antenna with Gt = Gr = 30 dB. The radar illuminates a σT = 50m2 target at a range of 2 km. (a) Calculate the expected reradiated power back at the radar receiver if fc = 94 GHz. (b) Calculate the reradiated power back at the radar receiver if fc = 9.3 GHz. (Assume the gain of the antenna remains the same). 5. An airborne platform carrying an LPI CW emitter is moving toward a target (σT = 100m2 ), at a speed of V = 150 m/s. The emitter is turned on at a distance of R = 20 km from the target. Every 100 ms the emitter adjusts its transmit power level to keep the required SNRRo a constant, and equal to the minimum acceptable value. The other characteristics of the emitter are Gt = Gr = 32 dB, fc = 10 GHz, and δR = 8 × 10−17 W. The target also carries a noncooperative intercept receiver with the following characteristics: δI = −80 dBmi (GI = 0 dB). (a) Plot the emitter transmitted power in dBW versus time, (b) Plot the radar’s maximum detection range and the interceptor’s maximum intercept range as a function of time for the entire engagement. (c) What can you conclude about the radar’s quietness? 6. Using the Taylor GUI software in the Chapter 1 folder, examine the antenna patterns for side lobe level of 10 to 50 dB (in increments of 5 dB). For each pattern, estimate the 3-dB beamwidth and plot these values as a function of the side lobe level.

Chapter 2

LPI Technology and Applications In this chapter, we examine the applications of LPI radar technology. Altimeters are discussed first. An altimeter is an instrument that measures the vertical distance (or altitude) of an object (such as a missile) with respect to a reference level. The next application discussed is LPI landing systems. A fully automatic LPI landing system can compensate for wind and platform roll, and can perform ship-based landings under day/night, all-weather conditions. Surveillance and fire control radar systems are also presented, and depend on LPI technology to remain functional on the battlefield. Finally, antiship capable missiles and torpedo seekers that use LPI technology are reviewed.

2.1 2.1.1

Altimeters Introduction

In 1928, German inventor Paul Kollsman changed the world of aviation with the invention of the world’s first accurate barometric altimeter, also called the “Kollsman Window.” Barometric altimeters are operated by air pressure but have two limitations: (a) If the atmospheric pressure changes while the platform is in flight the altimeter reading will change, and (b) the barometric altimeter indicates height above sea level, or some other preset level, and does not reveal the actual platform altitude above the surface. In 1924, Lloyd Espenschied invented the first radio altimeter. The radio altimeter is a device, most often used in aircraft and cruise missiles, that makes use of the reflection of radio waves from the land or water to 41

42

Detecting and Classifying LPI Radar

determine the height of the platform above the surface. In 1938, the frequency modulation (FM) radio altimeter was first demonstrated in New York by Bell Labs. In the first public display of the device, radio signals were bounced oﬀ the ground, showing pilots the altitude of an aircraft. Another choice for an altimeter is the use of a pulse-modulated radar. Altimeters that work on this principle give satisfactory results if the platform is at a high altitude. At low altitudes, however, they have significant problems. This is because pulse-modulated radar have a blind zone area surrounding their installation where no targets can be detected. The blind zone area depends upon the pulse width. For example, with a pulse width of 0.2 μs, no target within 100 feet of the radar can be detected. Consequently, altimeters of this type are not useful for aerial vehicles such as cruise missiles flying near the surface. For vehicles that fly near the surface, it is necessary to detect and to measure the distance from the surface to the radar, down to almost zero feet. Frequency modulation continuous wave radar is the simplest of radar ranging techniques, and the most resistant to false-lock to undesired targets such as the missile structure. For example, in a typical FMCW altimeter, the transmitter’s carrier frequency changes linearly over a 120-MHz modulation bandwidth that ranges from 4.24 to 4.36 GHz. The transmitter works continuously to produce the CW output, and changes frequency at a constant rate in either a sawtooth pattern or a triangular pattern. A fixed, broad-beam antenna system is used to illuminate a large area of the underlying terrain. The broad beam allows for correct operation over the normal range of missile pitch and roll. The FMCW ranging process occurs by mixing a sample of the linearly varying frequency with the signal reflected from the surface. The diﬀerence produced after mixing is a low-frequency beat signal proportional to the range of the surface being measured. A simple limiter then selects the strongest signal from the surface directly below the vehicle. With proper antenna installation, the FMCW processor can accurately select the surface directly below the missile and ignore any atmospheric variations.

2.1.2

Fielded LPI Altimeters

The NavCom Defense Electronics Inc. Combined Altitude Radar Altimeter (CARA) AN/APN-232 uses a solid-state, FMCW emitter centered on 4.2 to 4.36 GHz with 100-MHz modulation bandwidth, and features a wideband LPI output and electronic protection (EP) features to prevent inoperability due to jamming or electronic attack (EA). The device assemblies are shown in Figure 2.1. LPI operation is achieved by using automatic power management that depends on the aircraft attitude and altitude, and the terrain type. That is, the transmitter output power is adjusted automatically so that the least amount required for signal acquisition and tracking is transmitted [1]. The AN/APN-232 measures the altitude from 0 to 50,000 ft. The system uses two

LPI Technology and Applications

43

Figure 2.1: Assemblies of the AN/APN-232 LPI radar altimeter [1] ( c 2003 Jane’s Information Group). identical antennas mounted along the bottom of the aircraft (one for transmit and one for receive) [2]. When the system is energized, it remains in search until the reflected signal strength is suﬃcient for the receiver portion to lock on to the return signal. The AN/APN-232 is used on the Lockheed Martin C-130 Hercules and its F-16 Fighting Falcon [3]. The display presented to the pilot is similar to that shown in Figure 2.2. The HG-9550 LPI radar altimeter system developed by Honeywell Sensor and Guidance Products uses power management by controlling the emitter power to produce an echo signal at a level 10 dB above the track threshold, and transmits less than 1W–making it virtually undetectable. Other programmable LPI features include high sensitivity, frequency agility, jittered code, and pulse repetition frequency. A microprocessor allows the track rate and EP response to be varied as a function of real-time inputs, or to be preprogrammed according to mission requirements [4]. The HG-9550 operates at a frequency of 4.3 GHz, has a range of 0 to 50,000 ft, and a track rate of ± 2,000 ft/s. It also maintains an altitude accuracy of ± 4 ft. The HG-9550 is an oﬀ-the-shelf system currently in production for U.S. Air Force HC-130J and C-17 Globemaster, U.K. C-130J, Argentine A-4 upgrade, the F-16 Block 60, the Boeing Joint Strike Fighter, and the Lockheed Martin Joint Strike Fighter aircraft. The cruise missile radar altimeter (CMRA) built by Honeywell Inc. Military Avionics was developed specifically for cruise missile programs, including the air launched cruise missile (ALCM) and Tomahawk missile. Honeywell’s CMRA is a derivative product in which a variety of features from other Honeywell altimeters are incorporated. The system has the capability to perform terrain correlation and navigation functions [5]. Another Honeywell LPI altimeter is the AN/APN-209 LPI radar altimeter that is standard on all U.S.

44

Detecting and Classifying LPI Radar

Figure 2.2: AN/APN-232 LPI radar pilot display. Army helicopters. Functions include transmitter power management, lowand high-altitude warnings, analog and digital outputs, and integration of the indicator, receiver, and transmitter [6]. The GRA-2000 LPI radar altimeter is being developed and tested by the integrated product team of NAVAIR’s Air Combat Electronics Program Oﬃce (PMA-2091), along with GEC-Marconi Hazeltine, General Microwave Corporation, and Systems Maintenance and Technology, Inc. The GRA-2000 LPI altimeter has been selected by the U.S. Joint Services Program Oﬃce to replace the AN/APN-194, -171, -209, and -232 series altimeters on the majority of tactical jet, helicopter, and transport aircraft employed by the U.S. Department of Defense [7]. The design is based on using a high gain receiver with a single-stage IF downconversion and specialized algorithms to provide LPI and jam resistance. The altimeter has a high-speed digital signal processor and achieves the LPI characteristics by combining a frequency hopping, phase-coded waveform with a low power transmitter output signal [8]. The assemblies for the GRA-2000 are shown in Figure 2.3. The small size enables easy mounting to a variety of platforms. The GRA-2000 has a range of 0 to 35,000 ft. It also maintains an altitude accuracy of ± 2 ft. (0—5,000 ft) and ± 50 ft. (5,000—35,000 ft). The PA-5429 pulsed airborne radar altimeter built by Tellumat, South Africa, provides the height between the altimeter and the underlying terrain/surface for heights from 0 to 5,000 ft. The altimeter operates in the mid-J-band (≈15 GHz) and features a self-contained installation, eliminating the need for separate RF feed cables and antennas. The altimeter has good EP

LPI Technology and Applications

45

Figure 2.3: GRA-2000 LPI radar altimeter set [6] ( c 2003 Jane’s Information Group). performance, with a low probability of intercept and comprehensive EP, making it suitable for a wide range of applications, including high-performance and transport aircraft, helicopters, and missiles. The accuracy of the PA-5429 is ± 3 ft for heights 0-100 ft and ± 3% for heights between 100 and 5,000 ft [9]. Other LPI altimeters include the Thales (originally Thompson CSF) AHV2100 digital radar altimeter [10] and the BAE AD1990, both operating at 4.3 GHz. The AHV-2100 uses power management of the RF output to reduce the probability of interception at low altitude over water, and the combination of a narrow receiver bandwidth with digital signal processing to provide EP from jamming. The AD1990 radar altimeter was designed for the U.K. Royal Air Force’s Tornado in the 1990s and has a maximum operating altitude of 5,000 ft down to ground level. The altimeter was ahead of its time with LPI being achieved by spreading the transmitted signal over a very wide bandwidth through the application of pseudorandom phase modulation and adaptive power management.

2.2 2.2.1

Landing Systems Introduction

Landing an aircraft and especially an unmanned aerial vehicle (UAV) is difficult for several reasons. Landing involves the air vehicle switching between diﬀerent modes of operation (e.g., takeoﬀ, landing, and hovering). The air vehicle must also coordinate with the landing site using voice or data links. Automatic and precision landing systems transmit a beacon and can aid in the landing operation, but must be LPI to remain active on the battlefield.

46

2.2.2

Detecting and Classifying LPI Radar

Fielded LPI Landing Systems

The AN/SPN-46 is an automatic precision approach and landing system (PALS) for aircraft carriers and amphibious assault ships. Built by Textron, the AN/SPN-46 PALSs are installed on all U.S. Navy aircraft carriers, and provide safe and reliable final approach and landing guidance for Marine Corps helicopters and AV-8B Harrier vertical and/or short takeoﬀ and landing (VSTOL) attack aircraft during day/night operations and adverse weather conditions. The PALS employs LPI technology using both an fc = 9.3 and 33.2-GHz carrier frequency mainly to obtain adequate accuracy. As in many other system examples where two bands are used, one band is used for search while another higher frequency band is used for tracking. Sometimes one lower band can be used for initial tracking through weather, and a higher frequency for more precision at short range. The PALS employs the 9.3-GHz coherent transmitter and receiver with monopulse tracking and Doppler processing on received signals for clutter rejection and rain attenuation at an operating range of 15 km [11]. The PALS is also capable of controlling up to two aircraft simultaneously in a “leapfrog” pattern, because of two dual-band radar antennas/transmitters. As each approaching aircraft being assisted by the system lands, another can be acquired. As of 2002, Jane’s sources were reporting the SPN-46(V) as being in service aboard the U.S. Navy aircraft carrier Enterprise (two radar installed), the Kitty Hawk, the John F. Kennedy (two radar installed), and the Nimitz (two radar installed) class aircraft carriers. The SPN-46(V) was also noted as being a retrofit option for the U.S. Navy’s “Wasp” class amphibious assault ships [12]. The Sierra Nevada tactical automatic landing system (TALS) is an allweather, transponder tracking radar system designed for land-based environments and interoperability with any ground control station (GCS). It is an upgrade of the AN/UPN-51(V) UAV Common Automatic Recovery System (UCARS) and features a millimeter wave (MMW) K-band (35 GHz) radar. It uses a narrow beamwidth antenna for close-range LPI acquisition in fog and rain, and an omnidirectional antenna for rollout. Due to its LPI signature, the TALS has minimal impact to the host aircraft [13]. At a range of 3.7 km, the transmit power for the airborne transponder is 100 mW with a 60% duty cycle, while the ground tracking radar transmits a maximum of 1W with a 0.04% duty cycle. A photo of the TALS system is shown in Figure 2.4. The ground tracking subsystem, contained in a portable unit, locates and accurately tracks the airborne transponder, using high-bandwidth tracking loops to cover touchdown and roll-out. Recovery software, proven in UCARS, performs air vehicle guidance and control calculations. The recovery of a UAV using the TALS is similar to the UCARS system shown in Figure 2.5 [14]. The TALS has been ordered for the AAI RQ-7A Shadow 200 tactical UAV system and recently underwent U.S. Army trials in 2000.

LPI Technology and Applications

47

Figure 2.4: The tactical automatic landing system (TALS) showing the 35GHz antenna [13] ( c 2002 Jane’s Information Group).

Figure 2.5: Steps in the recovery of a UAV using a UCARS [14] ( c 2002 Jane’s Information Group).

48

2.3 2.3.1

Detecting and Classifying LPI Radar

Surveillance and Fire Control Radar Battlefield Awareness

On the battlefield, situational awareness and threat evaluation are achieved using tactical surveillance radar to detect and track targets. For covert operations, the detection and tracking of targets should be as quiet as possible. These systems employ LPI technology to decrease the probability of passive detection by hostile forces; that is, “to see without being seen.” The role of multimode airborne fire control radar is to provide the eyes for tactical fighter aircraft within an air dominance mission and also require LPI operation.

2.3.2

LPI Ground-Based Systems

Ericsson Microwave Systems has produced several LPI radar systems for fire control and surveillance, including the Improved Helicopter and Aircraft/Radar Detection (HARD)-3D, the Eagle, and the Pointer. The Improved Hard-3D is a solid-state, 3D search and acquisition radar that has been designed for use in short-range air defense systems. The Improved HARD features an LPI capability that is due to a low output peak power of 240W (30W average), broadband frequency agility, low side lobes, and a narrow antenna beam [15]. The 3D capability is achieved by an electronically scanned beam in elevation with intelligent beam control, providing a short reaction time after the target is detected. The elevation coverage is obtained by steering the antenna beam to a number of fixed elevations on a pulse-topulse basis. Figure 2.6 shows the HARD-3D radar mounted on a Hagglunds vehicle. The elevation search pattern covers up to 35 degrees in elevation within two antenna revolutions. Upon target detection, the beam pattern is controlled so that a secondary detection will always occur in the next revolution for immediate confirmation and track initiation [15]. In a special pop-up mode, the track will start automatically after the first detection. Up to 20 targets and five jammers can be tracked automatically in range, azimuth, and elevation. Instrumented ranges are 12 and 20 km. The Ericsson Microwave Systems Eagle is a fire-control LPI radar intended for mobile ground and naval-based air defense systems. The equipment operates in the K-band (35 GHz) and is used to track low-flying targets and perform air-to-surface missile alert and closed-loop fire control. The Ka-band waveform provides a narrow antenna beam for low-altitude tracking at short range, as is required for gun fire control. The Eagle system is shown in Figure 2.7 and achieves LPI operation by using a low-output peak power (20W), pulse compression, high antenna gain with extremely low side lobes [16]. The radiation pattern and a new transmission technique claim to make it impossible for escort or stand-oﬀ jammers to degrade the radar performance. It can track two targets simultaneously with an angular error of less than 0.2 mrad

LPI Technology and Applications

49

Figure 2.6: HARD-3D radar on Hagglunds vehicle [15] ( c 2002 Jane’s Information Group).

Figure 2.7: Missile control and launch vehicle with the mast-mounted Eagle radar [16] ( c 2003 Jane’s Information Group).

50

Detecting and Classifying LPI Radar

Figure 2.8: Pointer LPI radar system antenna [17] ( c 2003 Jane’s Information Group). at 10 km. The Ericsson Microwave Systems Pointer radar system is a short-range LPI air surveillance 3D solid state radar system that was designed to be integrated into short-range air defense missile systems such as the Mistral, Stinger, and Starburst [17]. Pointer is a fully autonomous system that includes an X-band radar and the antenna shown in Figure 2.8. The range of Pointer is typically over 20 km, and 9 to 10 km in altitude. Pointer can be brought into action in 1 minute by a single operator. Most functions of Pointer, including track initiation, tracking, classification of fixed-wing aircraft and helicopters, threat evaluation, and data distribution via radio or wire are fully automatic. Target information can be sent to the firing unit 2 or 3 seconds after the target enters the line of sight. All the missile system operator then has to do is to acquire, track, and engage the target [17]. The Pointer operator can be positioned a long distance from the radar, using the radar remote control laptop computer shown in Figure 2.9. The Pointer was designed to increase the overall eﬀectiveness of short-range air defense systems by reducing target acquisition time, as well as enabling more targets to be engaged [17]. Pointer builds on Ericsson Microwave Systems’ experience in the development of both the HARD-3D and Eagle LPI radar. Hollandse Signaalapparaten is developing a LPI radar as an alternative

LPI Technology and Applications

51

Figure 2.9: Pointer operator’s radar remote control unit that is deployed away from the radar unit [17] ( c 2003 Jane’s Information Group). to the use of infrared sensors for short-range missile and gun systems. The company’s PAGE (portable air-defense guard equipment) is a lightweight and inexpensive 8—10 GHz (I-band) FMCW emitter with a transmit power of only 10—20W, providing a detection range of 10—15 km [18]. The PAGE LPI radar system, shown in Figure 2.10, exploits Signaal’s experience in developing its Scout family of naval and land-based FMCW ground surveillance LPI radars.1 It is also being developed as a private venture by Thales Nederland as a lowlevel air surveillance radar which provides early warning and cueing data for short-range networked air defense applications. Especially of interest are the man-portable surface-to-air missiles (SAM) and light anti-aircraft guns. The PAGE can survive the most extreme EA conditions and is nearly undetectable by ES and radar warning receivers. The PAGE system consists of an antenna unit including a solid-state transceiver, a radar processor unit, an operator unit, and a small generator. It also has the capability to integrate an identification friend-or-foe (IFF). (An automated datalink and weapons terminal can be added to PAGE for real-time data processing at remote fire units). Configurations include a man-portable tripod version, a light vehicle or trailer mounting and installation on existing self-propelled anti-aircraft gun or SAM systems [18].

1 The GB-Squire is a variant of the PAGE, and has detected artillery shells and Browning 0.50-calibre machine gun bullets in flight during testing.

52

Detecting and Classifying LPI Radar

Figure 2.10: PAGE LPI radar system [18] ( c 2006 Jane’s Information Group). The Thales Nederland (formerly Signaal) Variant shown in Figure 2.11, is a dual-band (4—6 GHz and 8—10 GHz) radar (one octave apart) that is relatively low-cost low-power, and lightweight making it ideal for a broad range of vessels, including fast patrol boats, amphibious vessels and support ships [19]. It has an autonomous target detection and tracking capability and is intended to fill three principal functions. These include surface target detection and tracking, air target detection and tracking, and gunfire targeting support. The Variant uses an integrated solid-state FMCW emitter with a transmit power Pavg = 10 mW. The antenna rotates at 14 rpm for long-range surveillance and at 28 rpm for a higher update rate (for self-defense applications). The system is fully coherent and provides pulse Doppler detection and tracking algorithms for optimal clutter suppression and air targeting. Spread spectrum techniques are used to enable detection and classification of helicopters. Surface gunfire support is provided for by three fire-control/splash-spotting windows, eliminating the need for a dedicated tracking radar for engagement of surface targets [19]. The system is able to detect air and surface targets out to instrumented ranges of 60 km and 70 km respectively. Important features include the ability to detect hovering and slow-moving helicopters, and a high resistance to jamming, weather clutter, and multipath propagation due to the dual-band operation and LPI operation.

LPI Technology and Applications

53

Figure 2.11: Variant LPI radar system [19] ( c 2006 Jane’s Information Group). The quiet naval radar CRM-100, built by Przemyslowy Instytut Telekomunikacji Telecommunications Research Institute in Poland, is a solid-state FMCW LPI radar that uses 10 switched frequencies in the 9.3- to 9.5-GHz subband. It has a modulation period of 1 ms and a modulation bandwidth of 54 MHz (max). The modulation bandwidth chosen depends on the selected range scale of 1.4, 3, 5.6, 11.1, 22.2, or 44.5 km, resulting in range cell sizes 3, 6, 12, 24, 48, and 96m, respectively [20]. The range resolution is three times the range cell size. Designed as a surface surveillance radar, this range coverage is similar to standard navigational radar that uses a pulsed signal. The transmit waveform is power managed, depending on the range to the target, and ranges from 1 mW to 1W. A line drawing of the CRM-100 antenna is shown in Figure 2.12. The radar has a beamwidth of 1.8 degrees in the horizontal dimension, and 25 degrees in the vertical dimension with side lobes −27 dB. The scan rate is 30 revolutions per minute (RPM). The receiver has an IF bandwidth of 500 kHz and a noise figure of 3 dB. The CRM-100 is designed to detect surface targets and determine their coordinates [20]. It provides automatic tracking of targets and automatic transfer of data on the tracked targets to command and control systems. The radar can be installed on a ground vehicle as shown in Figure 2.13 (shore version) or on board a ship (marine version). The Chinese JY-17A, shown in Figure 2.14, is a fully coherent, mediumrange pulse Doppler battlefield surveillance radar that is designed to detect, locate, and identify moving ground or low-altitude air targets. Built by the

54

Detecting and Classifying LPI Radar

Figure 2.12: The CRM-100 quiet naval radar antenna (measurements shown in millimeters) [20] ( c 2003 Jane’s Information Group).

Figure 2.13: The CRM-100 quiet naval radar installation [20] ( c 2003 Jane’s Information Group).

LPI Technology and Applications

55

Figure 2.14: JY-17A medium-range ground surveillance radar [21] ( c 2003 Jane’s Information Group). East China Institute of Electronic Engineering, the radar can be vehicle— mounted or ground—deployed. The radar features a solid-state, LPI transmitter in the 8- to 12-GHz range, and a high-stability frequency synthesizer [21]. It also has a selective linear and circular polarization antenna with low side lobes and digital phase coding, random frequency shift keying, with pulse Doppler processing that has automatic target detection and tracking. It can detect a single pedestrian at 10 km, a light vehicle at 15 km, a helicopter at 20 km, and a ship at 30 km [21]. The Raytheon multirole survivable radar (MRSR) is a tactical target acquisition and tracking LPI radar for the U.S. Army Missile Command to meet the tactical air defense requirements in the high-to-medium air defense and forward-area air defense mission areas. The radar is a 3D track-while-scan, phased array in elevation radar; designed to acquire and track multiple airborne targets over a 360-degree azimuth at extended ranges and at all tactical altitudes. Targets include tactical aircraft, UAVs, and hovering and slowly moving helicopters. The LPI radar incorporates a solid-state, low noise transmitter, and operates over a wide bandwidth with frequency agility [22]. The radar aperture is optimized to resist advanced EA and antiradiation missiles by employing very low side lobes combined with the LPI waveform. Multiple beams are moved electronically in elevation, with one continuously scanning the horizon with its bottom edge touching the ground, producing hot spots

56

Detecting and Classifying LPI Radar

to confuse antiradiation missile seekers [22].

2.3.3

LPI Airborne Systems

The AN/APS-147 multimode radar is an inverse synthetic aperture radar (ISAR) system designed to support the multimission capability of the light airborne multipurpose (LAMPS) SH-60B helicopter system during maritime surveillance and patrol missions. Power management and frequency agility give the operators the ability to perform missions at output power levels lower than traditional maritime surveillance radar. This enables the radar to detect medium-to-long-range targets with an LPI capability against enemy intercept receivers. Radar modes include target imaging, small target (periscope) detection, long-range surveillance, weather detection and avoidance, all-weather navigation, short-range search and rescue, and enhanced LPI search and target designation [23]. The AN/APQ-181 is the LPI radar designed specifically for the Northrop Grumman B-2 Spirit stealth bomber. The B-2 is in use by the U.S. Air Force and is shown in Figure 2.15. The radar operates in the J-band (12.5—18 GHz), using 21 separate modes for terrain following and terrain avoidance, navigation system updates, target search, location, identification and acquisition, and weapons delivery [24]. The radar employs two electronically scanned antennas and advanced LPI techniques that match the aircraft’s overall stealth qualities. The antenna is electronically steered in two dimensions and features a monopulse feed design to enable fractional beamwidth angular precision. It is designed to have a low RCS with respect to both in- and out-of-band RF illumination [25]. The AN/APG-77 is an advanced multimode tactical radar and is the primary sensor for the F-22 Raptor fighter aircraft built by Northrop Grumman (with Raytheon). A photo of the F-22 Raptor is shown in Figure 2.16. The LPI nature of the APG-77 radar provides a significant advantage for the F22. The F-22 is able to detect RWR/ES-equipped fighter aircraft without them knowing they are being illuminated [26]. The APG-77 emits low energy pulses over a wide frequency band. That is, the emitter changes frequency and power levels after every pulse, in order that no two transmitted pulses are alike. When multiple echoes are sent back to the radar, the signal processor converts the signals together instead of individually. The radar antenna is a fixed, elliptical, electronically scanned active array that contains 2,000 transmit and receive (TR) modules [27]. The antenna also contains circulators, radiators, and manifolds assembled into subarrays and then integrated into a complete array. The active array requires significantly less volume and prime power than a gimbaled slotted array. The antenna is integrated both physically and electromagnetically with the airframe and has a low radar cross section. The active array provides frequency agility, low radar cross section, agile beam steering, and a wide bandwidth capability typical of LPI radar.

LPI Technology and Applications

57

Figure 2.15: The Northrop Grumman B-2 bomber carries the Raytheon Electronic Systems AN/APQ-181 radar [24] ( c 2002 Jane’s Information Group).

Figure 2.16: The F-22 Raptor employs the LPI AN/APG-77 radar [27] ( c 2003 Jane’s Information Group).

58

Detecting and Classifying LPI Radar

The low-altitude navigation and targeting infrared for night (LANTIRN) is a system consisting of two pods that allow aircrew to fly their aircraft by day or night and in adverse meteorological conditions. The LANTIRN consists of a navigation pod and a targeting pod. The navigation pod contains a wide field of view forward looking infrared (FLIR) and a Ku-band LPI terrain following radar, the AN/APN-237A, that can be linked directly to the F-16’s autopilot to automatically maintain a preset altitude down to 100 feet while flying over virtually any kind of terrain. It has five modes: normal, weather, EP, LPI, and very low clearance [28]. The targeting pod contains another FLIR and a laser designator/rangefinder. The LANTIRN is deployed on the F-16C/D, F-15E/I/S, and F-14 platforms.

2.4 2.4.1

Antiship Capable Missile and Torpedo Seekers A Significant Threat to Surface Navies

Antiship capable missiles (ASCMs) are a significant threat to navy surface ships. Active RF ASCM seekers that radiate substantial transmitter power, however, allow themselves to be detected by relatively modest intercept receivers in both the main and side lobes. The intercept of seeker transmissions ultimately leads to vulnerability through the use of antiradiation missiles, missile interceptors, or EA. In the future, RF seekers will have LPI, powermanaged operation in the 8- to 20-GHz range as well as the 35- and 96-GHz ranges, by incorporating a number of advanced electronic technologies. These technologies will enable the missile to generate a broad collection of wideband reprogrammable waveforms with bandwidths reaching 500 MHz to 1 GHz. Using a variety of wideband techniques and coherent range-Doppler processing, these seekers will eﬀectively target low radar cross section ships, while simultaneously allowing the seeker to escape detection and reject decoys such as chaﬀ. Chapter 7 examines ASCM seeker technology and explores a missile-ship engagement scenario where the missile uses a power-managed, LPI seeker to detect a low RCS ship in several sea states.

2.4.2

Fielded LPI Seeker Systems

The Saab Bofors Dynamics AB’s RBS-15 medium-range, radar-guided, airto-surface missile is one of a family of long-range ASCMs produced in Sweden that can be launched from the air, land, or sea [29]. The missile makes use of low RCS materials to reduce the likelihood of early detection by enemy radar and also has a low infrared signature to reduce the probability of detection by infrared search and track systems. A picture of the RBS-15 is shown in Figure 2.17. In the 1990s, the company developed and tested an LPI radar

LPI Technology and Applications

59

Figure 2.17: RBS-15 missile. seeker for the RBS-15 (Mk 2). The seeker uses FMCW technology and has output power in the milliwatt range that is progressively reduced as the missile approaches the target. In 1994, Saab began work on the next generation RBS-15 (Mk 3) that incorporates an updated version of the current turbojet engine, providing a range in excess of 200 km [29]. Saab is developing a future land-attack version of the RBS-15 Mk 3 and is working on several new seeker technologies that may be applicable and that may also be retrofitted to existing variants. These include synthetic aperture radar, which would boost seeker resolution by more than 100% and substantially increase the seeker’s target discrimination capability as well as the terminal aimpoint accuracy. Another option is an LPI radar seeker that would use long, coded pulses that are diﬃcult to detect and diﬃcult to jam. Prototypes for both the synthetic aperture and LPI seekers are currently under test [29]. The improved Mk 3 version uses a global positioning system (GPS) data link, and the range has been increased to 400 km. Sweden is also developing automatic target recognition (ATR) systems that would give the missile a better discrimination capability. One option is for a dual-mode seeker version that combines the LPI radar with an imaging infrared (IIR) seeker, using ATR for terminal guidance. Figure 2.18 shows the RBS-15 missile being fired from a ground-based launch site. Another type of LPI approach is the random noise emitter. DARPA is investigating this type of seeker for the miniature air-launched interceptor (MALI). The MALI is a supersonic armed version of the miniature airlaunched decoy (MALD) and is used to intercept cruise missiles in flight from the rear. Figure 2.19 shows the MALI mounted on an aircraft ready for launch. The noise seeker is a Ka-band (35 GHz) seeker with 1-GHz bandwidth, and transmits randomly generated noise signals to detect and home in on the cruise missile. The randomly generated noise signals are copied and stored in seeker memory in order to correlate with the radar return. Not only does the randomness of the noise seeker make it harder for an intercept

60

Detecting and Classifying LPI Radar

Figure 2.18: RBS-15 missile firing.

Figure 2.19: Miniature air-launched interceptor [30] ( c 2003 Aviation Week and Space Technology).

LPI Technology and Applications

61

Figure 2.20: Spearfish being loaded [31] ( c 2003 Jane’s Information Group). receiver to detect the seeker’s transmission, the wide bandwidth provides an imaging capability that makes it easier to distinguish low-flying cruise missiles from the clutter. The large bandwidth provides excellent range resolution and a large processing gain, while the random noise pulse eliminates range ambiguities and is resistant to certain advanced countermeasures. This approach has been made possible by recent advances in high-speed, low-power processing [30]. Torpedo-homing performance in littoral regions has traditionally suﬀered due to poor acoustics found in the shallow-water environment. For example, shallow water has more pronounced temperature gradients (particularly in equatorial regions) that distort the sound-ray path and can result in nondetection or skip zones. Also, active sonar performance is degraded by the proximity of the surface- and bottom-reflecting boundaries, while passive sonar suﬀers as a result of wave noise and marine life. Conceived during the Cold War, the Spearfish torpedo was optimized to defeat fast, deep-diving, Soviet nuclear-powered submarine threats [31]. With the emphasis now on operating in littoral zones against small, ultra-quiet diesel-electric submarines, BAE Systems and QinetiQ have been researching torpedo sonar and signal-processing techniques that form the basis for an upgrade to the British Royal Navy’s Spearfish heavyweight torpedo shown in Figure 2.20. The Advanced Spearfish update program is intended to improve substantially the weapon’s performance against quiet targets in shallow water environments, while at the same time solving obsolescence issues aﬀecting Spearfish’s existing hybrid processing architecture. Digital signalprocessing (DSP) techniques have been considered, along with microprocessor technology, to handle the high computational loads demanded. New technology includes wide bandwidth processing, complex waveforms with additional modulations, LPI active waveforms, adaptive beam forming, neural net clas-

62

Detecting and Classifying LPI Radar

sification, and advanced tracking [31]. Adaptive beam-forming is also used to overcome the eﬀects of EA by noise jammers.

2.5

Summary of LPI Radar Systems

This chapter presented several LPI radar system applications where their design intentionally (and sometimes unintentionally) makes their transmission diﬃcult to intercept. Table 2.1 summarizes the systems discussed, along with their application or use. It is important to note that indentifying an LPI radar as any radar system that uses higher than conventional duty cycles (through pulse compression or CW operation), solid state transmitters, low side-lobe antennas, or low transmitter power, can end up leading to a misclassification. For example, under this definition, the new ballistic missile early warning system (BMEWS), Pave phased array warning system (PAWS) radar, airborne warning and control system (AWACS) radar, air route surveillance radar model 4 (ARSR-4), and any police CW radar would be classified as LPI, which is certainly not correct. In the next few chapters, details on the LPI technology and the important pulse compression techniques used in the above applications are presented.

LPI Technology and Applications

63

Table 2.1: LPI Radar Systems Developer

System

LPI Use

NavCom Defense Electronics Honeywell NAVAIR Tellumat, South Africa Honeywell Thompson CSF BAE Textron Systems Sierra Nevada Saab Bofors Signaal Signaal Ericsson Microwave Systems Ericsson Microwave Systems Ericsson Microwave Systems Thales Nederland Thales Nederland PITT Research Institute, Poland China Inst. of Elec. Engineering Raytheon TI Raytheon Northrop Grumman Raytheon TI Saab Dynamics BAE

AN/APN-232 HG-9550 GRA-2000 PA-5429 CMRA AHV-2100 AD1990 AN/SPN-46 (V) TALS Pilot Scout Smart-L HARD-3D Eagle Pointer PAGE Variant CRM-100 JY-17A MRSR AN/APS-147 AN/APQ-181 AN/APG-77 AN/APG-70 LANTIRN RBS-15MR Spearfish

Combined altitude radar altimeter Radar altimeter Tri-service radar altimeter Radar altimeter Cruise missile radar altimeter Radar altimeter Radar altimeter Precision approach, automatic landing Tactical automatic landing system Surveillance, navigation Surveillance, navigation Surveillance Fire control and surveillance Fire control Air surveillance radar Air surveillance Surface and air target, gun fire detection Surface target detection Battlefield surveillance radar Target acquisition and tracking radar Enhanced search and target designation Tactical multimode fire control radar Multimode tactical radar Multimode tactical radar Terrain following radar Radar guided air-to-surface missile Torpedo for littoral environments

64

Detecting and Classifying LPI Radar

References [1] “AN/APN-232 combined altitude radar altimeter,” Jane’s Avionics - Military CNS, FMS, Data and Threat Management, Feb. 10, 2003. [2] http://www.osmpf.wpafb.af.mil/. [3] “Lockheed Martin Aeronautics Company,” Jane’s All the Worlds AircraftFixed Wing-Military, Jan. 10, 2003. [4] “HG9550 LPI radar altimeter system,” Jane’s Avionics - Military CNS, FMS, Data and Threat Management, April 26, 2002. [5] “Cruise missile radar altimeter,” Jane’s Radar, July 17, 1994. [6] “AN/APN-209 radar altimeter,” Jane’s Avionics - Military CNS, FMS, Data and Threat Management, Feb. 10, 2003. [7] “GRA-2000 low probability of intercept (LPI) altimeter,” Jane’s Avionics Military CNS, FMS, Data and Threat Management, Feb. 5, 2003. [8] http://www.cni.na.baesystems.com/html/low probability of intercept a.html [9] “PA-5429 radar altimeter,” Jane’s Avionics - Military CNS, FMS, Data and Threat Management, Feb. 5, 2003. [10] “AHV-2100 digital radar altimeter,” Jane’s Avionics - Military CNS, FMS, Data and Threat Management, Feb. 10, 2003. [11] http://www.fas.org/man/dod-101/sys/ship/weaps/an-spn-46.htm. [12] “AN/SPN-46(V) approach radar,” Jane’s Radar and Electronic Warfare Systems, Military Air Traﬃc Control, Instrumentation and Ranging Radars, Feb. 7, 2003. [13] “Sierra Nevada TALS,” Jane’s Unmanned Aerial Vehicles and Targets - Launch and Recovery Systems, April 17, 2002. [14] “Sierra Nevada UCARS,” Jane’s Unmanned Aerial Vehicles and Targets Launch and Recovery Systems, April 17, 2002. [15] “Ericsson Microwave Systems Improved HARD-3D radar system,” Jane’s Land-Based Air Defence-Anti-Aircraft Control Systems, Oct. 23, 2002. [16] “Eagle fire-control radar,” Jane’s Radar and Electronic Warfare Systems, Battlefield, Missile Control and Ground Surveillance Radar Systems, Jan. 30, 2003. [17] “Ericsson Microwave Systems Pointer radar system,” Jane’s Land-Based Air Defence-Anti-Aircraft Control Systems, 1999. [18] Hewish, M., “Low-level air defense—new sensors enhance eﬀectiveness,” Jane’s Defence Equipment and Technology, Vol. 27, No. 6, pp. 43, June, 1994. [19] “Aﬀordable performers: surveillance radars balance cost with capability,” International Defence Review, Mar., 2008. [20] “CRM-100 surveillance radar,” Jane’s Radar and Electronic Warfare SystemsNaval/Coastal Surveillance and Navigation Radar, Jan. 30, 2003. [21] “JY-17 battlefield reconnaissance radar,” Jane’s C4I Systems-Land Based Surveillance and Location, April, 22, 2002.

LPI Technology and Applications

65

[22] “Multi-role survivable radar - Tactical target acquisition and tracking,” Jane’s Air Defence Radar - Land and Sea, Jan. 1997. [23] “AN/APS-147 multimode airborne radar,” Jane’s Avionics - Military CNS, FMS, Data and Threat Management, Feb. 10, 2003. [24] “AN/APQ-181 radar for the B-2,” Jane’s Avionics - Military CNS, FMS, Data and Threat Management, Jan. 17, 2003. [25] http://www.raytheon.com/products/apq181/. [26] http://f22rap.virtualave.net/avionics.html. [27] “AN/APG-77 multimode airborne radar,” Jane’s Radar and Electronic Warfare Systems-Airborne Fire Control Radar, Nov. 11, 2002. [28] http://www.f-16.net/reference/armament/lantirn.html. [29] “RBS 15F,” Jane’s Air-Launched Weapons-Air to Surface Missiles, Sept. 12, 2002. [30] R. Wall, “USAF eyes decoy, jammer as MALI demonstration ends,” Aviation Week and Space Technology, Jan. 13, 2003. [31] “Spearfish,” Jane’s Underwater Warfare Systems - Torpedos, May 3, 2002.

Problems 1. In an FMCW altimeter such as the CARA, the frequency is swept over the modulation bandwidth ∆F during the modulation (coherent processing) period tm . Ranging (determining the altitude) occurs by mixing a sample of the transmitted signal with the reflected signal from the surface to derive a diﬀerence frequency (or beat frequency) δf . (a) Write an expression for the time interval that corresponds to the measured beat frequency δf as a function of the sweep rate ∆F˙ . (b) Determine the beat frequency (in Hz) for the CARA if the modulation period is 1 ms and the altimeter is at a height of 30m. HINT: the wavefront takes 6.7 μs/km to travel a round-trip path. 2. Estimate the maximum intercept range of the TALS ground tracking radar if its MMW antenna is 60% eﬃcient and the intercept receiver sensitivity is δI = −100 dBmi. 3. Estimate the HARD-3D pulse width τR if the maximum unambiguous range is 20 km. 4. Determine the maximum detection range of the Eagle radar, considering that the antenna is 90% eﬃcient.

Chapter 3

Ambiguity Analysis of LPI Waveforms In this chapter, the ambiguity (delay-Doppler) analysis of LPI waveforms is addressed. Ambiguity analysis is important to understand the properties of the CW waveform and its eﬀect on measurement accuracy, target resolution, ambiguities in range, and radial velocity, and its response to clutter. The periodic autocorrelation function (PACF) is introduced, and it is shown that CW signals can have a perfect PACF with zero side lobes. The periodic ambiguity function (PAF) is also introduced, to analyze the response of a matched receiver that uses N copies of the reference (transmitted) function to cross-correlate the return CW signal and perform target detection. The PAF is similar to the ambiguity function often used to represent the magnitude of the matched receiver output for a coherent pulse train. The cut of the PAF at zero Doppler (ν = 0) is the PACF, and cuts of the PAF along zero delay (τ = 0) yield the response of the correlation receiver at a given Doppler shift. Several important properties of the PAF are presented. The MATLAB low probability of intercept toolbox (LPIT) is described (Appendix A) and is used to generate a CW Frank signal in order to demonstrate the PACF and PAF concepts. The MATLAB code used to calculate the PACF and PAF is also described (Appendix B). Modifying the reference waveform in the receiver with a weighting function (mismatched receiver) can help reduce the Doppler side lobes that appear. This subject is addressed, and three important weighting functions are presented.

67

68

3.1

Detecting and Classifying LPI Radar

The Ambiguity Function

A matched radar receiver performs a cross-correlation of the received signal and a reference signal, whose envelope is the complex conjugate of the envelope of the transmitted signal. The ambiguity function describes the response of this matched receiver to a finite duration signal. In ambiguity analysis, the receiver is considered matched to a target signal at a given delay and transmitted frequency. The ambiguity is then a function of any added delay and additional Doppler shift from what the receiver was matched to. If u(t) is the complex envelope of both the transmitted signal and received signal, the ambiguity function is given by [1] e e8 ∞ e e u(t)u∗ (t − τ )ej2πνt dtee (3.1) |χ(τ, ν)| = ee −∞

where τ is the time delay and ν is the Doppler frequency shift. The 3D plot, as a function of τ and ν, is called the ambiguity diagram. The maximum of the ambiguity function occurs at the origin (τ = 0, ν = 0), and |χ(0, 0)| is the output if the target appears at the delay and Doppler shift for which the filter was matched. The delay-Doppler response of the matched filter output is important for understanding the properties of the radar waveform [2]. Ideally, the ambiguity diagram would consist of a diagonal ridge centered at the origin, and zero elsewhere (no ambiguities). The ideal ambiguity function, however, is impossible to obtain. For a coherent pulse train consisting of NR pulses with pulse duration τR and pulse repetition interval Tr , the ambiguity function indicates that the Doppler resolution is the inverse of the total duration of the signal NR Tr while the delay resolution is the pulse duration [3].

3.2

Periodic Autocorrelation Function

LPI signals are typically low-power CW waveforms that are modulated by a periodic function, such as a phase code sequence or linear frequency ramp. A major advantage of the periodically modulated CW waveforms is that they can yield a perfect PACF. For example, consider a phase-coded CW signal with Nc phase codes each with subcode duration tb s. The transmitted CW signal has a code period T = Nc tb s and a periodic complex envelope u(t) given as u(t) = u(t + nT ) (3.2) for n = 0, ±1, ±2, ±3 . . . . The values of the PACF as a function of the delay r (which are multiples of tb ) are given by R(rtb ) =

Nc 1 3 u(n)u∗ (n + r) Nc n=1

(3.3)

Ambiguity Analysis of LPI Waveforms and ideally we would like a perfect PACF or F 1, r = 0(modNc ) R(rtb ) = 0, r = 0(modNc )

69

(3.4)

Since the CW signal is continuous, the perfect PACF is possible. Note however, that finite duration signals, such as a pulse train, cannot achieve this ideal autocorrelation since as the first sample (or last sample) enters (or leaves) the correlator, there is no sample that can cancel the product to yield a zero output.

3.3

Periodic Ambiguity Function

The periodic ambiguity function or PAF, introduced by Levanon and Freedman [4], describes the response of a correlation receiver to a CW signal modulated by a periodic waveform with period T , when the reference signal is constructed from an integral number N of periods of the transmitted signal (coherent processor length N T ). The target illumination time (dwell time) P T must be longer than N T (see Figure 1.9). As long as the delay τ is shorter than the diﬀerence between the dwell time and the length of the reference signal 0 ≤ τ ≤ (P − N )T , the illumination time can be considered infinitely long and the receiver response can be described by the PAF given as [5] e e e 1 8 NT e e e u (t − τ ) u∗ (t) ej2πνt dte (3.5) |χN T (τ, ν)| = e eNT 0 e

where τ is assumed to be a constant, and the delay rate of change is represented by the Doppler shift ν. The PAF for N periods is related to the single-period ambiguity function by a universal relationship e e e sin(N πνT ) e e e (3.6) |χNT (τ, ν)| = |χT (τ, ν)| e N sin(πνT ) e where

1 |χT (τ, ν)| = T

e8 e e T e e ∗ j2πνt e u(t − τ )u (t)e dte e e 0 e

(3.7)

is the single period ambiguity function. The single period ambiguity function is multiplied by a universal function of N and T that is independent of the complex envelope of the signal and that does not change with τ . The PAF shows the eﬀect of using a reference receiver consisting of N code periods (see Section 1.3). Examination of (3.6) reveals that for a large number of code periods N , the PAF is increasingly attenuated for all values of ν except at multiples of 1/T . It also has main lobes at νT = 0, ±1, ±2, . . . . Equation (3.6) also reveals that the PAF has relatively strong Doppler side lobes.

70

Detecting and Classifying LPI Radar

The PAF serves CW radar signals in a similar role to which the traditional ambiguity function serves finite duration signals. Note that for a large N , the PAF is compressed to zero for all ν, except near ν = n/T, n = 0, ±1, ±2, . . . . For an infinitely large N , the function |χN T (τ, ν)| becomes a train of impulses. For large N , the PAF of a sequence exhibiting perfect periodic autocorrelation will strongly resemble the ambiguity function of a coherent pulse train.

3.3.1

Periodicity of the PAF

The PAF formulation given in (3.5) is not unique, and alternate definitions have also been adopted [6]. The form of the PAF in (3.5), however, represents the straightforward implementation of a matched filter to the signal u(t) delayed by τ and Doppler shifted by ν. It can easily be shown that the cut along the PAF’s delay axis |χNT (τ, 0)| (zero Doppler) is the magnitude of the PACF of the signal given by (3.3) [4, 6]. The cut along the Doppler axis (zero delay) is 8 NT 1 |u(t)|2 ej2πνt dt (3.8) χN T (0, ν) = NT 0 Assuming a constant amplitude signal, |u(t)| = 1 (e.g., phase-modulated CW signals) e e e sin(πνN T ) e e |χN T (0, ν)| = ee (3.9) πνN T e and

|χN T (0, 0)| = 1

(3.10)

For any integer n, the periodicity on the delay axis is |χN T (nT, ν)| = |χNT (0, ν)|

(3.11)

For the ν axis, for m = 0, ±1, ±2, . . . |χN T (τ, m/T )| = |χNT (τ + nT, m/T )|

(3.12)

The symmetry cuts are a function of the three parameters: the code period T , the number of phase codes Nc , and the number of code periods used in the correlation receiver N . Additional symmetry and periodicity properties are discussed in [4, 6].

3.3.2

Peak and Integrated Side Lobe Levels

The time side lobe levels in the autocorrelation function (ACF) help quantify the LPI waveform in its ability to detect targets without interfering side lobe targets. That is, if the ACF has high side lobes, a second nearby target might be able to hide in a side lobe and go undetected. To quantify the LPI

Ambiguity Analysis of LPI Waveforms

71

waveform characteristics, the peak side lobe level (PSL) of the ACF can be defined as ] } ] } max side lobe power max R2 (k) PSL = 10 log10 (3.13) = 10 log (peak response)2 R2 (0) where k is the index for the points in the ACF, R(k) is ACF for all of the output range side lobes except that at k = 0, and R(0) is the peak of the ACF at k = 0. The integrated side lobe level is } ] M 3 total power in side lobes R2 (k) (3.14) = 10 log ISL = 10 log10 2 (peak response) R2 (0) k=−M

and is a measure of the total power in the side lobes as compared with the compressed peak. The PSL is a useful measure when a single point target response is of concern. Values for the PSL depend on the number of subcodes in the code sequence Nc as well as the number of code periods N within the receiver. The ISL is considered a more useful measure than the PSL when distributed targets are of concern. Typical matched filter ISL values range from −10 to −20 dB.

3.4

Frank Phase Modulation Example

To demonstrate the properties of the ACF, PACF, and PAF, we look briefly at one important type of phase modulation called the Frank code [7]. The Frank code is a polyphase code (more than two phase states). It has a variable length and can be used to phase modulate a complex signal every subcode period tb .

3.4.1

Transmitted Waveform

The transmitted signal can be written as + s(t) = Ae(j2πfc t+φk )

(3.15)

2π (i − 1) (j − 1) M

(3.16)

where fc is the carrier frequency and φk is the phase modulation that is used to shift the phase of the carrier in time every subcode period according to the particular phase modulation used. Note that the carrier frequency remains constant. The Frank phase modulation code is derived from a step approximation to a linear frequency modulation waveform using M frequency steps and M samples per frequency. If i is the number of the sample in a given frequency and j is the number of the frequency, the phase of the ith sample of the jth frequency for the Frank code is φi,j =

72

Detecting and Classifying LPI Radar

Figure 3.1: Frank phase modulation for M = 8 (Nc = 64). where i = 1, 2, . . . , M , and j = 1, 2, . . . , M . The Frank code has a length of Nc = M 2 subcodes, which is also the corresponding pulse compression ratio or processing gain P GR . For tb s (the subcode period), if cpp represents the number of carrier cycles per subcode, then tb = cpp/fc s resulting in a transmitted signal bandwidth B = 1/tb = fc /cpp. The code period can also be expressed as (3.17) T = Nc tb = M 2 tb Below we examine the ACF, PACF, and PAF properties of this signal. Chapter 5 discusses the Frank code in more detail.

3.4.2

Simulation Results

A signal containing the Frank phase modulation can easily be generated with the MATLAB low probability of intercept toolbox distributed on the enclosed CD and described in Appendix A. The LPIT can also generate a host of other LPI signals discussed in Chapters 4—7. Figure 3.1 shows the Frank phase modulation (3.16) with M = 8 (Nc = 64). The plot is generated within the LPIT. The carrier frequency is fc = 1 kHz, fs = 7 kHz, and cpp = 1. Figure 3.2 shows the power spectral

Ambiguity Analysis of LPI Waveforms

73

Figure 3.2: Power spectral density for Frank phase modulation for M = 8 (Nc = 64) with fc = 1 kHz, fs = 7 kHz, and cpp = 1. density of the Frank signal. This plot is also generated within the LPIT. Note that since the cpp = 1, the 3-dB bandwidth B = 1 kHz, as illustrated. The ACF and PACF are shown in Figure 3.3 for the number of code periods N = 1. These results can be obtained by using the output waveforms from the LPIT in conjuction with Levanon’s ambfn7.m code as described in Appendix B with r = 1, F ∗ M tb = 10, T = 1, N = K = 100. The PSL can be read from Figure 3.3(a). The largest side lobe level is 28 dB down from the peak. This is in agreement with the theoretical result PSL = 20 log10 (1/M π) = −28 dB (voltage ratio). Also note from Figure 3.3(b) that the CW Frank signal has a perfect PACF (zero side lobes). The PAF for N = 1 is shown in Figure 3.4. The phase modulation signals generated using the LPIT contain cppfs (3.18) bsc = fc number of samples per subcode. The total number of samples within a code period is then Nc bsc . When ambfn7.m is used to examine the signals from the LPIT, the delay axis is normalized by the subcode period tb and so the PAF repeats at Nc bsc since the waveform is sampled. That is, dividing this axis by the number of samples per subcode bsc gives the delay axis in terms of the subcode number. For the LPIT default Frank signal (cpp = 1, fs = 7 kHz, fc = 1 kHz), bsc = 7 and, as illustrated in the plot, the code repeats

74

Detecting and Classifying LPI Radar

Figure 3.3: Frank (a) ACF (PSL = −28 dB down) and (b) PACF for M = 8 (Nc = 64), cpp = 1 with number of reference waveforms N = 1.

Figure 3.4: PAF for Frank phase modulation for M = 8 (Nc = 64), cpp = 1 with number of reference waveforms N = 1.

Ambiguity Analysis of LPI Waveforms

75

Figure 3.5: Frank (a) ACF (PSL = −40 dB down) and (b) PACF for M = 8 (Nc = 64), cpp = 1 with number of reference waveforms N = 4. every τ = 448/bsc = 64 = Nc . The Doppler axis is normalized with respect to the entire signal duration Nc tb . Therefore, depending on the number of code periods N integrated into the PAF calculation, the Doppler lobes appear at kN for k ∈ {0, 1, 2, . . .} as illustrated in Figure 3.4 for N = 1. Increasing the number of code periods N used in the receiver can help to decrease the Doppler side lobes as well as the time side lobes in the ACF. Figure 3.5 shows the ACF and PACF for when N = 4 code periods are used within the reference receiver (r = 1, F ∗ M tb = 40, T = 0.3, N = K = 100). Including N in the estimation of the peak side lobe level W w 1 dB (3.19) PSL = 20 log10 NMπ Using N = 4, PSL = −40 dB down from the peak as shown in Figure 3.5. Figure 3.6 shows the PAF for the Frank code with N = 4 and demonstrates that by using more copies of the reference signal within the correlation receiver, the delay-Doppler side lobe performance improves.

3.5

Reducing the Doppler Side Lobes

To reduce the Doppler side lobes it is necessary to modify the reference signal with a weighting function w(t) that converts the receiver from a matched receiver to a mismatched receiver (with a corresponding degradation in SNR

76

Detecting and Classifying LPI Radar

Figure 3.6: PAF for Frank phase modulation for M = 8 (Nc = 64), cpp = 1 with number of reference waveforms N = 4. and decrease in resolution). Following the development in [5], the reference signal u∗ (t) in (3.5) is divided into a product of two signals: r(t) which is periodic with the same period as u(t), and w(t) an aperiodic weighting function. That is, u∗ (t) = r(t)w(t). The delay-Doppler response of the mismatched receiver is e e8 ∞ e e j2πνt e e u(t − τ )r(t)p(t)w(t)e dte |ψ(τ, ν)| = e (3.20) −∞

where p(t) is an aperiodic rectangular window function F 1 0 ≤ t < NT p(t) = 0 elsewhere

(3.21)

Since (3.20) is the Fourier transform of two products (except for the missing negative sign in the exponential) it can be described by the convolution (denoted ⊗) of two Fourier transforms as e8 ∞ e u(t − τ )r(t)ej2πνt dt |ψ(τ, ν)| = ee −∞ e 8 ∞ e ⊗ p(t)w(t)ej2πνt dtee (3.22) −∞

Ambiguity Analysis of LPI Waveforms

77

With the first transform, since both u(t) and r(t) are infinitely long and periodic with period T , the Fourier transform of their product (for any τ ) can be shown to be a series of delta functions at ν = n/T , n = 0, ±1, ±2, . . . or 8 ∞ ∞ p 3 nQ u(t − τ )r(t)ej2πνt dt = δ ν− (3.23) gn (τ ) T −∞ n=−∞ where

gn (τ ) =

1 T

8

0

T

u(t − τ )r(t)ej2πnt/T dt

(3.24)

The second integral in (3.22) is the Fourier transform of the product of the rectangular window and the weight function 8 ∞ p(t)w(t)ej2πνt dt (3.25) W (ν) = −∞

or W (ν) =

8

NT

w(t)ej2πνt dt

(3.26)

0

Finally, the delay-Doppler response of the weighted correlation receiver is obtained from the convolution between (3.23) and (3.26) yielding [5] e e ∞ e 3 p n Qee e g (τ )W ν − |ψ(τ, ν)| = e (3.27) e en=−∞ n T e

The significance of this equation is that at any given coordinate (τ, ν), the delay-Doppler receiver response is determined by contributions from gn (τ ) and the weight function. The set of functions gn (τ ) is determined by (3.24) and depend on the transmitted signal modulation that is used. Three important amplitude weighting windows have been described in [5] and can be defined by selecting the parameter c in the following expression w W 1−c 2πt 1 1− cos (3.28) p(t)w(t) = NT c NT where 0 ≤ t ≤ N T and zero elsewhere. For uniform, Hann, and Hamming weight windows, c is selected as c = 1.0, 0.5, and 0.53836 respectively. Using (3.25) to transform p(t)w(t) yields w W (1 − c)(νN T )2 sin(πνN T ) 1+ ejπνN T (3.29) W (ν) = πνN T c[1 − (νN T )2 ] with the exponent indicating that the weight function is not centered at t = 0. Still to be determined is the modulation function gn (τ ). This is discussed in detail in the following chapters since it depends on the waveform being

78

Detecting and Classifying LPI Radar

considered. Note that a smooth weight, covering N periods of the signal, aﬀects only the Doppler behavior. It has no influence on the PACF (the zero Doppler cut of the PAF). In phase-coded signals, the delay response remains a triangle with base 2tb , regardless of any amplitude taper along N periods of the signal.

References [1] Levanon, N., Radar Principles, John Wiley & Sons, New York, 1988. [2] Skolnik, M., Introduction to Radar Systems, 3rd Edition, McGraw Hill, Boston, p. 331, 2001. [3] Levanon, N., “CW alternatives to the coherent pulse train - signals and processors,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 29, No. 1, pp. 250—254, Jan. 1993. [4] Levanon, N. and Freedman, A. “Periodic ambiguity function of CW signals with perfect periodic autocorrelation,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 28, No. 2, pp. 387—395, April 1992. [5] Getz, B. and Levanon, N., “Weight eﬀects on the periodic ambiguity function,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 31, No. 1, pp. 182—193, Jan. 1995. [6] Freedman, A. and Levanon, N., “Properties of the periodic ambiguity function,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 30, No. 3, pp. 938—941, July 1994. [7] Frank, R. L., “Polyphase codes with good nonperiodic correlation properties,” IEEE Trans. IT-9, pp. 43—45, 1963.

Problems 1. When the reference signal is of duration N T , the response of the correlation receiver is the PAF for N periods. Another form of the PAF can be defined by the relationship 1 χN T (τ, ν) = NT

8

0

NT

p τQ ∗p τ Q j2πνt u t+ dt u t− e 2 2

Starting from here, show the universal result e e e sin(πνN T ) e e |χN T (τ, ν)| = |χT (τ, ν)| ee N sin(πνT ) e

Hint: Split the integral into N sections and use the transformation of variables t = t + (n − 1)T .

Ambiguity Analysis of LPI Waveforms

79

2. The complex envelope of a signal with periodic phase modulation can be expressed as Nc 3 un (t − (n − 1)tb ) u(t) = n=1

where 0 ≤ t ≤ Nc tb and

un (t) = ejφn

for 0 ≤ t < tb . There are periodic two-valued phase sequences that can also yield a perfect periodic autocorrelation. That is, φn = 0 or φn = φ and un can either be 1 or β where β = ejφ For Nc = 7, and

φn = {0 0 0 φ φ 0 φ} φ = cos−1 (−3/4)

For Nc = 11, and

φn = {0 0 0 φ φ φ 0 φ φ 0 φ} φ = cos−1 (−5/6)

For both the Nc = 7 and Nc = 11 sequences, (a) generate the complex CW signal using beta.m. Save the phase shift plot showing the Nc phase values being used within a code period. (b) For the signal only, plot the PACF and PAF (delay versus Doppler) when N = 1 and N = 4 to verify the periodicity (how often the ambiguity function repeats itself) and the reduction of the PSL. (c) Add the beta.m signal to your LPIT menu. 3. Plot the weighting function (3.29) for (a) a uniform window, (b) a Hann window, and (c) a Hamming window, for N = 1 and N = 5 for a code period T = 0.021s (consistent with a CW LPI waveform with fc = 1 kHz, M = 7, and cpp = 3). 4. Using the LPIT, generate the Frank signal with M = 8, fc = 1 kHz, fs = 7 kHz, and cpp = 1. Plot the ACF, PACF, and PAF for N = 8, and compare your results with Figures 3.5 and 3.6. 5. A phase code signal is generated with a carrier of fc = 5 kHz. The processing gain of the signal is 24 dB and the bandwidth of the signal is B = 1.25 kHz. Determine (a) the subcode period tb and (b) the code period T in s. (c) If the signal is intercepted with a receiver that has an ADC with fs = 25 kHz, how many samples are within a subcode period (bsc )?

Chapter 4

FMCW Radar This chapter examines the advantages of the frequency modulation CW LPI technique, gives detailed expressions for the transmitted signal and the received signal, and discusses the isolation required when using a single antenna. LPI search and track mode processing are discussed, and several FMCW emitter configurations are presented. Also investigated are the eﬀects of frequency modulation nonlinearities. Moving target indication filtering is discussed, as well as the FMCW periodic ambiguity function. The experimental PANDORA multifrequency FMCW radar is presented as an example of FMCW technology. Electronic attack considerations are also addressed. Finally, the technology trends for FMCW emitters are examined.

4.1

Advantages of FMCW

CW radars that use unmodulated waveforms cannot measure a target’s range. To measure the target’s range and/or speed, the transmit frequency must be varied in time, and the frequency of the return signal from the target measured. Correlation of the return signal with the transmit signal can give a measure of both the range and Doppler information of the target. Since the modulation cannot be continually changed in one direction (e.g., up or down), a periodic modulation is normally used. Frequency modulation can create a wideband LPI waveform and take many forms, with sinusoidal and linear modulation being used most frequently. The most popular linear modulation utilized is the triangular FMCW emitter, since it can measure the target’s range and range rate.1 1 Sinusoidal frequency modulation is mathematically more tractable than linear frequency modulation and is presented well in [1].

81

82

Detecting and Classifying LPI Radar

FMCW is an eﬀective LPI technique for many reasons. In some applications, such as radio altimeters, a key advantage is the simple architecture, which is capable of giving a very high range resolution. Due to the very low energy transmitted (low radiation hazard), the noncooperative intercept receiver’s interception range is significantly reduced. This means that an FMCW radar may be used in otherwise restrictive emission-control (EMCON) conditions that would preclude the operation of pulsed emitters. The frequency modulation spreads the transmitted energy over a large modulation bandwidth ∆F , providing good range resolution that is critical for discriminating targets from clutter. The power spectrum of the FMCW signal is nearly rectangular over the modulation bandwidth, so noncooperative interception is diﬃcult. Since the transmit waveform is deterministic, the form of the return signals can be predicted. This gives it the added advantage of being resistant to interference (such as jamming), since any signal not matching this form can be suppressed. Consequently, it is a diﬃcult matter for a noncooperative receiver to detect the FMCW waveform and measure the parameters accurately enough to match the jammer waveform to the radar waveform (a subject we take up in Part II). FMCW modulation is also readily compatible with solid-state transmitters, and represents the best use of output power available from these solid state devices. The return signal is correlated with the transmitted signal, and is often done using analog techniques. The correlation receiver can also be implemented using digital techniques. The frequency processing performed to obtain the range information from the digitized IF signals can be done very quickly with FFTs. The ease with which the range resolution can be changed, and the way in which very high range resolutions can be obtained without requiring wide IF and video bandwidths is also a significant advantage. That is, the IF and video bandwidths can be matched to the required data rate rather than to the RF bandwidth required to give the range resolution [2]. Due to the fourth power relationship between a radar’s return signal power and the target’s range, an adequate amount of sensitivity time control (STC) must be used in the receiver to selectively attenuate the returns from closein targets in order to control the dynamic range and prevent saturation [3]. Due to the frequency-range relationship in the FMCW radar, this technique may be easily implemented in the frequency domain early on in the signal processing. FMCW is also easier to implement than phase code modulation, as long as there is no strict demand on linearity specifications over the modulation bandwidth. The ability to use weighting to control the range and Doppler side lobes (mismatched correlation receiver) also allows for eﬃcient use of the spectrum. Finally, the advanced transceiver design allows FMCW radars to be connected to, and operated in parallel with, any available pulsed I-band navigation radar using a common antenna. This means that the very presence of the LPI radar cannot be ascertained by external observation.

FMCW Radar

83

Figure 4.1: Block diagram of a homodyne triangular FMCW radar.

4.2

Single Antenna LPI Radar for Target Detection

A block diagram of a homodyne triangular FMCW emitter is shown in Figure 4.1. In this search mode configuration, both the target range and Doppler information can be measured unambiguously, while maintaining a low probability of intercept. The system uses a single antenna. A triangular waveform generator is used to modulate the CW source for transmission. For low power single antenna systems, a circulator can be used to allow simultaneous transmission and reception [4]. With higher power systems, the transmitter noise side bands can hide valid targets and desensitize the receiver. In this case, separate transmit and receive antennas must be used. To enable the FMCW emitter to operate more eﬃciently using a single antenna for both transmission and reception, a reflected power canceler (RPC) is shown [3, 5]. The RPC adaptively cancels the transmit/receive feedthrough that can limit the dynamic range of single antenna CW radar. In the case of a linear ramp, a simple RPC can adapt during the sweep to handle a wide modulation bandwidth, since the instantaneous bandwidth is small. The target echo is received through the antenna and consists of a delayed replica of the transmitted waveform. The instantaneous frequency diﬀerence between the received signal and the transmitted signal is a constant propor-

84

Detecting and Classifying LPI Radar

Figure 4.2: Envelope approximation detection GOCFAR processor. tional to the round trip delay, so a measurement of this frequency diﬀerence yields the target range. The frequency diﬀerence is obtained by a homodyne mixing process, and the frequencies of the received echos (beat frequencies) are recovered by a spectral analysis of the mixer-lowpass filter output. The lowpass filter is used to pass only the beat frequencies of interest (maximum expected beat frequency fb ), and also to reduce the possibility of strong interfering signals reaching the low noise amplifier (LNA), where they can generate inband spurious signals and distortion that could prevent the detection of the desired target signal. The LNA amplifies the signal after the mixing/LPF operation. An analog-to-digital converter samples and quantizes the complex LNA output, and an FFT computes the frequency spectrum in order to derive the range profile for each sweep. The complex FFT output is detected using an envelope approximation detector x = a max{|I|, |Q|} + b min{|I|, |Q|} (4.1) where a and b are simple multiplying coeﬃcients (e.g., a = 1, b = 1) [6, 7]. This provides a reasonable approximation to the envelope detector but avoids the squares and square roots of the envelope detector which impose additional hardware complexity. A greatest of constant false alarm rate (GOCFAR) processor shown in Figure 4.2 is used to detect the targets in the presence of possible clutter edges within a single modulation period. The envelope approximation detector output values are strobed into the n reference cells with the test cell located in the center. Both reference cell neighborhoods have n cells that are used to determine the noise power levels y1 and y2 on each side of the test cell.

FMCW Radar

85

Figure 4.3: State transition diagram of the Markov chain used for postdetection integration. Note that the width of each reference cell or filter is ∆f Hz. The threshold voltage Vt is obtained by choosing the greatest of y1 and y2 , normalizing by the number of reference cells n and multiplying by the threshold multiplier T . Targets are declared in range for both up slope and down slope (beat frequencies f1b , f2b ), when the amplitude of the test filter is greater than the threshold voltage. Other CFAR architectures can be used, depending on the operating environment. For each modulation period, a single target can result in a number of GOCFAR range detections, depending on the target’s extent and the size of the range resolution ∆R. Each detection is tagged by its range RT and its azimuth angle θa . To reduce the chance of declaring a false target, postdetection integration can be used within a single scan. A simple method of performing postdetection integration for each range detection is through the use of a discrete time Markov chain [8] with NM states followed by a single scan angle threshold processor. A state transition diagram of a postdetection integration Markov chain is shown in Figure 4.3. When the state reaches NX , Θstart = θa , and this marks the beginning of the target position in azimuth. For each detection at RT , the state of the chain advances one level (with probability of detection p). Upon receiving subsequent reports for this range bin from the GOCFAR, the state either moves up or down. For each subsequent miss at RT , the state drops one level (with probability q = 1 − p). When the state drops below NY , Θstop = θa and this marks the end of the

86

Detecting and Classifying LPI Radar

target’s extent in azimuth. Each postdetection integration output has both the target’s range RT , and its extent in azimuth ∆Θ = |Θstart − Θstop |. The single scan angle threshold processor then compares ∆Θ and declares a target at this range and scan if TA ≤ ∆Θ ≤ TB . The thresholds TA (lower limit) and TB (upper limit) depend on the signal-to-noise ratio and are a function of the target’s range, RCS, and any frequency domain STC that is applied. The targets declared on each scan are normally entered into a track file after going through a gating process followed by a scan-to-scan correlation.

4.3

Transmitted Waveform Design

There are two main challenges in designing a high dynamic range FMCW radar for the detection of small targets against a high density clutter background. The first is generating a frequency sweep that is linear. The second challenge is controlling the leakage of transmitter phase noise into the receiver. We begin by examining a triangular FMCW waveform and the Doppler shifted received signal as shown in Figure 4.4. The triangular modulation consists of two linear frequency modulation sections with positive and negative slopes. With a triangular waveform, the range and Doppler frequency of the detected target can be extracted unambiguously by taking, respectively, the sum and the diﬀerence of the two beat frequencies. In this section, the triangular waveform is described, and ways of generating the LPI waveform are discussed.

4.3.1

Triangular Waveform

The frequency of the transmitted waveform for the first section is [9, 10] f1 (t) = fc −

∆F ∆F + t 2 tm

(4.2)

for 0 < t < tm and zero elsewhere. Here fc is the RF carrier, ∆F is the transmit modulation bandwidth, and tm is the modulation period. The modulation (sweep) bandwidth ∆F is chosen to provide the required range resolution ∆R =

c 2∆F

m

(4.3)

Note that the larger the bandwidth, the smaller the resolution and the more LPI the signal becomes. The rate of frequency change or chirp rate F˙ is ∆F F˙ = tm

(4.4)

FMCW Radar

87

Figure 4.4: Linear frequency modulated triangular waveform and the Doppler shifted received signal. The phase of the transmitted RF signal is 8 t f1 (x)dx φ1 (t) = 2π

(4.5)

0

Assuming that φ0 = 0 at t = 0, W ] }w ∆F 2 ∆F t+ φ1 (t) = 2π fc − t 2 2tm for 0 < t < tm . The transmit signal is given by W ] }w ∆F 2 ∆F t+ s1 (t) = a0 sin 2π fc − t 2 2tm

(4.6)

(4.7)

The frequency of the transmitted waveform for the second section is similarly f2 (t) = fc +

∆F ∆F − t 2 tm

(4.8)

88

Detecting and Classifying LPI Radar

Figure 4.5: A block diagram of an FMCW emitter simulation. for 0 < t < tm . Finally, the transmit baseband signal is given by W ] }w ∆F 2 ∆F t− t s2 (t) = a0 sin 2π fc + 2 2tm

(4.9)

Figure 4.5 shows a block diagram of an FMCW emitter simulation. The sinusoidal carrier is 9.3 GHz and the modulation bandwidth ∆F = 1 GHz. Also shown is the triangular waveform with modulation period tm = 0.5 × 10−6 s. The power spectral density for the fc = 9.3-GHz FMCW signal with ∆F = 1.0 GHz is shown in Figure 4.6 with an SNR = 0 dB. The SNR is defined in terms of the signal and noise power as SNR =

A2 2σ 2

(4.10)

where A is the amplitude of the signal and σ 2 is the white Gaussian noise power. Note the simulation shows that the power spectrum of the linear FMCW waveform is nearly rectangular over the band fc − ∆F/2 < f < fc + ∆F/2 adding to the LPI properties of the transmitted signal.

FMCW Radar

89

Figure 4.6: The FMCW signal with fc = 9.3 GHz, ∆F = 1.0 GHz, and SNR = 0 dB.

4.3.2

Waveform Spectrum

Without loss of generality, the instantaneous frequency for the first section (4.2) in transmitted waveform can be rewritten as f1 =

∆F t + fc tm

(4.11)

for |t| ≤ tm /2 where the carrier frequency fc lies at the beginning of the sweep in frequency. The phase of the signal with instantaneous frequency (4.11) can be calculated as 8 t π∆F 2 f1 (t )dt = t + 2πfc t (4.12) φ(t) = 2π tm 0 where the signal has constant amplitude. To compute the spectrum of the waveform we use the complex form of the transmit signal as [11] s(t) = ejφ(t) and obtain the Fourier transform as 8 ∞ s(f ) = s(t)e−j2πf t dt

(4.13)

(4.14)

−∞

Substituting in (4.13) and letting α = π∆F/tm and β = π(fc − f ) 8 ∞ 2 ej(αt +2βt) dt s(f ) = −∞

(4.15)

90

Detecting and Classifying LPI Radar

Using the integral relationships 5 F w 2W w 2W k 8 β β π 2 cos(αt + 2βt)dt = cos C(x) + sin S(x) 2α α α

and 8

sin(αt2 + 2βt)dt =

5

π 2α

F w 2W w 2W k β β cos S(x) − sin C(x) α α

where

5

2 (αt + β) πα and C(x) and S(x) are the Fresnel integrals w 2W 8 x πt C(x) = dt cos 2 0 w 2W 8 x πt dt S(x) = sin 2 0 the spectrum of a single sweep is then 5 π −jβ 2 /α x(tm /2) s(f ) = e [C(x) + jS(x)]|−x(t m /2) 2α x=

(4.16)

(4.17)

(4.18)

(4.19) (4.20)

(4.21)

and the magnitude squared spectrum is tm {[C(x2 ) − C(x1 )]2 + [S(x2 ) − S(x1 )]2 } (4.22) |s(f )|2 = 2∆F Using (4.22), the spectrum sidelobe roll-oﬀ rate may be approximated in the side lobe region using the Fresnel integral approximations for large x > 5 as [11] w 2W w 2W 1 1 1 πx πx sin − 2 3 cos (4.23) C(x) ≈ + 2 πx 2 π x 2 and w 2W w 2W 1 1 πx 1 πx cos − 2 3 sin (4.24) S(x) ≈ − 2 πx 2 π x 2

This shows that the dominant frequency relationship is an inverse x2 term since x ∝ f through β, and thus the roll-oﬀ rate w W f2 = −20dB per decade (4.25) s(f ˙ ) = 10 log10 (10f )2

This spectral behavior is important when considering the out-of-band emissions that can degrade the LPI nature of the waveform. Various techniques can be employed for reducing out-of-band emissions of FMCW waveforms. These include amplitude tapering on a sweep-by-sweep basis (sometimes referred to as curbing) and using a smooth and finite flyback at the end of each sweep.

FMCW Radar

4.3.3

91

Generating Linear FM Waveforms

Linear FM waveforms may be generated by either analog or digital methods. One method consists of using a voltage controlled oscillator (VCO) to produce an approximately linear FM sweep, with the nonlinearities being compensated in the control voltage ramp [4]. The problem with this approach is being able to achieve adequate linearity over a wide bandwidth. The oscillators can also drift with temperature. Another commonly used technique involves a dispersive delay line using surface acoustic wave (SAW) technology, but this has limitations with large time-bandwidth product waveforms tm ∆F . Another approach is to synthesize the sweep in frequency directly by digital means [12]. Advantages of the direct digital synthesizer (DDS) method include: Only the waveform bandwidth (not the time-bandwidth product) is limited by the technology (and circuit complexity), and digital circuits are less likely to be susceptible to temperature drift. Modern DDSs are fully integrated, low-cost, single chip solutions that only need an external clock source for generating the sinusoidal output signals. The DDS benefits from the totally digital generation of the output signal, which allows full control of the signal’s frequency and phase, both with very high precision and resolution. The sequence of waveform samples can be precomputed, stored, and clocked out of memory. The waveform can be generated at IF or baseband. If generated at IF, a high clock rate is required (that depends on the bandwidth). The preferred approach is generating the complex (I and Q) waveform at baseband and using a single sideband modulator to put the waveform on a carrier for transmission. The clock rate for this approach is equal to the chirp bandwidth (rather than twice the chirp bandwidth as in the IF approach). From Figure 4.4, note that the frequency of the waveform increases linearly with time. The phase for the upsweep is given by (4.6). To synthesize the waveform in discrete steps, t is replaced by the sample index i and F˙ = ∆F/tm becomes the angular frequency increment per sample F˙ [12]. The sampled frequency for the first section for N samples is then N p Q ∆F 3 ˙ + f1 N, F˙ = fc − F 2 i=0

(4.26)

The corresponding phase is then

or

N N p Q p Q 3 3 ∆F + F˙ N φ1 N, F˙ = 2π f1 N, F˙ = 2π fc − 2 i=0 i=0

p Q φ1 N, F˙ = F˙ N 2 + φ1 (0)

(4.27)

(4.28)

From these phases, the complex baseband amplitudes can be generated with two accumulators as shown in Figure 4.7. The first (frequency) accumulator

92

Detecting and Classifying LPI Radar

Figure 4.7: Generation of linear FMCW waveform using two accumulators. is preloaded with the starting frequency fc − ∆F/2. The second (phase) accumulator is loaded with zero. In each clock cycle, the frequency increment is added to the frequency accumulator and the new frequency is added to the phase accumulator [see (4.26) and (4.27)]. The width of the data path in the accumulators is given by [12] ] } tm fclk ∆F (4.29) n = log2 δF where δF is the bandwidth increment and fclk is the clock frequency. The phase accumulator output (e.g., 2’s complement) is then used to address both a sine look-up table (LUT) and a cosine LUT. Only one cycle of the sine and cosine waveform needs to be stored in the LUT, since the waveform repeats every 2π. The output LUT resolution depends on the fidelity of the signal required, and the bandwidth and resolution of the digital-toanalog converter (DAC) that is available. The lowpass filter (LPF) is needed to reject the repeated spectra around the clock frequency and multiples of the clock frequency [13]. If not eliminated, the high frequency components cause spurious signals out of the single-sideband modulator (SSBM) used for upconversion on to the RF carrier fc . The SSBM uses the DDS as a reference for a phase-locked-loop stabilized VCO, where the DDS is driven by a high speed reference clock.2 2 Software-driven digital upconversions are also an area of development that is promising for FMCW generation. They can currently provide an intermediate stage upconversion,

FMCW Radar

93

Figure 4.8: Staircase approximation of the phase φ(t). The SSBM mixes the video modulating signal fm with the carrier fc and suppresses either fc + fm or fc − fm . How well the sideband is suppressed can be quantified as a function of |I|, |Q|, and the phase error from perfect quadrature ∆φ as } ] |I|2 |I|2 − 2 cos ∆φ (4.30) s = 10 log10 1 + |Q|2 |Q|2 A detailed noise analysis of the approach above was completed by [14]. The analysis investigates a staircase phase approximation of the FMCW chirp, and examines the spectrum of the transmitted and received signal. The noise caused by the quantization error is then analyzed. It shows that the FMCW signal can be digitally generated using a staircase approximation of its quadratic phase term, without requiring a filter to smooth the signal on transmission or reception. The noise on the transmitted waveform is not usually a problem, except that demodulation of the return signal uses this transmitted waveform as a reference. A digital approximation of the parabolic phase is shown in Figure 4.8, and ensures that each step of the phase staircase is a rectangular function. Also shown is the holding time or subpulse width. The amplitude and phase noise produce a noise power spectral density on the transmitted signal that depends on the subpulse width T and the number of bits of the uniform quantizer n. The requirement for good spectral conditions is [14] T <

1 5Ba

(4.31)

where Ba is the bandwidth after demodulation (on the order of 100 Hz). If the amplitude and phase noise errors are both uniformly distributed over the relaxing the requirements on the DAC and LUT resolution.

94

Detecting and Classifying LPI Radar

bandwidth of 1/T , and the spectral contributions of individual subpulses each contain a constant error, the power spectral density (PSD) is W w T V2 ωT 2 PSD = (4.32) sinc 12 × 22n 2 Hz Example 1: Determine the number of bits required in the accumulator data path if the modulation period tm = 5.0 μs, ∆F = 500 MHz, the clock frequency fclk = 500 MHz, and the bandwidth increment δF = 1 MHz. Using (4.29) J o (4.33) n = log2 1.25(106 ) = 20 bits Example 2: Consider a subpulse period T = 8 μs and a 12-bit quantizer. (a) Determine the bandwidth over which the total noise power will be spread. (b) Determine the noise level due to amplitude and phase noise errors.

For (a), 1/T = 1/8μs = 125 kHz. Note that this is much larger than the low frequency stages of the radar receiver (e.g., 100 Hz). For (b), from (4.32) above, W w V2 8 μs (4.34) = 134 dB PSD = 10 log 12 × 224 Hz

below the received carrier, which is quite good. Recently a DDS was reported using InP double heterojunction bipolar transistor technology. With a single 12-bit phase accumulator and a read only memory LUT phase converter, the DDS is capable of synthesizing output frequencies up to 12 GHz in steps that are 1/4,096 of the 24 GHz clock rate [15]. The measured spurious free dynamic range (SFDR) is 30.7 dB and the average SFDR over all frequency control words is 40.4 dB. The significance of this is that the radar signals can be generated directly in the desired RF band. In summary, the DDS is a more complex approach to generating the FMCW waveform than using a VCO. It has the advantage however, that it provides a perfectly linear sweep and has greater stability which is especially important in LPI emitters where sweep-to-sweep Doppler processing is required.

4.4

Receiver-Transmitter Isolation

One of the greatest problems facing CW radar designers is detecting target returns on the order of a picowatt or less in the presence of a few watts of transmitted power. This is due to the problem of achieving suﬃcient isolation between transmitter and receiver, since the transmission and reception are simultaneous. The main two problems are:

FMCW Radar

95

• Transmitter noise sidebands can hide valid targets. • Power leakage desensitizes the receiver. Although a dual antenna configuration that is well isolated is a possible solution, numerous applications require only a single antenna (e.g., a missile seeker). In this section, a review of transmission line basics is presented, followed by a discussion of two single antenna systems; one using a circulator, and one using an RPC.

4.4.1

Transmission Line Basics

In the analysis of transmission line performance [16], the voltage reflection coeﬃcient, Γ of a transmission line-antenna interface is defined as Γ=

reflected voltage incident voltage

(4.35)

and is generally a complex quantity Γ = |Γ|ejθl

(4.36)

where |Γ| is the magnitude, and never greater than unity (|Γ| ≤ 1). The phase θl is the angle between the incident and reflected voltages at the receiving end, and is usually called the phase angle of the reflection coeﬃcient. The general solutions of the transmission line equations consist of two waves traveling in opposite directions with unequal amplitudes. These waves are called standing waves. The ratio of the maximum voltage of the standing wave pattern to the minimum voltage is defined as the voltage standing wave ratio ρV |VMax | (4.37) ρV = |VMin |

and is usually found using Smith charts. The standing wave ratio results from the fact that the two traveling wave components add in phase at some points, and subtract it at other points. The standing wave ratio ρV is related to the reflection coeﬃcient by 1 + |Γ| (4.38) ρV = 1 − |Γ| and solving for |Γ|,

|Γ| =

ρV − 1 ρV + 1

(4.39)

These results can be used to quantify the various antenna configurations for FMCW emitters.

96

Detecting and Classifying LPI Radar

Figure 4.9: Computing power at receiver using a single circulator including losses.

4.4.2

Single Antenna Isolation Using a Circulator

One solution to isolate the single antenna transmit and receive functions is to use a circulator. To highlight the problems with using a single antenna and circulator, consider the configuration shown in Figure 4.9. To receive a target echo signal and derive the correct beat frequencies, a significant amount of isolation must be present between the transmitted waveform and the received waveform. The transmitter sends an average power Pt to the circulator. A certain fraction of the incident power Ic is leaked at the circulator output, due to the finite amount of isolation. Circulators provide the best isolation when they are terminated correctly (impedances matched). The isolation between any two ports is the return loss due to third port mismatch. Including transmission line loss (LRT = LRR = Lx ≥ 1) and circulator loss (Lc ≥ 1), the average power into the antenna is Pt /Lx Lc . From above, the amount transmitted out of the antenna is Pt (1 − |Γ|2 )/Lx Lc and the amount reflected back to the receiver is Pt |Γ|2 /Lx Lc . The power received from the target is Pr and that portion of received power entering the receiver is Pr (1 − |Γ|2 )/Lx Lc . In summary, the total signal appearing at the receiver is the addition of the target return, the leakage, and the antenna mismatch or Ptot = Pr

|Γ|2 Pt (1 − |Γ|2 ) + Ic Pt + Lx Lc (Lx Lc )2

(4.40)

Example 3: Calculate the total power at the receiver if the standing wave ratio ρV =2:1, the transmission line loss Lx = 0.5 dB, the circulator isolation is Ic = −60 dB, and the circulator loss Lc =1 dB. The CW transmitter provides Pt =10 dBW at fc = 9.375 GHz. The antenna has a transmit, receive gain Gt , Gr =30 dB. The target is located at a range or 28,000m and has a

FMCW Radar

97

RCS σT = 50m2 . The first step is to calculate the magnitude of the reflection coeﬃcient. From (4.39), Γ =0.333. Next, the power transmitted out of the antenna is calculated as Pt (1 − |Γ|2 ) (4.41) PCW = Lx Lc or PCW =6.3W. Using (1.23) with PCW = 6.3W and recognizing that (4.40) takes into account the transmission line losses, the return power from the target is Pr = PRT = 2.6(10−16 ) (or −156 dBW). Using this value in (4.40), Ptot = 0.56W or -2.5 dBW. This example shows that the amount of power from the target that reaches the receiver is minimal, and highlights one of the main problems with using a single circulator FMCW emitter.

4.4.3

Single Antenna Isolation Using a Reflected Power Canceler

The reflective power canceler was discussed briefly in the first section and shown schematically in Figure 4.1. It was developed in the early 1960s as a coherent device that could be used to cancel the transmitter feedthrough in an FMCW emitter [17, 18]. Many of the recent improvements have been made possible by the availability of new microwave and digital components. The RPC is shown in Figure 4.10. The RPC takes a sample of the signal being transmitted and vector modulates it, so that it is of equal amplitude and opposite in phase to the transmitter leakage signal. By adding this signal into the receiver, using a directional coupler, the leakage and noise sidebands of the transmitted signal can be canceled out [3, 5]. The eﬀectiveness of the RPC depends on how accurately the amplitude and phase can be adjusted. To perform adequately, the RPC must operate in a closed-loop fashion, with suﬃcient gain and bandwidth to track the leakage variations. The principle of leakage cancellation is to generate a signal with equalamplitude and opposite-phase to the original leakage. This signal summing up with the original leakage signal realizes the cancellation. A good cancellation requires accurate match of amplitudes and phases. If the signal to be cancelled or leakage signal is the complex signal A, and the cancellation signal or feedthrough signal under vector modulator control is B, assuming a certain phase diﬀerence ∆φ and amplitude diﬀerence ∆A between them, the cancellation signal is (4.42) B = (A + ∆A)ej∆φ The cancellation ratio or cancellation depth is given by [19] e e eB − Ae e e Rcancel,dB = 20 log10 e A e

(4.43)

98

Detecting and Classifying LPI Radar

Figure 4.10: Schematic diagram of a reflective power canceler. or D i Rcancel,dB = 10 log10 1 − 2(1 + ∆A/A) cos ∆φ + (1 + ∆A/A)2

(4.44)

The cancellation depth is very sensitive to the phase error and the amplitude error. For example, to achieve a 30 dB cancellation depth, an amplitude diﬀerence of less than 0.25 dB (3%) and a phase diﬀerence of less than 1◦ is required. An accurate phase match within 1o of error is very diﬃcult to realize using wideband analog microwave and millimeter wave circuits which can vary with temperature and environmental changes. One recent RPC that uses PIN (p into n) diodes and is also used by the Pilot radar, is shown in Figure 4.10. The amplitude and phase of the leakage power are estimated by measuring the dc levels of the I and Q outputs of the receiver mixer. These I and Q signals are then used to control the amplitude and phase of the leakage signal, forming a closed loop controller. The RPC is quite robust to phase errors, on the order of 45 degrees around the loop. Consequently, the vector modulation and quadrature mixer requirements can be relaxed. The Pilot radar uses modern microwave components to improve the transmit/receive isolation from about 20 dB (without RPC) to over 50 dB, and is comparable to the isolation achieved by a dual antenna configuration. The block diagram of a FMCW radar system that uses DDS technology coupled with an RPC and a single antenna for shipboard surveillance is shown in Figure 4.11 [20]. The DDS uses a clock frequency of 300 MHz integrated with a phase-locked loop at L band which is upconverted to X band using a

FMCW Radar

99

mixer. The radar uses a solid state transmitter module for power management (maximum transmit power of 1 W) and the modulation bandwidth can be varied from 50 MHz to 200 MHz. The RPC provides 30 dB of cancellation and has a vector modulator fabricated with PIN diodes, a commerical I-Q demodulator, and a low frequency control circuit (to filter and amplify the signals from the demodulator and apply them to the vector modulator to generate the cancellation signal).

Figure 4.11: Block diagram of an FMCW radar using DDS technology, an RPC, and a single antenna for shipboard surveillance (adapted from [20]). In [19], a heterodyne scheme based on real-time digital signal processing (DSP) is presented for leakage cancellation. In this approach, heterodyne processing is used to generate an error signal modulated at a pre-selected reference frequency. In this manner, the DC oﬀset of the mixer can be separated from the modulated error signal using a band pass filter. Since the modulated error signal contains the amplitude and phase information of the leakage signal, the generation of the controlling error vector is carried out in DSP by comparing the reference signal and the modulated error signal. Then the error vector is used to adjust the vector modulator. Over 30 dB cancellation of the leakage was achieved over a modulation bandwidth ∆F = 1.7 GHz and modulation period tm = 1.4 ms [19]. A quadrature FMCW radar topology using a leakage cancellation circuit at 24 GHz is presented in [21]. The canceller is composed of four branch-line hybrid couplers, a 90o delay line and a Wilkinson combiner. For this architecture, a 35 dB cancellation was achieved.

100

4.5

Detecting and Classifying LPI Radar

The Received Signal

The received signal from a stationary target is the transmit signal delayed in time by the round-trip propagation time (or transit time) to the target and back (td ), with reduced amplitude b0 [3] sr (t) = or

b0 s1 (t − td ) a0

W ] }w ∆F ∆F 2 (t − td ) + s1r (t) = b0 sin 2π fc − (t − td ) 2 2tm

(4.45)

(4.46)

For the homodyne FMCW emitter, the receive signal is mixed with the transmit signal. The beat frequencies are derived as the diﬀerence between the transmitted and received signals. The beat frequency is sometimes referred to as an intermediate frequency, although the information is not modulated onto a conventional carrier [9]. The mixer output beat frequency signal is W }w ] ∆F ∆F 2 ∆F td − t + td t (4.47) s1b (t) = c0 cos 2π fc − 2 2tm d tm For the second segment of the triangular waveform, the mixer output beat frequency signal is W }w ] ∆F ∆F 2 ∆F td + td − td t (4.48) s2b (t) = c0 cos 2π fc + 2 2tm tm Equations (4.47) and (4.48) contain a frequency term that is time varying and phase terms that are not. The beat frequency is the third term in (4.47) and (4.48) ∆F 2R∆F 2R ˙ td = = F (4.49) fb = tm ctm c where the delay time td = 2R/c for a stationary target at a range of R. If the target is moving with velocity V , the beat frequency for the first segment is f1b =

2R ˙ 2R∆F 2V 2V = − F− ctm λ c λ

(4.50)

and the beat frequency for the second segment is f2b =

2R ˙ 2R∆F 2V 2V = + F+ ctm λ c λ

(4.51)

where the second term is due to the target’s Doppler frequency. For multiple targets, multiple beat frequencies would be present and would depend on each target’s range and velocity.

FMCW Radar

101

Figure 4.12: ASCM LPI emitter-ship scenario. In summary, the advantages of the linear FMCW waveform include: (a) the presence of LPI operation with an eﬃcient utilization of the spectrum, (b) the waveform is easier to implement than phase-coded modulation if there are no strict demands on linearity over a wide bandwidth, and (c) the received signal can be processed using one multiplication with a matched reference signal, with the range being resolved using spectral analysis.

4.6

LPI Search Mode Processing

To illustrate LPI search mode processing, consider an antiship cruise missile with a seeker (fc = 9.375 GHz) flying inbound to a target ship with RCS = σT . The incremental backscattering coeﬃcient of the sea surface is σo . The LPI seeker comes on at a range of R = 28,000m (15 nmi) from the ship. Figure 4.12 shows the missile-ship scenario being investigated. The emitter is flown at 300 m/s (Mach 1) at an altitude of h = 70m toward the ship for a period of 91s. Note that this scenario assumes initially that the ship is not moving. The scenario is analogous to the LPI radar being stationary and the target approaching at 300m/s. In the search mode, the emitter uses, for example, the conventional scan shown in Figure 1.4(a) and makes a single scan every 3s with a scan rate of 70 deg/s. At end game (700m from target), the missile dives to the ship for impact. The first step in designing the LPI seeker is to determine the modulation bandwidth ∆F (peak-to-peak frequency deviation) in order to give the required range resolution. For example, the ASCM might require a ∆R = 0.3m

102

Detecting and Classifying LPI Radar

range resolution, in order to calculate the ship orientation and select a waterline aimpoint with good accuracy. With this range resolution, the ship returns could easily extend over a large number of range bins, depending on the aspect angle. Recall that the ideal range resolution is ∆R =

c 2∆F

m

(4.52)

For ∆R = 0.3m, a ∆F = 500 MHz is chosen. To increase the signal to clutter ratio, a ∆R equivalent to the size of the ship may be selected so that the entire ship’s return lies within a single range bin. This approach would require a smaller ∆F . The modulation period is chosen next, and two factors must be considered. The first consideration is that tm <

∆R Vt

(4.53)

where Vt is the maximum closing velocity of the target. This relationship requires that the target must remain in a range bin for at least an entire modulation period tm . Otherwise, the target return will smear across several range bins. The second consideration is that tm should be several times the maximum round-trip delay td , of the target’s return signal. This is in order to minimize the loss in eﬀective transmit bandwidth and power and to also provide a high velocity resolution [9]. Since an acquisition range of R = 28, 000m corresponds to a maximum round-trip delay td = 186.7 μs, a modulation period of tm = 1 ms is chosen (≈ 5.5td ). The resulting coherent processing interval is t0 = tm − td

(4.54)

The spectral width of the beat frequency is the inverse of the coherent processing interval or 1 1 1 = ≈ (4.55) ∆w = t0 tm − td tm and is the Doppler shift that causes a range error of exactly one range bin. The eﬀect that a Doppler shift can change the apparent range of the target is the well-known FMCW range-Doppler cross-coupling eﬀect. That is, the unambiguous Doppler frequency is fu = ±1/2t0 Hz. The corresponding velocity resolution or first blind speed is ∆v =

λ∆w m/s 2

(4.56)

The first blind speed is the speed at which the Doppler goes through one complete cycle from one sweep to the next (beat frequency increases by one cycle per sweep) [3]. For our example, with a target acquisition range

FMCW Radar

103

R = 28 km and a td = 186.7 μs, the coherent processing interval t0 = 0.81 ms and the spectral width ∆w = 1.23 kHz. The resulting first blind speed is ∆v = 19.7m/s. For the first section of the triangular waveform, the partial overlap results in a reduced processed bandwidth. The eﬀective bandwidth is W w td Hz (4.57) ∆F = ∆F 1 − tm with an eﬀective time bandwidth product of t0 ∆F . The range resolution is also slightly degraded as c c m (4.58) = ∆R = 2∆F 2∆F (1 − td /tm ) Continuing the example above, with td = 186.7 μs, ∆F = 406.7 MHz, ∆R = 0.37m, and the eﬀective time-bandwidth product t0 ∆F = 330.75 × 103 . The large time-bandwidth product contributes to the LPI nature of the radar. The resulting beat frequencies are of the form f1b =

2R∆F 2V − ct0 λ

(4.59)

and

2R∆F 2V (4.60) + ct0 λ Using the numbers from the example above with Vmax = 300m/s, the corresponding maximum beat frequency is fbmax = 93.35 MHz. The analog-to-digital converter section of the LPI radar receiver must sample at least twice the highest beat frequency or W w 2R∆F 2V samples/s (4.61) + fs = 2 ct0 λ f2b =

resulting in the number of samples within a coherent processing interval of N F = fs t0 . With fbmax = 93.35 MHz, fs = 186.7 MS/s. To resolve the multiple echoes from the clutter and targets, an FFT process is used for frequency analysis. The signal after frequency analysis is a coherent video signal. Since the FFT requires integer powers of 2, the FFT size is chosen to be N = 2x ≥ N F . To capture this many samples, the ADC sampling frequency must be fs =

N t0

samples/s

(4.62)

with the sampling frequency and an FFT size of N , the resulting filter width is f (4.63) ∆f = s N

104

Detecting and Classifying LPI Radar

Table 4.1: Eight LPI Emitter Designs for Comparison Examples ∆F (MHz) ∆R (m) ∆F I (MHz) ∆RI (m) fbmax (MHz) FFT size t0 ∆F I

1 15 10.0 12.2 12.3 2.8 8,192 9,923

2 20 7.5 16.2 9.2 3.8 8,192 13,230

3 25 6.0 20.3 7.4 5.0 8,192 16,537

4 30 5.0 24.4 6.1 5.6 16,384 19,845

5 35 4.3 28.5 5.3 6.6 16,384 23,153

6 50 3.0 40.7 3.7 9.4 16,384 33,075

7 500 0.3 406.7 0.37 93.3 262,144 330,755

8 1000 0.15 813.3 0.18 186.7 524,288 661,511

and agrees with (4.55). For the example, N F = fs t0 = 151,853 samples and N = 218 = 262,144 so fs = 322 MS/s giving a filter width of ∆f = 1.23 kHz or 19.7m/s. Since the signal processed by the FFT is complex, the unambiguous range is Ru = N ∆R =96,993m. Since this exceeds the required detection range of the target, the number of range cells processed by the FFT can be limited by filtering the input to the FFT processor. This reduces the input bandwidth, as well as the complexity of the digital processing. Weighting can also reduce the frequency and range side lobes, but will increase the overall frequency and range resolution [10]. For a Hamming weighting we include the loss by multiplying by a factor of 1.8 or ∆R = 0.67m. Table 4.1 shows, for comparison, eight emitter design examples. For all examples shown, fc = 9.375 GHz, t0 = 0.81 ms, and ∆f = 1.23 kHz. After the GOCFAR detects the beat frequencies f1b , f2b from both transit waveform sections, the target’s range is calculated as R=

ctm (f1b + f2b ) 4∆F

m

(4.64)

and the target’s range rate is calculated as λ R˙ = (f2b − f1b ) 4

(4.65)

The Markov chain counts up the range hits during a scan, and sends the start and stop angles of the detected target to a single-scan detection process that thresholds the diﬀerence between the start and stop angle (see Section 4.2). After target declaration, the emitter fixes the antenna position at the angle of the target, and the track mode processing takes over.

4.7

Track Mode Processing Techniques

The LPI emitter starts at a range of R = 28,000m (15 nmi) from the ship. Figure 4.12 shows the emitter-ship scenario being examined. For the track mode processing, consider the return from a target showing up in a particular filter fb with bandwidth ∆f . This frequency will correspond to a target at a

FMCW Radar

105

range R where cfb t0 (4.66) 2∆F Consequently if the target range is varying, it may be tracked by adjusting the sweep bandwidth ∆F in order to keep the beat frequency equal to fb . This relaxes the LPF requirements at the receiver frontend. Also recall that the range resolution ∆R = c/2∆F . The ratio of these gives the range resolution expressed as a fraction of the range R=

1 ∆R = R fb t0

(4.67)

and is a constant. That is, the emitter will measure the range to the target with a resolution that is proportional to the range. As the range-to-target gets smaller, the bandwidth ∆F gets larger. For example, if the target at R = 28,000 is acquired on the first transmit waveform, the target shows up at filter number 75,675 or fb = 75, 675 ∗ 1.23 kHz = 93.1 MHz. In order to keep the target at this beat frequency, the sweep bandwidth is calculated as ∆F =

1.13 × 1013 cfb t0 = 2R R

Hz

(4.68)

For an endgame range-to-target of R = 700m, ∆F = 16.2 GHz. A block diagram of the track processing is shown in Figure 4.13. Note that the major advantage of this technique is that the (narrow) bandpass filter is now centered on fb . Since the range to the moving target is changing with time, a range tracker (in Doppler space) is required that is constantly adjusted to keep the target locked in range. After the range is computed, the required sweep bandwidth is recalculated and sent to the triangular waveform generator. Another approach to the track processing is to keep the sweep bandwidth constant, and to allow the target’s beat frequency to change. The target’s position can be followed in signal processing by monitoring the position of the FFT peak detector output. The advantage of this approach is that the receiver LPF used in the search mode can also be used for the track processing, at the expense of integrating a larger noise component.

4.8

Eﬀect of Sweep Nonlinearities

Frequency sweep nonlinearities (frequency instability in the transmitter) act to broaden the spectral width of the target’s beat frequency. The requirement on frequency stability in the transmitter is investigated in [10, 22], and techniques to correct for these nonlinearities are examined in [23]. To quantify these eﬀects, a nonlinear term can be added to (4.8) as [10]

106

Detecting and Classifying LPI Radar

Figure 4.13: Block diagram of the track processing, for the triangular homodyne FMCW emitter.

f2n (t) = fc +

∆F ∆F − t + An sin 2πfn t 2 tm

(4.69)

where 0 < t < tm and An is the amplitude of the sinusoidal nonlinearity, and fn is the frequency of the sinusoidal nonlinearity. The transmitted signal is W }w ] ∆F 2 ∆F An t− t + (1 − cos 2πfn t) (4.70) s2n (t) = a0 sin 2π fc + 2 2tm 2πfn The corresponding mixer output beat frequency signal can be shown to have the form W }w ∆F ∆F 2 ∆F td + t − td t s2bn (t) = c0 cos 2π fc + 2 2tm d tm ] An + [cos 2πfn (t − td ) − cos 2πfn t] 2πfn for 0 < t < tm . From this expression, the eﬀects of the nonlinearity can be evaluated and their significance evaluated.

FMCW Radar

107

Figure 4.14: Performance of a three-sweep canceler on S-band FMCW radar (i-canceled, ii-uncanceled) [3] ( c IEE 1992).

4.9

Moving Target Indication Filtering

A moving target indication (MTI) filter can also be added to the FMCW signal processing chain, and operates in a manner similar to a pulsed radar [3]. Figure 4.14 shows the operation of an MTI canceler, an experimental Sband FMCW radar built at Philips Research Laboratories. The upper trace shows the video A-scope picture from one sweep of the radar. The lower trace shows the signal at the output of a digital three-sweep MTI canceler with more than 40 dB of cancellation. Moving target Doppler (MTD) processing can be implemented by measuring the rate of change of phase of the output of each FFT range bin, from one sweep to the next, as shown in Figure 4.15. This capability can be added quite easily to existing FMCW radars.

108

Detecting and Classifying LPI Radar

Figure 4.15: MTD processing applied to FMCW radar with output a set of range-Doppler cells [3] ( c IEE 1992).

4.10

Matched Receiver Response

For the FMCW emitter design shown in Figure 4.1, the weighting is uniform. That is, no weighting is applied to the homodyne detector during the correlation process. Recall that the unweighted PAF describes the rangeDoppler response of a matched receiver, when the receiver’s reference signal is constructed from an integral number of periods N of the transmitted signal (reference signal duration N tm ). Figure 4.16(a) shows the unweighted ACF for an FMCW waveform with tm =20 ms and ∆F =500 Hz, where the receiver uses N = 1 reference signals for correlation. Note the peak side lobe level PSL ≈ −15 dB. The PACF is shown in Figure 4.16(b) and indicates that the FMCW does not have a perfect PACF. The PAF is shown in Figure 4.17. The plot shows the two peaks left out from the two diagonal ridges, bifurcating from the main lobe at a level of 1/2. The high side lobes are unwanted, since additional targets could possibly hide at these positions. Note that the main and side lobes do not have deep nulls, a situation that can be rectified with additional copies of the reference signal used in the receiver. Figure 4.18(a, b) shows the ACF and PACF, respectively, for the triangular FMCW with N = 4. Note the well-defined main lobe repeating at every 2tm fs = 280 samples, resulting from the use of N = 4 copies of the reference signal in the correlation receiver. Figure 4.19 shows the PAF for N = 4 and demonstrates the more pronounced Doppler lobes appearing at kN for

FMCW Radar

109

Figure 4.16: Triangular FMCW (a) ACF and (b) PACF with ∆F = 500 Hz, tm = 20 ms, and N = 1.

Figure 4.17: Triangular FMCW PAF with ∆F = 500 Hz, tm = 20 ms, and N = 1.

110

Detecting and Classifying LPI Radar

Figure 4.18: Triangular FMCW (a) ACF and (b) PACF with ∆F = 500 Hz, tm = 20 ms, and N = 4. k ∈ {0, 1, . . .}. The side lobes are reduced significantly.

4.11

Mismatched Receiver Response

Recall from Chapter 3 the weighted PAF e ∞ We w e 3 n ee e g (τ )W ν − |ψ(τ, ν)| = e e en=−∞ n tm e

where

1 gn (τ ) = T

8

0

(4.71)

T

u(t − τ )r(t)e2πnt/T dt

(4.72)

describes the performance of a mismatched correlation receiver. That is, for any (τ, ν) the receiver response is determined by contributions from all the gn functions. To study close up the mismatched response, we follow the development by Levanon and present the function gn (τ ) for a sawtooth FMCW signal [24]. In the receiver, the envelope of the reference signal (before adding weights) is the complex conjugate of the envelope of the transmitted signal (r(t) = u∗ (t)). The complex envelope of the transmitted signal is 3 u(t) = uT (t − ntm ) (4.73) n

FMCW Radar

111

Figure 4.19: Triangular FMCW PAF with N = 4. for n = 0, ±1, ±2, · · · , and jπ∆F uT (t) = exp

w

t−

tm

tm 2

W2

(4.74)

where 0 ≤ t ≤ tm and zero elsewhere. Using (4.74) and (4.73) and the reference signal r(t) = u∗ (t) in (4.72) ] w W } τ sin(πn − α) jπnτ /tm τ sin α gn (τ ) = + (−1)n 1 − e (4.75) tm α tm πn − α where α=

πτ [∆F (tm − τ ) + n] tm

(4.76)

and is shown in Figure 4.20(a) for ∆F = 500 Hz and tm = 20 ms (tm ∆F = 10) to demonstrate the extensive range side lobes that appear in the delayDoppler response for the FMCW signal. The weight function in (4.71) suppresses the Doppler side lobes. To reduce the range (or time) side lobes, frequency weighting is often used (similar to the STC processing). Since the frequency deviation is linearly swept within

112

Detecting and Classifying LPI Radar

Figure 4.20: gn (τ ) for FMCW waveform with tm ∆F = 10 (a) unweighted and (b) weighted (c = 0.53836 Hamming).

FMCW Radar

113

one modulation period tm , frequency weighting can be implemented by a repetitive time weight function with a period of tm 3 r(t) = u∗tm (t − ntm )wtm (t − ntm ) (4.77) n

where n = 0, ±1, ±2, . . . . Using the same weighting function discussed previously, the new function to reduce the time (range) side lobes can be shown to be 1−c [gn+1 (τ ) + gn−1 (τ )] (4.78) gnw (τ ) = gn (τ ) − 2c The result for the tm ∆F = 10 waveform is shown in Figure 4.20(b) and demonstrates the reduction in the range (time) side lobes using c = 0.53836 (Hamming window).

4.12

PANDORA FMCW Radar

The parallel array for numerous diﬀerent operational research activities (PANDORA) is an experimental LPI radar that is designed to generate eight separate (but simultaneous) narrowband FMCW signals at X-band, that are additively mixed and radiated. A block diagram of a four-channel PANDORA radar is shown in Figure 4.21 [25]. The multichannel multifrequency emitter consists of an FMCW waveform generator and a power combiner block. The receiver contains a wideband LNA, a power resolver block, stretch processing for each FMCW channel, a noncoherent processor, and a high resolution FFT. The radar operates on two well-isolated antennas; one for transmission and one for reception. In order to eliminate near field clutter, pencil beams are used for transmission and reception. The range is unambiguous, and the ambiguity in Doppler is controlled by ensuring that the change in Doppler across the modulation bandwidth for a particular target is less than the spectral width ∆f (confined to a single range bin). The major contribution of the PANDORA LPI radar is the ultrawideband processing capability without the need for an ultrawideband instantaneous bandwidth. The center frequency of each channel diﬀers by the modulation bandwidth (f1 = 48 MHz) plus a guard channel (fg = 56 MHz). The guard channel helps to ensure channel isolation, as well as enabling a higher resolution to be obtained than the individual sweeps by themselves. A total modulation bandwidth of 776 MHz is achieved from eight channels (from 9.378 GHz to 10.154 GHz) resulting in a range resolution of ∆R = 0.19m instead of ∆R = 3.1m characteristic of a ∆F = 48 MHz. The narrowband FMCW signals are generated in each channel as shown in Figure 4.22 [26]. A single channel has been demonstrated covering the entire bandwidth.

114

Detecting and Classifying LPI Radar

Figure 4.21: Block diagram of the PANDORA radar [25] ( c IEEE 2000).

Figure 4.22: PANDORA narrowband FMCW channel configuration [26] ( c IEEE 2000).

FMCW Radar

4.13

115

Electronic Attack Considerations

FMCW radars are hard to detect due to their wideband waveforms and consequently, potential jammers have a significant problem measuring the waveform parameters with suﬃcient accuracy in order to match the jamming waveform to the radar waveform. In a realistic environment with a large number of other radar systems operating in the same frequency band, an FMCW radar is significantly more diﬃcult to detect. These types of jammers and their requirements are discussed in Part II. Also, since the FMCW transmit waveform is deterministic, a good deal of robustness against electronic attack is inherent. This stems from the fact that with this deterministic transmitted signal, the return target signature has a general form that may be predicated. This leads to a significant suppression of many interfering waveforms that are uncorrelated, such as narrowband interference and pulsed radar emissions. Of course, if the modulation period tm and bandwidth ∆F can be determined, then coherent deception jamming is feasible and very eﬀective, since the jammer waveform looks like the radar waveform. Antijam aspects of linear FM waveforms using simulations have also been performed [27]. White Gaussian noise, continuous wideband jamming, and jamming signals that were identical to the transmitted chirp signal were evaluated. They conclude that the FMCW signal can be recovered in moderate noise conditions, but the radar has a hard time distinguishing a genuine chirp signal from a hostile jammer signal when the jammer produces signals that have a similar frequency spectrum to the chirp signal.

4.14

Technology Trends for FMCW Emitters

The FMCW limitations discussed above are quickly being overcome, with such devices as solid-state transmitters and high-speed DSPs. This section discusses some of the recent advances and their impact on the FMCW radar performance. As shown in Figure 4.1, the same antenna is used for both transmission and reception, and the signals are separated with a circulator connected to the antenna. In the FMCW emitter, transmission and reception are simultaneous, and it is necessary to detect target returns on the order of a picowatt or less in the presence of watts of transmitted power. The transmitter noise can swamp out the valid targets, and the power leakage can desensitize the receiver. Although two antennas (one transmit, one receive) can solve the problem, many FMCW emitters (e.g., LPI missile seekers) must use a single antenna. Consequently, the leakage must be canceled before it desensitizes the receiver performance. Conventionally, the vector modulator RPC adjusts a sample of the signal being transmitted so that it is of equal amplitude to, and directly out of

116

Detecting and Classifying LPI Radar

Figure 4.23: Block diagram of C-band FMCW radar MMIC with electronic circulator and photograph of GaAs chip (1.08 × 2.15 × 0.25 mm) [28] ( c IEEE 1989). phase to the transmitter leakage signal [3, 4]. By adding the signal into the receiver via a directional coupler, the leakage, including the noise sidebands of the transmitted signal, can be canceled out. This reflected power-canceling circuit must operate closed loop, with suﬃcient gain and bandwidth to track the leakage variation. The demand for the low cost and small size makes modern front-end solutions based on microwave monolithic integrated circuits (MMICs) the most favored approach. In order to allow single antenna operation, the first lowpower C-band FMCW radar MMIC chip that incorporated an electronic circulator in a single gallium arsenide (GaAs) integrated circuit was reported in [28] and shown in Figure 4.23. The chip also included the VCO, buﬀer amplifier, and the mixer. In this circuit, the VCO drives a two-stage amplifier to form the FM transmitter. The receiver consists of an active field eﬀect transistor (FET) mixer with a bandpass input filter. The electronic circulator circuit provides the interface to transmitter and receiver. The reference or local oscillator signal for the mixer is provided by the reflected power from the antenna mismatch. The signal reflected from the antenna mismatch is suﬃciently greater than the inherent circulator leakage to capture the mixer and serve as the local oscillator signal [28]. The circulator can also be a passive ferrite device, but this typically has to be placed outside the MMIC circuitry. The use of a power divider has also been suggested, but wastes one half of both the transmitted and received power. The FET transceiver is one promising approach to separate two signals that are closely spaced in frequency [29]. A circuit diagram of the FET transceiver is shown in Figure 4.24, and overcomes the disadvantages associated with diode circuits as well as being well suited to MMIC technology. The circuit eliminates the need for dual antennas, a circulator, or a coupler for the separation of the transmit and receive signal paths. The FET is used simultaneously as an amplifier for the transmitted signal, and as a resistive mixer to downconvert the received signal. At optimum bias point, the cir-

FMCW Radar

117

Figure 4.24: Circuit diagram of the X-band FET transceiver [29] ( c IEEE 2000). cuit has an output power of 7 dBm and a conversion loss of 9 dB. Although the output power in this technology is limited, by 2011 the output power capabilities are expected to be suitable for missile seeker applications. An indium phosphide (InP)-based MMIC for use in millimeter wave FMCW emitters was reported in [30] for a two-antenna system. For the transistor of this MMIC, an indium aluminum arsenide/indium gallium arsenide (InAlAs/InGaAs) on InP pseudomorphic high electron mobility transistor (HEMT) was used with a 0.5m gate length. Because of the high electron mobility and the high sheet charge density, the HEMT performed with 8 dBm output power gain in the millimeter wave frequency range. The millimeter wave circuitry consisted of a 30-GHz voltage-controlled oscillator, a 30/60-GHz frequency doubler, a 60-GHz amplifier, and a 60-GHz singlebalanced mixer. Other GaAs HEMT technology for W-band FMCW receivers have been recently reported in [31—33]. A 25-GHz nonlinear, single antenna FMCW front-end, that uses a highprecision 2.45-GHz surface acoustic wave (SAW) reference and adaptively compensates for phase errors (linearizing the target signal) by software, is reported in [34]. The compensation of phase errors is based on measuring the target signal against an exactly known distance standard. This standard is implemented using the SAW delay line. By moving the VCO and the reference delay line to a 2.45-GHz IF, a complete planar design of the 24-GHz front-end is realized as shown in Figure 4.25. A control voltage m(t) sweeps the frequency of the 2.45-GHz VCO monotonically over the sweep bandwidth. The VCO feeds the SAW delay line and a mixer yielding the reference signal sr(t). The other part is upconverted with a 21.7-GHz LO signal, bandpass filter, amplified and fed through a directional coupler to the antenna. The transmit/receiver hybrid diverts the delayed echo signal from the an-

118

Detecting and Classifying LPI Radar

Figure 4.25: Block diagram of a 24-GHz FMCW sensor with 2.45-GHz SAW reference [34] ( c IEEE 1997). tenna to the downconverter that is pumped by the LO. The resulting delayed 2.45-GHz IF signal is then mixed with the IF transmit signal, providing the sensor signal sm (t) for further digital signal processing. A 77-GHz version of the architecture incorporating a flip-chip MMIC VCO was also reported in [35]. The precision of FMCW emitters depends largely on the linearity of the frequency ramp generator. Many frequency synthesizer concepts have been explored. One method is to directly linearize the VCO. The linearity, however, that is achievable with a direct linearization circuit at the VCO input is poor [36]. The linearity can also be improved by controlling it within a phaselocked loop (PLL) that uses a stable crystal-controlled oscillator. This can result in linearity better than 10-4. The conventional PLL linearization circuit consists of a programmable frequency divider with a unity division ratio N . The analog ramp frequency results from the moving average of the reference frequency fref multiplied by N . To increase the number of steps the divider executes on the ramp, a fractional divider circuit can be used to make any desired step size. This way, many more division ratio steps can be executed on the ramp [36]. A block diagram of the FMCW system with a fractional ramp generator is shown in Figure 4.26, and includes a modified setup for measuring the ramp quality. Digital techniques to generate the sweep signals have also gained much attention. Use of a direct digital synthesizer, for example, has many advantages over analog methods, including good flexibility in changing the sweep bandwidth and sweep rate. Also, these techniques are not as susceptible to environmental factors. High-temperature superconductor (HTS)-based systems have made the

FMCW Radar

119

Figure 4.26: Block diagram of an FMCW system with fractional ramp generator [36] ( c IEEE 1999). transition from the laboratory to the field. The use of HTS systems has recently gained significant attention, since they can solve a number of recurring problems in digital receiver designs, such as noise figure, bandwidth, gain, loss, size, and dynamic range. For example, the insertion loss in the preLNA filter shown in Figure 4.1 can degrade the system noise figure and dynamic range. Superconductor tunable filters are very attractive due to the low loss that is achievable. A compact superconducting-ferrite filter operating at 77K with insertion loss of 1 dB is reported in [37]. An HTS filter with noise figure on the order of 0.3 dB is reported in [38]. Note that these filters have a flat passband, sharp filter edge skirts, and superior out-of-band rejection characteristics. The filter and the LNA are often contained together in a cryo-cooled Dewar. The use of HTS for an FMCW radar is discussed in [39]. Here, a self-contained FMCW radar incorporating a compact 2.2-ns broadband superconducting delay line operating at 80K is described and is the first demonstration of an integral microwave system utilizing HTS circuitry that incorporates a closed-cycle cooler, and a long-life permanently sealed Dewar.

References [1] Mahafza, B. R., Radar Systems Analysis and Design Using MATLAB, Chapman & Hall/CRC, Boca Raton, Jan. 2000. [2] Stove, A. G., “Modern FMCW radar - techniques and applications,” European Radar Conference, Amsterdam, pp. 149—152, 2004. [3] Stove, A. G., “Linear FMCW radar techniques,” IEE Proc. F, Vol. 139, No. 5, pp. 343—350, Oct. 1992. [4] Griﬃths, H. D., “New ideas in FM radar,” IEE Electronics and Communications Engineering Journal, pp. 185—194, Oct. 1990. [5] Beasley, P. D. L., et al., “Solving the problems of a single antenna frequency modulated CW radar,” Record of the IEEE 1990 International Radar Conference, pp. 391—395, 1990.

120

Detecting and Classifying LPI Radar

[6] Nathanson, F. E., and Luke, P. J., “Loss from approximations to squarelaw detectors in quadrature systems with postdetection integration,” IEEE Trans. on Aerospace and Electronic Systems, AES-8 pp. 75—77, Jan. 1972. [7] Filip, A. E. “A baker’s dozen magnitude approximations and their detection statistics,” IEEE Trans. of Aerospace and Electronic Systems, AES-12, pp. 86—89, Jan. 1976. [8] Cassandras, C. G., Discrete Event Systems Modeling and Performance Analysis, Aksen and Irwin Associates, Homewood, IL, 1993. [9] Piper, S. O., “Receiver frequency resolution for range resolution in homodyne FMCW radar,” Proc. National Telesystems Conference, Commercial Applications and Dual-Use Technology, pp. 169—173, 1993. [10] Piper, S. O., “Homodyne FMCW radar range resolution eﬀects with sinusoidal nonlinearities in the frequency sweep,” Record of the IEEE International Radar Conference, pp. 563—567, 1995. [11] Turley, M. D. E., “FMCW radar waveforms in the HF band,” ITU-R JRG 1A-1C-8B meeting, Nov. 2006. [12] Griﬃths, H. D., and Bradford, W. J., “Digital generation of high timebandwidth product linear FM waveforms for radar altimeters,” IEE Proc. F, Vol. 139, No. 2, pp. 160—169, April 1992. [13] Pace, P. E., Advanced Techniques for Digital Receivers, Artech House, Inc., Norwood, MA, July 2000. [14] Abousetta, M. M., and Cooper, D. C., “Noise analysis of digitized FMCW radar waveforms,” IEE Proc. F, pp. 209—215, Aug. 1998. [15] Turner, S. E., Chan, R. T., and Feng, J. T., “ROM-based direct digital synthesizer at 24 GHz clock frequency in InP DHT technology,” IEEE Microwave and Wireless Components Letters, Vol. 18, No. 8, pp. 566—568, Aug. 2008. [16] Liao, S. Y., Microwave Devices and Circuits, 2nd Edition Prentice Hall, Upper Saddle River, New Jersey, 1980. [17] Harmer, J. D., and O’Hare, W. S., “Some advances in CW radar techniques,” IRE 5th Mil-E-Con Record, pp. 311—323, 1961. [18] O’Hara, F. J., and Moore, G. M., “A high performance CW receiver using feedthrough nulling,” Microwave Journal, Vol. 6, No. 9, pp. 63—71, Sept. 1963. [19] Lin, K., Wang, Y. E., Pao, C.-K., and Shih, Y.-C., “A Ka-Band FMCW radar front-end with adaptive leakage cancellation,” IEEE Trans. on Microwave Theory and Techniques, Vol. 54, No. 12, pp. 4041 — 4048, Dec. 2006. [20] Grajal, J., Asensio, A. and Requejo, L., “From a high-resolution LFM-CW shipborne radar to an airport surface detection equipment,” Proceedings of the IEEE Radar Conference, pp. 157—160, Madrid, Spain, 2004. [21] Kim, C.-Y., Kim, J.-G., and Hong, S., “A quadrature radar topology with Tx leakage canceller for 24-GHz radar applications,” IEEE Trans. on Microwave Theory and Techniques, Vol. 55, No. 7, pp. 1438—1444, July 2007.

FMCW Radar

121

[22] Tujaka, S., “On frequency stability of transmitter in LFMCW MTD radar,” 12th International Conference on Microwaves and Radar, MIKON ’98, Vol. 3, pp. 776—780 May 1998. [23] Fuchs, J., et al., “Simple techniques to correct for VCO nonlinearities in short range FMCW radars,” IEEE MTT-S International Microwave Symposium Digest, pp. 1175—1178, 1996. [24] Levanon, N., and Getz, B., “Comparison between linear FM and phase-coded CW radars,” IEE Proc. F, Vol. 141, No. 4, pp. 230—240, Aug. 1994. [25] Jankiraman, M., Wessels, B. J., and van Genderen, P., “Pandora multifrequency FMCW/SFCW radar,” Record of the IEEE International Radar Conference, pp. 750—757, 2000. [26] Jankiraman, M., de Jong, E. W., and van Genderen, P., “Ambiguity analysis of Pandora multifrequency FMCW/SFCW radar,” Record of the IEEE International Radar Conference, pp. 35—41, 2000. [27] Fu, J. S., and Ke, Y., “Anti-jamming aspects of linear FM and phase coded pulse compressions by simulation,” CIE International Conference of Radar Proc., pp. 605—608, Oct. 8—10, 1996. [28] Reynolds, L., and Ayasli, Y., “Single chip FMCW radar for target velocity and range sensing applications,” Technical Digest of 11th Annual GaAs IC Symposium, pp. 243—246, 1989. [29] Yhland, K., and Fager, C., “A FET transceiver suitable for FMCW radars,” IEEE Microwave and Guided Wave Letters, Vol. 10, No. 9, pp. 377—379, Sept. 2000. [30] Sasaki, K., et al., “InP MMICs for V-band FMCW radar,” IEEE MTT-S International Microwave Symposium Digest, pp. 937—940, 1997. [31] Tessmann, A., et al., “A 77 GHz GaAs pHEMT transceive MMIC for automotive sensor applications,” Proc. of the GaAs IC Symposium, pp. 207—210, 1999. [32] Lamberg, J. R., et al., “A compact high performance W-band FMCW radar front-end based on MMIC technology,” IEEE MTT-S International Microwave Symposium Digest, pp. 1797—1800, 1999. [33] Haydl, W. H., et al., “Single-chip coplanar 95 GHz FMCW radar sensors,” IEEE Microwave and Guided Wave Letters, Vol. 9, pp. 73—75, Feb. 1999. [34] Nalezinski, M., Vossiek, M., and Heide, P., “Novel 25 GHz FMCW frontend with 2.45 GHZ SAW reference path for high precision distance measurements,” IEEE MTT-S International Microwave Symposium Digest, pp. 185—188, 1997. [35] Vossiek, M., Kerssenbrock, T. V., and Heide, P., “Novel nonlinear FMCW radar for precise distance and velocity measurements,” IEEE MTT-S International Microwave Symposium Digest, pp. 511—514, 1998. [36] Musch, T., Rolfes, N., and Schiek, B., “A highly linear frequency ramp generator based on a fractional divider phase-locked loop,” IEEE Trans. Instrumentation and Measurement, pp. 634—637, April 1999.

122

Detecting and Classifying LPI Radar

[37] Oates, D. C., Dionne, G. F., and Anderson, A. C., “Magnetically tunable superconductor filters,” GOMAC Session 15, Advanced Receiver Technology, Monterey, CA, pp. 396—399, March 1999. [38] Terrell, J., “High temperature superconducting filters for military applications,” GOMAC Session 15, Advanced Receiver Technology, Monterey, CA, pp. 400—403, March 1999. [39] Kapolnek, D. J., et al., “Integral FMCW radar incorporating an HTSC delay line with user-transparent cyrogenic cooling and packaging,” IEEE Trans. on Applied Superconductivity, Vol. 3 No. 1, pp. 2820—2823, Aug. 1992.

Problems 0 1. Calculate the error between the envelope detector output xe = I 2 + Q2 and the envelope approximation detector output (4.1) when I = 1.3 and Q = −3.1 for (a) a = 1, b = 1/2, and (b) a = 1 and b = 1/4. 2. An LPI emitter scans at a rate of 65 deg/s using a triangular FMCW waveform with modulation period tm = 1 ms. The GOCFAR range processor sends the report sequence {0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0} for a target at RT , to a Markov chain with NX = 6 and NY = 3. Calculate the target’s azimuth extent Θ. 3. An FMCW LPI waveform is shown in Figure 4.27. If the modulation period tm = 5 ms, the noise factor FR = 10, and the signal-to-noise ratio required at the receiver output is 13 dB, determine the receiver’s sensitivity in dBmW. 4. For the FMCW waveform shown in Figure 4.27, if the modulation bandwidth ∆F = 1 GHz, determine the range resolution.

Figure 4.27: FMCW LPI waveform.

FMCW Radar

123

5. A range resolution of ∆R= 5m is required to contain a ship target completely within a range bin. (a) Calculate the modulation bandwidth ∆F required. (b) If the modulation period tm = 1 ms, what is the chirp rate required of the radar? 6. Using the results in Section 4.3.2, plot the FMCW magnitude spectrum for ∆F = 500 kHz and tm = 1 ms. 7. The program lpi fmcw design.m, is useful for understanding FMCW radar systems and can be used to evaluate the trade-oﬀs in the emitter design. (a) Use the MATLAB program lpi fmcw design.m to design an FMCW LPI emitter at 9.3 GHz, with an ideal range resolution ∆R = 5.5m for a V = 200 m/s target velocity and a maximum target distance of 18 km. Choose your modulation period to be tm = 5.5td . Make a table listing the parameters of your design, including: the target’s Doppler frequency; the maximum delay td ; the coherent processing interval; the spectral width; the eﬀective transmitted modulation bandwidth; the degraded resolution, and minimum sampling frequency of the ADC; the FFT size; the adjusted sampling rate of the ADC; the maximum beat frequency; and the time bandwidth product. (b) What is the unambiguous range and unambiguous Doppler of your design? 8. The receiver design.m program computes the beat frequencies for a particular target configuration and FMCW radar design (from the program lpi fmcw design.m). The program asks for the range of the target and the velocity. Keeping the velocity at 200 m/s, run the program 10 times where, with each iteration, the range is decreased by 1m. For each iteration, save both the range-to-the-target and the target velocity computed by the FFT. Plot both of these parameters separately, as a function of range along with the error (diﬀerence between the true values and the measured values). Comment on the size of this error that is computed. 9. If the maximum target velocity is VT = 30 m/s, calculate the required modulation period such that the target moves a maximum of two range cells during the coherent processing interval. What is the resulting velocity resolution and spectral width?

Chapter 5

Phase Shift Keying Techniques In Chapter 4, we discussed the LPI technique of frequency modulation of the CW signal. This chapter presents the phase shift keying techniques that are useful for LPI radar waveform design. Although not a LPI modulation technique, Barker binary PSK is discussed first, since it is the first PSK technique to be investigated and is still widely used today. This is followed by a discussion of polyphase shift keying techniques. These include Barker polyphase sequences and the Frank code. Also presented are the P1, P2, P3, and P4 codes, and polytime codes T1, T2, T3, and T4. Each of these codes is shown to be useful as an LPI CW PSK technique due to its wideband characteristics and the fact that it forces the intercept receiver to initially have a large processing gain. For each code, the phase characteristics are examined, along with the power spectrum magnitude. To quantify the usefulness as a CW LPI waveform, the ACF, PACF, and PAF are examined. As an example of a PSK LPI radar, the omnidirectional LPI radar which uses the Frank code, is discussed.

5.1

Introduction

While linear FMCW has established itself as one of the most popular LPI waveforms, PSK CW waveforms have recently been a topic of active investigation, due to the their wide bandwidth and inherently low PAF side lobe levels achievable. For the LPI radar (as with pulsed radar), it is important to have a low side lobe level to avoid the side lobes of large targets from masking the main peak of smaller targets. The choice of PSK code aﬀects the radar performance and the implementation. For the PSK waveforms, the 125

126

Detecting and Classifying LPI Radar

bandwidth (inverse of the subcode period) is selected first by the designer, in order to achieve the range resolution desired. Encompassing a large target (such as a ship) within a single resolution cell can aid in detection, but results in a narrow bandwidth signal. On the other hand, a wideband transmitted signal can be chosen to divide the target echo into many resolution cells, and is a technique that is useful for target recognition. The trade-oﬀ here is that the radar requires a larger transmitted power to detect a target that has a small cross section, decreasing the ability of the radar to remain quiet. Binary phase shifting codes (e.g., 0 or 180 degrees) are popular, but provide little in the way of low side lobes and Doppler tolerance. Most useful for the LPI radar designer are the polyphase codes where the phase shift value within the subcode can take on many values (not just two) and the code period T can be made extremely long. These codes have better side lobe performance and better Doppler tolerance than the binary phase codes.1 The PSK techniques can result in a high range resolution waveform, while also providing a large SNR processing gain for the radar. The average power of the CW transmission is responsible for extending the maximum detection range while improving the probability of target detection (as compared to a pulsed signal of equal peak power). PSK techniques are also compatible with new digital signal processing hardware, and a variety of side lobe suppression methods [1—4] can be applied. Compatibility with solid state transmitters enables power management techniques to be used that lower the average power requirements of the transmitted CW signal. Power management allows the radar to keep a target’s SNR constant within the receiver, as the range to the target changes. An example of this technique is described in Chapter 9. In addition, the LPI radar designer can choose from a large selection of PSK codes that are available, which is the subject of this chapter.

5.2

The Transmitted Signal

In the PSK radar, the phase shifting operation is performed in the radar’s transmitter, with the timing information generated from the receiver-exciter. The transmitted complex signal can be written as s(t) = Aej(2πfc t+φk )

(5.1)

where φk is the phase modulation function that is shifted in time, according to the type of PSK code being used, and fc is the angular frequency of the carrier. The inphase (I) and quadrature (Q) representation of the complex signal from the transmitter can be represented as I = A cos(2πfc t + φk ) 1 Doppler

(5.2)

tolerance is measured by how well the code compresses in the matched receiver, when the received signal is Doppler shifted with respect to the reference code.

Phase Shift Keying Techniques

127

and Q = A sin(2πfc t + φk )

(5.3)

Within a single code period, the CW signal is phase shifted Nc times, with phase φk every tb seconds, according to a specific code sequence. Here tb is the subcode period. The resulting code period is T = Nc tb s

(5.4)

Rc = 1/Nc tb s−1

(5.5)

and the code rate is The transmitted signal can be expressed as Nc

uT = k=1

uk [t − (k − 1)tb ]

(5.6)

for 0 ≤ t ≤ T and zero elsewhere. The complex envelope uk is uk = ejφk

(5.7)

for 0 ≤ t ≤ tb and zero otherwise. The range resolution of the phase coding CW radar is ctb (5.8) ∆R = 2 and the unambiguous range is Ru =

cNc tb cT = 2 2

(5.9)

If cpp is the number of cycles of the carrier frequency per subcode, the bandwidth of the transmitted signal is B = fc /cpp = 1/tb Hz

(5.10)

The received waveform from the target is digitized and correlated in the receiver using a matched (unweighted) or mismatched (weighted) filter that contains a cascade of N sets of Nc reference coeﬃcients. The results from each correlation are combined to concentrate the target’s energy and produce a compressed pulse having a time resolution equal to the subcode duration tb and a height of Nc . For this reason, the number of phase code elements Nc is also called the compression ratio. Recall that the PAF describes the rangeDoppler performance of this type of receiver, and depends on the number of reference sets used.

128

5.3

Detecting and Classifying LPI Radar

Binary Phase Codes

In 1953, R. H. Barker presented binary sequences for synchronization purposes in telecommunications [5]. The binary Barker sequences are finite length, discrete time sequences with constant magnitude, and a phase of either φk = 0 or φk = π. The formal definition of a Barker sequence is given below [6]. Definition 5.1 A Barker sequence is a finite length sequence A = [a0 , a1 , . . . , an ] of +1’s and −1’s of length n ≥ 2 such that the aperiodic autocorrelation coeﬃcients (or side lobes) n−k

rk =

aj aj+k

(5.11)

j=1

satisfies |rk | ≤ 1 for k = 0 and similarly r−k = rk . Consequently, a binary Barker sequence has elements ai ∈ {−1, +1}, which are only known for lengths Nc = 2, 3, 4, 5, 7, 11, and 13. A list of the nine known Barker sequences is shown in Table 5.1 along with their PSL (dB) and ISL (dB). The longest code is of length Nc =13. The nine sequences are listed where a +1 is represented by a + and a −1 is represented by a −. It has been shown that binary Barker sequences with lengths greater than 13, with Nc odd, do not exist. Also, it has been proven that binary Barker sequences with 4 < Nc < 1, 898, 884 with Nc even do not exist. It has been conjectured that sequences with Nc ≥ 1, 898, 884 with Nc even also do not exist [7]. Compound Barker codes (Barker code within a Barker code) can also be created to have a large compression gain. An example of a compound Barker code made from a Barker sequence of length Nc = 4 is shown in Figure 5.1. Although a larger compression gain is achieved, the peak side lobes are not proportionally decreased. The Nc = 169 compound Barker code is frequently used and consists of a 13 Barker code inside a 13 Barker code. This represents the longest binary code sequence from a single concatenation. The Barker codes are the most frequently used binary code since they result in an ambiguity function with side lobe levels, at zero Doppler, not higher than 1/Nc relative to a main lobe of level 1. In fact, due to this property, Barker codes are often called perfect codes. Figure 5.2(a) shows the ACF (rk ) of a CW signal phase coded with an Nc = 13−bit Barker sequence, and reveals the side lobe structure of the code. For this signal, fc = 1 kHz and the sampling frequency fs = 7 kHz. Note the side lobe characteristics reflecting the perfect nature of the Barker codes. For the Nc = 13−bit code

Phase Shift Keying Techniques

129

Figure 5.1: A compound Nc = 4 Barker code.

Table 5.1: Nine Barker Codes with Corresponding PSL and ISL Code Length 2 3 4 4 5 7 11 13

Code Elements

PSL (dB)

ISL (dB)

−+, +− ++− + + −+ + + +− +++−+ +++−−+− +++−−−+−−+− +++++−−++−+−+

−6.0 −9.5 −12.0 −12.0 −14.0 −16.9 −20.8 −22.3

−3.0 −6.5 −6.0 −6.0 −8.0 −9.1 −10.8 −11.5

130

Detecting and Classifying LPI Radar

Figure 5.2: (a) ACF and (b) PACF for the Nc = 13-bit Barker binary PSK signal (PSL = −22 dB). shown, PSL = 20 log10 (1/Nc ) = −22.3 dB. The number of cycles per phase cpp = 1. Figure 5.2(b) shows the PACF and reveals the fact that the Barker codes do not have a perfect PACF side lobe characteristic (zero side lobes), but have a lowest side lobe level that equals the PSL shown for the ACF (−22 dB). In Figure 5.3, a plot of the PAF is shown for N = 1. The delay axis is normalized by the bit period tb so the PAF repeats every τ = Nc bsc = 91 samples. Note the presence of the large Doppler side lobes. Upon reception of the target’s return signal, the receiver uses a detector to generate a + or − for each subcode. Figure 5.4 demonstrates the binary phase coding technique and receiver architecture using an Nc = 13-bit Barker code. In this figure, the receiver output uses a single tapped delay line matched filter to compress the transmitted waveform. When the return signal vector is centered within the filter, the + filter coeﬃcients line up with the signal +’s and − filter coeﬃcients line up with signal −’s, and a maximum output results as shown. In addition to having a limited code length, Barker codes are very sensitive to Doppler shifts, as illustrated by the large PAF Doppler lobes shown in Figure 5.3. The Doppler shift of the return waveform (due to a motion of the target) can compress the waveform within the filter such that the matched filter gives incorrect results. This characteristic restricts binary Barker code applications. As a final note, Barker codes are not considered LPI since they are easily detected by an intercept receiver that uses frequency doubling. This simple technique involves multiplying the received signal by itself and

Phase Shift Keying Techniques

131

Figure 5.3: PAF for 13-bit Barker binary PSK signal showing the large Doppler side lobes.

132

Detecting and Classifying LPI Radar

Figure 5.4: Binary phase coding techniques and receiver architecture using a 13 Barker code (Nc = 13).

Phase Shift Keying Techniques

133

processing the result with an envelope detector. Barker BPSK signals can easily be generated using the LPIT contained on the enclosed CD (see Appendix A). The BPSK code generates three types of CW Barker sequences (Nc =7, 11, or 13). Also selectable are the carrier frequency fc , the sampling frequency fs , the number of code periods to generate, the cycles per subcode cpp, and the SNR.

5.4

Polyphase Codes

Polyphase sequences are finite length, discrete time complex sequences with constant magnitude but with a variable phase φk . Polyphase coding refers to phase modulation of the CW carrier, with a polyphase sequence consisting of a number of discrete phases. That is, the sequence elements are taken from an alphabet of size Nc > 2. Increasing the number of elements or phase values in the sequence allows the construction of longer sequences, resulting in a high range resolution waveform with greater processing gain in the receiver or equivalently a larger compression ratio. The trade-oﬀ is that a more complex matched filter is required compared to a Barker code filter. Note that a greater sequence length Nc does not aﬀect the signal bandwidth at the antenna and/or change the transmitted signal bandwidth (B = 1/tb ). Polyphase sequences that satisfy the Barker criteria (so-called polyphase Barker codes) are currently under investigation in order to try and find longer sequences. Polyphase compression codes have also been derived from stepapproximation-to-linear-frequency modulation waveforms (Frank, P1, P2) and linear-frequency modulation waveforms (P3, P4). These codes are derived by dividing the waveform into subcodes of equal duration, and using a phase value for each subcode that best matches the overall phase trajectory of the underlying waveform. An alternate approach to approximating these waveforms is to quantize the underlying waveform into a user-selected number of phase states, where the time spent at each phase state changes (in time) throughout the duration of the waveform. These codes are referred to as polytime codes. Other codes, such as the P (n, k) polyphase codes, have been derived using a step approximation of the phase function from a nonlinear frequency modulation waveform with a favorable energy density. The importance of polyphase coding to the LPI community is that by increasing the alphabet size Nc , the autocorrelation side lobes can be decreased significantly while providing a larger processing gain. By narrowing the subcode width tb (so there are fewer cycles per phase), the transmitted signal can also be spread over a large bandwidth, forcing the receiver to integrate over a larger band of frequencies. Polyphase signals can easily be generated using the LPIT contained on the enclosed CD (see Appendix A). The user can select any sequence length, carrier frequency fc , sampling frequency fs , and number of code periods to generate. The cycles per subcode cpp and the

134

Detecting and Classifying LPI Radar

SNR are also selected.

5.5

Polyphase Barker Codes

Polyphase Barker codes allow the LPI emitter a large amount of flexibility in generating the phase modulated waveforms. Since the number of diﬀerent phase terms (or alphabet) is not two-valued, there is considerable advantage to their use since they are unknown to the noncooperative intercept receiver. Over the years Nc ≤ 63 codes have been discovered and are presented below. Consider the generalized Barker sequences {aj } of finite length n where the terms aj are allowed to be complex numbers of absolute value 1 where the correlation is now the Hermitian dot product2 n−k

aj a∗j+k

rk =

(5.12)

j=1

where z ∗ represents the complex conjugate of z and the same restrictions in Definition 5.1 apply (|r(k)| ≤ 1 for k = 0). A class of transformations can be developed that leave the absolute value of the correlation function unaltered, so that, in particular, generalized Barker sequences are changed into other generalized Barker sequences [6]. For example, let {ur } be a complex sequence of length k and let its autocorrelation function be n−τ

ur u∗r+τ

rru =

(5.13)

j=1

Now define a new complex-valued sequence {vr } of length n as vr = ur ej2πr/m

(5.14)

where m is any nonzero integer. We can then observe the fact that the autocorrelation function rτv satisfies k−τ ∗ vr vr+τ

(5.15)

ur u∗r+τ e−j2πτ /m = rτu e−j2πτ /m

(5.16)

rτv = r=1

or

k−τ

rτv = r=1

for all τ . Since |e−j2πτ /m | = 1, |rτv | = |rτu | for all τ Also from (5.13) |vr | = |ur |. A more general transformation between vr and ur is given in [6]. 2 The Hermitian n x y∗ . i=1 i i

dot product of two vectors (x1 , x2 , . . . , xn ), (y1 , y2 , . . . , yn ) is

Phase Shift Keying Techniques

135

Table 5.2: Seven Alternating Quarternary Barker Codes [6] Code Length 2 3 4 5 7 11 13

Code Elements +1, +j +1, +j, +1 +1, +j, −1, +j +1, +j, −1, +j, +1 +1, +j, −1, +j, −1, +j, +1 +1, +j, −1, +j, −1, −j, −1, +j, −1, +j, −1 +1, +j, −1, −j, +1, −j, +1, −j, +1, −j, −1, +j, +1

Taking m = 4 in (5.13), the sequence (u1 , u2 , u3 , u4 . . . , uk ) is transformed into (u1 , ju2 , −u3 , −ju4 , . . . , (−1)k−1 uk ) which sets up a one-to-one correspondence between ordinary (binary) Barker sequences and four-symbol (±1, ±j) Barker sequences in which the real and imaginary terms alternate. This set of sequences is shown in Table 5.2. Note that the alternating Barker sequences of odd length are all palindromic (i.e., read the same forward and backward) and show a symmetry that is obscured in the binary representation. For a list of all the generalized Barker sequences whose terms are restricted to the complex sixth roots of unity with Nc ≤ 13 the reader is referred to [6]. Until recently, construction methods for generating Nc −phase Barker sequences with low autocorrelation side lobes were not known and exhaustive search routines were used. These methods and results are discussed below. In [8] an exhaustive search for all sixth-root Barker sequences was conducted through Nc = 22, for all eighth-root sequences through Nc = 15, and for all 12th-root sequences through Nc = 15. Table 5.3 shows these results. In the results, the sequence values ai are rth roots of unity. That is, they are the roots of the polynomial z r − 1 = 0. Their search extended the list of known Barker sequences up to Nc = 19 where the terms of the sequence are sixtieth roots of unity. In Table 5.3, the terms ai are expressed in terms of their phase angles as multiples of 6 degrees. Their results illustrate the smallest r known for each Nc where r divides 60. An iterative algorithm based on constrained iteration techniques is applied to generate polyphase Barker sequences in [9]. Uniform sequences meeting the Barker condition with Nc = 3 up to Nc = 25 elements are reported (except for Nc =20 elements). The sequence values ai are shown in Table 5.4. The list of uniform sequences was extended up to Nc =31 using the great

136

Detecting and Classifying LPI Radar

Table 5.3: Polyphase Barker Sequences Nc = 1 to 19 [8] ( c IEEE 1989) Nc

r

1 2 3 4 5 6 7

1 1 2 2 2 6 2

8

6

9

3

10

6

11

2

12

6

13

2

14

6

15

4

16

12

17

15

18

60

19

60

Sequence ai 0 0 0 0 0 0 0 30 0 50 0 0 0 0 0 0 0 20 0 30 0 0 40 50 0 45 0 0 45 0 0 0 0 0 4 54 0 41 31 42

0 0 0 0 0 0 0 10 0 40 0 30 0 30 0 40 0 0 0 40 20 0 45 30 0 45 30 0 48 20 0 7 57 0 3 56

30 30 0 10 0

0 30 30 30

0 0 30

40 0

0

0

30

20

0 20 0 10 0 30 10 0 0 0

0

20

40

0 50 30 0 0 40 0 30

20

40

30 30 50 10 0 0

30 20 30 30 30

0 10

10 20

10 40

0 10

0 15 0 0 15 0 0 40 4 9 35 35 9 58 32

15 30

15 45

0 15

15 30 35 4 4 32 8 32 3 4 20 28

15 45

0 15

20 28 56 53 15 30 16 43 11

16 32 47 37 8 15 57 2

Phase Shift Keying Techniques

137

Table 5.4: Polyphase Barker Sequences Nc = 3 to 25 [9] ( c IEE 1989) Nc

ai

3 4 5

−0.0121 −2.5016 +1.3354 +0.2608 +1.3630 +1.6235 +0.8688 +1.7924 −0.3131 −2.9788 −0.6896 −0.7098 +2.8670 −0.5887 −1.7728 +1.6298 +2.0760 −0.8944 −1.2395 +2.2363 −1.5832 +1.9194 +2.7188 +1.6773 +0.6941 +1.2749 −0.7019 +2.0131 +2.5855 +2.9666 +0.5655 −0.9322 +1.8799 −2.8457 −0.3146 −0.0918 +0.0895 −0.1218 −1.6448 +0.7623 −2.9279 −0.3226 −1.9249

6 7 8 9 10 11 12 13

14

15

16

17

−1.1943 −2.7749 −0.8992

+0.1409 −1.2319 −1.8595

+3.0246 +1.1919 +0.9106 +0.0223 −1.2660 −1.4428 −2.6573 −1.7158

−0.5804

+3.1349

−0.9048 +2.6777 +2.8067 +2.1516 +7.2661 −0.6370

−0.6238

Nc

ai

18

+2.1297 −2.5280 +0.2331 −0.8630 +2.4890 −1.9461 +2.1067 −2.7650 −0.4287 +1.1451 +0.4786 +2.2135 −2.5136 −2.8818 +2.4420 +1.8087 +1.3209 −0.1876 −0.0882 −1.7205 +0.9588 +2.7208 +1.5822 −2.1716 −1.3843 −1.6386 +2.6576 +0.0179 +3.1247 −2.7484 +2.3777 −1.4822 +2.3422 +1.4496 −1.4167 −1.5464 −1.1339 −0.8155 +2.8658 +2.6251 −1.5638 −2.0911 −1.3895 −0.1824 −2.8375 −2.0333

+2.1417 −1.4368 19 +2.6116 −1.8044 −1.0342 +1.5811

−1.8332 −0.8423 +2.8294 −0.6452 +1.5958 −1.1485 −2.6854 +3.0342 −0.6520 +1.3744 −0.2793 −2.8756

+2.1561 −1.9530

−0.3414 −0.7544

+2.3212 +1.8337 −1.6531 +3.1305 −0.0850 −0.3623 +2.0519 +3.0833 −1.8306

+1.9586 +1.6372

−2.2825 +2.2090 +2.4207 −2.6327 +0.2147 +2.6090 +2.0924 −0.4439 +0.1656 +1.2243 +2.8601 −1.1910 +0.8837 −2.4826 −2.7891 −0.0768

+1.2537 +1.7266 −0.6031

−1.4914 +2.9683 +0.1768

−0.4469 +1.0432 −2.9651 +1.5204 +0.1834 −2.7713 +0.2766 −2.9903 −2.7783 +2.1345 −2.5196 −1.8421

−0.5837 −0.8091 −0.6062

−2.8078 +2.2462 −3.0102 +0.6899 +2.2955 −0.4901

+0.4540 −1.9528 +2.5677 +1.6009 −0.0189 −0.1942 −0.3109 −1.9773

20

21

22

23

24

25

−2.4221 −0.2354 +2.3578 +0.5150 +3.7406 +2.6015 +0.5609 −0.4415 +1.5349 +0.3446 +0.6706 −2.1501 +0.0993 +0.0677 +2.5909 +0.7662 +0.0701 −1.9735 +0.2233 +2.1529

−1.6995 −0.1811 −0.4065 −1.6150

+0.3822 +1.3279 +0.0976 −2.7582

−0.0648 +2.4323 +1.6424 +2.3556 +0.7259 +1.5770 +0.8608 +1.7860 −1.3544 +1.1860 −0.5432 −0.8463 +1.7062 +1.3810 −2.4726

−1.3004 −1.6685 −1.4620 +1.0432

+2.7943 +1.7885 −0.9320 +0.8799 +1.3802 +0.6222 +1.1156 −2.6283 −1.6192 −1.6192 −2.6283 +1.1156 −0.3890 +2.3177 −2.5852 +1.2976 −0.1505 +3.0213 +2.9578 −0.4785 −0.9913 −1.5432 −2.7280 +0.6143

+2.4522 −2.9352 +0.8861 −2.1043 −0.2948

+2.0044 −1.3904 +2.2276 +2.4527 −1.8923

+2.3422 −1.4822 +2.3777 −2.7484 +3.1247 +0.0179 −2.1404 +0.2333 +0.8093 −3.0525 +2.1155 +2.3375 +1.8614 −1.0745 +1.2308 −2.6046 −2.8259 −2.2693

+1.8448 +1.2732 −0.5946 +1.2732 +1.8448

+1.8712 +1.1924 −0.3836 −2.4389 −0.6338 −1.5944 −1.4062 −1.4345 +2.8241 −0.5451

+1.4554 +0.4296 +2.0150 −0.8208 +2.6104 +2.6871 +2.4892 −0.9767 +2.8284 +1.4961 −0.1689 +1.4167

138

Detecting and Classifying LPI Radar

Table 5.5: Polyphase Barker Sequences Nc = 20 to 31 [10] ( c IEE 1994) Nc

20

26

27

28

29

30

31

ai

0.000000 0.000000 4.553049 4.086800 2.215325 1.894461 3.945793 3.770581 0.092210 0.967971 2.931040 1.003241 2.452194 3.460843 1.330362 3.745265 1.916620 4.431156 2.297439 4.416524

0.000000 0.000000 0.895841 2.043260 2.412575 4.632634 4.659854 3.061830 2.055563 4.540587 3.491350 2.376147 2.690606 3.123204 1.322308 5.951858 3.270461 5.356688 3.393189 1.614152 3.319561 0.300302 1.920568 4.368801 0.674586 3.485233

0.000000 0.000000 0.184756 0.381913 0.501476 5.667001 5.383231 4.897648 2.065845 1.731439 1.958458 4.965856 3.500713 5.477305 2.029632 5.701172 3.226034 0.931898 0.153375 3.384669 1.694949 4.205310 5.841580 1.796881 3.989645 5.794346 1.622635

0.000000 0.000000 5.463798 4.811496 3.381014 3.739787 2.796088 4.448612 4.248550 5.258279 4.368063 0.595450 5.859119 2.969228 5.908823 2.858973 5.257347 0.584991 4.028262 1.763293 0.929504 4.128530 4.342097 0.824984 1.073402 3.249433 4.575381 0.561518

0.000000 0.000000 0.120401 5.552993 4.186235 4.619877 4.174523 2.799691 5.262097 5.715868 0.326038 5.580307 1.481594 1.894634 3.910927 0.109814 0.547566 3.212265 2.928542 1.569419 5.675662 3.971280 2.537828 5.757173 1.598000 4.602239 1.641441 4.413265 1.039439

0.000000 0.000000 0.577184 0.603685 0.587563 0.207471 5.237221 4.913640 0.461842 0.945976 2.715992 3.698029 4.041807 2.346154 1.326526 5.544522 4.813630 1.179540 5.217885 3.222122 1.267677 2.683552 0.115401 4.583854 1.642393 4.237597 6.267467 2.612215 5.346838 1.248448

0.000000 0.000000 0.495357 2.054263 2.880816 4.126907 5.387150 5.322754 4.127543 3.776533 5.713595 4.877785 3.687515 4.313581 3.350924 1.665117 0.296297 4.764131 0.920844 5.779411 3.908770 5.301284 2.568618 0.379536 4.286983 0.511796 2.539604 5.184811 1.089083 3.330664 0.135490

deluge algorithm (GDA) in [10]. The GDA is a stochastic optimization routine that outperforms other routines such as simulated annealing or threshold accepting. First, a quality factor Q is established based on the autocorrelation properties. Searching for a global maximum value for the quality factor Q, the GDA allows every phase step size that does not result in a Q value lower than a certain threshold. During optimization, this threshold is continuously increased. The algorithm terminates when the phase step size becomes smaller than a predefined minimum phase step size. These results are shown in Table 5.5 for 20 ≤ Nc ≤ 31. In [11] uniform complex sequences of lengths 32 ≤ Nc ≤ 36 are presented. These sequences are also derived using a stochastic optimization algorithm to optimize a set of continuous phase values after properly selecting the starting vectors. After optimization, the phase values are quantized into a finite alphabet. The results are shown in Table 5.6. Exhaustive search routines are not feasible for large alphabet sizes. In addition, a suitable initial value for the quality factors must be chosen. In [12], a systematic method is presented

Phase Shift Keying Techniques

139

Table 5.6: Polyphase Barker Sequences Nc = 32 to 36 [11] ( c IEEE 1996) ai = P φi /2π, i = 2 · · · Nc − 1

Nc

P

32

720

27 33 181 220 190 121 666 614 578 563 171 328 497 670 343 152 128 443 596 220 74 545 359 39 358 576 165 584 266 659

33

720

286 307 678 665 361 267 38 217 332 433 451 455 637 477 369 452 283 227 150 72 371 654 453 217 605 233 546 700 376 713 329

34

360

11 1 307 245 200 184 231 293 300 348 45 227 247 57 335 1 127 249 68 91 315 221 57 116 238 58 287 127 273 127 5 216

35

11,520

36

180

2,984 6,322 9,634 7,826

2,094 1,797 4,748 2,363

5,326 4,236 11,012 8,940 10,804 9,642 1,176 295 10,427 10,697 782 5,051 9,316 3,612 4,521 9,491 4,120 4,014 10,924 4,157 10,287 5,043 9,622 3,440 8,140

41 59 114 114 29 30 77 54 10 117 106 131 118 98 110 58 6 113 89 61 63 38 133 57 128 54 160 50 133 15 62 123 30 93

based on a modified stochastic optimization procedure (similar to that in [11]). These eﬀorts extended the Nc −phase Barker sequences to 37 ≤ Nc ≤ 45 and are shown in Table 5.7. Recently, the number of known polyphase Barker sequences was extended to a length of Nc = 63 [13]. This set was discovered using an algorithm that applies stochastic methods and calculus to the problem of finding the polyphase sequences that are a good local minima for the base energy (sum of the side lobe energies) [13]. Barker sequences of phase values with lengths 46 ≤ Nc ≤ 54 are shown in Table 5.8. The Barker sequences of phase values with lengths 55 ≤ Nc ≤ 63 using the smallest alphabet size K are shown in Table 5.9. In summary, the search for longer polyphase Barker sequences is continuing rapidly. Because the complexity of the applied numerical procedures increases significantly with longer sequence lengths, the search will become more and more demanding in terms of algorithm eﬃciency and computer resources. The entire set of polyphase Barker codes are contained within an EXCEL file (ppbc.xls) and are called out by the MATLAB LPIT code (ppbc.m).

5.6

Frank Code

In 1963, R. L. Frank devised a polyphase code that is closely related to the linear frequency modulation and Barker codes [14]. The Frank code is well

140

Detecting and Classifying LPI Radar

Table 5.7: Polyphase Barker Sequences Nc = 37 to 45 [12] ( c IEE 1998) Nc

P

ai = P φi /2π, i = 2 · · · Nc − 1

37

60

0 0 11 15 20 39 39 54 2 46 37 55 0 46 33 55 8 54 42 48 27 23 13 59 20 3 51 20 59 39 7 29 51 17 30 59 23

38

90

0 0 10 24 28 57 64 71 85 59 53 70 84 57 46 74 15 56 11 73 3 43 86 6 63 74 44 34 9 9 59 13 78 49 89 54 30 89

39

90

0 0 10 23 21 47 62 58 76 55 68 44 59 49 78 26 50 41 83 89 46 49 1 79 56 52 21 47 2 12 67 72 34 71 35 9 65 29 85

40

90

0 0 7 6 11 14 23 18 83 76 63 53 10 85 47 38 51 19 8 55 2 85 46 39 58 76 21 20 74 33 59 79 15 45 10 61 13 54 1 41

41

120

0 0 18 21 10 1 1 8 32 38 74 79 111 101 68 47 28 26 0 86 52 102 101 40 49 98 29 26 78 115 68 22 103 54 104 29 71 6 61 117 52

42

120

0 0 3 13 12 45 58 63 75 27 26 36 44 17 109 21 51 119 58 117 26 74 12 116 96 67 56 6 14 88 80 5 52 80 22 3 65 118 68 27 97 47

43

120

0 0 16 25 31 21 18 24 32 65 84 118 8 28 112 86 57 33 90 119 4 75 63 10 62 75 30 32 6 103 30 91 110 60 101 41 102 57 28 91 23 80 21

44

120

0 0 10 3 14 19 104 102 117 94 16 2 63 39 40 55 104 84 44 118 15 93 82 110 45 22 52 27 99 105 63 31 77 82 16 19 73 117 30 94 45 85 12 54

45

90

0 0 7 1 76 71 76 63 56 73 87 9 9 14 25 53 62 5 32 35 85 69 40 76 57 26 9 83 56 57 21 5 52 89 48 11 68 26 62 6 37 73 19 58 12

Phase Shift Keying Techniques

141

Table 5.8: Barker Sequences 46 ≤ Nc ≤ 54 With Alphabet Sizes K ( c IEEE 2005) Nc 56

K 190

55

150

54

200

53

100

52

185

51

50

50

150

49

90

48

70

47

80

46

90

Phase 0, 0, 13, 37, 43, 95, 83, 115, 109, 145, 111, 12, 117, 86, 127, 116, 184, 109, 65, 121, 125, 116, 36, 92, 79, 85, 12, 1, 72, 183, 156, 135, 62, 139, 95, 16, 67, 134, 17, 138, 59, 92, 161, 46, 79, 176, 10, 127, 114, 48, 23, 148, 162, 88, 117, 35 0, 0, 8, 18, 18, 19, 22, 105, 100, 127, 119, 128, 117, 118, 53, 33, 112, 147, 132, 46, 30, 1, 133, 48, 117, 83, 31, 35, 38, 64, 144, 129, 100, 56, 39, 92, 104, 32, 140, 49, 110, 88, 14, 91, 134, 38, 84, 3, 111, 33, 95, 140, 43, 101, 19 0, 0, 23, 43, 16, 9, 40, 51, 20, 7, 67, 126, 178, 180, 71, 120, 144, 151, 61, 25, 45, 100, 86, 9, 172, 161, 142, 22, 85, 8, 96, 128, 81, 1, 18, 137, 0, 95, 132, 59, 44, 155, 16, 129, 157, 98, 47, 174, 73, 18, 145, 65, 170, 100 0, 0, 5, 3, 4, 5, 9, 13, 23, 58, 79, 99, 42, 68, 66, 99, 2, 41, 68, 29, 41, 76, 22, 25, 94, 98, 74, 59, 16, 58, 35, 62, 22, 93, 85, 19, 54, 17, 56, 94, 64, 92, 43, 26, 13, 70, 47, 95, 57, 21, 13, 86, 51 0, 0, 20, 11, 30, 26, 15, 27, 57, 26, 133, 97, 177, 149, 123, 45, 11, 140, 76, 85, 105, 3, 133, 31, 28, 58, 150, 103, 149, 39, 32, 137, 170, 100, 122, 58, 42, 86, 2, 172, 50, 128, 163, 49, 136, 76, 122, 17, 20, 108, 171 0, 0, 4, 4, 18, 20, 27, 25, 25, 26, 24, 15, 15, 14, 9, 32, 36, 2, 21, 17, 9, 27, 46, 49, 19, 29, 9, 32, 7, 43, 21, 46, 22, 47, 18, 35, 0, 22, 9, 31, 44, 5, 29, 21, 4, 49, 33, 24, 9, 49, 29 0, 0, 16, 20, 44, 48, 72, 66, 103, 40, 142, 59, 4, 92, 129, 96, 112, 82, 58, 71, 94, 67, 1, 52, 58, 112, 92, 37, 14, 59, 107, 3, 68, 146, 71, 102, 40, 58, 0, 124, 62, 67, 129, 41, 51, 138, 136, 76, 66, 13 0, 0, 5, 12, 7, 1, 0, 88, 6, 25, 43, 68, 72, 51, 29, 13, 55, 62, 10, 21, 78, 79, 28, 23, 63, 50, 81, 57, 37, 5, 9, 23, 84, 61, 47, 54, 24, 75, 23, 88, 51, 7, 43, 78, 35, 65, 15, 51, 7 0, 0, 1, 5, 14, 23, 35, 36, 26, 22, 17, 5, 68, 16, 16, 51, 53, 0, 21, 13, 63, 50, 59, 43, 21, 1, 52, 27, 53, 62, 28, 28, 0, 55, 24, 51, 5, 22, 51, 15, 50, 8, 44, 21, 64, 24, 52, 12 0, 0, 10, 13, 15, 11, 9, 15, 31, 41, 66, 74, 5, 77, 46, 35, 65, 53, 32, 15, 77, 59, 37, 30, 42, 4, 8, 39, 74, 71, 25, 57, 60, 24, 54, 23, 41, 75, 19, 58, 13, 55, 11, 61, 33, 65, 28 0, 0, 3, 14, 21, 34, 50, 70, 75, 79, 57, 61, 47, 61, 79, 22, 55, 71, 71, 25, 44, 85, 9, 67, 5, 56, 81, 59, 26, 64, 11, 58, 25, 14, 83, 85, 62, 42, 4, 56, 23, 81, 50, 24, 11, 71

142

Detecting and Classifying LPI Radar

Table 5.9: Barker Sequences 55 ≤ Nc ≤ 63 with Alphabet Sizes K ( c IEEE 2005). Nc 63

K 2000

62

3000

61

1930

60

210

59

340

58

500

57

240

56

190

55

150

Phase 0, 0, 88, 200, 250, 89, 1832, 1668, 1792, 145, 308, 290, 528, 819, 1357, 1558, 1407, 1165, 930, 869, 274, 97, 10, 1857, 731, 789, 1736, 150, 1332, 1229, 390, 944, 1522, 1913, 648, 239, 1114, 1708, 200, 666, 1870, 1124, 1464, 265, 845, 1751, 1039, 53, 737, 1760, 798, 1880, 851, 1838, 1103, 419, 1711, 1155, 546, 1985, 1325, 754, 44 0, 0, 459, 324, 361, 2987, 152, 432, 2963, 2907, 112, 598, 1276, 1489, 2216, 1814, 1505, 2536, 2949, 197, 1039, 1241, 2809, 2780, 1388, 590, 2233, 1352, 2458, 2284, 962, 172, 1453, 2245, 799, 558, 2461, 1258, 34, 1666, 2834, 1364, 2755, 1369, 2284, 796, 724, 2118, 198, 1327, 2858, 2962, 2021, 1774, 1604, 698, 1059, 100, 2995, 1923, 2278, 884 0, 0, 58, 1761, 1762, 1703, 1724, 193, 721, 241, 247, 1855, 187, 416, 1379, 1421, 1385, 922, 362, 784, 1401, 1383, 584, 1709, 284, 807, 285, 373, 1404, 1739, 1173, 179, 750, 1, 1239, 1215, 1691, 1092, 490, 17, 160, 1047, 704, 536, 1515, 820, 1892, 1138, 1630, 139, 288, 1065, 1780, 733, 613, 1309, 1452, 550, 1673, 1049, 143 0, 0, 16, 208, 180, 153, 126, 161, 135, 78, 83, 98, 143, 127, 162, 153, 183, 141, 72, 207, 149, 167, 15, 13, 146, 58, 23, 109, 169, 208, 74, 143, 173, 199, 51, 50, 31, 142,152, 84, 74, 6, 147, 205, 151, 66, 31, 151, 27, 101, 170, 75, 172, 91, 20, 131, 1, 78, 166, 68 0, 0, 5, 321, 293, 253, 251, 285, 268, 262, 286, 14, 96, 65, 33, 43, 152, 220, 235, 71, 142, 49, 262, 176, 285, 31, 181, 150, 305, 337, 108, 138, 13, 209, 274, 163, 24, 100, 320, 169, 221, 4, 48, 209, 339, 109, 192, 33, 222, 301, 128, 45, 228, 130, 299, 188, 45, 288, 134 0, 0, 1, 47, 209, 191, 154, 364, 437, 363, 420, 51, 437, 413, 277, 382, 78, 4, 428, 267, 308, 352, 238, 115, 205, 179, 474, 425, 234, 52, 443, 311, 482, 491, 400, 234, 297, 495, 492, 169, 397, 464, 75, 259, 476, 121, 437, 183, 34, 263, 0, 64, 242, 496, 292, 68, 318, 127 0, 0, 18, 51, 31, 37, 6, 39, 43, 64, 128, 167, 187, 19, 22, 226, 163, 103, 97, 238, 200, 172, 111, 201, 72, 95, 75, 172, 2, 91, 49, 220, 209, 57, 212, 168, 116, 206, 110, 102, 25, 131, 2, 30, 143, 182, 42, 107, 216, 89, 10, 161, 29, 170, 106, 205, 86 0, 0, 13, 37, 43, 95, 83, 115, 109, 145, 111, 12, 117, 86, 127, 116, 184, 109, 65, 121, 126, 116, 36, 92, 79, 85, 12, 1, 72, 183, 156, 135, 62, 139, 95, 16, 67, 134, 17, 138, 59, 92, 161, 46, 79, 176, 10, 127, 114, 48, 23, 148, 162, 88, 117, 35 0, 0, 8, 18, 18, 19, 22, 105, 100, 127, 119, 128, 117, 118, 53, 33, 112, 147, 132, 46, 30, 1, 133, 48, 117, 83, 31, 35, 38, 64, 144, 129, 100, 56, 39, 92, 104, 32, 140, 49, 110, 88, 14, 91, 134, 38, 84, 3, 111, 33, 95, 140, 43, 101, 19

Phase Shift Keying Techniques

143

Figure 5.5: Phase relationship between the quantized linear FM and Frank coded signals with M = 4. documented and has recently been used successfully in LPI radars (such as the OLPI). The Frank code is derived from a step approximation to a linear frequency modulation waveform using M frequency steps and M samples per frequency. The Frank code has a length or processing gain of Nc = M 2 . In the case of a single side band detection, the result is the Frank code [15]. As an example, consider that a local oscillator is at the start of the sweep of the step approximation to the linear frequency waveform. The first M samples of the polyphase code are 0 phase. The second M samples start with 0 phase, and increase with phase increments of (2 π/M ) from sample to sample. The third group of M samples start with 0 phase and increase with (3-1)(2π/M ) increments from sample to sample and so on. Figure 5.5 shows the phase relationship between the quantized linear FM and Frank code signal for M =4. If i is the number of the sample in a given frequency and j is the number of the frequency, the phase of the ith sample of the jth frequency is φi,j =

2π (i − 1) (j − 1) M

(5.17)

where i = 1, 2, . . . , M , and j = 1, 2, . . . , M . The Frank polyphase code can

144

Detecting and Classifying LPI Radar

also be written as an M × M matrix ⎡ 0 0 0 ⎢ 0 1 2 ⎢ ⎢ 0 2 4 ⎢ ⎢ .. .. .. ⎣ . . . 0 (M − 1) 2(M − 1)

··· 0 · · · (M − 1) · · · 2(M − 1) .. . ···

(M − 1)2

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(5.18)

where the numbers represent multiplying coeﬃcients of the basic phase angle 2π/M . For the Frank code, the PSL = 20 log10 (1/(M π)) [16, 17]. For M =8, Nc =64, the PSL = −28 dB. Figure 5.6(a) shows the discrete phase values that result for the Frank code for M = 8 (Nc = 64). Figure 5.6(b) shows the signal phase modulo 2π, and demonstrates that the Frank code has the largest phase increments from sample to sample in the center of the code. Consequently, when the Frank code is passed through a bandpass amplifier in a radar receiver, the code is attenuated most heavily in the center of the waveform. This attenuation tends to increase the side lobes of the Frank code ACF. Figure 5.7 shows the power spectrum magnitude of a Frank signal with fc =1 kHz, fs =7 kHz, and cpp = 1 with M = 8. Figure 5.7(a) shows the power spectrum for the signal only, and shows the wideband characteristics (B =1 kHz) resulting from the phase modulation. Figure 5.7(b) shows the power spectrum for the SNR = 0 dB case. Figure 5.8(a) shows the ACF and the PACF for the Nc = 64 Frank code with N = 1. The ACF reveals the peak side lobe level PSL = −28 dB. Figure 5.8(b) shows the PACF, and the fact that the Frank code has a perfect PACF. Figure 5.9 shows the PAF for the Frank code for Nc = 64 and N = 1. Note the delay and the Doppler side lobe levels are much lower than the BPSK code examined in Section 5.3. Another formulation to generate the Frank code can be found by examining a linear transformation. In a linear transformation of the Frank code, the kth phase element can be expressed as [18] φk =

2π M

k − k(mod M ) [k(mod M )] M

(5.19)

where M is any positive integer that defines the code sequence length Nc = M 2 . If the phase-coded signal given in (5.1) is converted into digital form with a sample period ∆t = tb , then the kth signal sample of the polyphase Frank code sequence envelope is sk = A exp [jφk ] = exp j

2π k − k(mod M ) k(mod M ) M M

(5.20)

for k = 0, 1, · · · , Nc − 1. In a radar application, the sampling rate must be higher. Assuming that the sampling period ∆t = tb /s where s is the number

Phase Shift Keying Techniques

Figure 5.6: Frank code phase values for M = 8 (Nc = 64), showing (a) discrete phase jumps and (b) signal phase modulo 2π.

145

146

Detecting and Classifying LPI Radar

Figure 5.7: Frank code power spectrum magnitude for M = 8 (Nc = 64 subcodes) for (a) signal only and (b) SNR = 0 dB.

Phase Shift Keying Techniques

Figure 5.8: Frank code (a) ACF and (b) PACF for Nc = 64, N = 1.

Figure 5.9: Frank code PAF for Nc = 64, N = 1.

147

148

Detecting and Classifying LPI Radar

of the samples per subcode, the kth sample of sk is 2π k − k(mod M s) k − k(mod M s) − (k mod M s) mod s M Ms s (5.21) where k = 0, 1, . . . , Nc s − 1. Note that the influence of the Doppler eﬀect is not taken into consideration with this model. sk = A exp j

5.7

P1 Code

The P1 code is also generated using a step approximation to a linear frequency modulation waveform. In this code, M frequency steps and M samples per frequency are obtained from the waveform using a double sideband detection with the local oscillator at band center [15, 16]. The length of the resulting code or compression ratio is Nc = M 2 . If i is the number of the sample in a given frequency and j is the number of the frequency, the phase of the ith sample of the jth frequency is φi,j =

−π [M − (2j − 1)][(j − 1)M + (i − 1)] M

(5.22)

where i = 1, 2, . . . , M , and j = 1, 2, . . . , M , and M = 1, 2, 3, . . .. For the P1 code the PSL = 20 log10 (1/(M π)) (the same as the Frank code). Figure 5.10(a) shows the phase values that result for the P1 code for M = 8 (Nc = 64). Figure 5.10(b) shows the signal phase modulo 2π and demonstrates that the P1 code has the largest phase increments from sample to sample at the ends of the code. When the P1 code is passed through the bandpass amplifiers in a radar receiver the attenuation is heaviest on the ends of the code. This tends to reduce the side lobes of the P1 AACF in the receiver [16].3 Figure 5.11 shows the power spectrum magnitude of an fc =1-kHz P1 signal (fs =7 kHz, cpp =1) with M = 8, and reveals the wideband nature of this phase modulation. Figure 5.11(a) shows the power spectrum for just the signal and Figure 5.11(b) shows the power spectrum for the SNR = 0 dB case. Figure 5.12(a) shows the ACF and the corresponding side lobe structure for the Nc = 64 P1 code with N = 1. Here PSL = −28 dB down from the peak as predicted. Figure 5.12(b) shows the PACF. Note that the P1 code has a perfect PACF with zero side lobes. Figure 5.13 shows the corresponding PAF for the P1 code. Note that the PAF repeats at Nc bsc = Nc (cppfs /fc ) = 448 samples. 3 Recall that the bandpass amplifier attenuation increased the side lobes of the Frank code AACF.

Phase Shift Keying Techniques

149

Figure 5.10: P1 code phase values for M = 8 (Nc = 64), showing (a) discrete phase jumps and (b) signal phase modulo 2π.

150

Detecting and Classifying LPI Radar

Figure 5.11: P1 code power spectrum magnitude for fc = 1-kHz signal (fs = 7 kHz, cpp = 1) with M = 8 (Nc = 64), for (a) signal only and (b) SNR = 0 dB.

Phase Shift Keying Techniques

Figure 5.12: P1 code (a) ACF and (b) PACF for Nc = 64, N = 1.

Figure 5.13: P1 code PAF for Nc = 64, N = 1.

151

152

5.8

Detecting and Classifying LPI Radar

P2 Code

For the P2 code M even, the phase increment within each phase group is the same as the P1 code, except that the starting phases are diﬀerent [15]. The P2 code also has a length or compression ratio of Nc = M 2 . The P2 code is given by [17] −π [2i − 1 − M ][2j − 1 − M ] (5.23) φi,j = 2M where i = 1, 2, 3 . . . , M , and j = 1, 2, 3 . . . , M , and where M = 2, 4, 6, . . .. The requirement for M to be even in this code stems from the desire for low autocorrelation side lobes [15]. For the P2 code, the PSL = 20 log10 (1/(M π)) and is the same as the Frank code and P1 code. Figure 5.14(a) shows the discrete phase values that result for the P2 code for M = 8. Figure 5.14(b) shows the signal phase values modulo 2π, and demonstrates the fact that the phase changes are largest toward the end of the code. Figure 5.15 shows the power spectrum magnitude of the P2 code for M = 8 (Nc2 =64) with fc = 1 kHz, fs = 7 kHz, and cpp = 1. Figure 5.15(a) shows the power spectrum for the signal only, and Figure 5.15(b) shows the power spectrum for the SNR = 0 dB. Figure 5.16(a, b) shows the corresponding ACF and PACF, respectively. Note that the P2 code does not have a perfect PACF. In fact, the PACF is identical to the ACF. Figure 5.17 shows the PAF for the P2 code for Nc = 64 and N = 1. An interesting observation is that the P2 PAF has an opposite slope compared to the other PSK sequences.

5.9

P3 Code

The P3 code is conceptually derived by converting a linear frequency modulation waveform to baseband, by using a synchronous oscillator on one end of the frequency sweep (single sideband detection), and sampling the I and Q video at the Nyquist rate (first sample of I and Q taken at the leading edge of the waveform) [15]. The phase of the ith sample of the P3 code is given by φi =

π (i − 1)2 Nc

(5.24)

where i = 1, 2, . . . , Nc , and Nc is the compression ratio. Figure 5.18(a) shows the quadratic discrete phase values that result for the P3 code for Nc = 64. Figure 5.18(b) shows the signal phase modulo 2π. In the P3 code, the largest phase increments occur at the center of the code. The P3 shares the intolerance to precompression band limiting associated with the Frank code [15]. Figure 5.19 shows the power spectrum magnitude of the P3 code for Nc = 64. Figure 5.19(a) shows the power spectrum magnitude for just the

Phase Shift Keying Techniques

153

Figure 5.14: P2 code phase values for M = 8 (Nc2 = 64), showing (a) discrete phase values and (b) signal phase modulo 2π.

154

Detecting and Classifying LPI Radar

Figure 5.15: P2 code power spectrum magnitude for M = 8, for (a) signal only and (b) SNR = 0 dB.

Phase Shift Keying Techniques

Figure 5.16: P2 code (a) ACF and (b) PACF for Nc = 64, N = 1.

Figure 5.17: P2 code PAF for Nc = 64, N = 1.

155

156

Detecting and Classifying LPI Radar

Figure 5.18: P3 code phase values for Nc = 64, showing (a) discrete phase steps and (b) signal phase modulo 2π.

Phase Shift Keying Techniques

157

signal, and Figure 5.19(b) shows the power spectrum magnitude for the SNR = 0 dB. Figure 5.20(a) shows ACF and the side lobe structure of the P3 for Nc = 64 and N = 1. The peak side lobe ratio for the P3 code is larger than the Frank, P1, and P2 codes. Here PSL = 20 log10 2/(Nc π 2 ) dB, down from the peak. With Nc = 64, PSL = −25 dB. This is revealed in Figure 5.20(a) which shows the corresponding ACF. Figure 5.20(b) shows the PACF for the P3 code and indicates that the P3 has a perfect PACF. The PAF for the P3 code is shown in Figure 5.21. Here Nc = 64 and N = 1. Note that the PAF slope for the P3 code is opposite to that of the P2 code.

5.10

P4 Code

The P4 code is conceptually derived from the same linear frequency modulation waveform as the P3 code, except that the local oscillator frequency is oﬀset in the I and Q detectors, resulting in coherent double sideband detection. Sampling at the Nyquist rate yields the polyphase code named the P4 [15, 16]. The P4 code consists of the discrete phases of the linear chirp waveform taken at specific time intervals, and exhibits the same range Doppler coupling associated with the chirp waveform. However, the peak side lobe levels are lower than those of the unweighted chirp waveform. Various weighting techniques can be applied to reduce the side lobe levels further. The phase sequence of a P4 signal is described by φi =

π(i − 1)2 − π(i − 1) Nc

(5.25)

for i = 1 to Nc where Nc is the pulse compression ratio. Figure 5.22(a) shows the discrete phase values that result for the P4 code for Nc = 64. Figure 5.22(b) shows the signal phase values modulo 2π. The P4 code has its largest phase increments from sample to sample on the ends of the code, similar to the P1 code. Figure 5.23(a) shows the power spectrum magnitude for just the signal, and Figure 5.23(b) shows the power spectrum for the SNR = 0 dB case, and for the P4 code PSL = 20 log10 2/(Nc π 2 ) (same as the P3 code). Figure 5.24(a) shows the ACF and its corresponding side lobe structure for the Nc = 64 P4 code with N = 1. Figure 5.24(b) shows the PACF. The P4 is a Doppler-tolerant perfect code in that it exhibits a perfect PACF—namely zero PACF side lobes. Figure 5.25 shows the PAF for the P4 code for Nc = 64 and N = 1. Note that the side lobe levels are smaller compared to nonperfect PACF codes, such as the BPSK and P2 code.

158

Detecting and Classifying LPI Radar

Figure 5.19: P3 code power spectrum magnitude for Nc = 64, for (a) signal only and (b) SNR = 0 dB.

Phase Shift Keying Techniques

Figure 5.20: P3 code (a) ACF and (b) PACF, for Nc = 64, N = 1.

Figure 5.21: P3 code PAF for Nc = 64, N = 1.

159

160

Detecting and Classifying LPI Radar

Figure 5.22: P4 code phase values for Nc = 64, showing (a) discrete phase steps and (b) signal phase modulo 2π.

Phase Shift Keying Techniques

161

Figure 5.23: P4 code power spectrum magnitude for Nc = 64, for (a) signal only and (b) SNR = 0 dB.

162

Detecting and Classifying LPI Radar

Figure 5.24: P4 code (a) ACF and (b) PACF, for Nc = 64, N = 1.

Figure 5.25: P4 code PAF for Nc = 64, N = 1.

Phase Shift Keying Techniques

5.11

163

Polytime Codes

The Frank, P1, P2, P3, and P4 codes discussed above were developed by approximating a stepped frequency or linear frequency modulation waveform, where the phase steps vary as needed to approximate the underlying waveform, and the time spent at any given phase state is a constant. Another approach to approximating a stepped frequency or linear frequency modulation waveform is to quantize the underlying waveform into a user-selected number of phase states. In this case, the time spent at each phase state changes throughout the duration of the waveform. The code sequences that use fixed phase states with varying time periods at each phase state are given the name polytime coding [19]. Two types of polytime coded waveforms can be generated from the stepped frequency model and are denoted as T1(n) and T2(n), where n is the number of phase states used to approximate the underlying waveform. The T3(n) and T4(n) polytime sequences are approximations to a linear frequency modulation waveform. Increasing the number of phase states increases the quality of the polytime approximation to the underlying waveform, but also reduces the time spent at any given phase state, complicating the generation of the waveform. The phase state (or bit) durations change as a function of time. The minimum bit duration sets the waveform bandwidth.

5.11.1

T1(n) Code

The T1(n) sequence is generated using the stepped frequency waveform that is zero beat at the leading segment. The expression for the wrapped phase versus time for the T1(n) polytime sequence is [19] φT 1 (t) = mod

jn 2π INT (kt − jT ) , 2π n T

(5.26)

where j = 0, 1, 2, . . . , k − 1 is the segment number in the stepped frequency waveform, k is the number of segments in the T1 code sequence, t is time, T is the overall code duration, and n is the number of phase states in the code sequence. An example of how a stepped frequency waveform is converted into a T1(2) polytime waveform with k = 4 segments and n = 2 phase states is shown in Figure 5.26 (one period with length T = 16 ms). Figure 5.26(a) shows the unwrapped phase change in the time domain. Figure 5.26(b) shows the wrapped phase quantized to phase states of 0 and 180 degrees. Figure 5.26(c) shows a resulting 1-kHz time domain signal incorporating the phase changes generated. In this example, the underlying waveform has k = 4 segments each, with duration of 4 ms (overall code period T = 16 ms). The frequency step between adjacent segments is 1/4 ms = 250 Hz (B = 1,000 Hz). In the T1 code, the first segment is zero frequency and the phase is constant

164

Detecting and Classifying LPI Radar

Figure 5.26: Stepped frequency waveform generating a polytime code T1(2) showing (a) the unwrapped stepped frequency phase shift, (b) wrapped phase quantized to phase state 0 and 180 degrees, and (c) the resulting time domain waveform with phase modulation.

Phase Shift Keying Techniques

165

at zero. The second segment accumulates one full cycle (360 degrees) over the duration of 4 ms. The third segment accumulates an additional two full cycles (720 degrees) over its duration of 4 ms. The fourth segment accumulates an additional three full cycles (1,080 degrees) over its duration of 4 ms resulting in a total accumulated phase change of 2,160 degrees. As the phase of the stepped frequency waveform crosses increments of 180 degrees, the quantized phase changes to the alternate state (between 0 degrees and 180 degrees) and remains there until the phase reaches the next 180-degree boundary as shown. The power spectrum magnitude of the T1(2) signal only is shown in Figure 5.27(a). Figure 5.27(b) shows the power spectrum magnitude for the SNR = 0 dB case. These plots serve to demonstrate the wideband nature of this type of phase modulation. Note that the bandwidth is not equal to B but is the result of the phase state with the smallest duration. Figure 5.28(a) shows the ACF and its side lobe structure for the T1(2) code with N = 1. The PSL is high (PSL ≈ −10 dB). From the PACF shown in Figure 5.28(b), it is clear that the T1(2) also does not have a perfect PACF. Figure 5.29 shows the PAF for the T1(2) code for N = 1. The plot reveals the high Doppler side lobes expected.

5.11.2

T2(n) Code

The T2(n) sequence is generated by approximating a stepped frequency waveform that is zero at its center frequency. For stepped frequency waveforms with an odd number of segments, the zero frequency is the frequency of the center segment. If an even number of segments is used, the zero frequency is the frequency halfway between the two centermost segments. The expression for the wrapped phase versus time for the T2(n) polytime sequence is φT 2 (t) = mod

2π INT (kt − jT ) n

2j − k + 1 T

n , 2π 2

(5.27)

where the variables are as defined above. An example of how a stepped frequency waveform is converted into a T2(2) polytime waveform, resulting from n = 2 phase states and k = 4 segments, is shown in Figure 5.30 for one period T = 16 ms. Figure 5.30(a) shows the unwrapped phase change in the time domain. Figure 5.30(b) shows the wrapped phase quantized to phase state 0 and 180 degrees. Figure 5.30(c) shows the resulting 1-kHz time domain signal, illustrating the imposed phase modulation. The underlying waveform has k = 4 segments, each with duration of 4 ms (overall code period T = 16 ms). The frequency step between adjacent segments is 1/4 ms= 250 kHz (B = 1,000 Hz). In the T2 code, the phase shift for the code period is significantly diﬀerent as reflected in the unwrapped stepped frequency phase shift and the wrapped phase that is quantized to n phase states.

166

Detecting and Classifying LPI Radar

Figure 5.27: Polytime code T1(2) power spectrum magnitude, for (a) signal only and (b) SNR = 0 dB.

Phase Shift Keying Techniques

Figure 5.28: T1(2) code (a) ACF and (b) PACF for N = 1.

Figure 5.29: T1(2) code PAF for N = 1.

167

168

Detecting and Classifying LPI Radar

Figure 5.30: Stepped frequency waveform generating a polytime code T2(2), showing (a) the unwrapped stepped frequency phase shift, (b) the wrapped phase quantized to phase state 0 and 180 degrees, and (c) the resulting time domain waveform with imposed phase modulation.

Phase Shift Keying Techniques

169

The power spectrum magnitude of the T2(2) signal for signal only is shown in Figure 5.31(a), and Figure 5.31(b) shows the power spectrum magnitude for SNR = 0 dB. Note again, that the bandwidth is not equal to B but is the result of the phase state with the smallest duration. Figure 5.32(a) shows the ACF for the T2(2) code with N = 1. The peak side lobe level is approximately the same as the T1(2) examined above, except that it occurs at a larger delay (τ /tb = 38). Figure 5.32(b) shows the PACF and reveals that the T2(n) code also does not have a perfect PACF. Figure 5.33 shows the PAF and, as also expected, has fairly large side lobes.

5.11.3

T3(n) Code

A linear FM waveform that is zero beat at its leading edge generates the T3(n). The equation for the wrapped phase versus time for a T3 polytime sequence is n∆F t2 2π INT , 2π (5.28) φT 3 (t) = mod n 2tm where tm is the modulation period and ∆F is the modulation bandwidth. An example of a T3(2) waveform generated using fc =1 kHz, ∆F =1 kHz, and tm =16 ms is given in Figure 5.34. Figure 5.34(a) shows the unwrapped phase change in the time domain. Figure 5.34(b) shows the wrapped phase quantized to phase state 0 and 180 degrees. Figure 5.34(c) shows the resulting 1-kHz time domain signal, illustrating the imposed phase modulations. The quadratic phase accumulates 2,880 degrees after 16 ms. The wrapped phase shifts between 0 and 180 degrees, as the quadratic phase of the linear FM waveform passes through increments of 180 degrees. The power spectrum magnitude of the T3(2) signal only is shown in Figure 5.35(a) and Figure 5.35(b) shows the power spectrum magnitude for SNR = 0 dB. Figure 5.36(a) shows the ACF for the T3(2) code with N = 1, and indicates that the side lobe performance is somewhat better than the T1(2) or T2(2) code (PSL ≈ −18 dB). Figure 5.36(b) shows the corresponding PACF, also indicating that the T3(2) does not have a perfect PACF. Figure 5.37 shows the PAF for the T3(2) code. As expected, the side lobes are relatively high.

5.11.4

T4(n) Code

If the linear frequency modulation waveform is zero beat at its center and is quantized into n discrete phase states, the T4(n) polytime sequence is generated. The equation for the wrapped phase versus time for a T4(n) polytime sequence is φT 4 (t) = mod

n∆F t2 n∆F t 2π INT , 2π − n 2tm 2

(5.29)

170

Detecting and Classifying LPI Radar

Figure 5.31: Polytime code T2(2) power spectrum magnitude, for (a) signal only and (b) SNR = 0 dB.

Phase Shift Keying Techniques

Figure 5.32: T2(2) code (a) ACF and (b) PACF for N = 1.

Figure 5.33: T2(2) code PAF for N = 1.

171

172

Detecting and Classifying LPI Radar

Figure 5.34: Stepped frequency waveform generating a polytime code T3(2) showing (a) the unwrapped phase shift, (b) the wrapped phase quantized to phase state 0 and 180 degrees, and (c) the resulting time domain waveform with phase shifts.

Phase Shift Keying Techniques

173

Figure 5.35: Polytime code T3(2) power spectrum magnitude, for (a) signal only and (b) SNR = 0 dB.

174

Detecting and Classifying LPI Radar

Figure 5.36: T3(2) code (a) ACF and (b) PACF for N = 1.

Figure 5.37: T3(2) code PAF for N = 1.

Phase Shift Keying Techniques

175

An example of a T4(2) waveform with fc =1 kHz, ∆F =1 kHz, and tm =16 ms is given in Figure 5.38. Figure 5.38(a) shows the unwrapped phase change in the time domain. Figure 5.38(b) shows the binary phase code corresponding to each phase shift. Figure 5.38(c) shows the resulting 1-kHz time domain signal illustrating the phase modulation. The power spectrum magnitude of the T4(2) signal only is shown in Figure 5.39(a). Figure 5.39(b) shows the power spectrum magnitude for SNR = 0 dB. Figure 5.40(a) and (b) shows the ACF and PACF, respectively. The T4(2) has side lobes that are higher than the T3(2). The T3(2) also does not have a perfect PACF. Figure 5.41 shows the PAF for the T4(2) code for N = 1, and shows similar performance to the T1(2) through T3(2). Other sequences can be formed by quantizing the phase into n > 2 phase states. Increasing the number of phase states increases the quality of the polytime approximation of the underlying waveform [19]. Since the polytime sequences approximate the underlying stepped frequency and linear frequency modulation waveforms, it is surprising that their properties do not follow more closely the properties of the underlying waveform. As more phase states are added to the polytime sequence, the agreement in time side lobe behavior improves. Polytime coding also has the advantage that arbitrary time-bandwidth waveforms can be generated with only a few phase states.

176

Detecting and Classifying LPI Radar

Figure 5.38: Stepped frequency waveform generating a polytime code T4(2) showing (a) the unwrapped stepped frequency phase shift, (b) the wrapped phase quantized to phase state 0 and 180 degrees, and (c) the resulting time domain waveform with phase shifts.

Phase Shift Keying Techniques

177

Figure 5.39: Polytime code T4(2) power spectrum magnitude, for (a) signal only and (b) SNR = 0 dB.

178

Detecting and Classifying LPI Radar

Figure 5.40: T4(2) code (a) ACF and (b) PACF for N = 1.

Figure 5.41: T4(2) code PAF for N = 1.

Phase Shift Keying Techniques

179

Figure 5.42: Photo of the OLPI radar (a) transmit antenna and (b) receive antenna.

5.12

Omnidirectional LPI Radar

The objective of the omnidirectional LPI radar concept is to provide mediumrange surveillance while avoiding antiradiation missile attacks [20, 21]. The transmitting antenna beam illuminates the observation space continuously using a Frank phase-coded CW waveform. The CW signal is transmitted from an antenna that uses a nonscanning main beam, as illustrated in Figure 1.4(c). The transmitter is separated from the receiving system by approximately 100m. By separating the transmit and receive antennas, no direct coupling exists, providing good isolation. In a tactical situation, several transmitters can be used (with diﬀerent frequencies and phase codes) to provide backup, or as decoys. Figure 5.42 shows a picture of both the OLPI transmitter antenna and receive antenna. In the transmitting antenna, eight vertical dipoles in a column are combined by a microstrip-feeding network, resulting in a fan-beam pattern with a width of 20 degrees in elevation and 120 degrees in azimuth. The gain of the transmitting antenna is Gt = 8π. The objective here is to distribute the energy evenly within the observation space. The transmitter power is 10W at 2.82 GHz [22]. The receive antenna uses a multiple beam array to provide continuous coverage of the illuminated space. The multiple beam antenna also provides

180

Detecting and Classifying LPI Radar

Figure 5.43: Block diagram of the OLPI radar signal processing. directional information from the detected targets. The echo from nearby objects is strong, while the echo from distant flying targets is weak. Consequently, Doppler processing is used to extract the targets from the background clutter. The receive antenna has a planar array of 64 columns, with each column containing eight dipoles combined by a network that is the same as for the transmit antenna. The total number of antenna elements is 512. The multiple beams in azimuth are formed by a 64-port Butler matrix that was manufactured using microstrip technology. The Butler matrix is an analog beamforming network, made up of 3-dB directional couplers and fixed phase shifts, to form N continuous beams with an N element linear array where N = 2x . The half-power beamwidth of each beam in the OLPI is 2 degrees, which is also the azimuth resolution. The gain of the receiving antenna is Gr = 512π. Since everything is illuminated by the transmit antenna, the signals received through the receive antenna side lobes can pose a problem, making side lobe cancelation in the receive beam particularly important. A block diagram of the OLPI radar signal processing is shown in Figure 5.43. The received signal from the Butler matrix is passed through a lownoise amplifier and downconverted to an IF frequency of 30 MHz, filtered, and then converted to baseband I and Q. The ADCs performing the baseband sampling are 12-bit devices sampling at a rate of 250 kHz. The received

Phase Shift Keying Techniques

181

signals for each resolution are integrated during a time of Ts =2s. The range resolution is matched to the azimuth resolution at 30 km, which is 600m. Therefore, the range resolution is 600m, resulting in a subcode width of tb = 4 μs. With fs = 250 kHz, each subcode period contains one I and Q pair. The Frank code length is Nc = 64, resulting in a code period of T = 256 μs and is equivalent to an Ru =38.4 km. The first step in the signal processing is to suppress the (mostly stationary) clutter echoes, using a recursive notch filter. After clutter suppression, the code compression is accomplished by using an FFT that eﬃciently compresses the Frank code. The processing gain due to code compression is Nc = 64. Because the phase is unknown, however, there is a loss of 1 dB compared to fully coherent integration resulting in a net processing gain of P GR = 10 log10 (Nc ) − 1 or 17 dB. The phase code compression is followed by Doppler filtering to extract the moving targets. To detect targets with velocity v =250m/s at 38 km within an integration time of Ts = 2s, the resulting Doppler spectral width is 2v 2 Ts 2∆v = (5.30) λ Rλ or 60 Hz. The filter width is matched to this value, resulting in a coherent integration time of 16 ms and corresponds to 64 code periods, each 256 μs long. That is, 64 code periods are integrated for each range bin. To simplify the hardware complexity of having to process 4,096 range bins, the signal is digitized into a single bit (±1) [22]. The processing gain due to the Doppler filtering of 64 phase codes is P G = 10 log10 (64) = 18 dB. Due to the digitization into a single bit, however, a loss of 2 dB is encountered. Also, since the Doppler frequency and phase are unknown, an additional loss of 2.5 dB is included, resulting in a processing gain due to Doppler filtering of P GR = 18 − 2.5 − 2 = 13.5 dB. The fourth step described in [22] is the noncoherent integration of the outputs of the Doppler filter bank. The noncoherent integration is carried out over the frame time (T = 2s). During the total integration time of Ts = 2s, a further 128 signals are integrated in amplitude individually. With 64 beams, 64 range bins, and 64 Doppler filters per range bin, a total of 262,144 resolution cells are available. The processing gain due to noncoherent integration is 12.7 dB. The total processing gain for all three stages is then P GR = 17 + 13.5 + 12.7 =43.2 dB. With an output detection threshold of SNRRo = 13 dB, the required input SNRRi = −30.2 dB. With BRi = 1/tb = 250 kHz and FR = 5.6 dB (including Butler matrix loss), the sensitivity of the OLPI can be estimated as ∆ω =

δR = kT0 FR BRi SNRRi = −174 dBW

(5.31)

The OLPI radar has been used experimentally to detect hovering helicopters (above terrain masking for only a short time), and is described more fully

182

Detecting and Classifying LPI Radar

in [22]. Although the OLPI is only one example of an LPI radar that uses phase modulation, there have also been others built that use much longer phase codes such as the Hughes Aircraft Company “quiet radar” built in the early 1980s.

5.13

Summary

In this chapter we have examined several popular PSK LPI radar schemes, as well as some new techniques recently developed. The phase structure was examined for each type of code, along with an analysis of the magnitude of phase change throughout the code. The power spectrum results were also presented. The correlation and ambiguity functions from Chapter 3 were used to examine each waveform’s ACF, PACF, and PAF in order to determine its suitability for use as an LPI waveform. In the next chapter we look at frequency shift keying techniques for LPI radar applications, as well as hybrid FSK/PSK techniques.

References [1] Lee, W. K., and Griﬃths, H. D., “Pulse compression filter generating optimal uniform range sidelobe level,” IEE Electronics Letters, Vol. 35, No. 11, pp. 873—875, May 1999. [2] Lee, W. K., Griﬃths, H. D., and Benjamin, R., “Integrated sidelobe energy reduction technique using optimal polyphase codes,” IEE Electronics Letters, Vol. 35, No. 24, pp. 2090—2091, Nov. 1999. [3] Grishin, Y. P., and Zankiewicz, A., “A neural network sidelobe suppression filter for a pulse—compression radar with powers-of-two weights,” IEEE 10th Mediterranean Electrotechnical Conference, Vol. 2, pp. 713—716, 2000. [4] Lee, W-K., and Griﬃths, H. D., “A new pulse compression technique generating optimal uniform range sidelobe and reducing integrated sidelobe level,” Record of the IEEE International Radar Conference, pp. 441—446, 2000. [5] Barker, R. H., “Group synchronizing of binary digital systems,” in Communications Theory, Butterworth, London, pp. 273—287, 1953. [6] Golomb, S. W., and Scholtz, R. A., “Generalized Barker sequences,” IEEE Trans. on Information Theory, Vol. IT-11, No. 4, pp. 533—537, Oct. 1965. [7] Eliahou, S., and Kervaire, A., “Barker sequences and diﬀerence sets,” L’ Enseignement Mathematique, Vol. 38, pp. 345—382, 1992. [8] Zhang, N., and Golomb, S. W., “Sixty-phase generalized Barker sequences,” IEEE Trans. on Information Theory, Vol. 35, No. 4, pp. 911—912, April 1989. [9] Bomer, L., and Antweiler, M., “Polyphase Barker sequences,” IEE Electronics Letters, Vol. 25, No. 23, pp. 1577—1579, 1989.

Phase Shift Keying Techniques

183

[10] Friese, M., and Zottmann, H., “Polyphase Barker sequences up to length 31,” IEE Electronics Letters, Vol. 30, No. 23, pp. 1930—1931, Nov. 1994. [11] Friese, M., “Polyphase Barker sequences up to length 36,” IEEE Trans. on Information Theory, Vol. 42, No. 4, pp. 1248—1250, July 1996. [12] Brenner, A. R., “Polyphase Barker sequences up to length 45 with small alphabets,” IEE Electronics Letters, Vol. 34, No. 16, pp. 1576—1577, Aug. 1998. [13] Borwein, P., and Ferguson, R., “Polyphase sequences with low autocorrelation,” IEEE Trans. on Information Theory, Vol. 51, No. 4, pp. 1564—1567, April 2005. [14] Frank, R. L., “Polyphase codes with good nonperiodic correlation properties,” IEEE Trans. IT-9, pp. 43—45, 1963. [15] Lewis, B. L., Kretschmer, F. F., and Shelton, W. W., Aspects of Radar Signal Processing, Artech House, Norwood, MA, 1986. [16] Lewis, B. L., “Range-time-sidelobes reduction technique for FM-derived polyphase PC codes,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 29, No. 3, pp. 834—840, July 1993. [17] Painchaud, G. R., et al., “An experimental adaptive digital pulse compression subsystem for multi-function radar applications,” Record of the IEEE International Radar Conference, pp. 153—158, 1990. [18] Lesnik, C. J., et al., “Eﬃcient matched filtering of signal with polyphase Frank coded sequences,” IEEE 12th International Conference on Microwaves and Radar, MIKON ’98, Krakow, Poland, Vol. 3, pp. 815—819, May 20—22, 1998. [19] Fielding, J. E., “Polytime coding as a means of pulse compression,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 35, No. 2, pp. 716—721, Apr. 1999. [20] Wirth, W. D., “Long term coherent integration for a floodlight radar,” Record of the IEEE International Radar Conference, pp. 698—703, 1995. [21] Wirth, W. D., “Polyphase coded CW radar,” Proc. of the IEEE Fourth International Symposium on Spread Spectrum Techniques and Applications, Mainz, Germany, Vol. 1, pp. 186—190, Sept. 22—25, 1996. [22] Wirth, W. D., Radar Techniques Using Array Antennas, IEE, London, United Kingdom, 2001.

Problems 1. For an LPI CW radar with an fc =9 GHz, (a) what is the subcode period tb of the transmitted waveform if the cycles per subcode cpp = 5? (b) What is the transmitted bandwidth of the signal? (c) If the number of phase codes used is Nc = 128, what is the code rate Rc and the range resolution?

184

Detecting and Classifying LPI Radar

Figure 5.44: LPI phase-coded waveform. 2. The generation of an LPI phase-coded CW signal is shown in Figure 5.44. If the carrier frequency is 0.5 MHz, (a) what is the code period (in seconds)? (b) What is the unambiguous range of the waveform (in km)? (c) What is the bandwidth of the transmitted signal (in MHz)? (d) What is the range resolution of the waveform (in m)? (e) If the phase code used is a P3 or P4 code, what would you expect the ACF peak side lobe level to be (in decibels down from the main lobe response)? 3. (a) Using the bpsk.m file as a template, generate a compound Barker code with fc = 1 kHz, cpp = 2, and Nc = 7. (b) Add this capability to the LPIT menu. (c) For this waveform, how many subcodes are contained within a code period? (d) What is the subcode period tb ? (e) Plot the ACF, PACF, and the PAF. (f) What can you say about the PSL and the Doppler side lobe levels? 4. (a) Generate three code periods of an fc = 1 kHz (fs = 7 kHz), cpp = 3 polyphase Barker code with length Nc = 16. (b) Plot the ACF, PACF, and PAF. (c) Compare these results with an fc =1 kHz (fs = 7 kHz), cpp = 3 polyphase P4 code with length Nc = 16. 5. Use the lpit.m file in the LPIT toolbox to generate the default BPSK, Frank, P1—P4 and T1—T4 codes, and both test signals by selecting the “no change” option for each signal to accept the defaults. Be sure to write down the default parameters for each case. The signals will be saved automatically to your LPIT directory. Move these signals to a separate folder for use in Part II of this text. 6. Run the LPIT and select the BPSK signal. (a) Change only the number of cycles per Barker bit to 1 (cpp = 1), and generate the signal. That is, each bit now contains only 1 cycle of the IF frequency. (b) Plot the power spectrum magnitude and record the approximate 3-dB bandwidth of the waveform, comparing this with a calculation of what you would theoretically expect. (c) Repeat for cpp = 7.

Phase Shift Keying Techniques

185

7. Consider a generalized Barker sequence with the general transformation vr = ur ej2π(r+α)/x where α and x are any real numbers, x = 0 with |vr | = |ur | and |rτv | |rτu |. Show that the transformation vr = uk−r+1 preserves the Barker property and runs the sequence backwards. 8. (a) Using the LPIT toolbox, generate polytime codes T1(8) and T2(8), with fc = 1 kHz, fs = 7 kHz, k = 4, and tm = 16 ms. (b) Plot the phase distribution within a code period for each signal. (c) Plot the ACF, PACF, and PAF for each signal. (d) Compare the phase distribution diagrams with those shown in Figure 5.26 and Figure 5.30. (e) Compare the correlation and ambiguity diagrams with those shown in Figure 5.28(a, b), Figure 5.29, Figure 5.32(a, b), and Figure 5.33. 9. (a) Using the LPIT toolbox, generate polytime codes T3(8) and T4(8), with fc = 1 kHz, fs = 7 kHz, k = 4, ∆F = 1 kHz, and tm = 16 ms. (b) Plot the phase distribution within a code period for each signal. (c) Plot the ACF, PACF, and PAF for each signal. (d) Compare the phase distribution diagrams with those shown in Figure 5.34 and Figure 5.38. (e) Compare the correlation and ambiguity diagrams with those shown in Figure 5.36(a, b), Figure 5.37, Figure 5.40(a, b), and Figure 5.41. 10. (a) Determine the maximum detection range of the OLPI radar for a σT = 5 m2 target if the losses total 14 dB. (b) How does this range compare with Ru ?

Chapter 6

Frequency Shift Keying Techniques CW waveforms with pulse compression allow the LPI radar to have a significant processing gain over an unintended intercept receiver, due to the code secrecy and the large bandwidth signals that are transmitted. In Chapter 4, it was shown that an FMCW waveform is the simplest technique to implement, with the compression of the waveform done using either analog or digital hardware. In Chapter 5, PSK techniques were shown to have significant promise, due to advances in digital hardware and the fact that many codes and code lengths are available to choose from. Another coding technique that increases the library of LPI radar waveforms is the use of frequency shift keying. In this chapter three important FSK or frequency hopping (FH) techniques for coding CW waveforms are presented.

6.1

Advantages of the FSK Radar

Much of the LPI radar technology fielded today is linear FMCW, with the simplicity of this technology being its main advantage.1 The FMCW approach spreads the transmitted energy out over the modulation bandwidth to eﬀectively reduce the power spectral density (PSD). The main disadvantage, as illustrated in Chapter 4, is the high side lobe values that occur on the order of 13 dB down from the peak response, and so this type of waveform requires that some type of weighting be applied to the matched filter response. The PSK radar uses polyphase codes to reduce the side lobe levels, and the waveforms are directly compatible with digital generation and 1A

review of fielded LPI radar systems is given in Chapter 2.

187

188

Detecting and Classifying LPI Radar

compression, making their use more attractive. In addition, the codes must be chosen carefully in order to maintain Doppler tolerance. An LPI radar that uses FH techniques hops or changes the transmitting frequency in time over a wide bandwidth in order to prevent an unintended receiver from intercepting the waveform.2 The frequency slots used are chosen from an FH sequence, and it is this unknown sequence that gives the radar the advantage in terms of processing gain. That is, the frequency sequence appears random to the intercept receiver, and so the possibility of it following the changes in frequency is remote. This prevents a jammer from reactively jamming the transmitted frequency.3 In contrast to the FMCW and PSK techniques, the FH technique of rapidly changing the transmitter frequency does not lower the PSD of the emission, but instead moves the PSD about according to the FH sequence. Consequently, the FH radar has a higher probability of detection than a PSK or FMCW waveform, but retains a significantly low probability of interception. In a PSK radar, all the control circuitry, modulators, and demodulators must have enough bandwidth in order to avoid transmitting second order eﬀects, thereby making the overall system expensive [1]. A major advantage of the FH radar is the simplicity of the FSK architecture, especially for track processing and generating large bandwidth signals. Large bandwidth frequency hopping radar waveforms can be generated by using coherent direct analog synthesizers that generate the output frequencies using standard VCOs and very simple digital circuitry. Drawbacks of this approach include spurious frequencies and high levels of phase noise, due to the complex analog circuitry required. Direct digital methods can also be used, and involve using a digital frequency synthesizer and a digital-to-analog converter, followed by a lowpass filter. The major disadvantage here is that the output bandwidth is limited by the speed of the digital devices. Single or multiple phaselocked loops can also be used and have the advantage of large bandwidths and the ability to filter spurious frequencies outside the loop bandwidth [2]. Another advantage of the FH radar is that the range resolution is independent of the hopping bandwidth (unlike that of the FMCW and PSK techniques). Range resolution in an FH radar depends only on the hop rate. A significant benefit also resides in the secrecy of the FH sequence that is used. FH radar performance depends only slightly on the code used, given that certain properties are met. This allows for a larger variety of codes, making it more diﬃcult to intercept. By comparison, a PSK radar must choose from a group of well-known codes, due to the ambiguity properties 2 A frequency hopping radar is diﬀerent than a frequency agile radar, in that the frequency agile radar is usually regarded as a pulse radar that uses a diﬀerent frequency on a pulse-to-pulse basis. The LPI frequency hopping radar transmits a CW frequency hopped signal. 3 A jammer can preemptively jam a FH radar if its bandwidth and power are large enough to cover the FH band.

Frequency Shift Keying Techniques

189

required. Although the length of the PSK code may be unknown to the intercept receiver, it may still cycle through, and attempt to correlate specific signal patterns for detection and jammer waveform construction (more about this in Part II). The order in which the frequencies are transmitted significantly aﬀects the ambiguity performance of the signal. The PAF for FH signals can easily be approximated, because the cross-correlation signals at diﬀerent frequencies approach zero when the frequency diﬀerence is large relative to the inverse of the signal duration (or multiples of that inverse) [1]. In a multiple LPI emitter environment, an important requirement is to keep the mutual interference between transmitters as low as possible. Mutual interference occurs when two or more emitters transmit the same frequency slot at the same time. The degree of mutual interference is related to the cross correlation properties of the FH sequences. Another advantage is that the glint (target scintillation) error spectrum is broadened significantly, since the glint error is eﬀectively decorrelated when the transmitter changes frequency.

6.2

Description of the FSK CW Signal

In an FSK radar, the transmitted frequency fj is chosen from the FH sequence {f1 , f2 , . . . , fNF } of available frequencies for transmission at a set of consecutive time intervals {t1 , t2 , . . . , tNF }. The frequencies are placed in the various time slots corresponding to a binary time-frequency matrix. Each frequency is used once within the code period, with one frequency per time slot and one time slot per frequency. The expression for the complex envelope of the transmitted CW FSK signal is given by s(t) = Aej2πfj t

(6.1)

The transmitted waveform has NF contiguous frequencies within a band B, with each frequency lasting tp s in duration.

6.3

Range Computation in FSK Radar

CW FSK radars using multiple frequencies can compute very accurate range measurements. To illustrate, consider a CW radar that transmits the waveform (6.2) s(t) = A sin(2πfj t) where the received signal from a target at a range RT is W w 4πfj RT s(t) = A sin(2πfj t − φT ) = A sin 2πfj t − c

(6.3)

190

Detecting and Classifying LPI Radar

Solving for RT RT =

c φT 4πfj

(6.4)

The unambiguous range occurs when φT is maximum or φT = 2π and therefore with one frequency, RT is limited to extremely small values that are not practical [3]. If two frequencies are used s1 (t) = A1 sin(2πf1 t)

(6.5)

s2 (t) = A2 sin(2πf2 t)

(6.6)

W w 4πf1 RT s1 (t) = A1 sin(2πf1 t − φT 1 ) = A sin 2πf1 t − c

(6.7)

W w 4πf2 RT s2 (t) = A2 sin(2πf2 t − φT 2 ) = A sin 2πf2 t − c

(6.8)

and the received signals are

and

After mixing with the carrier frequency in the receiver, the phase diﬀerence between the two signals is ∆φT =

4πRT 4πRT (f2 − f1 ) = ∆f c c

(6.9)

Since RT is maximum when ∆φ = 2π, the maximum unambiguous range is Ru =

c 2∆f

(6.10)

and is very large since ∆f << c. From the measurement of the phase diﬀerence, ∆φT , the range of the target is then RT =

c∆φT 4π∆f

(6.11)

This can also be written as a function of just the phase diﬀerence as RT = Ru

∆φT 2π

(6.12)

Since the range to the target depends on the frequency diﬀerence, the range resolution then depends on the duration of each frequency as ∆R =

ctp 2

(6.13)

Frequency Shift Keying Techniques

191

The transmitted power for each frequency must be such that the energy content within the target echo is suﬃcient for detection, and enough to ensure that accurate phase measurements can be made. In summary, for the FSK CW radar, the frequency diﬀerence ∆f determines the maximum unambiguous detection range. The target’s range is computed by measuring the return signal phase diﬀerence from two consecutive transmitted frequencies. The range resolution, ∆R, depends only on the FH period.

6.4

Costas Codes

In a study by J. P. Costas, techniques were presented for generating a sequence of frequencies that produce unambiguous range and Doppler measurements while minimizing the cross talk between frequencies [4]. In general, the Costas sequence of frequencies provides an FH code that produces peak side lobes in the PAF, that are down from the main lobe response by a factor of 1/NF for all regions in the delay-Doppler frequency plane. That is, the order of frequencies in a Costas sequence or array is chosen in a manner to preserve an ambiguity response with a thumbtack nature (the narrow main lobe and side lobes are as low as possible). The firing order of these frequencies is based on primitive roots (elements) of finite fields.

6.4.1

Characteristics of a Costas Array or Sequence

A Costas array or (frequency) sequence f1 , · · · , fNF is a sequence that is a permutation of the integers 1, · · · , NF satisfying the property fk+i − fk = fj+i − fj

(6.14)

for every i, j, and k such that 1 ≤ k < i < i + j ≤ NF . An array that results from a Costas sequence in this way is called a Costas array [5]. The nonequivalence condition in (6.14) can be checked easily when the frequency sequence is expressed in an NF − 1 × NF diﬀerence triangle. As an added bonus, the diﬀerence triangle can also be used to derive the PAF. We discuss how to derive Costas sequences in the next section and in Appendix C. Consider the frequency sequence fj = {2, 4, 8, 5, 10, 9, 7, 3, 6, 1} kHz. Figure 6.1(a) shows the binary time-frequency matrix for this sequence. The frequencies are fired at each ti and are indicated by a “1” in the matrix. The power spectral density of the signal is shown in Figure 6.1(b). Also indicated is the firing order for each frequency. If the subperiod tp (frequency duration) is constant, the cycle density or number of cycles per frequency varies as tp fj .

192

Detecting and Classifying LPI Radar

Figure 6.1: Costas sequence fj = {2, 4, 8, 5, 10, 9, 7, 3, 6, 1} kHz, showing (a) the binary time-frequency matrix, and (b) the power spectrum magnitude for several code periods.

6.4.2

Computing the Diﬀerence Triangle

The first step to verifying (6.14) and deriving the PAF is to form a diﬀerence triangle. To form the diﬀerence triangle, we start by writing the NF frequency values in the sequence (fj where j = 1, . . . , NF ) as column headers across the top as illustrated in Figure 6.2(a). The NF − 1 rows in the diﬀerence triangle correspond to the delays, with each row number i representing the delay value. To calculate each cell value in the diﬀerence triangle ∆i,j ∆i,j = fj+i − fj

(6.15)

where i = 1 . . . NF − 1, j = 1 . . . NF − 1, and i + j ≤ NF . For example, the first row (delay i = 1) is formed by taking diﬀerences between adjacent frequencies. By (6.14), all results in this row must be unique [6, 7]. The second row in the diﬀerence matrix is formed by taking diﬀerences between next-adjacent terms (delay i = 2). Results in this row must also be unique. The process is repeated until the i = NF − 1 delay is computed. All values of ∆i,j must be unique within each row, and is the defining criterion of a Costas sequence.

6.4.3

Deriving the Costas Sequence PAF

The PAF can be approximated by overlaying the binary time-frequency matrix upon itself, and shifting one relative to the other according to a particular

Frequency Shift Keying Techniques

193

delay (horizontal shifts) and particular Doppler (vertical shifts). At each combination of shifts, the sum of coincidences between points of the fixed and the shifted matrix, represents the relative height of the PAF. An easier way to derive the PAF is using the diﬀerence triangle, as shown in Figure 6.2(a). In Figure 6.2(b) the PAF of the 10-frequency Costas signal is derived from the diﬀerence triangle. The PAF is constructed by considering each row (delay) in the diﬀerence triangle, and placing a “1” in the PAF delay-Doppler cell corresponding to each ∆i,j . The delay i = 1 is shaded as an example. The PAF derived from this complex Costas signal with fs = 27.5 kHz (power spectrum magnitude shown in Figure 6.1) is shown for comparison in Figure 6.2(c).

6.4.4

Welch Construction of Costas Arrays

There are many analytical procedures for constructing Costas frequency hopping arrays. Although Costas arrays may exist in principle for any positive integer NF , these analytical construction methods are typically limited to values of NF related to prime numbers [6, 8, 9]. Most construction methods to produce a large number of Costas arrays of equal length are based on the properties of primitive roots (see the tutorial in Appendix C). For the Welch construction of a Costas array, an odd prime number p is chosen first. The number of frequencies and the number of time slots in the Costas sequence are then NF = φ(p) = p− 1 where φ(p) is the Euler function. Next, a primitive root g modulo p is chosen. As discussed in Appendix C, if g is a primitive root modulo p, then g is an integer belonging to the Euler-φ(p) function modulo p. Since g is a primitive root modulo p, g, g 2 , . . . , g φ(p) are mutually incongruent and form a permuted sequence of the reduced residues p. Welch showed that this reduced residue sequence is a Costas sequence. Theorem 6.1 Let g be a primitive root of an odd prime number p. Then the (p−1) by (p−1) permutation matrix A has elements ai,j =1 iﬀ j ≡ g i (mod p) for 1 ≤ i, j ≤ p − 1 and this is a Costas array [10]. Example: The first step is choosing a prime number p. We choose the prime number p = 7. For p = 7, NF = 6, which is the number of frequencies in the FH code. The complete residue system is {0, 1, 2, 3, 4, 5, 6}. With p prime, we know that the number of elements in the reduced residue system is φ(p) = p − 1 = 6. The reduced residue system is {1, 2, 3, 4, 5, 6} (deleting the one element that is divisible by p). From Appendix C, for p = 7 we know there are exactly φ{φ(7)} = φ{6} = 2 mutually incongruent primitive roots modulo p = 7. We start with the smallest value g = 2, but the order of g =2 is 3 (not 6). Next we pick g = 3 and get the desired result {3, 2, 6, 4, 5, 1}, which is the Costas array as shown below. The left-hand column shows i from 1 to p − 1, and the right-hand column shows the frequency j using

194

Detecting and Classifying LPI Radar

Figure 6.2: Costas sequence with (a) the diﬀerence triangle, (b) the PAF derived from the diﬀerence triangle, and (c) the PAF derived from the complex signal.

Frequency Shift Keying Techniques

195

Theorem 6.1.

i 1 2 3 4 5 6

j = g i (mod7) 31 = 3 32 = 2 33 = 6 34 = 4 35 = 5 p−1 = 36 = 1 3

where i, j = 1, 2, . . . , 6. Consequently, the Costas frequency sequence is f = {3, 2, 6, 4, 5, 1}

(6.16)

Note from the symmetry that f = {5, 4, 6, 2, 3, 1} is also a Costas sequence. The Welch construction is also singly periodic [5]. That is, the sequence fi , fi+1 , . . . , fi+p−2 is also a Costas sequence. Any circular shift of the sequence is also a Costas sequence. The costas.m program within the LPIT allows the user to quickly add additional sequences that may be of interest.

6.5

Hybrid FSK/PSK Technique

The hybrid LPI radar technique discussed in this section combines the technique of FSK (FH using Costas sequences) with that of a PSK modulation using sequences of varying length [11, 12]. This type of signaling can achieve a high time-bandwidth product or processing gain, enhancing the LPI features of the radar. Ambiguity properties of the signal are retained by preserving the desirable properties of the separate FSK and PSK signaling schemes. The FSK/PSK techniques can maintain a high Doppler tolerance, while yielding an instantaneous spreading of the component frequencies along with an enhanced range resolution [11]. Below, a Costas-based FSK/PSK signal (Barker 5-bit PSK over each frequency) is investigated as an example. Other PSK techniques from Chapter 5 can also be investigated using the LPIT.

6.5.1

Description of the FSK/PSK Signal

Recall that for the FH LPI radar, the CW waveform has NF contiguous frequencies within a bandwidth B, with each frequency lasting tp s in duration. The hybrid FSK/PSK signal further subdivides each subperiod into NB phase slots, each of duration tb as shown in Figure 6.3. The total number of phase slots in the FSK/PSK waveform is then NT = NF NB

(6.17)

196

Detecting and Classifying LPI Radar

Figure 6.3: General FSK/PSK signal containing NF frequency subcodes (hops) each with duration tp s. Each frequency subcode is subdivided into NB phase slots, each with duration tb . with the total code period T = tb NB NF . The expression for the complex envelope of the transmitted CW FSK/PSK signal is given by s(t) = Aej2πfj t+φk

(6.18)

where φk is one of NB Barker codes for this example, and fj is one of NF Costas frequencies. During each hop, the signal frequency (one of NF frequencies) is modulated by a binary phase sequence, according to a Barker sequence of length NB = 5, 7, 11, or 13. As an example, the FSK/PSK signal generated by using the NF = 6 Costas sequence (6.16), and phase modulating it with a Barker binary phase modulation of length NB = 5 gives the signal: S = 3+ , 3+ , 3+ , 3− , 3+ , 2+ , 2+ , 2+ , 2− , 2+ , 6+ , 6+ , 6+ , 6+ , 6− , 4+ , 4+ , 4+ , 4− , 4+ , 5+ , 5+ , 5+ , 5− , 5+ , 1+ , 1+ , 1+ , 1− , 1+ . The final waveform is a binary phase modulation within each frequency hop, resulting in five phase subcodes equally distributed within each frequency, for a total of NP NF =30 subcodes. Figure 6.4 shows the power spectrum magnitude that reveals the spread spectrum characteristic of the phase-modulated Costas signal f = {3, 2, 6, 4, 5, 1} kHz. For this signal, the sampling frequency fs = 15 kHz, the subperiod for each frequency is tp =6 ms (B = 167 Hz) and an NB = 5-bit Barker code is used. Figure 6.4(a) shows the Costas sequence power spectrum magnitude before phase modulation. Figure 6.4(b) shows the power spectrum magnitude of the Costas sequence FSK/PSK after phase modulation. Figure 6.5(a, b) shows the ACF and the PACF, respectively, of the FSK/PSK sequence. Note the phase modulation spikes that are present with regular periodicity. Figure 6.6 shows the PAF and the Doppler side lobes present. The fsk psk costas.m program within the LPIT allows additional phase modulations to be included with the Costas sequences (which can also be easily changed). In this manner, the side lobe structure for various phase modulations can be easily compared.

Frequency Shift Keying Techniques

Figure 6.4: Power spectrum magnitude plot for a Costas waveform, with (a) no phase modulation and (b) 5-bit phase modulation.

197

198

Detecting and Classifying LPI Radar

Figure 6.5: (a) ACF and (b) PACF plot for the Costas sequence with a 5-bit Barker phase modulation.

Figure 6.6: PAF plot for the Costas sequence with a 5-bit Barker phase modulation.

Frequency Shift Keying Techniques

6.6

199

Matched FSK/PSK Signaling

The matched FSK/PSK radar concept uses a pulse compression technique that allows it to synthesize uniform envelope signals with an arbitrary spectral density. This type of radar, proposed in [13], concentrates the signal energy in spectral locations of most importance within the spectrum bandwidth, but does so with a random sequence. The radar uses FSK/PSK signals as above but, instead of selecting the frequency from a Costas sequence, the frequency is chosen randomly with a probability distribution that is defined by the spectral characteristics of the target of interest. That is, the frequencies transmitted most often are those that correspond to the spectral peaks of the target signature. Since the FH sequence still appears random, this type of radar can achieve a relatively low probability of intercept. One method to estimate the spectral characteristics of a target (magnitude and phase) is by Fourier-transforming the range profile. The range and spectral characteristics depend on the details of the target structure and aspect angle at which the target is observed. If the target is known ahead of time, several range and frequency profiles for the various aspect angles anticipated can be precomputed and stored in the radar’s bulk memory. A random binary phase shift is also added to reduce the ambiguity function side lobes. A correlation receiver with a phase-mismatched reference signal is used in order to allow the radar to generate signals that can match a target’s spectral response in both magnitude and phase. Figure 6.7 shows a block diagram of the signaling scheme proposed in [13]. The implementation starts with the complex range response of a selected target with NF range samples. The target’s range response is Fouriertransformed, to give a magnitude spectrum with NF unique frequencies. The frequency components with their corresponding magnitude and phase are collected, to represent the probability density function of the transmitter. A random selection process then chooses each frequency, with a probability defined by the spectral characteristics of the target [14]. Consequently, the frequencies corresponding to the spectral peaks of the target (highest magnitudes) are transmitted more often. Each frequency from the NF sequence is transmitted a certain number of times and is also modulated in phase. Each frequency starts with its initial phase value (from the FFT), but is modified by a pseudorandom binary code with values zero or π equally likely. Note that although the spectral density function of the target may contain only NF points, the frequencies are chosen randomly NC NT times in a particular code period T , in order to obtain the proper probability density function. Note that in the LPIT, the complex range response of only one target is available and is configured to closely represent that shown in [13]. Figure 6.8(a) shows NF = 32 complex points describing the target’s range response. Figure 6.8(b) shows the probability density function or, equivalently, the power spectrum magnitude computed from the target’s range

200

Detecting and Classifying LPI Radar

Figure 6.7: Block diagram of the generation of an FSK/PSK target matched waveform.

Frequency Shift Keying Techniques

201

response. The histogram of the transmitted frequency hopping signal is shown in Figure 6.9(a). This figure shows how many times each one of NF = 32 frequencies is transmitted in the NC =512 frequency code. Note the similar appearance to the probability density function shown in Figure 6.9(b), and the power spectrum magnitude given in Figure 6.8(b). Increasing the number of random frequency selections NC > 512, will result in an even better match. Figure 6.10 shows the resulting power spectrum magnitude for the transmitted signal, revealing the wideband nature of this type of hybrid FSK/PSK signaling. Figure 6.11(a) shows the ACF of the transmitted waveform. Note the near-uniform side lobes that are down close to −30 dB. The PACF is shown in Figure 6.11(b), and shows the absence of any periodic components. The PAF shown in Figure 6.12 shows a spike at (τ /tb = 0, ν ∗ Nc tb = 0) and very low side lobes, resembling the PAF of random noise.

6.7

Concluding Remarks

FSK signals provide a higher probability of detection compared to PSK and FMCW signals, but oﬀer many advantages for LPI signaling. Combined with PSK, significant LPI results can be obtained. The FSK, FSK/PSK pulse compression signals discussed in this chapter can help a radar achieve LPI goals. The waveforms can be generated using the LPI toolbox main menu program lpit.m contained on the MATLAB CD. The hybrid modulations presented in this chapter tend to make the transmitted signal appear as noise-enhancing its low probability of intercept nature. These hybrid techniques are a subset of a larger group of radar architectures known as random signal or noise radar. Random signal radar techniques can derive target detections using correlation, spectrum analysis, or anticorrelation. Random signal radar modulations include: noise FMCW, sine plus noise FMCW, random binary PSK CW, and random pulse modulation [15]. Because of the random nature of the transmitted waveform, random signal radar also provides a good deal of electronic protection and has a counterelectronic support capability [16]. These techniques are examined in detail in the next chapter.

202

Detecting and Classifying LPI Radar

Figure 6.8: Transmitted signal showing (a) 32 complex points describing the simulated range response and (b) the normalized power spectrum magnitude representing the probability density function. (After [13].)

Frequency Shift Keying Techniques

203

Figure 6.9: (a) Synthetic or transmitted signal histogram and (b) the original histogram defined by the spectral characteristics of the target.

Figure 6.10: Transmitted signal power spectrum magnitude.

204

Detecting and Classifying LPI Radar

Figure 6.11: Transmitted signal (a) ACF and (b) PACF.

Figure 6.12: Transmitted signal PAF.

Frequency Shift Keying Techniques

205

References [1] Sanmartin-Jara, J., Burgos-Garcia, M., and Retamosa-Sanchez, J., “Radar sensor using low probability of interception SS-FH signals,” IEEE Aerospace and Electronics Magazine, pp. 23—28, April 2000. [2] Benn, H. P. and Jones, W. J., “A fast hopping frequency synthesizer,” Second International Conference on Frequency Control and Synthesis, pp. 69—72, April 1989. [3] Mahafza, B. R., Radar Systems Analysis and Design Using MATLAB, Chapman & Hall/CRC, New York, 2000. [4] Costas, J. P., “A study of a class of detection waveforms having nearly ideal range-Doppler ambiguity properties,” Proc. of the IEEE, Vol. 72, No. 8, pp. 996—1009, August 1984. [5] Golomb, S. W., and Moreno, O., “On periodicity properties of Costas arrays and a conjecture on permutation polynomials,” IEEE Trans. on Information Theory, Vol. 42, No. 6, pp. 2252—2253, Nov. 1996. [6] Golomb, S. W., and Taylor, H., “Construction and properties of Costas arrays,” Proc. of the IEEE, Vol. 72, No. 9, pp. 1143—1163, Sept. 1984. [7] Levanon, N., Radar Principles, John Wiley & Sons, New York, NY 1988. [8] Maric, S. V., Seskar, I., and Titlebaum, E. L., “On cross-ambiguity properties of Welch-Costas arrays,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 30, No. 4, pp. 1063—1071, Oct. 1994. [9] O’Carroll, L., et al., “A study of auto- and cross-ambiguity surface performance for discretely coded waveforms,” IEE Proc. F Radar and Signal Processing, Vol. 137, No. 5, pp. 362—370, Oct. 1990. [10] Lemieux, J. A., “Analysis of an optimum hybrid radar waveform using frequency hopping and locally optimum signals,” Proc. of the IEEE National Radar Conference, pp. 98—102, March 12—13, 1991. [11] Donohoe, J. P., and Ingels, F. M., “The ambiguity properties of FSK/PSK signals,” Record of the IEEE 1990 International Radar Conference, 1990, pp. 268—273 May 7—10, 1990. [12] Skinner, B. J., Donohoe, J. P., and Ingels, F. M., “Simplified performance estimation of FSK/PSK hybrid signaling radar systems,” Proc. of the IEEE 1993 National Aerospace and Electronics Conference, NAECON, Vol. 1, pp. 255—261, May 24—28, 1993. [13] Skinner, B. J., Donohoe, J. P., and Ingels, F. M., “Matched FSK/PSK radar,” Record of the 1994 IEEE National Radar Conference, pp. 251—255, March 29—31, 1994. [14] Marsaglia, G., “Random variables and computers,” Proc. of the Third Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, Liblice, pp. 499—512, June 5—13, 1962. [15] Guosui, L., Hong, G., and Weimin, S., “Development of random signal radars,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 35, No. 3, pp. 770— 777, July 1999.

206

Detecting and Classifying LPI Radar

[16] Garmatuk, D. S., and Narayanan, R. M., “ECCM capabilities of an ultrawideband bandlimited random noise imaging radar,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 38, No. 4, pp. 1243—1255, Oct. 2002.

Problems 1. An FSK CW radar is required to perform ranging up to a maximum of 15 nmi. What is the required frequency diﬀerence ∆f ? 2. Derive the Costas frequency sequence given in Figure 6.1. Hint: Start by choosing the correct prime modulus p and writing down the two primitive roots. 3. The frequency hopping sequence {3, 9, 10, 13, 5, 15, 11, 16, 14, 8, 7, 4, 12, 2, 6, 1} is being considered for a new LPI radar. (a) Show that this is a Costas sequence. (b) If so, how many primitive roots are there? (c) Derive the sequence by determining p and the primitive roots. 4. Consider the Welch construction of a Costas frequency hopping sequence with p = 13. (a) How many frequencies are contained in the frequency hopping sequence? (b) Write the elements of the reduced residue system. (c) How many primitive roots are there in the system? Do not forget to show your work. (d) What are the primitive roots of the system? (e) Write out the Costas sequence for each primitive root. (f) For the sequence resulting from the largest primitive root, show that the sequence is Costas by forming the diﬀerence triangle. (g) Draw a contour grid of the periodic ambiguity function for the sequence in (f) making sure that you label the side lobe levels and main peak amplitude. 5. (a) Edit the costas.m file to include the Costas sequence given in (6.16). (b) Compute the power spectrum magnitude and PAF of this sequence. 6. Using the fsk psk costas.m file, generate the power spectrum, ACF, PACF, and PAF for the first Costas sequence with (a) NB = 5 and (b) NB = 13. What is the diﬀerence in the side lobe level you observe?

Chapter 7

Noise Techniques In this chapter the principles of random noise radar are presented. A discussion of each noise technology is then described in detail including a comparative discussion of the advantages and the disadvantages of each. The major focus is on the radar system’s transmitted waveform. Mathematical models of each transmitter have been developed in MATLAB and are included on the CD within the Part I, LPIT Toolbox folder. The autocorrelation function (ACF), the periodic autocorrelation (PACF) and the periodic ambiguity function (PAF) for each transmitted waveform are examined in order to compare their Doppler side lobe and time side lobe characteristics. The four types of noise technology radar systems discussed include: random noise radar, random noise plus FMCW, random noise FMCW plus sine, and random binary phase modulation.

7.1

Historical Perspective

The concept of random noise radar (RNR) is not new but was considered as early as the 1950s as a way to eliminate all the range-Doppler ambiguities in the radar (i.e., thumbtack ambiguity function). RNR systems transmit a random or random-like low power microwave noise waveform that may (or may not be) modulated by a lower frequency waveform. The peak value of a cross-correlation process (delayed copy of the transmitted signal corresponds with the echoes of the target) can be used to determine the distance to the target. The earliest reported investigations of noise technology used as a range measurement system are given by Horton [1] and Craig [2] in the Institute of Radio Electronics. A short time later Grant et al. [3], Cooper et al. [4], and McGillem [5] at Purdue University put forth a theoretical analysis and some prototypes were built. Further experimental results of a complete noise radar 207

208

Detecting and Classifying LPI Radar

system were obtained in [6] showing that it was possible to detect a target in very poor SNR conditions even with nonoptimum hardware. The research however, was quickly dropped since the development of noise waveform sources with the required bandwidth was diﬃcult. Also since crosscorrelation processing of the transmitted and received signal was necessary the use of variable microwave delay lines was required [7]. Before the 1960s, the manufacturing of these devices was complicated. From the 1960s to the 1970s, the research into RNR ramped up quickly and several experimental systems were built and tested. A good overview of the diﬀerent techniques is given in [8] and an extensive bibliography of the early development in RNR is given in [9]. With the development of solid-state microwave techniques and high-speed integrated VLSI circuits the technology began to support the RNR concepts and implement the required processing. Today the RNR waveform can be generated digitally followed by a digital-to-analog converter and up-conversion onto a carrier signal. They are also relatively inexpensive to build and many diﬀerent variants on the RNR are possible including the use of UWB waveforms. Noise technology radar can be used to detect targets in both range and Doppler. RNR emitters have good electronic protection properties by possessing a natural immunity to jamming and interference from other radar systems operating in the same theater of operations [10, 11]. The use of a RNR provides the advantage that it is uncorrelated with the intentional and unintentional interference as well as other noise sources. That is, the correlation process used in the receiver allows it to sort out the incoming signals even within the same band making it attractive in multi radar environments [10]. These advantages are due to the properties of the RNR featureless waveform. These include transmitting the lowest obtainable instantaneous power spectral density possible by spreading its energy over a wide signal bandwidth and the use of non-redundant waveforms that appear random and are concealed in the ambient thermal noise and interference environment [12]. The exception is the use of deception. Deception is a repeater technique (constant gain) in which false targets are created in the radar receiver that are interpreted as valid targets. The jam-to-signal ratio is independent of the range between the repeater jammer and the radar. Post detection integration of target signal returns can normally provide a significant decrease in jam-tosignal ratio however, for deception techniques, the integration gain is equal for valid and false targets. RNR systems that use random noise also have a significant processing gain unavailable to the noncooperative intercept receiver since their low mean power and noise-like characteristics result in a very low SNR. Even if the signal is detected, it is unlikely to be identified making these types of emitters important for many LPI and LPID applications. RNR systems and waveforms are becoming useful in certain (limited) ap-

Noise Techniques

209

plications such as acoustic radar—usually called sodar (sound detection and ranging) [13]. Also of growing importance are the high-resolution measurement of range profiles for foliage- and ground-penetrating detection of buried objects such as mines [14—17], inverse synthetic aperture radar (ISAR) and synthetic aperture (SAR) imaging [18, 19]. Covert tracking of targets using RNR monopulse techniques are discussed in [20—22]. Car collision warning and avoidance systems and UAV landing systems are also being investigated [7]. The detection of small-RCS targets in surface clutter depends on the signal-to-clutter ratio (SCR) in the target range resolution cell and the ability to resolve the target signal in Doppler. The SCR (in the absence of range ambiguity) is the ratio of target RCS to clutter RCS, and for diﬀerent waveforms the clutter RCS depends on the signal bandwidth and the possible presence of range side lobes. Surface clutter (especially at low grazing angles) is notably spiky, with peaks having dimensions on the order of 1m, so a range resolution cell smaller than the target length is of limited value in target detection. There are many waveform options that can be matched to the radial dimension of a small-RCS target, or to the dimension of dominant scatterers within the target and noise waveforms have no unique advantage in this respect. For the noise waveforms, the range cells are formed by stepwise delay of the transmitted reference signal however, the use of a nonperiodic waveform suppresses the range ambiguity. The Doppler cells are created by step-wise varying the time compression of the reference signal at the correlation operation. The Doppler resolution depends on the coherent processing interval and is limited by the same factors for all waveform types and therefore noise waveforms do not have any particular advantage here as well. Due to the randomness of the waveform, a noise floor is present in the correlation integral that limits the possible side lobe suppression. In strong clutter, the integrated side lobe contribution can be very large and clutter cancelation methods are required. Recently, there has been much interest in multiple-input multiple-output (MIMO) radar systems. MIMO techniques have been well studied in communications oﬀering advantages where multipath environments can cause fading. Radar waveform rejection of multipath requires that the range resolution cell be smaller than the range diﬀerence δ between the direct and multipath echoes (even if range side lobes are absent). The range diﬀerence between the direct path and the multipath echoes can be expressed as δ≈

2hr ht R

where hr and ht are the radar and target altitudes and R is the range. For a low-grazing-angle target not resolvable by the antenna beamwidth, the range diﬀerence can be quite small. Even if the waveform bandwidth were increased to make the resolution smaller than this range diﬀerence, the scatterers in

210

Detecting and Classifying LPI Radar

the initial range cell of the target would have to be large enough to provide a signal for tracking, before the multipath catches up with the direct signal and generates a tracking error. Whether a noise waveform or other type of waveform is used, resolution of this sort has not provided significant tracking advantages in any known system. The majority of MIMO radar configurations have focused on multistatic arrays that have suﬃcient spatial separation to decorrelate the target’s radar cross section scintillation. These networks combine the received data noncoherently to average out the scintillations. Another form of MIMO radar uses multiple orthogonally coded waveforms from individual transmitter elements of a phased array which are then combined coherently upon receive to form multiple beams [23]. Recently, the extension of noise radar to MIMO configurations has been explored. Two transmission techniques are described and include an element-space and beam-space approach [24]. In the elementspace approach, K channels of independent (noncoherent) noise are transmitted separately by K omnidirectional antennas. In the beam-space approach, each independent noise source is fed into each antenna but is either delayed or phase shifted so as to form a beam illuminating a selected sector of the radar system’s field of view-eﬀectively coding each sector according to a particular noise source. The direction of each noise sector is determined by the phase shifts and the sector width is determined by the beamwidth of the array.

7.2

Ultrawideband Considerations

The combination of RNR and ultrawideband (UWB) technology can give significant benefits and overcome inherent drawbacks of narrowband radar. A few definitions concerning UWB waveforms are given below. Consider for example a wideband RNR signal with bandwidth spanning fmin to fmax . The first definition is for the absolute bandwidth B, Definition 7.1 The absolute bandwidth B defines the width of the frequency interval occupied by the signal’s spectrum and is the diﬀerence between the maximum frequency and the minimum frequency or B = fmax − fmin

(7.1)

The term ultrawideband (UWB) refers to waveforms that have an instantaneous fractional bandwidth greater than 0.25 (25%) with respect to the center frequency.

Noise Techniques

211

Definition 7.2 The instantaneous fractional bandwidth ∆f is defined as the ratio of the absolute bandwidth (fmax − fmin ) to the mean frequency (fmin + fmax )/2. Thus the fractional bandwidth is defined as [25] } ] 2(fmax − fmin ) 100% ∆f = (7.2) 100% = fmin + fmax 0.5 + fmin /B The maximum fractional bandwidth is 200% and is reached if fmin = 0. Note that this value is not fmax dependent. A small fractional bandwidth ∆f indicates that the behavior of the radar system devices being used are not likely to change much within the absolute bandwidth B. With a large ∆f , the device behavior may show changes throughout B because the device characteristics may be diﬀerent across the large number of transmit frequencies. That is, it is more diﬃcult to build devices which cover a large bandwidth with the same eﬃciency or properties. Another important term used to evaluate UWB RNR signal bandwidth when the waveform is produced by random binary phase shifts is the spreading ratio (or processing gain) [26]. Definition 7.3 The spreading ratio or processing gain of a random binary phase shift keying signal is defined as P GR =

T = Nc tb

(7.3)

where T is the code period, tb is the subcode period and Nc is the number of subcodes within a period. The motivation to use UWB random noise emitters comes from the need to have fine range resolution and range measurement accuracy. In contrast to conventional narrowband systems, the UWB radar obtains much more information about the material properties and the structure of scanned targets. In the case of high SNR and precise calibration, range accuracy may even approach millimeter wave (mm) and submillimeter levels. It also has an enhanced clutter suppression capability which could someday lead to a solution for the diﬃcult task of detecting a sea-skimming antiship capable missile. Foliage-, wall- and ground- penetrating detection and imaging also benefit. For through-the-wall UWB radar, 1.99 GHz—10.6 GHz are allowed in

212

Detecting and Classifying LPI Radar

the United States (FCC) and 30 MHz—18 GHz frequency range is envisioned for wall and ground penetrating radar in Europe [25]. An important aspect of the UWB radar in addition to its LPI and LPID characteristics are its immunity from electromagnetic radiation eﬀects which enable frequency spectrum sharing and a significant immunity from deceptive jamming. Note that noise jamming has the same eﬀect on radar systems that use noise waveforms as it does on systems that use of any other type of waveforms of similar bandwidth. On the other hand, there are worries in the community about the influence of the UWB RNR on small signal receiver devices such as GPS, cell phone and wireless LAN communications [27]. Another major problem in the radar application of UWB noise waveforms is that they exhibit the “thumbtack” ambiguity function and require the use of a correlator that covers many range-Doppler cells to detect targets whose range and velocity are unknown. The techniques examined in this chapter describe systems in which the correlator covers a single cell, requiring two-dimensional sequential search to detect targets with unknown position. Although useful for some geophysical applications, the technology is currently inadequate for most military radar applications. Detection of buried mines and tracking a target after it has been detected by other conventional waveforms are examples of current military applications. The processing throughput for parallel coverage of large regions in range-velocity space is a major problem that must still be addressed.

7.3

Principles of Random Noise Radars

The ability to simultaneously measure range and Doppler is important for target detection and imaging and requires that the radar be phase coherent [28]. This simultaneous measurement would be especially advantageous if it were implemented in a real-time range-Doppler processor covering a useful field in both coordinates. Today no noise radars have this capability, and this absence currently constitutes a major disadvantage being addressed. Although RNR is by definition, totally incoherent, it is possible to inject phase coherence into the radar using the technique of heterodyne correlation. Figure 7.1 shows the main components of a RNR system. A microwave CW noise signal S(t) is transmitted, and the return signal from the target’s reflectivity, delayed by td , is received and coherently detected. A copy of the transmitted noise, delayed by Tr (RF delay line), is used as a reference signal that is cross-correlated with the received signal. The amount of delay of the reference signal is a measure of the target’s distance. The down range performance of a random noise radar depends mainly on the cross-correlation function in the radar receiver. When Tr is varied, a strong correlation peak is obtained for Tr = td , which gives an estimate of the target’s range as R = ctd /2. Doppler processing can also be performed and the output of the

Noise Techniques

213

Figure 7.1: Main components of a noise radar using a delay line. (After [28].) Doppler filters following the correlator can be used to calculate the velocity of the target. Consider the detection of a point target. Following the development by Axelsson, the transmitted noise signal can be modeled as a stationary process in complex form as [29, 30] S(t) = [X(t) + jY (t)] exp(j2πfc t)

(7.4)

where 2πfc is the frequency of the carrier and X(t) and Y (t) are stationary Gaussian processes with zero means and bandwidth B. For moving targets, the received signal is compressed or expanded in time as a result of the relative velocity between the point target and the noise radar. For a point target positioned at R with a relative velocity v, the received signal is S(αt − td ), c. where as before td = 2R/c. Also α = (c − v)/(c + v) ≈ 1 − 2v/c when v Cross-correlation of S(αt − td ) with the reference signal S(αr t − Tr ), which is delayed by Tr and time compressed by αr = 1 − 2vr /c, becomes proportional to [29] 8 Tint w(t)S(αt − td )S ∗ (αr t − Tr )dt (7.5) C(td , α; Tr , αr ) = 0

where Tint is the measurement time and a window function w(t) is included in the correlation integral to improve the Doppler side lobe suppression. After

214

Detecting and Classifying LPI Radar

insertion of (7.4) into (7.5) C(td , α; Tr , αr ) =

8

Tint

w(t) [X(αt − td ) + jY (αt − td )]

0

(7.6)

· [X(αr t − Tr ) − jY (αr t − Tr )] · exp [−jωc (td − Tr ) + j(α − αr )ωc t] dt The correlation output is close to its mean value when the time-bandwidth product BTint is large. The average of (7.6) is found with ∆α = α − αr and ∆T = td − Tr 8 Tint Rc (∆T, ∆α) = 2 exp(−jωc ∆T ) w(t) [RX (∆αt − ∆T ) (7.7) 0

−jRXY (∆αt − ∆T )] exp [j∆αωc t] dt

where RX (·) and RXY (·) are the autocorrelation and cross-correlation functions of X(t) and Y (t). For a symmetric noise power spectrum about the carrier frequency, the cross-correlation term can be neglected and Rc (∆T, ∆α) = 2 exp(−jωc ∆T )

8

0

Tint

w(t)RX (∆αt − ∆T ) exp [j∆αωc t] dt

(7.8) The parameters Tr and αr are varied until the maximum is found, represented by αr0 and Tr0 , from which range and velocity are estimated: R = cTr0 /2 fc ), the phase and v = c(1 − αr0 )/2. For narrowband noise processes (B term of (7.7) and (7.8) generates the dominant decorrelation. Hence, ∆αωc t should be kept small over the integration time to avoid a degradation of the correlation peak [30]. As in previous LPI waveforms, the range resolution depends upon the bandwidth B. There is a limiting relationship between the range resolution ∆R = c/(2B), the relative velocity of the target, v, and the available correlation time Tint . Note that this is similar to the FMCW range-Doppler cross coupling eﬀect discussed in Chapter 4. The time taken for the target to pass through a range resolution cell Tp = ∆R/v should be greater than the measurement time Tint , giving the limitation ∆R/v = c/(2Bv) > Tint . If the number of statistically independent samples is represented by N = 2BTint , an upper limit can be derived as [29] N = 2BTint < c/v

(7.9)

As an example, for v < 300 m/s, N < 106 is required. Longer sequences can be applied if the delay of the reference signal is made variable and is adapted to the predicted target velocity. From (7.7) and (7.8), the correlation peak degrades as a result of the ∆αt term in RX (∆αt − ∆T ) if ∆αTint =

Noise Techniques

215

2|∆v|Tint /c exceeds the correlation time (1/B) of the noise process. This gives the requirement 2BTint < c/|∆v|, which is equivalent to (7.9). The RNR system shown in Figure 7.1 uses a noise source working at a microwave frequency. Equally eﬀective is the use of a baseband noise source followed by the upconversion to a carrier frequency. A digital implementation could also generate the noise signal and provides the flexibility to include other noise waveforms. For example, the use of tailored or colored noise waveforms can be used and have been shown to enhance target detectability [31]. The receiver can also include a homodyne or heterodyne detection of the in-phase and quadrature components of the received signal and an I/Q demodulator used to generate the correlation response. As in a typical CW LPI radar, leakage or lack of isolation between transmit and receive antennas can degrade the receiver sensitivity and can aﬀect long range target detection performance. One approach to eliminate the leakage is the reflected power canceler (discussed earlier in Chapter 4). In a bistatic configuration, the noise radar can also use external transmitters where the correlation is between the direct wave from one antenna and the target reflection from another antenna. Another approach that can eliminate the CW leakage between the transmitter and receiver entirely is to use an interrupted CW waveform (long noise pulses). This technique improves the isolation by using a transmit/receive (T/R) switch to switch the antenna between transmitter and receiver several times per transmitted noise waveform. Typically, T/R switches can receive more than 60 dB of isolation between transmitter and receiver. The system is no longer a true continuous wave noise radar but under certain conditions the essential properties of noise radars are preserved.

7.4

Narayanan Random Noise Radar Design

A well published hardware example of a UWB random noise radar is the system first introduced by Narayanan et al. [32]. Figure 7.2 shows the block diagram of the system configuration. An UWB Gaussian noise waveform is transmitted and target detection is accomplished by employing a heterodyne correlation receiver which cross-correlates the received signal with a timedelayed and frequency shifted replica of the transmit signal. The transmitter uses a microwave noise diode OSC1 that is band-limited using a bandpass filter BPF and amplified using a broadband power amplifier AMP1. The transmitted signal has a Gaussian amplitude distribution and an average power output of 0 dBm (1 mW) in the 1—2 GHz frequency range. The power is divided by PD1 that splits the transmitted waveform into two equal in-phase components (the transmitted waveform and the reference signal). The reference signal is connected to a fiber optic fixed delay line DL1

216

Detecting and Classifying LPI Radar

that is used to set the minimum range to the target [33].1 For example, in a ground-penetrating system this minimum delay ensures that the correlation operation is performed only at depths below the air-soil interface [14]. A programmable delay line DL2 is also used to step through the entire range of available delays so that various probing depths can be obtained. The delay line output is mixed with a 160 MHz phase locked oscillator OSC2 in a lower sideband up converter MXR1. The upconverter output (0.84—1.84 GHz) feeds the mixer MXR2 that receives the 1—2 GHz return signal. The mixer MXR2 output is the 160 MHz correlation output (correlation coeﬃcient) and is filtered in a 160 MHz BPF of 5 MHz and then fed to the I and Q detector which is also fed by the 160 MHz oscillator OSC2 [34]. The output of the I and Q detector is then sampled, integrated and the envelope of the signal is extracted. Worthy of mention in Figure 7.2 are a few points on the Doppler resolution. The Doppler return from the slow-moving target will show up at roughly 50 Hz about the carrier frequency, when using fc = 1.5 GHz. Seeking to isolate and keep this Doppler information, the model uses a low-pass filter at 100 MHz. This filtering also rejects the undesirable harmonics of the 160 MHz LO frequency. Although not shown the system also houses a second receive chain that may be used for fully polarimetric measurements or spaced receiver interferometry [32]. A polarimetric noise radar system measures the complex scattering matrix of a target [S] given by ] } SV V SV H (7.10) [S] = SHV SHH where Sij represents the target scattering coeﬃcient for transmit and receive polarizations i and j respectively. Subscripts V and H stand for vertical and horizontal respectively. Reciprocity implies that SV H = SHV . The measured scattering coeﬃcients of obscured targets are multiplied by the product TA TB where Tk is the one-way complex transmission coeﬃcient through the medium for the polarization k. The transmit polarization alternately switches between V and H while the receiver processes both polarizations simultaneously [17]. Simulation and field test results have been shown to demonstrate the potential of combining a UWB waveform with coherent processing for high-resolution subsurface imaging.

7.4.1

Operating Characteristics

The system shown in Figure 7.2 can achieve a significant probability of detection Pd with arbitrarily small probability of false alarm Pf a . Taking the real 1 Erbium-doped fiber amplifiers can also been used as an ultrawideband microwave noise source. Based on their amplified spontaneous emission characteristics, the low coherence output light can have an absolute bandwidth approaching B = 1,200 GHz [33].

Noise Techniques

217

Figure 7.2: Block diagram of a random noise radar (from [34]). part of (7.4), the transmitted Gaussian noise signal centered at 2πfc , with a bandwidth B (bandpass process) can be expressed as St (t) = Re{S(t)} = X(t) cos(2πfc t) − Y (t) sin(2πfc t)

(7.11)

where

B 2 The received signal back at the radar can be expressed as [35] 2πfc >

Sr (t) = X (t) cos{ωc [(1 + α)t − td ]} − Y (t) sin{ωc [(1 + α)t − td ]}

(7.12)

(7.13)

where X (t) and Y (t) are given by X (t) = AX[(1 + α)t − td ]

(7.14)

Y (t) = AY [(1 + α)t − td ]

(7.15)

and where A2 is the power reflection coeﬃcient that is related to the target’s range, radar antenna gain, and target geometry. The delayed reference signal

218

Detecting and Classifying LPI Radar

Sd (t) at the output of the up converter MXR1 can be written as ] } X(t − Tr ) cos{(ωc − ωIF )t − ωc Tr } Sd (t) = 2 } ] Y (t − Tr ) − sin{(ωc − ωIF )t − ωc Tr } 2

(7.16)

where ωIF is the intermediate frequency (IF) and Tr is the delay provided by the delay line. The cross-correlator MXR2 extracts the normalized complex correlation coeﬃcient ρejφ between the input signals Sr (t) and Sd (t) as $T Sr (t)Sd (t)dt 0 ρejφ = lim (7.17) =1/2 $T T −∞ $ T 2 2 |Sr (t)| dt 0 |Sd (t)| dt 0

or

ρejφ = lim

T −∞

$T 0

Xr (t)Xd (t)dt σ1 σ2

(7.18)

where σ1 is the total received power (signal + noise) and σ2 is the total power in the delayed replica. In practice, T cannot go to infinity and one has to use the short-time correlation function over a finite time Tint . The maximum value of the correlation coeﬃcient occurs when the received and delayed reference signal are completely correlated. The data acquisition, storage and analysis performs an integration of the I and Q channels and then a square law detector i1/2 D (7.19) Z = I 2 + Q2

is used to compute the response. Expressions for the characteristic function and joint PDF for the integrator output and the PDF and CDF for the detector output are given in [35]. For the sum of a large number of uncorrelated and independent samples N with no target present, the envelope of the detector output is approximately Rayleigh-distributed W w 8Z −4Z 2 (7.20) exp PN (Z) ≈ N (σ1 σ2 )2 N (σ1 σ2 )2 The probability of false alarm Pf a for a threshold Th can then be found by integration of (7.19) W w −4Th2 (7.21) Pf a ≈ exp N (σ1 σ2 )2

For large N , the threshold Th is related to the Pf a by Th ≈

σ1 σ2 [−N ln Pf a ]1/2 2

(7.22)

Noise Techniques

219

No closed form expressions are available for the probability of detection Pd and numerical results for the Pf a vs. Pd are shown in [35] for N = 1, 25, 50 and 100. This maximum value of the correlation coeﬃcient is related to the input signal to noise ratio SNRi as ρmax ≈

}

SNRi 1 + SNRi

]1/2

(7.23)

2 2 2 and SNRi = σsr /σn1 where σsr = A2 σs2 is the power in the received signal; σs2 is the transmitted signal power and A2 is the power reflection coeﬃcient that is related to the antenna gain, target’s range and geometry. The term 2 is the receiver noise power. σn1 Depending on the interference that corrupts the return signal, the correlation coeﬃcient can have a value anywhere from 0 to 1.

7.4.2

Model of RNR Transmitter

The RNR transmitter uses a random white Gaussian microwave noise source that is band-limited and amplified. To evaluate the characteristics of the transmitted waveform, Figure 7.3 shows a block diagram of the transmitter configuration used in this chapter to evaluate the PACF and PAF characteristics [36]. The transmitter is modeled in MATLAB and is part of the LPIT (contained on the CD). With inputs consisting of the carrier frequency fc , bandwidth B, amplitude A, and noise power level, the model produces the in-phase and quadrature components of the waveform as it would appear at the output of a noncooperative intercept receiver with an ADC sampling at 3 GS/s. Figure 7.4 illustrates the wideband white Gaussian noise magnitude that is generated prior to bandlimiting. A key performance element is the transmitted noise bandwidth. For good range resolution, clutter discrimination, and LPI characteristics, the noise signal needs to spread the energy over a large modulation bandwidth. Without loss of generality, our example models the transmitted noise to have an absolute bandwidth of B = 300 MHz (200 MHz ≤ B ≤ 500 MHz) giving a range resolution of 0.5 m. Figure 7.5 shows the white Gaussian noise after bandlimiting. The carrier frequency is fc = 350 MHz. Note from (7.2) that this model demonstrates a UWB waveform with a fractional bandwidth of ∆f = 85%.

7.4.3

Periodic Ambiguity Results

To examine the periodic ambiguity side lobe characteristics, Figure 7.6 shows the ACF and the PACF for the CW noise signal shown in Figure 7.5. The number of transmitted code periods used in the correlation receiver is N = 1. The delay oﬀset axis is normalized by the subcode period tb which in this case

220

Detecting and Classifying LPI Radar

Figure 7.3: Random noise radar transmitter model (from [36]).

Figure 7.4: Wideband microwave noise signal.

Noise Techniques

221

Figure 7.5: Band-limited microwave CW noise signal.

Figure 7.6: Random noise CW radar autocorrelation function and periodic autocorrelation function with N = 1.

222

Detecting and Classifying LPI Radar

Figure 7.7: Random noise CW radar periodic ambiguity function with N = 1. With an integration period of is the sampling period (1/fs ). Tint = 2 μs, the PACF mainlobe repeats every 6,000 samples. With N = 1 copies of the reference in the correlation receiver the peak side lobe level revealed after close examination of the ACF and PACF is −3 dB at 3 normalized delay oﬀsets. The side lobe level however drops oﬀ quickly to −15 dB at 8 oﬀsets. Figure 7.7 shows the PAF for the transmitted waveform. The zero Doppler cut of the PAF is the PACF and the mainlobe repeats at every integer multiple of the code length (6,000 samples). Note the relatively large Doppler spread and high Doppler side lobes in the PAF at each code period. Dawood et al. [28] examine expressions for the generalized ambiguity function and show that the UWB RNR waveforms are not suitable for unambiguous range rate estimation due to this extended Doppler-spread parameter (product of transmit bandwidth and range rate) unless the cross-correlator is matched in the delay rate.

7.5

Random Noise Plus FMCW Radar

The random noise plus FMCW radar (RNFR) was first introduced by Liu et al. in 1984 [37]. In the RNFR, a white Gaussian noise source is linearly frequency modulated by an FMCW waveform. Figure 7.8 shows the radar

Noise Techniques

223

Figure 7.8: Block diagram of random noise plus FMCW radar system (from [38]). system and illustrates both the transmit and the receive functions. A portion of the transmitted signal is used as a local oscillator input to the receiver’s front-end mixer where the correlation between target echo and transmitted signal takes place [38]. The mixer output is a beat frequency that represents the target’s range. The output spectrum of the mixer is a single Doppler frequency for a zero-range target and becomes gradually larger with the target range increasing. Following the mixer is an amplifier and two bandpass filters [9]. Optimized filters pass either the target’s Doppler signal with some noncorrelation signal or strictly the noncorrelation signal. The power detectors detect the signal envelope and a diﬀerence amplifier selects the correct channel to determine the target’s range from the measured power diﬀerence output. The emitter design has good electronic protection capability and also good resolution for precise, simultaneous distance and velocity measurements [7—9]. Its low mean power and noise-like characteristics result in a very low SNR in the intercept receiver that does not have access to the noise waveform to compress the signal. The RNFR has good distance measurement capability but the CW leakage makes it diﬃcult to measure target speed and detect long range targets [9].

7.5.1

RNFR Spectrum

The RNFR transmitter uses a white Gaussian noise source that is linearly frequency modulated by a triangular FMCW waveform. The transmitted noise plus FMCW signal is e(t) = E cos[ωc t + θ(t)]

(7.24)

224

Detecting and Classifying LPI Radar

where θ(t) =

8

t

Df ξ(t1 )dt1

(7.25)

0

and E is the amplitude and Df is the angular frequency per volt of the FMCW and ξ(t1 ) is the noise voltage of a stationary process with zero mean. Following the development given in [38], the power spectrum of e(t) is ] } 1 (ω − ωc )2 2 (7.26) We (f ) = E √ exp − 2∆F 2 2π∆F where ∆F is the angular frequency deviation of the transmitted noise signal. The echo of the moving target is eR (t) = ER cos[(ωc + ωd )(t − td ) + θ(t − td )]

(7.27)

where ER is the amplitude of the echo, td is the delay between the echo and the transmitted signal and fd = ωd /2π is the Doppler frequency. At the mixer output (7.28) V (t) = A cos[ωd (t − td ) − ωc td + θ(t − td ) − θ(t)] The correlation function at the mixer output is then given approximately by [38] } 2 ] σ1 (td )t2 A2 Rv (t) = exp − cos(ωd t) (7.29) 2 2 and σ12 (td ) = K 2 t2d and assumes that K is a normalizing constant, and σ 2 (td ) = σ12 (td )/4π2 . The Fourier transform of Rv (t) is ] } 1 f2 (7.30) SR1 (f ) = √ exp − 2 2σ (td ) 2πσ(td ) Assuming that σ(td ) >> fd Sv (f ) =

A2 A2 A2 SR1 (f − fd ) + SR1 (f + fd ) = SR1 (f ) 4 4 2

and the spectrum after correlation by the mixer is approximately ] } A2 f2 1 √ exp − 2 Sv (f ) = 2 2πσ(td ) 2σ (td ) for f > 0. Note the spectrum behavior as a function of td .

(7.31)

(7.32)

Noise Techniques

225

Figure 7.9: Model of random noise plus FMCW transmitter (from [36]).

7.5.2

Model of RNFR Transmitter

A block diagram of the RNFR transmitter is shown in Figure 7.9 [36]. A MATLAB model of the RNFR is also contained in the LPIToolbox. Indicated on the diagram in parentheses are the places where intermediate results of the model are shown below. A wideband microwave noise generator first produces a signal that is band-limited to 300 MHz (200 ≤ f ≤ 500 MHz) centered at fc = 350 MHz. After bandlimiting, the noise signal modulates a triangular FMCW signal with a modulation bandwidth ∆F = 300 MHz and modulation period tm = 1μs. The magnitude of the FMCW signal in Figure 7.9 (1) with ∆F = 300 MHz, and fc = 350 MHz are shown in Figure 7.10. The resultant signal is then high-pass-filtered to remove the lower sideband modulation leaving the transmitted signal with B = 600 MHz. The final noise modulated FMCW signal with ∆F = 300 MHz, and fc = 350 MHz is shown in Figure 7.11. In Figure 7.12 the magnitude of the noise FMCW high-pass filter output signal in Figure 7.9 (3) is shown (transmitted waveform) with ∆F = 300 MHz and fc = 350 MHz.

7.5.3

Periodic Ambiguity Results

Using the same signal duration as in Section 7.4, the ACF and the PACF of the RNFR waveform are shown in Figure 7.13. For the RNFR waveform the peak side lobes occur at approximately −21 dB down from the main lobe showing the advantages of the FMCW modulation over a strictly random noise modulation. To examine the side lobe performance in the delay-Doppler

226

Detecting and Classifying LPI Radar

Figure 7.10: Magnitude of the FMCW signal shown in Figure 7.9 (1) with ∆F = 300 MHz, and fc = 350 MHz.

Figure 7.11: Magnitude of the noise modulated FMCW signal in Figure 7.9 (2) with ∆F = 300 MHz, and fc = 350 MHz.

Noise Techniques

227

Figure 7.12: Magnitude of the noise FMCW high-pass filter output signal in Figure 7.9 (3) with ∆F = 300 MHz, and fc = 350 MHz. oﬀset domain the PAF is then calculated and is shown in Figure 7.14. The PAF main lobe repeats every code period or 6,000 samples. Note that the zero delay Doppler side lobes are also less compared to the RNR results. As a final note for comparison, closed form expressions for the average ambiguity function for the RNFR waveform are given in [38].

7.6

Random Noise FMCW Plus Sine

The random noise FMCW plus sine radar (RNFSR) uses an additional sine signal at a frequency of fm that modulates the noise source [8]. The composite signal is then modulated by the FMCW waveform. The additional sine signal that is added helps minimize the leakage from the transmitter to the receiver as explained below. A block diagram of the RNFSR is shown in Figure 7.15. The receiver is similar to the RNFR receiver with the received signal correlated to a time-delayed version of the emitted waveform using a mixer. The mixer output contains the noise and all the sinusoidal harmonics. The amplifier is a wideband automatic gain control circuit with a large dynamic range [7]. To account for the injected sine wave, the receiver uses two bandpass filters to expand the receiver’s frequency range for the Doppler plus noncorrelation signal and for the noncorrelation signal only. The transmitted

228

Detecting and Classifying LPI Radar

Figure 7.13: Random noise plus FMCW autocorrelation function and periodic autocorrelation function.

Figure 7.14: Random noise plus FMCW periodic ambiguity function.

Noise Techniques

229

signal for the RNFSR is [38] ec (t) = E cos[ωc t + θ1 (t) + θ2 (t)] where θ1 (t) =

8

(7.33)

t

∆F cos(ωm t1 )dt1 = D1 sin(ωm t)

(7.34)

0

with

D1 = and θ2 (t) =

8

∆F ωm

(7.35)

t

Df V (t2 )dt2

(7.36)

0

where the variable Df is the angular frequency per volt and V (t2 ) is the modulated noise voltage of a normal stationary process with zero mean and ωm is the additional tone frequency. As expected, the derivation of the mixer output spectrum for the RNFSR is considerably more complicated and the reader is referred to [7]. The major diﬀerence between the RNFR and the RNFSR are the filters shown in Figure 7.15. The filters have bandwidths expanded to include multiples of the added sine signal within the return signal. The bandwidth of the first bandpass filter is selected to be B1 = nfm + fdmin and the bandwidth of the second bandpass filter is selected to be B2 = nfm + fdmax where n represents the nth harmonic of the added sine waveform that is picked up by the radar. This technique takes advantage of the harmonic characteristics of the sinusoidal signal to eliminate the CW leakage at and close to zero range [7—9]. This zero range hole characteristic does not let the radar respond to close-in targets and only produces an output detection when a target is present between the two chosen ranges determined by the filter bandwidths. Even with the addition of the sinusoidal modulation, the RNFSR cannot measure the speed of a moving target or detect a long-range target (similar to the RNFR). The RNFSR is suitable for short-range LPI applications such as harbor control, missile fuse systems and UAV landing systems.

7.6.1

Model of RNFSR Transmitter

The RNFSR noise technology employs an additional tone signal that is modulated by the white Gaussian noise, which further modulates the FMCW waveform. Figure 7.16 shows a block diagram of the transmitter model used in this chapter [36]. A microwave noise generator produces a white Gaussian noise waveform. After this, the signal is band-limited to 300 MHz, centered on fc = 350 MHz. After band-limiting, the noise signal is added (added in frequency, multiplied in time) to a single tone with a frequency of fm = 350 MHz. The upper band is centered at 700 MHz (from the modulation

230

Detecting and Classifying LPI Radar

Figure 7.15: Random noise FMCW plus sine radar block diagram (from [9]). product) and this new signal modulates an FMCW signal with a modulation bandwidth of ∆F = 300 MHz. After noise modulation, the resultant signal is low-pass-filtered to remove the upper sideband modulation products. Finally, the 600-MHz bandwidth signal with center frequency of 350 MHz is amplified before transmission. To examine the model development, Figure 7.17 shows the noise source with the added tone modulation fm = 350 MHz. Note the frequency shift of the waveform to a center frequency of 700 MHz. Figure 7.18 shows the magnitude spectrum of the FMCW signal that is used to modulate the noise with the added tone. The signal has a modulation bandwidth of ∆F = 300 MHz. In Figure 7.19, the modulation of the sine plus noise by the FMCW signal is shown. Shown are the resulting upper and lower sideband products. The upper sideband is not needed and eliminated. Figure 7.20 shows the magnitude spectrum of the output waveform.

7.6.2

Periodic Ambiguity Results

For the RNFSR transmitted waveform, a sine wave is added to the noise plus FMCW modulation. To compare the side lobe performance of this waveform with the other noise modulations, the autocorrelation function and periodic autocorrelation function are shown in Figure 7.21 for a 2-μs period of the waveform. In this case the peak side lobe level is approximately −21 dB. Note that the side lobe structure is nearly the same as the RNFR waveform and the peak side lobe is not the first side lobe. The periodic ambiguity function is shown in Figure 7.22. Of interest here is the lower Doppler side lobe level and the smaller extent of the Doppler side lobes.

Noise Techniques

231

Figure 7.16: Random noise FMCW plus sine transmitter model (from [36]).

Figure 7.17: Sine plus random noise FMCW model in Figure 7.16 showing (1) the magnitude spectrum of the tone modulation of noise.

232

Detecting and Classifying LPI Radar

Figure 7.18: Sine plus random noise FMCW model in Figure 7.16 showing (2) the magnitude spectrum of FMCW signal.

Figure 7.19: Sine plus random noise FMCW model in Figure 7.16 showing (3) the magnitude spectrum of noise plus sine after modulation by the FMCW signal.

Noise Techniques

233

Figure 7.20: Sine plus random noise FMCW model in Figure 7.16 showing (4) the magnitude spectrum of output waveform after eliminating the upper sideband.

Figure 7.21: Sine plus random noise FMCW autocorrelation and periodic autocorrelation function.

234

Detecting and Classifying LPI Radar

Figure 7.22: Sine plus random noise FMCW periodic ambiguity function.

7.7

Random Binary Phase Modulation

The random binary phase code (RBPC) emitter is also a correlation CW noise radar that uses a random phase modulation of a carrier frequency to achieve LPI noise characteristics. The range resolution of a RBPC CW emitter depends on the width of the subcode as ctb 2

(7.37)

Nc ctb 2

(7.38)

∆R = and the maximum range performance is Rmax =

The Doppler tolerance depends on the length of the pulse compressor as fd max =

1 2Nc tb

(7.39)

where Nc is the number of phase codes and tb is the subcode width. Note that simultaneously extending the Doppler tolerance and the range performance is not possible since they are inverse relationships. To improve the performance of the RBPC emitter, several pulse compressors can be used in series. A block diagram of this RBPC emitter is shown in

Noise Techniques

235

Figure 7.23: Random binary phase modulation radar (from [39]). Figure 7.23 [39]. The transmitted microwave signal is phase-modulated by a random binary phase code (0 or π), which can be generated for example by Bernoulli trials. The received target echo signal is detected at zero IF, amplified and digitized by an ADC. To cross-correlate the echo signal and the delayed reference, a series of M parallel pulse compressors (transverse filters) PC1, PC2, ... PC(M) are used. The pulse compressor outputs are rearranged and range side lobe suppression techniques are used to limit the peak side lobes to PSL < −30 dB [5]. The CFAR and threshold detector then give the target range and velocity information. The maximum distance performance is dependent on the total length of the pulse compressor group as Rmax =

M Nc ctb 2

(7.40)

The maximum Doppler frequency that is measurable is set by the length of a single pulse compressor. Consequently, the RBPC radar can detect long range targets and high-speed targets simultaneously. That is, a reduction of the length Nc of the pulse compressor can easily extend the Doppler tolerance while an increase in the number of pulse compressors M in the receiver can satisfy a needed performance distance. The RBPC emitter also has good Doppler sensitivity and overcomes the limitations of target velocity measurement and long-range detection. The problem of CW leakage however, is still

236

Detecting and Classifying LPI Radar

Figure 7.24: Block diagram of a random binary phase code radar (from [36]). present.

7.7.1

Model of RBPC Transmitter

A block diagram of the RBPC transmitter is shown in Figure 7.24 [36]. For the example shown, the CW tone fc = 900 MHz and the phase change for each subcode is randomly selected as either 0 or π. The number of carrier cycles per subcode cpp = 3 (B = 300 MHz) with number of subcodes Nc = 600. This allows comparisons to be made with the previous noise radar configurations.

7.7.2

Periodic Ambiguity Results

To compare the peak side lobe performance of the RBPC waveform, fc = 900 MHz, cpp = 3, fs = 3 GS/s and Nc = 600. This results in bsc = 6,000 samples being processed within the code period. The ACF and PACF are shown in Figure 7.25. The peak side lobe level is approximately −19 dB. The PAF is shown in Figure 7.26. Note that although the peak range side lobe is a bit higher, the Doppler side lobe performance is considerably superior in that its extent is not as great.

Noise Techniques

237

Figure 7.25: Random binary phase code autocorrelation and periodic autocorrelation function.

Figure 7.26: Random binary phase code periodic ambiguity function.

238

7.8

Detecting and Classifying LPI Radar

Millimeter Wave Noise Radar

Millimeter wave (MMW) signals are most appropriate for applications such as environment monitoring, remote sensing, short range target detection, vehicle collision warning and automatic landing systems [40]. Several MMW solidstate noise transmitters have been investigated. These systems rely on the use of a chaotic waveform generator as a source of CW noise and a digitalanalog correlator with an electronically controllable delay line as the main part of the correlation receiver. Three MMW noise sources were investigated. Dynamical chaotization2 was undertaken for: (1) microwave oscillations in a waveguide multiresonant system (2—5 resonant frequencies) containing one or more Gunn-diodes that can couple two or more modes, (2) microwave oscillations in a microstrip ring or linear resonator, and (3) angle modulation of a VCO signal by an RF noise signal [41]. Ka- and W-band solid state noise generators have also been developed on the principles of chaotization of nonlinear systems using both IMPATTand Gunn-diodes. Power outputs on the order of 300 mW with bandwidths ranging from 30 MHz to 300 MHz were generated. Special designs have also been tested oﬀering bandwidths up to 2 GHz with an output power of 40 maw. To process the received signal from the target, fast digital real-time correlators were developed with clock frequencies on the order of 500 MHz. The use of ADCs were avoided by using a simple two-level quantization of the reference signal.

7.9

Correlation Receiver Techniques

The received noise signal reflected from the target is the delayed version of the transmitted signal. By measuring the delay, the receiver can determine the location of the target. To compute the position of the target, the receiver computes the cross-correlation between the time delayed, conjugated transmit signal and the received signal. The analog cross-correlation function is defined as in (7.5). The correlation coeﬃcient or normalized correlation function is defined as in (7.17). Signals are said to be correlated or alike to the extent that their correlation coeﬃcient approaches unity. Below we examine the diﬀerent approaches to implementing the cross-correlation function in the receiver. It can be shown that the received target response is a convolution between the target reflectivity profile γ(t) and the ACF of the radar transmit waveform p(τ ) [42] g(τ ) = γ(t) ⊗ p(τ ) (7.41) where 8 T /2

p(τ ) = lim

T →∞

2 Chaotization

−T /2

S(t)S ∗ (t − τ )dt

(7.42)

is the theoretical and experimental study of chaos in dynamical systems.

Noise Techniques

239

If there is a point scatterer at a distance R, with amplitude a0 and initial phase φ0 , the target reflectivity function can be expressed as γ(t) = a0 ejφ0 δ(t − td )

(7.43)

where δ denotes the Dirac impulse function. With the radar transmit waveform a band limited Gaussian noise signal with carrier frequency fc , bandwidth B, and a square spectrum with power σ 2 , the ACF is given by p(τ ) = σ 2 sinc(Bτ )ej2πfc τ

(7.44)

That is, for a radar that uses a band-limited Gaussian noise waveform as the transmit signal, its ACF is a sinc-pulse modulated by the carrier frequency fc [14].

7.9.1

Ideal Correlation

Figure 7.27 shows the block diagram of an ideal analog correlation receiver. The receiver consists of a noise source and an ideal time delay line that produces a delayed copy of the transmit signal. A mixer followed by a lowpass filter performs the correlation integration between the received target returns and the delayed transmit signals. The response is generated using an I & Q demodulator. The cross-correlation function for the ideal analog correlation receiver has been shown to be [42] CI (τ ) = a0 σ2 sinc(Bτ )e(j2πfc τ −φ0 )

(7.45)

and preserves both the target amplitude and the initial phase.

7.9.2

Digital-Analog Correlation

A digital-analog correlation receiver is shown below in Figure 7.28 [42]. In this architecture, the delay line is implemented with a digital radio frequency memory (DRFM) device. These devices use high-speed sampling and fast digital memory for storing and replicating the transmitted RF noise signal. They provide the ability to capture the transmitted signal and generate a precise, coherent replica for use in the correlation process. In the DRFM, the signal is digitized and then multiplexed into high-speed dual-ported memory for storage and delay processing [43]. The delayed signal is then converted back to an analog signal using a digital-to-analog converter before being sent to the mixer and lowpass filter. Expressed as a function of CI , the cross-correlation function of a digital-analog cross-correlation with a 2N −level ADC is [42] CDA (τ ) =

N a0 3 − i2 ∆22 e 2σ CI (τ ) πσ i=0

where ∆ is the quantization step size.

(7.46)

240

Detecting and Classifying LPI Radar

Figure 7.27: Ideal analog correlation receiver (from [42]).

Figure 7.28: Digital-analog correlation receiver (after [42]).

Noise Techniques

241

Figure 7.29: Fully digital correlation receiver. (After [42].)

7.9.3

Fully Digital Correlation

A fully digital cross-correlation receiver can also be used. In this configuration, both the received target echo signal and the copy of the transmit signal are digitized and the cross-correlation is done digitally. A block diagram of this approach is shown in Figure 7.29. To avoid the use of ADCs, the principle of two level quantization of the reference signal has been proposed. Fast correlator hardware can be developed since only the monobit (two-level) version of the noise waveform reference is delayed in a fast controllable digital delay line made up of shift registers or fast random access memory. For the case when the delayed transmit signal and the received signal are both clipped to be either −1 or +1 before performing correlation, the cross-correlation function has been shown to be [42] CD (τ ) =

2 sin−1 [sinc(Bτ )] π

(7.47)

Work on fast digital signal processing algorithms for computation of the cross-correlation are of high interest recently since this presents the major computational burden in random noise radar. By increasing the sample size N being processed, the requirements for the discrete Fourier transform processors and fast convolution processors which calculate the cross-correlation increase sharply. Recently a system of orthogonal real-imaginary basis functions representing a new version of Walsh functions were compared to using a

242

Detecting and Classifying LPI Radar

set of Walsh Cooley functions for calculating the correlation [44]. Parametric and nonparametric algorithms are compared in [45].

7.9.4

Acousto-Optic Correlation

Due to the physical delay lines that are used a limited number of range bins is available. This either limits the range gate extent (maximum detectable range scanned by the variable delay line) or the range resolution must be sacrificed. In addition, the slow switching speed (several seconds) of the variable delay lines can limit the data acquisition rate and constrain the ability to do realtime signal processing. This ultimately limits the ability to do range-Doppler processing to detect fast moving targets. Acousto-optic (AO) devices are well known for their utility in correlation processing [46]. The use of an AO processor oﬀers another approach to correlation processing in the random noise radar. The receiver still employs a fiber optic fixed-delay line to choose the coarse range delay but an acousto-optic (AO) time-integrating correlator is used to allow parallel range bin processing [47]. Here the received signal is heterodyned using the AO as the time integrating correlation receiver as shown in Figure 7.30. The noise signal is transmitted through the transmit antenna and the replica of the transmitted

Figure 7.30: Acousto-optic correlation receiver for noise radar (from [47]).

Noise Techniques

243

noise signal is delayed in the fixed fiber delay line (sets minimum detectable range). After addition of a fixed bias and level adjustments, the signal modulates the laser diode of the AO correlator. The laser diode light is then collimated with a lens and focused on the AO device. The received signal is used to drive a piezoelectric transducer, which launches a traveling acoustic wave into the AO device. The correlation of the delayed transmit and received signal is achieved by imaging the AO device aperture onto a 1-D CCD. The time-integrated correlation signal is produced by detecting the interference between the undiﬀracted beam and the polarization switched, diﬀracted traveling wave received signal by projecting both optical beams through a polarizer that can be rotated to optimize the beam ratio for good interferometric modulation depth. 0 The correlator provides the amplitude as a function of range as A = I 2 + Q2 . Further details and experimental results can be found in [47]. The use of the AO crystal provides up to 1,000 range cells that work simultaneously over the aperture of the crystal providing the capability for real-time data acquisition. The sensitivity is also improved up to 60 dB. Dynamic range and linearity are limited by the acoustic nonlinearities and scattering and by the limited dynamic range of CCD but could be increased by improved CCD detector arrays providing higher bit resolution (e.g., 16 bits). There is also a noise figure penalty for the electrical to fiber to electrical conversion in the fiber delay line and AO correlator. This was oﬀset by the processing gain achieved by the long integration time.

7.10

Concluding Remarks

Today noise waveforms can be generated digitally followed by a digital-toanalog converter and up-conversion onto a carrier signal. With the increasing integration of solid-state microwave techniques and high-speed VLSI circuits, the correlation signal processing required for noise radar is leading the way to real-time range-Doppler implementation. They are also relatively inexpensive to build and there is considerable interest in relating the technology to military applications such as covert surveillance and reconnaissance, target detection and tracking, through-the-wall imaging, ground-penetration, foliage-penetration profiling, synthetic aperture radar and inverse synthetic aperture imaging. The use of wideband noise waveforms can result in high resolution and reduced ambiguities in range and Doppler estimation. The periodic ambiguity analysis for the four noise technology emitters are compared in this Chapter. Table 7.1 summarizes the peak range side lobe level (in dB) and the peak Doppler side lobe level of the noise radar configurations simulated in this chapter. These results do not include any side lobe suppression techniques which can lower these values significantly. The use of noise waveforms

244

Detecting and Classifying LPI Radar

can result in a large mismatch in processing gain between the radar and the noncooperative intercept receiver making their presence hard to detect. The most significant consequence on the traditional intercept receiver is a slight increase in the receiver’s noise floor. Finally, the use of several noise waveforms in a netted radar configuration can minimize the mutual interference between emitters while providing an increase in surveillance volume and also lowering the CW power required even further (see Chapter 9). Table 7.1: Summary of Ambiguity Peak Side Lobe Performance Noise Technique RNR (Figures 7.6 and 7.7) RNFR (Figures 7.13 and 7.14) RNFSR (Figures 7.21 and 7.22) RBPC (Figures 7.25 and 7.26)

Range Side Lobe −3 dB −21 dB −21 dB −19 dB

Doppler Side Lobe −6 −6 −7 −2

References [1] Horton, B. M., “Noise-modulated distance measuring system,” Proceedings of the IRE, Vol. 49, No. 5, pp. 821—828, May 1959. [2] Craig, S. E., Fishbein, W. and Rittenbach, O. E., “Continuous-wave radar with high range resolution and unambiguous velocity determination,” IRE Transactions MIL-6, pp. 153, April 1962. [3] Grant, M. P., Cooper G. R., and Kamal, A. K., “A class of noise radar systems,” Proceedings of the IEEE Vol. 51, No. 7, pp. 1060—1061, July, 1963. [4] Cooper, G. R., and McGillem, C. D., “Random Signal Radar,” Final Report NASA Grant-NSG 543, Purdue University, Lafayette, IN, June 1967. [5] McGillem, C. D., Cooper, G. R., and Waltaman, W. B., “An experimental random signal radar,” Proceedings of the National Electronics Conference, Dayton, Ohio, pp. 409—411, Oct. 1967. [6] Smit, J. A., and Kneefel, W. B. S. M., “RUDAR—An experimental noise radar,” De Ingenieur, Vol. 83, No. 32, ppm. 99-110, Aug. 1971. [7] Guosui, L., Hong, G., and Weimin, S., Hongbo, S., Jianhui, Z., “Random Signal Radar—A Winner in Both the Military and Civilian Operating Environments,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 39, No. 2, pp. 489—498, April 2003. [8] Guosui, L., Hong, G., Xiaohua, Z., and Weimin, S., “The Present and Future of Random Signal Radars,” IEEE Aerospace and Electronic Systems Magazine, Vol. 12, No. 10, pp. 35—40, October 1997. [9] Guosui, L., Hong, G., and Weimin, S., “Development of random signal radars,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 35, No. 3, pp. 770—777, July 1999.

Noise Techniques

245

[10] Garmatyuk, D. S., and Narayanan, R. M., “ECCM Capabilities of an Ultrawideband Bandlimited Random Noise Imaging Radar,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 38, No. 4, pp. 1243—1255, October 2002. [11] Xianyi, Z., Weimin, S., and Hong, G., “Anti-jamming performance analysis for random noise UWB imaging radar,” Proceedings of the International Conf. on Radar (CIE ’06), Shanghai, China, 16—19 Oct. 2006. [12] Turner, L., “The evolution of featureless waveforms for LPI communications,” Proceedings of the NAECON, Dayton, OH, pp. 1325—1331, May 1991. [13] Axelsson, S. R. J., “Random noise radar/sodar with ultrawideband waveforms,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 45, No. 5, pp. 1099—1114, May 2007. [14] Narayanan, R. M., and Dawood, M., “Radar Penetration Imaging Using Ultra-wideband Random Noise Waveforms,” IEEE Trans. on Antennas and Propagation, Vol. 48, No. 6, pp. 868—878, June 2000. [15] Lai, C-P., Ruan, Q., and Narayanan, R. M., “Hilbert-Huang transform (HHT) processing of through-wall noise radar data for human activity characterization,” Proceedings of the IEEE Workshop on Signal Processing Applications for Public Security and Forensics (SAFE), Washington DC, April 2007. [16] Xu, X., and Narayanan, R. M., “FOPEN SAR Imaging Using UWB StepFrequency and Random Noise Waveforms,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 37, No. 4, pp. 1287—1300, October 2001. [17] Xu, Y., and Narayanan, R. M., “Polarimetric Processing of Coherent Random Noise Radar Data for Buried Object Detection,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 39, No. 3, pp. 467—478, March 2001. [18] Bell, D. C., and Narayanan, R. M., “Inverse synthetic aperture radar imaging using a coherent ultrawideband random noise radar system,” Optical Engineering, Vol. 40, No. 11, pp. 2612—2623, November 2001. [19] Garmatyuk, D. S., and Narayanan, R. M., “Ultra-Wideband ContinuousWave Random Arc-SAR,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 40, No. 12, pp. 2543—2552, December 2002. [20] Zhang, Y., and Narayanan, R. M., “Design Considerations for a Real-Time Random-Noise Tracking Radar,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 40, No. 2, pp. 434—445, April 2004. [21] Zhang, Y., and Narayanan, R. M., “Monopulse radar based on spatiotemporal correlation of stochastic signals,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 1, pp. 160—173, Jan. 2006. [22] Zhang, Y., Narayanan, R. M., and Xu, X., “Theoretical and simulation analysis of random noise monopulse radar,” Proceedings of the IEEE Antennas and Propagation Symposium, San Antonio, TX, pp. 386—389, July 2002. [23] Donnet, B. J., and Longstaﬀ, I. D., “MIMO radar, techniques and opportunities,” Proceedings of the 3rd European Radar Conference, pp. 112—115, Manchester UK, Sept. 2006.

246

Detecting and Classifying LPI Radar

[24] Gray, D. A., and Fry, R., “MIMO noise radar — element and beam space comparisons,” Proceedings of the International Waveform Diversity and Design Conference, Pisa Italy, pp. 344—347, June 2007. [25] Zetik, R., Sachs, J. and Thoma, R. S., “UWB short range radar sensing,” IEEE Instrumentation & Measurement Magazine, Vol. 10, No. 2, pp. 39—45, April 2007. [26] Sun, H. “Possible ultra-wideband radar terminology,” IEEE Aerospace and Electronic Systems Magazine, Vol. 19, No. 8, pp. 38, Aug. 2004. [27] Sun, H. Lu, Y., and Guosui, L., ”Ultra-Wideband Technology and Random Signal Radar: An Ideal Combination,” IEEE Aerospace and Electronic Systems Magazine, Vol. 18, No. 11, pp. 3—7, November 2003. [28] Dawood, M., and Narayanan, R. M., “Generalized wideband ambiguity function of a coherent ultrawideband random noise radar,” IEE Proceedings-F Radar, Sonar, Navigation Vol. 150, No. 5, pp. 379—386, Oct. 2003. [29] Axelsson, S. R. J., “Noise Radar for Range/Doppler Processing and Digital Beamforming using Low-bit ADC,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 41, No. 12, pp 2703—2720, December 2003. [30] Axelsson, S. R. J., “Noise Radar Using Random Phase and Frequency Modulation,” IEEE Trans. on Geoscience and Remote Sensing Vol. 42, No. 11, pp. 2370—2384, Nov. 2004. [31] Narayanan, R. M., Henning, J-A, and Dawood, M., “Enhanced detection of objects obscured by dispersive media using tailored noise waveforms,” Proceedings of the SPIE Conf. on Detection and Remediation Technologies for Mines and Minelike Targets III, Orlando, FL, Vol. 3392, pp. 604—614, April 1998. [32] Narayanan, R. M., Xu, Y., Hoﬀmeyer, P. D., and Curtis, J. O., “Design performance and applications of a coherent ultra-wideband random noise radar,” Optical Engineering, Vol. 37 No. 6, pp. 1855—1869, June 1998. [33] Jiang, R., Wolfe, K. W., and Nguyen, L., “Low coherence fiber optics for random noise radar,” Proceedings of the IEEE Military Communications Conference (MILCOM), Los Angeles, CA, pp. 907—911, Oct. 2000. [34] Li, Z., and Narayanan, R. M., “Doppler visibility of coherent ultrawideband random noise radar systems,” IEEE Trans. in Aerospace and Electronic Systems, Vol. 42, No. 3, pp. 904—916, July 2006. [35] Dawood, M., and Narayanan, R. M., “Receiver operating characteristics for the coherent UWB random noise radar,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 37, No. 2, pp. 586—594, April 2001. [36] Heuschel, E. R., III, “Time-Frequency, Bi-Frequency Detection Analysis of Noise Technology Radar,” U. S. Naval Postgraduate School Master’s Thesis, Sept. 2006. [37] Liu, G., and Xiangquan, S., “Average ambiguity function for random FMCW radar signal,” International Conference on Radar, Paris, pp. 339—346, 21—24 May 1984.

Noise Techniques

247

[38] Guosui, L., Xiangquan, S., Jinhui, L., Guoyu, Y., and Yaoliang, S., “Design of noise FM-CW radar and its implementation,” IEE Proceedings-F Radar, Sonar, Navigation , Vol. 138, No. 5, pp. 420—426, October 1991. [39] Hong, G., Guosui, L., Xiaohua, Z., Weimin, S., and Xi, L., “A new kind of noise radar—random binary phase coded CW radar,” Proceedings of the IEEE National Radar Conference, Syracuse, NY, pp. 202—206, May 1997. [40] Lukin, K. A., “Millimeter wave noise radar technology,” Proceedings of the 3rd International Symposium on Physics and Engineering of Microwave, Millimeter Wave and Submillimeter Waves, Kharkov Ukraine, Sept. 15—17, 1998. [41] Lukin, K. A., “Millimeter wave noise radar applications: Theory and Experiment, Proceedings of the 4th International Symposium on Physics and Engineering of Microwave, Millimeter Wave and Submillimeter Waves, Kharkov Ukraine,, June 4—9, 2001. [42] Xu, X., and Narayanan, R. M., “Impact of diﬀerent correlation receiving techniques on the imaging performance of UWB random noise radar,” Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, IGARSS, Toulouse, France pp. 4525—4527, 21—25 July, 2003. [43] Pace, P. E., Advanced Techniques for Digital Receivers, Artech House, Norwood, MA, 2000. [44] Sinitsyn, R. B., and Beletsky, A. J., “Fast signal processing algorithms for noise radar,” Proceedings of the 3rd European Radar Conference, Manchester, U.K., pp. 245—248, Sept. 2006. [45] Yanovsky, F. J., and Sinitsyn, R. B., “Ultrawideband signal processing algorithms for radar and sodars,” Proceedings of the Ultrawideband and Ultrashort Impulse Signals, Sevastopol, Ukraine, pp. 66—71, 18—22 Sept. 2006. [46] Hecht, D., “Characteristics of acoustooptic devices for signal processing,” Proceedings of the IEEE Symposium on Ultrasonics, San Francisco, CA, pp. 369—380, 1985. [47] Narayanan, R. M., Zhou, W., Wagner, K. H., and Kim, S., “Acoustooptic Correlation Processing in Random Noise Radar,” IEEE Geoscience and Remote Sensing Letters, Vol. 1, No. 3, pp. 166—170, July 2004.

Problems 1. Determine the instantaneous fractional bandwidth of a noise waveform if the absolute bandwidth B = 3 GHz and the maximum bandwidth fmax = 4 GHz. 2. Consider a moving target. The instantaneous Doppler frequency is not a constant but varies due to the varying nature of the instantaneous wavelength λ. Since λ varies between λmin and λmax , the Doppler frequencies vary from fdl to fdh . If fdc = (fmin + fmax )/2 is the average

248

Detecting and Classifying LPI Radar Doppler corresponding to transmit frequency of fc , (a) show that the minimum and maximum Doppler frequency are fdl =

2fmin fdc fmin + fmax

(7.48)

fdh =

2fmax fdc fmin + fmax

(7.49)

and

(b) Derive the expression for the target’s velocity as a function of fdl and also as a function of fdh . (c) Calculate fdl , fdh and the target’s velocity if λmin = 0.15m and λmax = 0.3m. 3. Show that a transmitted noise signal (7.11) St (t) = Re{S(t)} = X(t) cos(2πfc t) − Y (t) sin(2πfc t)

(7.50)

can be expressed as St (t) =

1 [sc (t)e2πfc t + s∗c (t)e−2πfc t ] 2

(7.51)

where sc (t) = X(t) + jY (t) is the complex conjugate envelope and denotes the complex conjugate.

∗

4. Using the algorithms in the noise folder, generate the four types of noise waveforms discussed in the chapter. Examine the ACF, PACF and PAF of each waveform and compare the highest time side lobe and Doppler side lobe level (in dB) for each waveform.

Chapter 8

Over-the-Horizon Radar In this chapter, we examine the sky wave over-the-horizon radar (OTHR) concept including the characteristics of the ionosphere on the propagation of the radio waves and the clutter spectrum. Sky wave processing and modern LPI waveform considerations are presented. The sky wave maximum detection range is also quantified for the Chinese OTH-B. Simulation results using PROPLAB PRO, an ionospheric radio propagation tool published by Solar Terrestrial Dispatch, are shown to demonstrate the coverage region of the emitter. Surface wave OTHR are also presented including the LPI waveform considerations. The surface wave radar equation is developed and simulation results of the maximum detection range are shown as a function of the required input SNR.

8.1

Two Types of OTHR

Today, many countries require an OTHR to provide a long-range, wide area surveillance capability due to modern day terrorists, smugglers and the need to monitor one’s economic zone and oﬀ shore resources [1]. OTHR systems operate in the high frequency (HF) band 3—30 MHz and use either surface wave propagation or sky wave propagation. Sky wave OTHR systems are installed inland and make use of the ionospheric refraction of the radio waves several hundred kilometers above the Earth’s surface to overcome the lineof-sight limitation caused by the Earth’s curvature. Surface wave systems operate in the lower part of the HF spectrum and are installed on the coastlines to make use of electromagnetic coupling of the emitted radio waves to the sea surface allowing propagation to extend over the horizon. OTHR surface wave systems were considered first and operated in the early 1950s with eﬀective sky wave systems coming along later [2]. Although work on sky wave 249

250

Detecting and Classifying LPI Radar

OTH radars continues around the world, systems that exploit surface wave propagation are attracting greater long-term interest due to their more convenient size and transportability. The significant diﬀerence between sky wave and surface wave radars is that sky wave radars have large detection ranges beyond the horizon (starting at about 800 km and extending out to 1,000— 4,000 km) while surface wave systems can see out to 400 km. The reason for the extended detection range for the sky wave propagation is that the losses caused by the ionization and absorption in the ionosphere are much less than the surface wave diﬀraction loss. Ionospheric eﬀects such as multipath and Doppler spreading are also significant. Targets such as cruise missiles, stealth aircraft, ballistic missiles and aircraft carriers can be detected with OTHR systems at distances well beyond the horizon. Several types of emitter waveforms for OTHR have been used in the past. Transmitted waveforms such as a simple pulse (e.g., cosine-squared), a chirped pulse or a pulse Doppler waveform have been used [3]. Due to the very small duty cycles, large peak powers were required to overcome the propagation losses incurred. With the necessity of having to operate across bands in which other authorized users were emitting many anti-interference measures had to be included [2]. The high-power, pulsed waveforms eﬀectively detected the targets however, they allowed the long-range interception of the emitter by noncooperative intercept receivers leading to direction finding, emitter identification, electronic attack (jamming), and deception. In order to provide a more covert military capability as well as a more eﬃcient use of the HF spectrum, the modern OTHR is moving towards the use of CW LPI waveform modulations such as CW phase modulation and frequency hopping [4]. Low power FMCW using multiple waveform repetition frequencies [5, 6] are being used that can relax the transmit power requirements to provide a more covert sky wave system. In addition these types of waveforms can resolve the range/Doppler ambiguity usually associated with HF FMCW radar. Surface wave systems using random low power FM interrupted CW (FMICW) are also being pursued [7]. The FMICW is a FMCW waveform that is gated on and oﬀ either randomly or with a well-defined sequence. The main problem caused by the spectra discontinuity is the high-range side lobes. Optimal sparse waveform designs [8] are being explored. They find the interference-free channels in the HF band by frequency monitoring, enabling the target detection to be accomplished using clear channels while also lowering the transmit power and minimizing the range side lobes. Shorter coherent integration times (CIT) [9], adaptive transmit frequency techniques [10], antijamming through the use of a radar waveform with discontinuous spectra using two carrier frequencies [11] and orthogonal MIMO waveforms [12] are also resulting in a quieter and more eﬀective OTHR. The ionospheric propagation and movement of the layers, contaminates the transmitted waveform resulting in a low, and fading SNR at the target. Traditionally, anti-interference measures such as adaptive frequency tuning,

Over-the-Horizon Radar

251

adaptive filtering (including tunable band reject filters) and spatial filtering have been used by the emitter [2]. Modern OTHR signal processing techniques such as adaptive interference suppression [13—15] and clutter cancelation algorithms [16] are now able to eliminate the ionospheric propagation path contaminants and compensate for the smearing of sea echo very eﬀectively. Adaptive time-frequency analysis has also been used to parameterize the radar signal so the interference can be identified and removed [17]. On the other hand, the ionospheric propagation makes the noncooperative detection of the OTHR more diﬃcult. The ionospheric contamination makes the polarization at the receiver indeterminable and consequently, the detection and DF (azimuth and elevation estimates) of the OTHR waveforms is tricky especially in the presence of the other interference within the HF band [18]. The antenna aperture required is large in size and must also be useful across the HF band with no grating lobes. Large shipboard multifunction arrays are hampered by limitations on the physical size of the aperture required and problems with electromagnetic interference and compatibility [19]. Single sight location techniques using complex time delay estimation algorithms have been used to DF the OTHR signals [20]. Furthermore, the received HF signals are nonstationary which limits the noncoherent integration eﬃciency within the signal processing. Due to multipath presence, high-resolution spectral estimation techniques such as multiple signal classification (MUSIC) and the cepstrum must also be used [18]. Since the HF signals have a large wavelength (10 ≤ λ ≤ 100m) the OTHR also has an inherent resistance to the ARM threat. This is because HF wavelengths are greater than 10m and any antenna mounted in a missile seeker (diameter = 0.5m) would have significant diﬃculty deriving any useful guidance information from the emitted HF waveform. In addition to counterARM capacity, the HF CW waveforms can also detect stealth aircraft and low level penetrators providing strategic and long distance early warning1 [21]. The OTHR systems are able to survey large areas of land and sea for air and maritime targets. The OTHR’s operating wavelength is nearly the same size as many of the targets being pursued which puts the targets in the resonant scattering region (increase in RCS and target detection performance). In this chapter, sky wave OTHR systems and the eﬀect the ionosphere has on the waveforms is presented. LPI waveforms are discussed and PROPLAB PRO simulation results are shown to demonstrate the typical footprint coverage as a function of the HF frequency. Example results for the Chinese OTH-B system are shown. MATLAB simulations showing the maximum detection range as a function of the minimum required SNR are also discussed. Surface wave systems are examined including the FM interrupted CW approach. With the focus on new emitter waveforms, incorporation of electronic protection, signal processing and spectrum management, the inter1 Stealth

aircraft are not optimized against bistatic over-the-horizon radars.

252

Detecting and Classifying LPI Radar

Figure 8.1: Sky wave radar concept (adapted from [23]). ception and direction finding (DF) of both the sky wave and surface wave OTHR systems present a significant challenge. For a review of the world’s OTHR systems, see [22].

8.2

Sky Wave OTHR

The emitted waveform from the sky wave OTHR system is bounced oﬀ the ionosphere and then down to the targets. Reflections from the targets are bounced back through the ionosphere to the receiver array as shown in Figure 8.1 [23]. Note the similarity to the MIMO (or spatially waveform diverse) architecture as discussed in Chapter 10. Due to the amount of sea clutter being returned the term backscatter is often used. Use of the term backscatter is intended to identify the system geometry, in which the small separation between transmitter and receiver results in an eﬀective monostatic radar, as opposed to a bistatic geometry in which the large angle between the transmit and receive path modifies the target and clutter RCS. These backscatter systems consist of two modes for detection of targets. Detection of air targets, and ballistic missiles during the launch phase constitute an air mode. Detection of surface targets is called a surface mode. Although they are typically separate operating modes, eﬀorts to combine the modes is also being pursued. Both modes are aﬀected significantly by the ionosphere and these eﬀects are presented below.

Over-the-Horizon Radar

253

Figure 8.2: Temperature and plasma density of neutral gas and ionized gas as a function of altitude (after [25]).

8.2.1

Characteristics of the Ionosphere

The ionosphere is defined as that part of the upper atmosphere where suﬃcient ionization can exist to aﬀect the propagation of radio waves [24]. Examining the LPI characteristics of OTHR systems requires an understanding of the ionosphere and its eﬀects. The structure of the neutral atmosphere and the ionosphere containing ionized gas surrounding the Earth is shown in Figure 8.2 [25]. The left side of the figure (neutral gas) shows the altitude (in kilometers) as a function of temperature (in Kelvin). The layer right above the Earth’s surface up to 10 km is the troposphere and all weather phenomena occur here. The layer above the troposphere is the stratosphere and the air flow is horizontal. The layer above the stratosphere is the mesosphere where the temperature increases with altitude. The layer above the mesosphere is the ionosphere. The right side of Figure 8.2 (ionized gas) shows the altitude

254

Detecting and Classifying LPI Radar

(km) as a function of plasma density (in units of cm−3 ). It also shows the layer structure in both daytime (solid line) and night time (dashed line). The plasma is typically the ionized gas and the plasma density refers to electron density. The ionosphere is the region at heights of above 80 km and is also the most outlying area from the center of the Earth [26, 27]. The ionosphere consists of ionized atoms. It makes long-distance propagation possible by reflecting the radio waves typically at a height between 90 and 350 km above the Earth’s surface. The free electron density is an indicator of the degree of ionization and is used to measure the structure of the ionosphere in layers. They are D-, E-, F1- and F2-layers in the daytime. There is always an F-layer at night and sometimes an E-layer is present as well. The radio waves that propagate through the troposphere are called surface waves or ground waves. The radio waves refracted from the ionosphere are called sky waves. The D-layer below the ionosphere is between the height of 48 and 80 km above the Earth’s surface. This layer only exists in daytime and its absorption causes the shorter propagation distance for the radio waves [28]. The distribution of layers in the ionosphere, except the D-layer, is shown in Figure 8.3. The E-layer exists between 88 and 145 km above the Earth’s surface. The maximum electron density in this layer is 1.5×105 electrons/cm3 at the height of about 110 km. The E-layer can refract the HF radio wave inducing propagation distances up to 2,000 km in the daytime. The F-layer splits into the F1- and F2-layers in the daytime and remains only the F-layer at night. The F-layer exists between 273 and 321 km. The F1-layer usually exists between 160 and 240 km and sometimes the electron density in this layer is not great enough to distinguish it as a separate layer. The F2-layer exists between 257 and 402 km and most HF radar signals are refracted from this layer to maximize the propagation range. The nominal height for each layer’s peak is 90 km for the D-layer, 110 km for E-layer, 200 km for F1-layer, and 300 km for F2-layer. The International Reference Ionosphere (IRI) is a joint project of the Committee of Space Research (COSPAR) and the Union of Radio Science International (URSI) [29]. The ionospheric model, IRI-2001, uses input data that includes the time (universal or local time), date and year, the latitude and longitude of the desired location, the profile type (height, latitude, longitude, year, month, day of month, day of year and hour profile), and the parameters of the profile itself. The optional input includes the sunspot number (SSN) and ionosphere index (IG) [30]. Figures 8.4 and 8.5, produced by the IRI model, illustrate diagrams of the electron density profile versus altitude at Nanjing, China (32.0 N and 241.7 W) for daytime and nighttime in the winter and summer, respectively. In Figure 8.4, the time was set to be 1000 and 2400 (local time) in January (winter). The same times were used in Figure 8.5 for July (summer). Both months are in the year of 2007. In these figures, the value along the abscissa

Over-the-Horizon Radar

255

Figure 8.3: Distribution of layers in the ionosphere during the daytime and nighttime. (from left to right) represents the electron density (electrons/cm3 ) for each altitude. The electron density is generated by semilog calculation method. The numbers along the ordinate of the figure correspond to the altitude above the ground (in kilometers). The first three lines on the top of the graph represent the information of the geographic coordinates, time, day, and month. The fourth line shows the optional inputs, SSN and IG index, that are generated by the model itself unless input by the user. In the daytime results shown in Figure 8.4(a) and Figure 8.5(a), the D, E and F2-layers are easily defined, but the F1-layer is not well defined. In the night time results shown in Figure 8.4(b) and Figure 8.5(b), both E and F-layer are well defined. These results demonstrate that the successful noncooperative interception of the OTHR waveforms depend heavily on the conditions of the ionosphere, time of day, and sun spot number (SSN) as well as the emitter power and range. Modeling the ionospheric electron density Ne and refractive index μ is useful for HF propagation studies and OTHR system planning and performance prediction. Exploitation of this predictability by the targets can also be used to avoid detection by the OTHR (e.g., by flying when the propagation losses and ionospheric modulation are the worst). The electron density

256

Detecting and Classifying LPI Radar

Figure 8.4: Electron density in (a) winter day (January 2007) and (b) winter night (January 2007). (electrons/cm3 ) of the ionosphere at the desired height from the Earth’s center can be calculated using a quasiparabolic ray path to represent the waveform within the ionosphere as [26—28] l W2 p Q M w rb 2 r − rm (8.1) Ne = Nm 1 − ym r for rb ≤ r ≤

rm rb rb − ym

where Ne is the electron density having a maximum value of Nm (electrons/cm3 ) at a radial distance rm (geocentric height of the maximum). The distance r is the radial distance from Earth’s center to the height of interest within the layer (r = re + h where re is the Earth’s radius and h is the height), rb is the value of r at the layer base (geocentric base height) and ym is the layer semithickness (half-thickness). This technique is developed for fitting quasiparabolic layers to measured vertical electron density profiles. Note that rb = rm − ym and the Earth’s radius re = 6,378.1 km. The parameters are illustrated in Figure 8.6.

Over-the-Horizon Radar

257

Figure 8.5: Electron density in (a) summer day (July 2007) and (b) summer night (July 2007). The critical frequency (kHz) is the maximum frequency of the emitted waveform that is returned from a layer at normal incidence. That is, when the emitted waveform is transmitted straight up towards the ionosphere (vertical incidence), the waveform will be returned to earth at all frequencies below the critical frequency fcr (kHz) which takes the form [2] 0 fcr = 81Nm (8.2)

Thus at normal incidence (φi = 0o ) a wave will penetrate the ionosphere if f > fcr . A negative refractive index occurs when f < fcr and this results in a ray at normal incidence being reflected from the ionosphere to return to the Earth. In case the frequency exceeds the critical frequency the influence the ionosphere layer has on the path of propagation depends upon the angle of incidence φi at the ionosphere. The angle of incidence φi is measured from the normal to the ionospheric layer. The critical frequency fcr is not the highest frequency that can be reflected from the layer. The maximum frequency that can be reflected back for a given distance of transmission is called the maximum usable frequency (MUF). The MUF is related to the critical frequency and the angle of incidence by [31] MUF = fcr sec φi

(8.3)

258

Detecting and Classifying LPI Radar

Figure 8.6: Ray path geometry. It has been shown that the attenuation varies approximately as the inverse square of the frequency. Therefore it is desirable to use as high a frequency as possible without approaching too close to the MUF. Due to the curvature of the Earth and the ionospheric layer, the largest angle of incidence φi that can be obtained in F-layer reflection is on the order of 74 degrees. The refractive index of the ionosphere μ can now be expressed as a function of the height parameters of the layer and the critical frequency as [2] W1/2 W2 w W2 w w 1 rm − r p rb Q2 81Ne = 1 − + (8.4) μ= 1− f2 F F ym r

where f is the HF frequency (in kHz) and F = f /fcr . The refractive index decreases as the wave penetrates into regions of greater electron density and the angle of refraction increases correspondingly. The minimum distance from the transmitter at which a sky wave of given frequency is returned to earth by ionosphere is called the skip zone or distance. If the OTHR increases frequency, the range of the footprint (and skip zone) also increases as shown in Figure 8.7. This summary set of skip zones were derived from the PROPLAB PRO modeling of the Chinese OTH-B discussed in Section 8.4.

Over-the-Horizon Radar

259

Figure 8.7: Coverage range for fc = 6, 8, 10, 12, 14, 16, 18, 20 and 22 MHz for SSN = 200 and the AI = 5 on 0:00 UTC 2007/7/31 [22].

8.2.2

Example of F2-Layer Propagation

Consider the electron density profile for the summer daytime in Figure 8.5. Here the maximum electron density Nm of the F2-layer is at the height of rm = 6618.1 km (240+6,378.1), with a value of 3 × 105 electrons/cm3 . The F2-layer semithickness (half-thickness) ym = 50 km or ym = 0.5(300 − 200), and the base height of the F2-layer rb = rm − ym or 6568.1 km, which means the base height of the F2-layer is 190 km above the Earth’s surface (also shown in Figure 8.5). At a desired height of 230 km above the Earth’s surface, the electron density is calculated from (8.1) as Ne = 2.8814 × 105 electrons/cm3 . The critical frequency depends only on the maximum electron density of the F2-layer fcr = 4.93 × 103 kHz. Based on (8.4), the refractive index μ is a function of electron density Ne and operating frequency f (kHz). If a frequency of f = 5.1 × 103 kHz is considered, the refractive index μ = 0.32. If the waveform is launched at an angle of incidence of φi = 10 degrees, MUF= 5 × 103 kHz.

8.2.3

Doppler Clutter Spectrum

How the targets appear in the Doppler space relative to the clutter is important in determining the HF frequency to be used. The excessive noise caused by ionospheric propagation is due to the electron density variations. This process decorrelates the radio signal as it propagates and broadens the Doppler spectrum. The Doppler radar spectrum of HF radiation backscattered from the ocean surface is shown in Figure 8.8 and characterized by two strong peaks appearing above and below the carrier frequency [32]. The phys-

260

Detecting and Classifying LPI Radar

Figure 8.8: Bragg peaks along with air and surface targets within the cluttertarget Doppler profile (after [32]). ical mechanism producing this phenomenon is single-bounce Bragg scattering from wave trains. The Bragg peaks represent the radiation being reflected. √ The Doppler frequencies of the Bragg peaks are ±0.102 fc Hz where fc is the operating frequency in megahertz and the sign ± indicates the resonant ocean waves advancing towards or receding away from the radar. The sidebands surrounding the Bragg peaks are due to wave-wave interactions and higher order Bragg scattering [33]. The ocean properties that can be extracted from features of the HF radar sea echo spectrum include (from easiest to measure) radial surface currents, sea state, surface wind speed, dominant wave period and direction [34]. Radial velocity variation of maneuvering targets (aircraft) with high speed may cause significant spread on the radar echo in the Doppler spectrum. These eﬀects make the echo energy disperse and degrades the eﬃciency of the coherent integration operation (coherent integration loss). Aircraft target speeds separate them well from surface targets and clutter for many geometries and provide a good match to the radar capabilities. Many ways have been proposed to deal with maneuvering targets in OTHR systems. For aircraft, the modulation periods are typically several seconds. Ships which have radial speeds between 5 and 25 ms−1 require coherent modulation periods longer than tens of seconds to achieve high resolution in the Doppler domain so as to distinguish the targets from the clutter [32]. The positioning accuracy

Over-the-Horizon Radar

261

can also be improved by the use of active transponders, clutter storage and display technology (to calibrate coast lines) and the use of one transmitting site and multiple receiving sites. Many targets of interest may be concealed by the clutter and this obscuration is predictable and hence exploitable by ships wishing to evade detection. For OTHR, reducing the severity of clutter masking is actively being investigated.

8.2.4

Example Sky Wave OTHR System

As an example, consider the Australia’s Jindalee Operational Radar Network. The Jindalee Over-the-horizon Radar Network (JORN) is a system that provides surveillance over 4,000 km of Australia’s northern coastline. Full implementation of JORN has involved the construction of two OTH backscatter radars that operate in the HF band and are able to detect airborne and ship targets at ranges of between 1,000 and 3,000 km, with a range resolution of 20—40 km. The JORN radars incorporate bistatic transmission and reception subsystems geographically separated to prevent mutual interference. The transmission subsystem comprises 28 transmitter chains, each of which incorporates a 20-kW power amplifier [35]. The receiver subsystem near Longreach, Queensland utilizes 480 receiver chains, while the one near Laverton, Western Australia incorporates 960 such chains. Figure 8.9 shows the JORN transmission site at Longreach, Queensland. An integral frequency management system determines which frequency within the operating band will yield the best SNR while spectrum and noise monitors identify clear channels and background noise levels. A backscatter sounder is used to monitor ionospheric propagation characteristics in the target area and operating frequency selection is made on the basis of independent data that is gathered. General ionospheric structure characteristics and target ground truths are obtained via a network of vertical and oblique sounding facilities and transponders located along Australia’s northern coastline [32]. The Longreach 3-km reception array is shown in Figure 8.10 and is positioned some 100 km from its associated transmitter. A JORN Coordination Center (JCC) is located at the Royal Australian Air Force (RAAF) base Edinburgh near Adelaide, South Australia. Here, the received data is processed into usable tracking data. The Longreach site is equipped with a 0.4-km transmission array.

8.2.5

Sky Wave Processing

For sky wave systems, the receivers and transmitters are almost always separated by as much as 100 km or more. Sky wave systems have large immovable antenna arrays that are spread out over a long distance and are positioned inland such that they are relatively immune to most forms of enemy attack by rockets and missiles. Sky wave OTHR transmitters use adaptive frequency

262

Detecting and Classifying LPI Radar

Figure 8.9: The JORN transmission site at Longreach, Queensland [35].

Figure 8.10: Jindalee receiving antenna [35].

Over-the-Horizon Radar

263

selection, low side lobe adaptive digital beam forming, and require sophisticated frequency management systems using ionosondes in order to operate via the ever-changing ionosphere [32]. Ionosondes are devices that send a spectrum of radio wave pulses straight up to measure: (a) the length of time it takes for a reflection to be returned, (b) the strength of the reflection, and (c) how high of a frequency can be reflected. From these three measurements (time, strength, frequency), the device can determine ionization density, altitude of the ionization, and the MUF. The transmitting system is usually implemented as a number of separate antenna arrays, each covering a certain frequency subband. Due to the large area being illuminated, these systems provide the users with a significant surveillance capability to detect targets at any altitude from the ionosphere to the surface of the Earth. The receive antenna is usually a long (> 1 km) array of monopoles sometimes with a backscreen to reduce the back lobe radiation. The receiver array is connected to a beamformer, receiver and ADC. The receiver output is digitized by an ADC and strobed into a bulk memory for target detection processing. The samples within a range gate (all range bins of interest) are added together coherently for a period of time that may vary anywhere from several seconds to several minutes depending on the targets being detected. Beyond the time where coherent integration is performed, the returns from the sea may be added noncoherently. That is, since the samples from beyond the horizon are stored digitally, a good deal of flexibility in the processing now exists (mostly to correct for the ionospheric modulation of the Doppler). Pulse OTHR systems use short pulses or pulse compression to obtain highrange resolution and a high peak power is required to obtain the necessary average power for target detection. This high transmitted power can lead to antenna design constraints and gives rise to impulsive interference that can easily be identified within the HF band. The engineering compromise to using high peak power, low duty cycle waveforms is to use CW frequency sweeping such as the FMCW. Modern sky wave emitters for example, take advantage of low power (30W in the case of WERA [36]) FMCW modulation. Although there is currently no military OTHRs that use tens or hundreds of W, the low power emitted makes it easy for them to hide within other HF radio services and interference. sky wave OTHRs for air vehicle detection must use much higher powers than 30W. JORN and the US OTH-B use hundreds of kW average power. The use of FMCW modulation to transmit and receive continuously maximizes the average power out of the transmitter’s amplifiers providing the range resolution inherent in a given transmission bandwidth. The disadvantages in using an FMCW are the spectral purity required in the waveform generator and the high dynamic range required in the receiver which has to handle the strong direct path (transmit antenna to receive antenna) and the weak signals from far ranges. Doppler information must also be derived by repeating the FM sweep a number of times (e.g., 64 or 128) and then performing the FFT in each range gate to examine the phase history

264

Detecting and Classifying LPI Radar

of any target in that gate. After these repeated FMCW sweeps in any given dwell or surveillance time, the OTHR moves to survey other azimuths and ranges that are part of the surveillance plan. Due to the frequency range of OTHR systems and the low volume data rates, new digital receivers can now directly digitize the returned CW signal with high resolution without the need for down conversion to intermediate frequencies (as is conventionally done for microwave emitters). The signal processor uses a primary FFT to sort the echo returns into range bins and a second FFT is used to calculate the range-Doppler map. For the OTHR, the unambiguous range of operation is given by [37] Ru =

c 2WRF

(8.5)

where WRF is the waveform repetition frequency WRF = 1/tm Hz and tm is the modulation period. The range resolution depends on the modulation bandwidth ∆F that is used. The return signals are accumulated over this bandwidth which determines the range resolution. The range resolution (m) is given by c (8.6) ∆R = 2∆F For a WRF, the blind speed which varies as a function of fc as [37] ν=

cWRF 2fc

(8.7)

For the surface-mode (detection of ships), a narrow modulation bandwidth ∆F is used with a high WRF. For the air-mode (detection of aircraft targets), a large modulation bandwidth is used with a smaller WRF. In both propagation cases the amount of energy scattered from the target back to the radar receiver is extremely small. In addition, the HF bandwidth used represents a wide percentage of the tunable bandwidth and the signals received after propagation are nonstationary. Each region within the coverage area is illuminated with the FMCW and coherent integration is performed over a number of modulation periods. The coherent integration time (CIT) must be long enough to extract the target echoes. The CIT is variable to accommodate the changing ionospheric, clutter conditions, and target types. Illumination for a long CIT however, works against the OTHR in terms of avoiding a noncooperative intercept. If the CIT is too short however, the low Doppler resolution cannot separate the ship from the large ocean clutter. For the aircraft target, a short CIT is not a problem since the speed separates it well from the clutter. A significant problem is the robust high-resolution Doppler processing of accelerating or decelerating targets [38]. The waveform parameters that can be set include the WRF, the operating frequency, the modulation bandwidth and the CIT. Multiple

Over-the-Horizon Radar

265

WRFs are used while the target is being illuminated and this solves the range Doppler ambiguity. Multiple carrier frequencies (either simultaneous or time multiplexed) are also used to enhance the target detection capability.

8.3

Sky Wave LPI Waveform Considerations

The repetitive nature of the frequency sweeping is one of the main drawbacks of the FMCW technique. The concentration of power into narrow HF bandwidths and the additional element of repetition (e.g., with the same WRF) makes the OTHR vulnerable to detection, which can lead to electronic attack and deception. Consequently, the move away from these traditional waveforms to the incorporation of new LPI modulations is being actively pursued. Changing the modulation parameters makes it even more diﬃcult to DF the emitter and identify the OTHR system location.

8.3.1

Phase Modulation Techniques

Phase modulation CW techniques such as Barker binary phase coding (with low time side lobes) have been considered [4]. For a coherent integration time CIT, more than one modulation period is integrated. Including the CIT, the peak side lobe level or PSL (see Chapter 3) is given by W w tb (8.8) PSL = 20 log10 WRF For example, for a tb = 50 μs subcode width and WRF = 5 s, a PSL = −100 dB is available everywhere in the ambiguity space. Time domain weighting is used to control the Doppler side lobes at the zero range cut (at the expense of Doppler resolution). Without weighting or uniform weighting, the zero-range cut follows the sinc pattern with −13 dB side lobes. Polyphase codes are also being explored since they provide low side lobes without the use of weighting. Using polyphase codes with Nc subcodes w W 1 (8.9) PSL = 20 log10 Nc For example, for Nc = 64, PSL = −36 dB. The polyphase codes however, have a significant Doppler tolerance and therefore are not useful as a Doppler sensitive waveform. As discussed in Chapter 5, polyphase codes oﬀer the LPI CW emitter good flexibility in achieving a large processing gain or timebandwidth product and can be quite useful in OTHR systems.

266

8.3.2

Detecting and Classifying LPI Radar

Costas Frequency Hopping

Frequency hopping Costas codes are also being explored. The peak side lobe level for a given Costas time-bandwidth product is W w 1 (8.10) PSL = 20 log10 B(WRF) For example, for B = 20 kHz and a WRF = 5 s, a PSL = 100 dB can be achieved in addition to a thumbtack ambiguity function. Increasing the time-bandwidth product of these CW modulations using larger bandwidths is also being pursued entailing operations over a discontinuous signal spectrum (due to all of the other radio traﬃc), an approach similar to the surface wave techniques that are used.

8.3.3

Reducing the CIT

In addition to the goal of LPI, a surveillance plan to scan, detect and track surface targets over large areas requires a short CIT in order that the tracker can receive the periodic updates in a timely fashion. To enable a short CIT, eﬃcient clutter cancelation algorithms are actively being pursued to improve signal-to-clutter ratio. Fourier-based clutter cancelation algorithms have shown success for OTHR and are based on modeling the first order clutter as a sinusoid and subtracting it from the data. The Fourier technique estimates the clutter frequency, amplitude and phase [9] from the Doppler spectrum. A high clutter-to-noise ratio for the Bragg peaks is required in order to estimate the initial phase for the clutter subtraction.

8.3.4

Multiple Waveform Repetition Frequencies

Unlike a pulsed signal, with FMCW, an ambiguous Doppler frequency is not folded within the same time delay resolution cell but is shifted to a nearby time delay cell. Recall that this cross-coupling eﬀect is the range-Doppler ambiguity of this waveform. One technique to overcome this ambiguity problem, which also leads to a more LPI waveform, is the use of multiple WRFs within a single illumination period [5]. It is also wellknown that ionospheric instability noise (due to polar and equatorial regions) has the potential to appear through a range ambiguity on top of the signals of interest if the WRF ≥ 7.5 Hz. This causes problems for aircraft which have Doppler frequencies of 5—60 Hz. Consequently, Doppler frequencies greater than this must be resolved without any range ambiguities. To understand the use of multiple WRF technique, we revisit the FMCW range-Doppler cross coupling eﬀect as presented in Chapter 4. Recall that the beat frequency is proportional to the range of a stationary target (or one

Over-the-Horizon Radar

267

that has a Doppler shift fd < ±1/2t0 ) as R=

cfb t0 2∆F

(8.11)

and the corresponding range resolution ∆R =

c c∆tmin = 2∆F 2

(8.12)

where ∆tmin = 1/∆F s is the minimum time delay that can be detected. Due to the range-Doppler cross coupling eﬀect, if the target is moving at a velocity such that fd > ±1/2t0 , the beat frequency is fm = fb ± fd and corresponding range of the target is given by Rm =

cfb t0 cfd t0 ± 2∆F 2∆F

(8.13)

and shows that the measured range is a function of the true range and an error due to the Doppler shift or Rm = R ± Rd . The range error due to the Doppler shift can be re-written in terms of range bins as [5] fd Rd =± ∆R WRF

(8.14)

where WRF = 1/t0 . This shows that the measured range is increased (or decreased) by one range bin as the Doppler shift is decreased (or increased) by a frequency equal to the WRF. In the multiple WRF technique, three WRFs are used during a single target illumination time as shown in Figure 8.11. Since the waveform repeti-

Figure 8.11: Coprime waveform repetition frequencies. tion frequencies of the waveforms are diﬀerent, aliasing causes the estimated Doppler shifts to be diﬀerent during each WRF. The Chinese remainder theorem can then be utilized to calculate the true Doppler shift where the maximum unambiguous Doppler range is limited by the least common multiple (LCM) of the selected WRFs [5, 6]. The duration and number of coprime

268

Detecting and Classifying LPI Radar

WRF sweeps are chosen to resolve the range ambiguities and to achieve the required Doppler resolution respectively. The Doppler shifts are unique for each WRF block and estimated sequentially using two FFTs as in normal FMCW processing. For OTHR surface mode targets, it is only necessary to extend the unambiguous Doppler to ±70 Hz so WRF3 = 7, WRF2 = 6, and WRF1 = 5 are suﬃcient giving a maximum unambiguous Doppler coverage of 3

fd = ±

1 WRFi = ±105 Hz 2 i=1

(8.15)

In selecting the WRF, the first limitation is the maximum unambiguous range Rmax ≤

ctm2 ctm1 ctm3 < < 2 2 2

(8.16)

where tmi are the corresponding modulation periods for the three WRFs (tmi = 1/WRFi ) [6]. The diﬀerence in range bins between the three WRFs should be large enough to separate the clutter. If NRB is the number of bins covered by the clutter then to ensure a clutter free range NRB =

∆F ∆F − WRF1 WRF2

(8.17)

NRB =

∆F ∆F − WRF2 WRF3

(8.18)

and also

which is the smallest diﬀerence. Rewriting (8.18), NRB WRF3 − WRF2 < ∆F WRF3 WRF2

(8.19)

and choosing WRF3 = WRF2 + 1, (8.19) is then ∆F > WRF22 + WRF2 NRB

(8.20)

A fixed waveform repetition frequency emitter is able to resolve Doppler frequencies within ±WRFi /2. With the WRFi satisfying WRF3 > WRF2 > WRF1 , the Doppler shift of the target can be written as [5] fd = n1 WRF1 + x1 = n2 WRF2 + x2 = n3 WRF3 + x3

(8.21)

where n1 , n2 and n3 are either a positive or a negative integer depending on the Doppler shifts and x1 , x2 and x3 are the corresponding fractions that are the measured Doppler shifts of certain targets with the limits −WRFi /2 ≤ xi ≤ WRFi /2.

Over-the-Horizon Radar

269

Below we present the alternate solution using the Chinese remainder theorem (CRT) and repeat the example in [5]. The problem is first set up as a set of simultaneous congruences fd ≡ x1 (mod WRF1 ) fd ≡ x2 (mod WRF2 ) fd ≡ x3 (mod WRF3 )

(8.22)

When WRFi are N positive integers that are coprime, the set of congruences have a unique solution modulo M=

N

WRFi

(8.23)

i=1

Any integer congruent modulo M to a given solution is also a solution. (The proof and straightforward computation of the CRT is given in [39].) The solution of the simultaneous congruences is fd =

N 3 j=1

or for N = 3

M bj xj WRFj

(8.24)

f0 = WRF2 WRF3 b1 x1 + WRF1 WRF3 b2 x2 + WRF1 WRF2 b3 x3 (mod M ) (8.25) The bi values are found by a repeated application of the Euclidean algorithm. So to complete the CRT solution we consider the example given in [5] where WRF1 = 5 Hz, WRF2 = 6 Hz, and WRF3 = 7 Hz and the corresponding ambiguous Doppler shifts are x1 = 2 Hz, x2 = −2 Hz, and x3 = 3 Hz. For b1 , since the greatest common divisor of 42 (M/WRF1 = WRF2 WRF3 ) and 5 (WRF1 ) is 1, the Euclidean algorithm is used to solve for x0 , y0 such that 42x0 + 5y0 = 1. Then we have 42x0 ≡ 1(mod 5), so b1 = x0 . Applying the algorithm [39] 42(1) + 5(0) = 42 42(0) + 5(1) = 5 42(1) + 5(−8) = 2 42(−2) + 5(17) = 1 and consequently, b1 = −2. Repeating the application of the Euclidean algorithm for b2 and b3 gives b2 = −1 and b3 = −3. The solution (8.25) is then (8.26) fd = −4(42) + 70 − 270(mod 210) = −368 which is out of the proper range (0 to 209). However, M = 210 goes into −368 two times, so −368 + 2(210) = 52 solves the problem and is the least positive solution. That is fd = 52 Hz as also solved in [5]. The technique presented here determines the actual Doppler frequency and is a more straightforward method using the CRT.

270

8.3.5

Detecting and Classifying LPI Radar

Out-of-Band Emission Suppression

In MIMO systems, the design objectives are transmitter element waveform orthogonality (using either temporal or spectral diversity). The implementation is limited by the performance of the transmission system especially the out-of-band emissions. New approaches to FMCW waveform design and to waveform generation have been adopted that are theoretically capable of achieving much lower out-of-band spectral levels [13]. Spectrum leakage that is out of band can be a significant beacon for HF/DF systems trying to noncooperatively identify the emitter. For FMCW sky wave emitters, out-of-band emission suppression is a major consideration and steps are usually taken to insure compliance with for example, the International Telecommunication Union (ITU). The ITU-R spectral management document SM.1541-1 provides recommendations on out-of-band emission advice for a number of radar waveforms including the FMCW waveform. The reduction of side lobes through time and frequency weighting can be done to improve the out-of-band emission spectrum while improving the in-band performance. One choice is to smooth the frequency transition region at the ends of each chirp by smoothing the signal in either the instantaneous frequency or amplitude domains [14]. Recall that a single sawtooth FMCW signal frequency can be written in the time domain as ∆F t + fc (8.27) fI (t) = tm for |t| ≤ tm /2. The complex signal is then v(t) = ejφ(t) where φ(t) =

π∆F 2 t + 2πfc t tm

(8.28)

(8.29)

for |t| ≤ tm /2. The spectral taper method begins by designing the waveform in the spectral domain and including a modulation with a taper function wST (f ) 8 ∞ wST (f )v(f )ej2πf t dt (8.30) vf m = −∞

The function vf m can then be inverse Fourier transformed to derive the signal. Taper functions such as the Hann taper function have been used. The taper however, does change slightly, the signal’s phase, amplitude and instantaneous frequency. The instantaneous frequency of the FMCW waveform is also a discontinuous function. A simple method to reduce this discontinuity is to introduce

Over-the-Horizon Radar a counter sloping chirp at the waveform end as [14] W w ∆F 1 fI (t) = t + fc 1 − γ tm

271

(8.31)

for −tm /2 ≤ t ≤ (1 − 2γ)tm /2 and fI (t) = −∆F t/(γtm ) + fc otherwise. Here 0 ≤ γ ≤ 1/2 is the flyback factor. The flyback factor accounts for the amount of time required for the sawtooth FMCW to return to the beginning frequency. To reduce the roll-oﬀ rate the application of amplitude tapering can be applied. For example, a cosine-Tukey amplitude taper wCT (t) in the time domain on the signal takes the form vam (t) = wCT (t)v(t)

(8.32)

This technique provides excellent out-of-band emission control even with low percentage tapering (e.g., 10%) causing only a small amount of loss in coherent gain. The penalty when using this approach is that the Fresnel ripples, which are usually a characteristic of the spectrum of the weighted chirp signal, now appear in the time domain waveform. The waveform to be transmitted has small amplitude ripples that must be preserved if the desired spectral performance is to be maintained [13]. That is, high linearity must be maintained at full output power levels.

8.4

Sky Wave Maximum Detection Range

The relative performance of the best known sky wave OTHR systems is shown in Figure 8.12. One of the important performance parameters of the OTHR is the maximum detection range. Figure 8.13 shows the OTH-B sky wave target detection geometry. The received power at the radar receiver from the target can be expressed as PRT =

PCW GT GR λ2 σT 2L (4π)3 RT2 RR P 2 LF L

(8.33)

where PCW is the average transmitter power in watts, GT is the transmit antenna gain, GR is the receive antenna gain, λ is the wavelength at the carrier frequency fc , σT is the target’s radar cross-section, the term LP 2 is the two-way transmission path loss and is on the order of 10—20 dB [21], L is the system losses which include the transmitter and receiver subsystem losses which are 15 dB [23]. LF is the Faraday polarization loss of the ionosphere which is typically 3 dB [21], RT is the distance of the ray path traveling from the radar, reflecting oﬀ of the ionosphere down to the target and RR is the distance of the return ray path traveling from the target to the receiver also reflecting

272

Detecting and Classifying LPI Radar

Figure 8.12: Relative performance of the best known sky wave OTHR systems (after [22]). oﬀ of the ionosphere. Understanding the ionosphere, and how it aﬀects the transmit and received waveform (from the target) is critical to predicting the OTHR capability. For example, the ionosphere can modulate the target’s Doppler profile making it undetectable. This is discussed in greater detail in the following sections. The minimum input signal-to-noise ratio SNRRi is related to the receiver’s sensitivity δR . The receiver can detect and process an incoming target signal at this signal level or higher. Substitution of the sensitivity for PRT in (8.34), the maximum detection range (reflecting oﬀ of the ionosphere) of the radar becomes W1/4 w PCW GT GR λ2 σT (8.34) RR max = (4π)3 δR LP 2 LF L where RRmax is calculated by assuming that the OTHR transmitter and receiver are located at the same range from the target RT = RR . The sensitivity δR is the product of the minimum SNR required at the input SNRRi times the noise power in the input bandwidth of the receiver or δR = kT0 FR BRi (SNRRi )

(8.35)

where k is the Boltzmann’s constant (k = 1.3807×10−23 J/K), T0 is the standard noise temperature (290 K), FR is the receiver noise factor and includes

Over-the-Horizon Radar

273

Figure 8.13: Target detection diagram. the fact that the additional noise is 20—50 dB larger than the receiver’s thermal noise, and BRi is the receiver’s input bandwidth in Hertz. The maximum detection range (reflecting oﬀ of the ionosphere) then can be expressed as W1/4 w PCW GT GR λ2 σT (8.36) RR max = (4π)3 kT0 FR BRi (SNRRi )LP 2 LF L Consider the Chinese FMCW OTH-B radar characteristics with PCW = 1.2 MW (61 dBW), GT = 18 dB and GR = 26 dB at 14.5 MHz, FR = 40 dB, BRi = 30 MHz, LP 2 = −15 dB, L = −15 dB, and LF = −3 dB [21, 40, 41]. The separation distance is typically 60—200 km for the Chinese OTH-B radar system [21]. We can calculate the modulation bandwidth ∆F from the published range resolution 15 km = ∆R = c/2∆F or ∆F = 10 kHz. Figure 8.14 shows the radar maximum detection range (reflecting oﬀ of the ionosphere) as a function of the required input SNR (SNRRi ) for 1, 10, and 100 m2 at operating frequencies fc = 14.5 MHz [22]. Assuming a flat Earth situation, the detection range Rfootprint along the Earth becomes w W2 RR max Rfootprint = 2 (8.37) − h2 F 2layer 2 where hF 2layer is the F2-layer height from the Earth’s surface. For this example, assume the F2-layer height is about 240 km. The geometry diagram for (8.37) is shown in Figure 8.15. The detection distance along the flat Earth (Rfootprint ) is calculated from (8.36) and (8.37) as shown in Figure 8.16.

274

Detecting and Classifying LPI Radar

Figure 8.14: FMCW OTH-B maximum detection range (RR max ) for σT = 1, 10, and 100 m2 [22]. From [21], the Chinese OTH-B radar has a skip zone or minimum detection range of 700 km and a maximum detection range of 3,500 km. For a maximum detection range along the flat Earth Rfootprint = 3,500 km, the RR max is calculated as 3,532 km from (8.36). The minimum required input SNR (SNRRi ) for fc = 14.5 MHz for σT = 1, 10, and 100 m2 is −107, −97 and −87 dB respectively from Figure 8.16. The processing gain of the emitter’s waveform used then provides the suﬃcient SNR for target detection. After target detection, coordinate registration is used for multipath tracking to convert the slant ranges and slant azimuth to surface coordinates. Several methods based on planar and spherical models have been reported recently [42—44]. Furthermore, with sophisticated processing to eliminate the coherent integration loss caused by irregular target motions, the transmit power can be lowered considerably.

8.5

Sky Wave Footprint Prediction

PROPLAB PRO is a propagation software for the personal computer that calculates the precise behavior of radio signals as they travel through the atmosphere. It simulates accurately, radio transmissions into the ionosphere using sophisticated ionospheric ray-tracing techniques [45]. One of the OTHR

Over-the-Horizon Radar

275

Figure 8.15: Geometry diagram of the detection range calculation. parameters that is of high interest to the noncooperative intercept receiver to predict is the emitter footprint or coverage area. For the Chinese OTHB radar, the transmitter is assumed to be located at Nanjing (32.05o N, 241.22o W) and the target is located at coordinates 30o N, 204.3o W which is 3,500 km distance away from the transmitter. A typical transmitter antenna radiation pattern is shown in Figure 8.17 with a maximum transmit gain of 18 dB at 14.5 MHz from a vertical dipole array pointed in azimuth 85o from true North (towards the United States). Simulation results for the summertime SSN 200 are shown below. The level of geomagnetic activity (A-Index, AI) = 5 on 21 July 2007. The electron density profile (Ne ) at the midpoint ( 32.37o N, 222.55o W) of the transmitter and the target along the great-circle path is shown in Figure 8.18. The D, E, F2 and topside layers are shown. The maximum usable frequency (MUF) profile (24-hour period) is shown in Figure 8.19 with the F2-layer MUF (the top-most line), optimum working frequency or FOT (the second line), average MUF of E and F-layer (the thin line next to FOT line), and the E-layer MUF (the bottom line). The most often used frequency range is between the FOT and the average MUF of E and F layer. From Figure 8.19, the maximum and minimum FOT values are 28 MHz at 08:00 UTC (coordinated universal time) and 20 MHz at 19:00 UT (universal time). Based on the maximum and minimum FOTs, the ray tracing screens can be generated as shown in Figures 8.20 and 8.21. To examine the footprint coverage and the skip zones generated as a function of frequency and elevation angle, the ray trace plots for fc = 6, 8, 10, 12, 14, 16, 18, 20 and 22 MHz were generated for angles between 0o and 20o . For these results SSN = 200 and the AI = 5 on 0:00 UTC 2007/7/31. Figure 8.20 shows the results for 10 MHz and 14 MHz. Two eﬀects can be noticed from the results. First, the increase of frequency toward the MUF results in an extended range and increased

276

Detecting and Classifying LPI Radar

Figure 8.16: FMCW OTH-B maximum detection range (Rfootprint ) for σT = 1, 10, and 100 m2 [22]. skip zone. In addition, when going from fc = 10 MHz to fc = 14 MHz, the 20o elevation launch angle finally penetrates the ionosphere. In Figure 8.7, a summary of the ray trace plots is shown. The range coverage for each frequency is shown (including the skip zone). Note that as the frequency approaches the MUF, the range increases. In Figure 8.21, fc = 18 MHz and fc = 22 MHz are shown. Considerable ionospheric penetration is occurring for SSN = 200 and the AI = 5 on 0:00 UTC 2007/7/31 as the frequency approaches the MUF.

8.6

Surface Wave OTHR

While the principles of HF surface wave or ground wave OTHR have been known for decades, they still present challenges to remain covert. Figure 8.22 shows the surface wave OTHR concept that uses a spatial separation of the transmit and receive system. The OTHR transmitter (XMTR) emits radio waves that follow the surface of the sea extending over the horizon. Surface wave radar works best when using vertically polarized antennas in contact with salty conducting water. The sea water is a good conductor and the air acts as the dielectric. As a result, the lowest layer of air and uppermost layer of sea form a waveguide in which the HF radiation is constrained by internal

Over-the-Horizon Radar

277

Figure 8.17: Example transmitter antenna radiation pattern for the OTH-B radar system [22].

Figure 8.18: Electron density profile for SSN = 200 and AI = 5 on 2007/6/21 [22].

278

Detecting and Classifying LPI Radar

Figure 8.19: Maximum usable frequency for SSN = 200 and AI = 5 on 2007/6/21 [22]. reflection. The antenna polarization is always chosen to be vertically polarized to avoid the higher attenuation associated with horizontal propagation. This coupling of the radiation to the sea surface provides a means to detect targets over the horizon beyond the line-of-sight limit experienced by conventional microwave radar systems. The surface wave method cannot be used over land, on freshwater lakes, or where fresh water dilutes the sea such as in the Baltic or the Nile Delta [23]. They do not require real-time knowledge of the ionosphere’s behavior. These systems are most applicable to naval applications. For example, monitoring a country’s exclusive economic zone and providing surface combatants with early warning of an attack by antiship cruise missiles. Being relatively inexpensive they are also widely used for collecting good quality wave, current and tidal information. Surface wave OTHR can detect surface and air targets from 10 to 400 km. The range is limited by the amount of power transmitted and the attenuation incurred. The attenuation can be predicted by examining the modified refractive index profile above the sea surface which is a function of the sea state and the atmospheric conditions. Computer programs such as the advanced refractive eﬀects prediction system (AREPS) [46] can give accurate predictions of current attenuation anywhere in the world. The range reso-

Over-the-Horizon Radar

279

Figure 8.20: Ray tracing results for SSN = 200 and the AI = 5 on 0:00 UTC 2007/7/31 for several elevation angles at (a) 10 MHz and (b) 14 MHz [22].

280

Detecting and Classifying LPI Radar

Figure 8.21: Ray tracing screen for SSN = 200 and the AI = 5 on 0:00 UTC 2007/7/31 for several elevation angles at (a) 18 MHz and (b) 22 MHz [22].

Over-the-Horizon Radar

281

Figure 8.22: Surface wave radar concept. lution varies widely from system to system and depends on the modulation bandwidth used which can be on the order of a few megahertz [8]. The optimum surface wave carrier frequency that is used depends critically on where the target of interest will appear in Doppler space relative to the clutter.

8.6.1

Example Surface Wave OTHR System

Raytheon Canada’s coastal surveillance radars are designed to detect and track ships, aircraft and ice formations out to ranges of up to 400 km [47]. The radars are shelter-mounted for ease of installation in remote locations and feature a comprehensive supervisory system for unattended operations. The also include spectrum management to enhance performance reliability. The SWR-503 (3.5—5.5 MHz) is optimized for long-range surveillance of targets out to a range of 407 km. The SWR-610 configuration (6—10 MHz) is designed for medium-range applications and features detection and tracking of smaller targets when compared with SWR-503. The transmit antenna is a monopole log periodic array and is shown in Figure 8.23. The receive array is a 16-element array on ground screen and is shown in Figure 8.24. The bandwidth is 3—80 kHz but is typically about 20 kHz (∆R = 7.4 km). Typical velocity resolution is 0.1 km/h (iceberg), 0.9 km/h (ship); 7.4 km/h

282

Detecting and Classifying LPI Radar

(aircraft). The average transmitter power is 3.2 kW with a peak power of 16 kW. The detection capability for the SWR-503 is shown in Figure 8.25 for several classes of air and surface targets.

Figure 8.23: SWR-503 transmit antenna configuration [47].

8.7

Surface Wave LPI Waveform Considerations

There are two problems with FMCW for surface wave systems. First, the necessary isolation between the transmitter and receiver for continuous-wave operation at HF frequencies is more diﬃcult to achieve. Second, due to the propagation losses, the signal levels decrease rapidly with distance and the dynamic range of the signals exceeds that of any available receiver hardware [7]. Due to heavy user congestion, surface wave OTHR systems are also restricted to operating within narrow frequency bands.

8.7.1

FMICW Characteristics

To overcome these problems, the spectrum must be made discontinuous and FMICW type signals are used [48]. The FMICW is an FMCW waveform that

Over-the-Horizon Radar

283

Figure 8.24: SWR-503 receive antenna configuration [47]. is gated on and oﬀ with a well defined sequence which is either pseudorandom (adding to the LPI nature of the emitter) or a deterministic sequence. The on and oﬀ gating or interruption process involves breaking the transmitted signal into an integral number of shorter bursts during the chirp period. To generate the FMICW, a synthesizer is used to produce a linear frequency swept waveform with frequency varying across the modulation bandwidth ∆F (chirp waveform). From Chapter 4 W ] }w ∆F 2 ∆F t+ (8.38) t s1 (t) = sin 2π fc − 2 2tm for 0 ≤ t ≤ tm . This waveform is then gated on and oﬀ to produce the pulsed waveform shown in Figure 8.26. The frequency sweep is pulsed P times by multiplying it by the gate signal which can be expressed as fT (t) = AT (t)s1 (t)

(8.39)

where the gating function is AT (t) =

P −1 3 n=0

rect[(t − nq − τR /2)/τR ]

(8.40)

284

Detecting and Classifying LPI Radar

Figure 8.25: SWR-503 detection capability for various classes of surface and air platforms [47]. where P is the number of short bursts, τR is the pulse width in seconds, rect(t/τR ) is a rectangular pulse of width τR centered at the origin and q is the gating period. The signal fT (t) = AT (t)s1 (t) represents a single FMICW sweep [49]. In Figure 8.26(a), the FMCW signal used to generate the FMICW is shown. In Figure 8.26(b, c) the transmitter gating sequence and the receiver gating sequence (complement of transmit sequence) are shown respectively. In Figure 8.26(d) the FMICW signal generated using the gating sequence in Figure 8.26(b) is shown. The eﬀect of target range on the received signal is shown in Figure 8.27 where for the same transmitted signal, the received signals are shown for two diﬀerent target ranges [7]. The FMICW concept is to transmit for a specific period of time and after the transmitter has been turned oﬀ, to receive during the quiet period. Both the transmit and receive waveforms are subjected to diﬀerent interrupt sequences. The FMICW allows the weak return signals to be more easily detected. With a duty factor of, for example, 50%, the average transmitted power is reduced by 3 dB compared to the FMCW waveform and the improved isolation typically decreases the system noise floor by more than 3 dB adding to the LPI nature of the emitter. It is important to remember that to prevent

Over-the-Horizon Radar

285

Figure 8.26: (a—d) FMICW generation showing transmit and receive gating (from [7]). eclipsing, the receiver must always be oﬀ whenever the transmitter is on. Further diﬀerences between the two sequences are introduced by soft gating which is used to suppress transients that would be caused if the interrupt sequences were switched rapidly between on and oﬀ states [7]. The radar returns from the targets are delayed by the two-way travel time td and are modified by the receiver gating sequence AR (t) as fR (t) = AR (t)AT (t − td )s1 (t − td )

(8.41)

fR (t + td ) = AR (t + td )AT (t)s1 (t)

(8.42)

or With the FMICW, the receiver must always be oﬀ whenever the transmitter is on so that the transmitter and receiver interrupt sequences are not identi-

286

Detecting and Classifying LPI Radar

Figure 8.27: FMICW radar echo from target with two-way travel time of (a) t1 s and (b) t2 s (from [7]). cal. This interrupted spectrum gives rise to high-range side lobes and consequently a low dynamic range [50]. Diﬀerences between the two sequences are introduced by the soft gating used to suppress these transients that would be caused if the interrupt sequences were switched rapidly between the on and oﬀ states. Depending on the target’s range, the transmitted waveform is generally not received at the radar in its entirety. There are three ways to extract the spectrum of the received echo from the target. The first method is to weight the return signal bursts individually and process the complete return as for a conventional FMCW receiver using a single long FFT. The second method is to weight each burst individually and pack the remainder of the signal with zeros and process the complete return as for a conventional FMCW receiver. The third method is to weight each burst individually and process each short section using an FFT matched to its length. Here an FFT with a duration equal to the burst period is used to produce a spectrum. The number of floating point operations required

Over-the-Horizon Radar

287

to generate the FFT is N log2 N where N is the number of record points in the FFT. Therefore it is more eﬃcient to generate a number of shorter FFTs and integrate them noncoherently than to generate a single long FFT. For example, for six bursts, the noncoherent integration improvement factor is about 6.2 dB compared with about 7.8 dB for coherent integration of the complete interrupted signal [7]. Conventional Doppler processing of FMICW is constrained by the limited time that a target is present in a range cell. Targets whose speed is outside the range of conventional processing have their signal energy smeared in range due to the target traversing several range cells within the processing period. This smearing however, can be removed with velocity-matched filters that perform phase corrections on the processed signal. The velocity-matched filters can accurately extract the range and velocity of a low-flying aircraft whose signal is aliased in velocity and smeared in range conventional processing.

8.7.2

FMICW Ambiguity Space

The relative time delays in the receiver gating sequences significantly change the actual signals gated into the receiver. The ambiguity function will also be diﬀerent for these two ranges and must be carefully considered for long range applications. Since the target Dopplers are very small, the zero Doppler ambiguity is suﬃcient to evaluate the performance of the waveform. The zero Doppler ambiguity function for the FMICW can be computed using 8 ∞ p p p τQ τQ τ Q j2πατ t AT t + dt (8.43) AR t + td − AT t − e χ(τ, α, td ) = 2 2 2 −∞ where α = ∆F/tm is the frequency sweep rate. The ambiguity function of the FMICW is evaluated in [7] and it is shown that the gating on the received signal varies with the target range and introduces a range dependence on the ambiguity function. That is, the performance of the FMICW emitter is dependent on the relationship between the transmit period and the round-trip time td and hence is range-dependent. The evaluation of the ambiguity function is diﬃcult for the FMICW due to the finite extent of the linear frequency sweep as well as the eﬀect of the interrupt sequence used. Note the inverse problem of determining the parameters of an FMICW waveform to realize a desired ambiguity function is more diﬃcult. Also, since the target velocities are typically very small, the zero-Doppler ambiguity function is suﬃcient to evaluate the performance of the waveform. It is very diﬃcult to find clear channels (30—100 kHz) in the HF band for use in FMICW. A sparse waveform design can help mitigate the interferences; however, it also gives rise to high-range side lobes. The cochannel interference that is present can be mitigated by using an adaptive coherent side lobe cancelation algorithm based on forming subarrays that use negative frequency

288

Detecting and Classifying LPI Radar

range bin samples to calculate the covariance matrix and correlation vector as described in [15]. Improvements in signal-to-interference ratio on the order of 20 dB can be achieved. The sparse waveform approach is to find the interference-free channels in the HF band and then transmit the signal in these clear channels. The main problem caused by the spectrum discontinuity is the range side lobes that are created [8]. Another interesting approach is to use a multiparametric generalization of the nonuniform FMICW train and by exploiting a factorization of the ACF based on genetic algorithms, an optimal solution has been proposed [8]. A new FMICW waveform is presented in [51] and provides high-range resolution using a larger modulation bandwidth and a narrow modulation period to achieve a longer coherent integration time for high-speed targets. To prevent the high speed targets from smearing into many range cells during the longer integration periods, two frequency sweep bandwidths with diﬀerent sweep repetition intervals are used to determine the required coherent integration time (CIT) and ∆R independently. The target velocities are estimated using one waveform and then applied to compensate the velocity phase terms to account for the target movement. Due to the ability of higher order correlation and spectral analysis methods to eﬀectively suppress symmetrical distributions such as Gaussian noise, these techniques have also been explored for interference cancelation and signal detection in OTHR [52].

8.8

Surface Wave Maximum Detection Range

The HF radar system planning and implementation problem is compounded by the influence of the conducting ground plane on the radiation resistance of radar antennas and target backscattering cross-section. The potential error resulting from basing a system design on a radar equation with an inconsistent set of parameter definitions is high. Without careful attention to detail, predicted received signal-to-noise ratios might be in error by 10 dB or more. To determine the maximum detection range as a function of the input required SNR, we develop the surface wave radar equation taking into account three eﬀects that do not occur in conventional radars [53]: 1. A doubling of field strength due to direct and ground reflected waves; 2. A mutual impedance between the antennas and their images in the ground plane; 3. A coupling between the target and its image in the ground plane. Eﬀects (2) and (3) are only significant when the antenna or the target is within approximately one wavelength of the ground. Due to the HF wavelength, most antennas and some classes of target will be within one wavelength of the ground and so the eﬀects cannot be ignored. The coupling of the antennas

Over-the-Horizon Radar

289

Table 8.1: RISP Gains for Some Example Antennas Antenna Isotropic in free-space Isotropic on a perfect ground plane Hertzian dipole in free-space Hertzian dipole on a perfect ground plane λ/4 monopole on a perfect ground plane

Gain (dB) RISP dBi 0 0 0 3 1.8 1.8 1.8 4.8 2.2 5.2

and target with their images in the ground modifies their radiation resistances and this is the root cause of eﬀects (2) and (3). In this section it is convenient to describe the gain of an antenna as Relative to an isotropic antenna at the same position (RISP). The RISP gain of some example antennas are presented in Table 8.1 along with the dBi value. To develop the surface wave equation we follow the development in [53] and begin with the power flux Fi , incident on a target due to transmission from a vertical Hertzian dipole over a perfectly conducting ground plane Fi =

E2 pt gt [2 sin θ cos(kht cos θ)]2 = Z0 4πd2 (1 + ∆t )

(8.44)

where E is the field strength, Z0 the impedance of free-space, pt the radiated power in the presence of the ground, the transmitting antenna has RISP gain gt and d is the distance between transmitter and target. The term (1+∆t ) is a factor to allow for coupling between the antenna and its image in the ground. The angle θ is the zenith angle of the target measured at the transmitter, k = 2π/λ, and ht is the dipole height above the ground. The term ∆ is given by ] ]} } sin(2kh) 3 − cos(2kh) (8.45) ∆= (2kh)2 2kh At h = 0, (1 + ∆) = 2. For h > λ, (1 + ∆) ≈ 1. The term in square brackets in (8.44) gives the vector sum of direct and ground reflected signals. When θ → π/2 pt gt 4 (8.46) Fi = 2 4πd (1 + ∆t ) The trailing factor of 4 is due to the in-phase addition of the direct and ground-reflected waves. For the collecting aperture of a target consider that the target is a matched antenna with RISP gain gx . The power available to the matched load is equal to that which is reradiated. The target power collecting aperture is given by 1 gx λ2 · 4π (1 + ∆x )

(8.47)

290

Detecting and Classifying LPI Radar

This expression comprises: 1. the aperture of an isotropic antenna in free-space, λ2 /4π; 2. a factor for additional gain, gx ; 3. a factor for coupling between the target antenna and its image in the ground (1 + ∆x )−1 . The power reradiated Prerad by the target is found by combining (8.46) and (8.47) as p 2Q λ gx 4π pt gt ·4· (8.48) Prerad = 4πd2 (1 + ∆t ) (1 + ∆x ) The power flux back at the receiver antenna FRR can be found by reapplying (8.46), to extend (8.48) as p 2Q λ g x 4π gx pt gt ·4· · ·4 (8.49) FRR = 4πd2 (1 + ∆t ) (1 + ∆x ) 4πd2 (1 + ∆x ) The second gx is the gain term for the power reradiated by the target, the trailing 4 indicates that the direct and ground-reflected waves from the target add in phase. The power available from the receiving antenna with RISP gain gr , when located above a perfectly conducting plane, is given by p 2Q λ gr 4π (8.50) (1 + ∆r ) Multiplying (8.49) and (8.50) gives the received power pr p 2Q p 2Q λ λ gx 4π gr 4π gx pt gt ·4· · ·4· pr = 4πd2 (1 + ∆r ) (1 + ∆t ) 4πd2 (1 + ∆x ) (1 + ∆t )

(8.51)

and is the main HF surface wave radar equation and includes the ground plane eﬀects on antennas, target, and propagation. The target backscattering term is evident only indirectly by the target gain gx . To be useful, it is necessary to relate gx to a target backscattering cross-section σT . Three definitions of the target backscattering cross-section coeﬃcient are considered. 1. Conventional microwave radar definition: w 2W 4gx2 λ σT = 2 (1 + ∆x ) 4π

(8.52)

Over-the-Horizon Radar

291

and relates the scattering cross-section of a matched antenna of RISP gain gx above a perfectly conducting ground plane with elevation h > λ. The factor (1 + ∆x )−2 accounts for the antenna collecting and reradiating properties. 2. Free-space backscattering cross-section definition: w 2W λ 2 σF S = gx 4π

(8.53)

and relates the backscattering cross-section of an isotropic antenna in free-space (absence of a ground plane). If the isotropic antenna were replaced by a target antenna with RISP gain gx , then its backscattering cross-section in free-space is given by σF S . 3. Shearman’s definition [54]: σs =

gx2

p

λ2 4π

Q

(1 + ∆x )2

(8.54)

which departs from the conventional microwave radar definition by a factor of 4 to allow for the ground reflection on the signal’s return to the receiver. By substituting for gx from (8.52), (8.53), and (8.54) into (8.49), we obtain three diﬀerent equations, all equally valid, but using diﬀerent definitions of the target cross-section: p 2Q λ 4π σT (1 + ∆x )2 pt g t D λ2 i · 4 · · (8.55) pr = 2 4πd (1 + ∆t ) (1 + ∆x ) 4 4π p 2Q λ g r 4π 1 · 4 · · 4πd2 (1 + ∆x ) (1 + ∆r ) p 2Q λ 4π σF S pt g t · 4 · · D λ2 i pr = (8.56) 4πd2 (1 + ∆t ) (1 + ∆x ) 4π p 2Q λ g r 4π 1 ·4· · 4πd2 (1 + ∆x ) (1 + ∆r ) p 2Q λ 4π σs (1 + ∆x )2 pt g t D λ2 i · 4 · · pr = (8.57) 2 4πd (1 + ∆t ) (1 + ∆x ) 4π p 2Q λ g r 4π 1 ·4· · 4πd2 (1 + ∆x ) (1 + ∆r )

292

Detecting and Classifying LPI Radar

The propagation loss must now be addressed to be included in the expression for pr . Two definitions are given below and are ratios of transmitted power to received power and thus are values greater than unity. ITU-R Definition: The internationally recognized definition of basic transmission loss Ib is the ratio of radiated power to power available from a matched receiving antenna when the actual antennas are replaced by isotropic antennas at the same location as the actual antennas. For a one-way path above a perfectly conducting ground plane W2 w 2πd (1 + ∆t )(1 + ∆r ) (8.58) Ib = λ For antennas on the ground plane ∆t = ∆r = 1 and Ib is the same as the 2 free-space value of (4πd/λ) . Barrick Definition: In 1971, Barrick [55] published curves of additional groundwave attenuation for propagation over the sea when it is roughed by wind waves. As part of the work, Barrick included curves showing basic transmission loss over a smooth sea. Barrick’s theory and curves are very widely used in HF groundwave radar design. Barrick’s basic transmission loss, IBar , for a one-way path above a perfectly conducting ground plane is given by W2 w 2πd (8.59) IBar = λ

Note the two propagation loss quantities Ib and IBar are related as Ib = IBar (1 + ∆t )(1 + ∆r )

(8.60)

and Ib can be up to 6 dB greater than IBar (i.e., a possible diﬀerence of 12 dB on the two-way radar path). The three expressions for pr (8.55), (8.56), and (8.57) corresponding to the three definitions of target cross-section can be combined with the two expressions for propagation loss. This leads to six expressions for pr , as presented below. All six are equally valid. For the ITU-R version of loss Ib and the microwave definition of cross-section σT : 1 σT (1 + ∆x )2 1 D λ2 i pr = pt gt · (8.61) · gr Ib Ib 4 4π

For the ITU-R version of loss Ib and the free-space definition of cross-section σF S : 1 σF S 1 (8.62) pr = pt gt · D λ2 i · gr Ib Ib 4π

Over-the-Horizon Radar

293

For the ITU-R version of loss Ib and the Shearman definition of cross-section σs : 1 σs (1 + ∆x )2 ) 1 D λ2 i pr = pt gt · (8.63) · gr Ib Ib 4π

For the Barrick version of loss IBar and the microwave definition of crosssection σT : pr

σT (1 + ∆x )2 1 D λ2 i · IBar (1 + ∆t )(1 + ∆x ) 4 4π 1 · gr · IBar (1 + ∆r )(1 + ∆x )

= pt gt

(8.64)

For the Barrick version of loss IBar and the free-space definition of crosssection σF S : pr = pt gt

σF S 1 1 · D λ2 i · · gr IBar (1 + ∆t )(1 + ∆x ) I (1 + ∆ Bar r )(1 + ∆x ) 4π

(8.65)

For the Barrick version of loss IBar and the Shearman definition of crosssection σs : pr

= pt g t ·

σs (1 + ∆x )2 1 · D λ2 i IBar (1 + ∆t )(1 + ∆x ) 4π

(8.66)

1 · gr IBar (1 + ∆r )(1 + ∆x )

The maximum detection range of the surface wave emitter can be determined by substituting the receiver’s sensitivity δI = kT0 FR BRi (SNRRi )

(8.67)

for the return power pr (given by the six equations) and then solving for the distance d. Figure 8.28 shows the results of two simulations (fc = 5 MHz and fc = 15 MHz) using the surface wave MATLAB code surface detect.m on the CD. Other (default) parameters include pt = 100 kW, gt = gr = gx 3 dB, ht = hr = 10m, hx = 5m. The emitter input bandwidth BRi = 30 MHz and the receiver has a noise factor of FR = 10 dB with kT0 = 4 × 10−21 W/Hz.

294

Detecting and Classifying LPI Radar

Figure 8.28: Surface wave emitter maximum detection range as a function of the required SNRRi for fc = 5 MHz and fc = 15 MHz.

Over-the-Horizon Radar

8.9

295

Concluding Remarks

Both surface wave and sky wave radars experience ionospheric clutter (unwanted backscatter from the moving ionosphere) that can sometimes hide the presence of the desired target echoes. Sky wave radars can also suffer significant polarization losses and focusing/defocusing problems due to ionospheric eﬀects. Military HF radars are susceptible to deliberate jamming and consequently they are incorporating LPI waveforms and techniques to prevent their detection while fulfilling their early warning role while avoiding electronic warfare measures (for example, see [4, 15]). Another significant problem in OTHR is robust high-resolution Doppler processing of accelerating or decelerating targets. The ionosphere often modulates the return signals and spreads the Doppler, which makes it diﬃcult to detect targets. This Doppler eﬀect arises during aircraft and ship target maneuvers and during observations of rockets in boost phase and mid-course phase flight. Most OTHR systems use classical Doppler processing, where one Doppler spectrum is computed using one full CIT. Typically, the CIT is on the order of 1—100 seconds in OTHR systems. Some systems use overlapped Doppler processing to provide a spectrogram analysis of time-varying Doppler [6]. Today, more than ever, the prediction of OTHR performance is important especially for naval systems that are trying to avoid being detected at a longrange distance. Sky wave simulation results show that for Rfootprint = 3500 km, the minimum required input SNR (SNRRi ) for fc = 14.5 MHz for σT = 1, 10, and 100 m2 is −107, −97 and −87 dB, respectively, from Figure 8.16. PROPLAB results have been shown for one day. The results however will change depending on the time of year as well as the time of day.

References [1] Wise, J.C., “Summary of Recent Australian Radar Developments,” IEEE Aerospace and Electronic Systems Magazine, pp. 8—10, Dec. 2004. [2] Kolosov, A. A., Over-the-Horizon Radar, Artech House Inc., Norwood, MA, 1987. [3] Headrick, J. M., and Skolnik, M. I., “Over-the-horizon radar in the HF band,” Proc. of IEEE, Vol. 62, No. 6, pp. 664—673, 1974. [4] Green, S. D., Kingsley, S. P., and Biddiscombe, J. A., “HF radar waveform design,” Proceedings of the HF Radio Systems and Techniques Conf., 4—7 July, pp. 202—206, 1994. [5] Musa, M., and Salous, S., “Ambiguity elimination in HF FMCW radar systems,” IEE Proc. Radar, Sonar and Navig. Vol. 147, No. 4, pp. 182—188, Aug. 2000.

296

Detecting and Classifying LPI Radar

[6] Musa, M., and Salous, S., “Evaluation of multiple WRF-HF-FMCW radar waveforms,” Proc. of the IEE HF Radio Systems and Techniques Conf., pp. 207—211, 2000. [7] Khan, R. H., and Mitchell, D. K., “Waveform analysis for high-frequency FMICW radar,” IEE Proc.-F, Vol. 138, No. 5, pp. 411—419, Oct. 1991. [8] Liu, W. X., Lu, Y. L., and Lesturgie, M., “Optimal sparse waveform design for HFSWR system,” International Waveform Diversity and Design Conf., pp. 127—130, 4—8 June 2007. [9] Guo, X., Ni, J. L., Liu, G. S., “Ship detection with short coherent integration time in over-the-horizon radar,” Proc. of the International Conf. on Radar, pp. 667—671, 3—5 Sept. 2003. [10] Anderson, S. J., Mei, F. J., and Peinan, J., “Enhanced OTHR ship detection via dual frequency operation,” Proc. of the CIE International Conf. of Radar, pp. 85—89, 2001. [11] Wei, Y., and Liu, Y., “New anti-jamming waveform designing and processing for HF radar,” Proceedings of CIE International Conf. of Radar, pp. 281—284, 2001. [12] Frazer, G. J., Abramovich, Y. I., and Johnson, B. A., “Spatially waveform diverse radar: perspectives for high frequency OTHR,” Proc. of the IEEE Radar Conf., pp. 385—390, 2007. [13] Topliss, R. J., Maclean, A. B., Wade, S. H., Wright, P. G., and Parry, J. L., “Reduction of interference by high power HF radar transmitters,” Proc. of the IEE HF Radio Systems and Techniques Conf., No. 411, pp. 251—255, July 1997. [14] Turley, M. D. E., “FMCW radar waveforms in the HF band,” Input to the ITU-R JRG 1A-1C-8B meeting, November 2006. http://www.its.bldrdoc.gov/meetings/itu-r/contributions4/jrg-73.pdf. [15] Xianrong, W., Hengyu, K., and Biyang, W., “Adaptive cochannel interference suppression based on subarrays for HFSWR,” IEEE Signal Processing Letters, Vol. 12, No. 2, pp. 162—165, Feb. 2005. [16] Lu, K., Liu, X., and Liu, Y., “Ionospheric decontamination and sea clutter suppression for HF skywave radars,” IEEE Journal of Oceanic Engineering, Vol. 30, No. 2, pp. 455—462, April 2005. [17] Guo, X., Hongbo, S., and Yeo, T. S., “Transient interference excision in overthe-horizon radar using adaptive time-frequency analysis,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 43, No. 4, pp. 722—735, April 2005. [18] Tarran, C. J., “Operational HF DF systems employing real time superresolution processing,” Proc. of the IEE HF Radio Systems and Techniques Conf., No. 411, pp. 311—319, July 1997. [19] Dawber, W. N., Pote, M. F., Turner, S. D., Graddon, J. M., Barker, D., Evans, G., and Wood, S. G., “Integrated antenna architecture for high frequency multifunction naval systems,” Proc. of the CIE International Conf. of Radar, pp. 1—5, 2006.

Over-the-Horizon Radar

297

[20] Huang, G., Meng, J., and Yang, L., “Time-delay estimation for sub-sampling sinusoidal signals,” Proc. of the International Conf. on Communications, Circuits and Systems, pp. 761—764, 2005. [21] Xiaodong, T., Yunjie, H., and Wenyu, Z., “Sky wave over-the-horizon backscatter radar,” Proceedings of the CIE International Conf. on Radar, pp. 90—94, 15—18 Oct. 2001. [22] Liu, B-Y, Pace, P. E., and Knorr, J. B., “HF skywave FMCW OTH-B systems expected emitter footprint,” Proc. of the IEEE System of Systems Engineering Conf., Monterey, CA, June 2008. [23] Kingsley, S., and Quegan, S., Understanding Radar Systems, Scitech, Mendham, NJ, 1999. [24] Davies, K., Ionospheric Radio, IEE Electromagnetic Waves Series, Vol. 31, IEEE Electromagnetic Waves Series, 1990. [25] http://www.utdallas.edu/research/spacesciences/ionosphere.htm (The Earth’s Ionosphere). [26] Dyson, P. L., and Bennett, J. A., “Exact ray path calculations using realistic ionospheres,” IEE Proc. - H, Vol. 139, No. 5, pp. 407—413, Oct. 1992. [27] Ong, C. Y., Bennett, J. A., and Dyson, P. L., “An improved method of synthesizing ground backscatter ionograms for spherical ionospheres,” Radio Science, Vol. 33, No. 4, pp. 1173—1185, 1998. [28] Croft, T. A., and Hoogasian, H., “Exact ray calculations in a quasi-parabolic ionosphere with no magnetic field,” Radio Science, Vol. 3, No. 1, pp. 69—74, Jan. 1968. [29] http://nssdc.gsfc.nasa.gov/nssdc news/june01/iri.html Ionospheric Model (IRI-2001). [30] http://modelweb.gsfc.nasa.gov/models/iri.html IRI Model, Space Physics Data Facility (SPDF). [31] Jordan, E. C., and Balmain, K. G., Electromagnetic Waves and Radiating Systems, Prentice Hall, Inc., Englewood Cliﬀs, NJ, 1968. [32] Barnes, R. J., “Automated propagation advice for OTHR ship detection,” IEE Proc. — Radar, Sonar, Navig., Vol. 143, No. 1, pp. 53—63, Feb. 1996. [33] Gill, E. W., Howell, R. K., Hickey, K., Walsh, J. and Dawe, B. J., “High frequency ground wave radar measurement of ocean surface parameters during the ERS-1 calibration-validation experiment,” Proc. of OCEANS ’93 Engineering in Harmony with Ocean, pp. I55—I60, 18—21 Oct. 1993. [34] Georges, T. M., and Harlan, J. A., “New horizons for over-the-horizon radar,” IEEE Antennas and Propagation Magazine, Vol. 36, No. 4, pp. 14—24, Aug. 1994. [35] Jindalee Operational Radar Network (JORN), Jane’s Radar and Electronic Warfare Systems, Land-Based Air Defence Radars, January 10, 2007. [36] Gurgel, K-W, Essen, H-H, Schlick, T., “HF surface wave radar for oceanography— a review of activities in Germany,” Proc. of the International Radar Conf., pp. 700—705, 2003.

298

Detecting and Classifying LPI Radar

[37] Hartnett, M. P. and Clancy J. T., “Utilization of a nonrecurrent waveform to mitigate range-folded spread Doppler clutter: Application to over-the-horizon radar,” Radio Science Vol. 33, No. 4, pp. 1125—1133, 1998. [38] Zhang, Y., Amin, M. G. Amin and Frazer, G. J., “High-resolution timefrequency distributions for manoeuvring target detection in over-the-horizon radars,” IEE Proc. — Radar Sonar Navig., Vol. 150, No. 4, pp. 299—304, Aug. 2003. [39] Pace, P. E., Advanced Techniques for Digital Receivers, Artech House Inc., Norwood, MA, 2000. [40] “Chinese OTH Radar,” Jane’s C4I Systems, Intelligence Systems in Direction Finding, June, 2000. [41] Li, N.-J., “A review of Chinese designed surveillance radars—past, present and future,” Record of the IEEE International Radar Conf., pp. 288—293, Alexandria, VA, May 8-11, 1995. [42] Krolik, J. L., Anderson, R. H., “Maximum likelihood coordinate registration for over-the horizon radar,” IEEE Trans. on Signal Processing, Vol. 45, No. 4, pp. 945—959, April 1997. [43] Torrez, W. C., and Blasch, E., “An application of generalized least squares bias estimation for over-the-horizon radar coordinate registration,” Proc. of the Third International Conf. on Information Fusion, Volume 1, 10—13 July, 2000. [44] Min, K., Wang, G-H, and Wang, X-B, “Coordinates registration and error analysis based on spherical model for OTH radar,” Proc. of the International Conf. on Radar, pp. 1—4, Oct. 2006. [45] PROPLAB-PRO version 2.0 User’s Manual, High Frequency Radio Program Laboratory, 1994-1997. [46] http://areps.spawar.navy.mil/ AREPS (Advanced Refractive Eﬀects Prediction System) [47] SWR series High-Frequency Surface Wave Radars (HFSWR), Naval/Coastal Surveillance and Navigation Radars, Canada, Jane’s Radar And Electronic Warfare Systems, April 10, 2007. [48] Yang, S., Ke, H., Wu, X., Tian, J., and Hou, J., “HF radar ocean current algorithm based on MUSIC and the validation experiments,” IEEE Journal of Oceanic Engineering, Vol. 30, No. 3, pp. 601—618, July 2005. [49] Kahn, R., Gamberg, B., Power, D., Walsh, J., Dawe, B., Pearson, W., and Millan, D., “Target detection and tracking with a high frequency ground wave radar,” IEEE Journal of Oceanic Engineering, Vol. 19, No. 4, pp. 540—548, Oct. 1994. [50] Green, S. D., and Kingsley, S. P., “Improving the range/time sidelobes of large bandwidth discontinuous spectra HF radar waveforms,” Proc. of the IEE HF Radio Systems and Techniques, No. 411 00. 246—250, July 1997. [51] Yiying, S., Ning, Z., and Yongtan, L., “New waveform with both high range resolution and long coherent integration time in a HF radar,” Proceedings of CIE International Conf. of Radar, pp. 285—288, 8—10 Oct. 1996.

Over-the-Horizon Radar

299

[52] Zongchuang, L., Zingzhao, L., and Yongtan, L., “A signal detection algorithm based on higher-order statistics for HFSW-OTH radar,” Proceedings of CIE International Conf. of Radar, pp. 996—1000, 2001. [53] Milsom, J. D., “HF groundwave radar equations,” Proc. of the IEE HF Radio Systems and Techniques, No. 411, pp. 285—290, July 1997. [54] Barrick, D. E., “First order theory and analysis of MF/HF/VHF scatter from the sea,” IEEE Trans. on Antennas and Propagation, AP-20, pp. 2—10, 1972. [55] Barrick, D. E., “Theory of HF and VHF propagation across the rough sea,” Parts I and II, Radio Science Vol. 6, No. 5, pp. 517—533, 1971.

Problems 1. A target’s range is measured with a t0 = 200 ms and shows up in range bin 15. If the target has a Doppler shift of 20 Hz, what is the corrected range bin of the target? 2. Wideband clutter covers 200—500 km. If a FMCW waveform with ∆F = 10 kHz is used, in what range bins will the clutter appear? 3. In the multiple WRF technique, if the ∆F = 10 kHz and if the number of range bins covered by the clutter is NRB = 40 (a) what is the maximum integer value for WRF2 ? and (b) what are the three WRFs? 4. Consider a multiple WRF FMCW radar with a bandwidth ∆F = 20 kHz and WRF1 = 7 Hz, WRF2 = 8 Hz, and WRF3 = 9 Hz and an integration time of 150s (each block is 50s). For the first block (WRF1 ), determine (a) the total number of range bins, (b) the range resolution, and (c) the corresponding maximum unambiguous range. (d) Repeat (a)—(c) for WRF2 and WRF3 . (e) What is the maximum clutter width (in km) in order that sea echoes and other unambiguous targets can be detected?

Chapter 9

Case Study: Antiship LPI Missile Seeker In Chapter 1 we examined the characteristics that make a radar LPI, and in Chapter 2 we looked at a number of important applications. A significant advantage can be gained over the noncooperative intercept receiver when the radar uses frequency, phase, and hybrid wideband waveform coding techniques. In Chapter 3 the periodic ambiguity function was presented as a means of quantifying the characteristics of the LPI waveforms, which are discussed in Chapters 4—8. In this chapter, we bring some of these concepts together in a case study that examines the detection capability of a powermanaged LPI antiship cruise missile seeker. In the scenario examined, the ASCM has an FMCW seeker that attempts to detect and track a low radar cross section ship at the horizon. RCS values considered include 50, 100, and 500 m2 . To predict the target detection capability, sea clutter models are developed, and the emitter is flown at 300 m/s in a scenario that starts at a range of 28 km from the target. Each sea state (0—4) is characterized by a second-order polynomial that describes the normalized mean sea backscatter coeﬃcient as a function of the grazing angle. The emitter transmit power level is adapted to be consistent with the RCS and range to the target, while keeping the output signal to noise ratio SNRRo at 20 dB. A brief history of ASCM seeker technology is given first.

9.1

History of ASCM Seeker Technology

Antiship cruise missiles have been a significant threat to navy surface ships for many years. The first generation of ASCM threats (prior to 1969) used a single-frequency RF pulse with a constant pulse repetition interval [1]. The 301

302

Detecting and Classifying LPI Radar

antenna scanned mechanically and was very susceptible to electronic attack. Second generation ASCMs (1969—1979) were marked by an increase in their electronic protection capability. Monopulse processing and the use of discrete computer circuits allowed additional RF capability, using both staggered and jittered PRI. In the third generation (1979—1989), the integration of multiple sensors was introduced along with the use of complex RF modulations and frequency agility. Coherent Doppler processing and a large amount of electronic protection were also incorporated. Computer-aided design also started to play a significant role. In the fourth generation (1990 to the present), the signal processing performed by the missile has been vastly improved. The use of embedded computers allows the seekers to do imaging and interleave modes such as track-while-scan. Dual-mode infrared (IR) and millimeter wave seekers using wideband frequency agility demonstrate the capabilities of these fourth-generation ASCMs. The most important trends under way are the use of LPI seekers with hybrid combinations such as LPI/imaging IR, LPI/antiradiation (ARM), and millimeter wave LPI/imaging IR.

9.2

The Future for ASCM Technology

Stealthy ship designs, such as the Lafayette-class frigate shown in Figure 9.1, are a response to the ASCM threat. Future ASCM threat technology will be the result of the balance between the available technology and required littoral warfare capabilities, and the aﬀordability and export sales potential that exist. The number of development programs for cruise missiles has greatly increased, following the publicity given to the use of the Tomahawk missiles during the 1991 Gulf War [2]. Including the United States, 19 countries now have cruise missile programs with missile ranges extending to 3,000 km (e.g., the Chinese HN-3, and the Russian AS-15C and Kh-101). Ship-based helicopters capable of firing ASCMs, such as the Saudi Dauphin II shown in Figure 9.2, are already gaining popularity in the international market. The capabilities that will be required for ASCMs in the future include fire-and-forget and man-in-the-loop. Cruise missiles such as the Chinese C802 ASCM are all-weather, fire-and-forget missiles that have a range greater than 400 km. The seekers will have the capability to select a target very accurately, ignoring any land clutter or other ships in the vicinity, and they will also ignore any decoys that are used. To defeat the protection systems that could possibly shoot down the missile on its way to the target, programmable way points will be commonly used in antiship threats, such as the Swedish RBS-15. The capability will also exist to come back around for a reattack in case the ship was missed. In order to strike the ship at the most vulnerable point, future ASCMs will have programmable aimpoints, along with the ability to adjust their attack aspect. With high-G maneuverability, integrated EA and self protection, and a stealthy cross section (with regard to both RF and IR),

Case Study: Antiship LPI Missile Seeker

303

Figure 9.1: Stealthy ship designs, such as this Lafayette-class frigate, are a response to the ASCM threat [1]. (Source: Horizon House c 1998. Reprinted with permission.)

Figure 9.2: Saudi Dauphin II firing an antiship cruise missile [1]. (Source: Horizon House c 1998. Reprinted with permission.)

304

Detecting and Classifying LPI Radar

the future ASCM penetration capability will be ominous. The capability to perform coordinated salvos (coordination of multiple launch platforms) with simultaneous arrival times will also increase the probability of hitting the ship. Several ASCMs approaching a ship from multiple aspects coordinated as a stream raid seem to make the odds of ship survival remote at best. A number of advanced electronic technologies such as field-programmable gate arrays in GaAs, and application-specific integrated circuits, will be used in future ASCMs. Low-probability-of-intercept, power-managed seekers operating in the 8- to 20-GHz range, as well as the 35- and 96-GHz ranges will use pulse-to-pulse spread-spectrum modulation with coherent range Doppler processing to target the ships. Phased arrays and active arrays will refine the targeting capability, allowing variable sectors to be scanned using multiple beams. Exclusion zones will also provide the ability to reject any decoys that might interfere with the target kill. The active seekers will also use other sophisticated modes, such as Doppler beam sharpening, unfocused synthetic aperture radar, and inverse synthetic aperture radar. Wideband ARM seekers with phased arrays will be able to easily recognize and discriminate targets, and will be especially robust against emissions control tactics (RF < −110 dBm). When faced with emissions-control tactics, these ARM seekers will also use a technique called loitering, in which a parachute is deployed to slow the missile until the radiation source comes back up. Although not as prevalent today as RF seekers, infrared seekers are fast becoming a force to be reckoned with. By 2010, large-scale InSb, HgCdTe, and PtSi imaging arrays on the order of 1,024 × 1,024 will be available. New cooling techniques and the development of detectors that do not require cooling will improve the fidelity of the IR images. Improvements in IR dome materials, and protection against laser jammers and interrogators, will allow the seeker to be very robust in the terminal phase of attack. Future dual-mode technologies that will appear include ARM/millimeter-wave and ARM/laser radar using high-accuracy inertial systems for the terminal phase. For flight guidance, most new missiles are using an inertial navigation system (INS) together with global positioning system updates. Whereas a modern INS will have an accuracy of about 2 km per flight hour at around Mach 0.85, a combined INS/GPS would have an accuracy of around 50 to 100m circular error probable (CEP)1 regardless of flight time. The use of fiber optics (instead of copper wire) will also make the weapon lighter and increase the range that it can travel. The RBS-15 shown in Figure 9.3 is an example of an advanced missile 1 A circular error probable is determined by a series of flight tests, and is usually calculated by taking the square root of the sum of the squares of the range and track errors. The resultant CEP indicates the radius of the circle that encompasses half the impact points during the flight tests. The other half of the results could spread out to many times the CEP radius, and the CEP may be diﬀerent for diﬀerent ranges, flight profiles or target sets [2].

Case Study: Antiship LPI Missile Seeker

305

Figure 9.3: Swedish RBS-15 ASCM in flight [3] ( c 2002 Jane’s Information Group). that is designed to operate in all surface attack roles, from littoral warfare to blue-water situations, and includes a day-and-night, all-weather, land-attack capability. Its long range (over 200 km) and flexible trajectory mean that it can attack hostile vessels well beyond the horizon, but also at very close ranges. The missiles, each individually prepared in a salvo, can be preprogrammed to enable attacks to be mounted from diﬀerent directions, with a preselected time of arrival for each missile to confuse air defenses. Using an advanced missile engagement planning system, the missiles can make use of terrain masking for a concealed approach, to minimize warning time.

9.3

Detecting the Threat

To adequately defend the ship, the ASCM must be detected before it comes over the horizon. The detection of an incoming cruise missile seeker at the horizon (≈ 24 km) is diﬃcult with modern ES intercept receivers. Since the missile usually flies just above the water surface, it is hard to detect and extract it from the clutter using radar, since the RCS can be very small. The ASCM is also hard to detect with infrared sensors. It can possibly be detected when the seeker turns on, but that does not give much time for the ship’s self defense. Ships receive insuﬃcient warning against the missiles being developed today. An even greater problem exists within the littoral theater, where anything can be fired in short order [4]. Detection techniques being researched today extend the first engagement of the cruise missile out to 300 km, expanding the ASCM area-defense capability. To detect the missile at this range requires an airborne adjunct system capable of 3-D surveillance with a high-fidelity tracking capability. The concept of using an airborne platform to guide ship-launched missiles for intercepting low-flying targets beyond the ship’s horizon was considered over two decades ago. Since the completion of the Mountain Top tests [5], infrared search and track (IRST) surveillance technology has also been investigated for airborne ASCM detection. Long-

306

Detecting and Classifying LPI Radar

wave IR focal plane arrays oﬀering 640 × 480 resolution were developed in 1994, with the resolution expected to exceed 960 × 1,280 by 2005. Sensor platforms include, for example, the E2-C Hawkeye flying at altitudes above 7,600m, extending the engagement range out past 220 km.

9.4

ASCM Target Scenario

In this case study we have used an FMCW waveform to illustrate the power management LPI technique, and assume that the problems of transmitterreceiver isolation and transmitter phase noise can be solved satisfactorily in the single-antenna seeker environment, even with the reflected power from antenna and radome mismatch near the 0.1W level. The ASCM-target scenario being evaluated in this case study was introduced in Chapter 4, and is shown in Figure 9.4. The FMCW technique separates the target echo in frequency from the transmission by a significant fraction of the modulation bandwidth, while tolerating relatively high levels of transmitter leakage into the receiver. Practical solutions to the leakage problems are becoming available to the seeker designer such as those discussed in Section 4.4. The missile contains an FMCW LPI emitter, and flies at the ship starting at a rangeto-target of R = 28 km at a height of 70m oﬀ the surface of the water at a speed of Mach 0.9 (300 m/s). Below the target model, the sea clutter model and the emitter model are described. Simulation results are described to predict the detection performance of the emitter. Note that this is a first-order analysis, and the results shown do not include any standard or nonstandard propagation eﬀects such as spherical spreading and ducting [6, 7].

9.4.1

Low RCS Targets

The future design of naval vessels will have a low RCS in addition to other signature reduction techniques. For example, the HMS Visby is the first of five Visby-class stealth corvettes under construction for the Swedish Navy by HDW-owned Kockums shipyard in Karlskrona, Sweden. It is shown in Figure 9.5 performing high-speed sea trials oﬀ the German Baltic coast [3]. The stealth corvette has a length of 72m, is constructed almost entirely from carbon fiber-reinforced plastic material, and features a variety of innovative signature-reduction techniques covering radar cross-section, infrared, acoustic, magnetic, and hydrodynamics. The most favorable situation for the seeker is when the ship is broadside (largest return within a range bin). To detect a stealthy target, the CW frequency should be between 30 and 960 MHz. This is also the frequency range that contains public broadcasting and mobile communication systems. At broadside, however, there is no Doppler separation between the ship and the clutter, which is why most nonimaging missile seekers do not use Doppler

Case Study: Antiship LPI Missile Seeker

307

Figure 9.4: ASCM-to-target scenario.

Figure 9.5: The Swedish stealth corvette HMS Visby conducting high-speed trials in the Baltic. (Source: Michael Nitz. c 2002 Jane’s Information Group.)

308

Detecting and Classifying LPI Radar

Table 9.1: Normalized Mean Sea Backscatter Coeﬃcients for Grazing and 0.1 to 10.0 Degrees for Sea States 0 to 4 in Decibels Below 1 m2 /m2 for 9.3 SEA STATE Grazing Angle (degrees) 0.1 0.3 1.0 3.0 10.0

0 70 62 57 52 46

1 60 58 50 45 42

2 56 52 44 41 36

3 51 45 39 38 32

4 48 43 37 35 29

processing. Also note that since the emitter is at a height of 70m within the model, the waterline of the ship is visible throughout the entire flight. If the height of the emitter is lower, then the waterline only becomes visible at a closer range. For example, with a sea-skimming missile at a height of 9m, the waterline is visible at a max range of about 13 km. This is why most seekers turn on at 7—13 km (in addition to minimizing the time the ship has to react). For the detection analysis below, we choose 50, 100, and 500 m2 as examples of low RCS values for the ship target.

9.4.2

Sea Clutter Model

To model the sea clutter, a set of normalized mean sea backscatter coeﬃcients for low grazing angles and sea states is given in Table 9.1. This figure gives the normalized mean sea backscatter coeﬃcients for grazing angles 0.1—10.0 degrees for sea states 0 to 4 in decibels below 1m2 /m2 for 9.3 GHz, vertical polarization (adapted from [8]). Sea clutter exhibits very diﬀerent spectral characteristics at higher frequencies compared to those at low frequencies. Some of the values have been estimated, since errors in the reported values are not unlikely, and some values are not reported at all (especially for low grazing angles) [8]. Other experimental sea clutter coeﬃcients as a function of the grazing angle for various frequencies are reported in [9, 10]. To extract the correct value for the mean sea backscatter coeﬃcient σ0i as a function of the grazing angle, a polynomial was developed for each sea state (9.1) σ0i = AΨ2 + BΨ + C (dB below 1 m2 /m2 ) where i is the sea state, Ψ is the grazing angle (in radians), and the coeﬃcients A, B, and C are given in Table 9.2. Using these coeﬃcients, the value of σ0i for the five sea states (σ00 − σ04 ) is shown in Figure 9.6. It is in-

Case Study: Antiship LPI Missile Seeker

309

Table 9.2: Polynomial Coeﬃcients A, B, and C to Determine σ0i as a Function of the Sea State (i) i 0 1 2 3 4

1.8289 −2.0882 −9.7730 4.6285 9.0787

A (10−4 ) (10−3 ) (10−4 ) (10−3 ) (10−3 )

1.1146 7.3396 1.5948 2.6412 5.3639

B (10−4 ) (10−4 ) (10−3 ) (10−3 ) (10−3 )

−2.5296 −1.4661 2.1903 2.6779 3.5646

C (10−8 ) (10−6 ) (10−6 ) (10−5 ) (10−5 )

Figure 9.6: Normalized mean sea backscatter coeﬃcient σ0i as a function of the grazing angle.

310

Detecting and Classifying LPI Radar

teresting to note that the sea state of one backscatter coeﬃcient does not increase as dramatically as the other sea states when the grazing angle gets larger. Also note that these clutter calculations minimize the fact that the clutter distribution becomes highly non-Gaussian at low grazing angles, due to sea spikes. For increased accuracy, lognormal, Weibull, or K-distributed analysis can be used and will typically increase the required SNR by 10—20 dB. In the next section, the transmitter power management is discussed. The backscatter coeﬃcient polynominals are then used to predict the detection capability of the LPI emitter design for three RCS values (50, 100, 500 m2 ).

9.4.3

Linear FMCW Emitter Power Management

In a power-managed seeker, the emitter transmits a power level consistent with the RCS and range of the target to be detected, thereby keeping the SNR a constant. When the missile first enters the engagement envelope and turns on the seeker, the most probable range cells are monitored, and the transmitter output power is at a level where detection of the target can be made on a single scan using only a few modulation periods. If the target is not detected, the power can be increased gradually on the next scan. Once the target is detected, the seeker shuts down and the missile moves up to a new location, making any subsequent targeting or exploitation of the emitter impossible. The emitter uses computer control so that the RF energy is only emitted when it is necessary to measure the target characteristics and update the track file. From (1.28), the average transmit power of an FMCW emitter can be written as w W w 4 W RT SNRRo (4π)3 kT0 FR L∆f RT4 SNRRo =K (9.2) PCW = G2t λ2 σT σT where L2 ≈ 1, FR is the receiver noise factor, kT0 = 4.0 × 10−21 W/Hz, L = LRT LRR represent the system losses, SNRRo is the required output signal-to-noise ratio required for target detection, ∆f = 1/tm is the filter bandwidth, RT is the range to the target (ship), and σT is the ship’s RCS. Continuing with the FMCW example discussed in Chapter 4, fc = 9.3 GHz and tm = 1 ms. The modulation bandwidth is chosen as ∆F = 15 MHz in order to provide a ∆R = 10m such that the ship return all lies within a range bin. Also, FR = 10 and L = 10, which is reasonable for a single antenna implementation. The antenna is a circular aperture with diameter da = 0.3m with uniform illumination. This antenna diameter will easily fit in the nose of an ASCM pod. The 3-dB beamwidth in the azimuth plane depends on the aperture size and is approximately [11] θa = 1.29

λ da

rad

(9.3)

Case Study: Antiship LPI Missile Seeker

311

Table 9.3: Summary of LPI Emitter Parameters Used in Simulation Results Carrier frequency Modulation period Coherent processing interval Modulation bandwidth Eﬀective modulation bandwidth Range resolution Eﬀective range resolution FFT size Time bandwidth product Average transmitter power ADC sampling speed Detection signal-to-noise Noise factor Range-doppler gate System losses Antenna diameter Antenna eﬃciency Beamwidth Antenna gain

fc tm t0 ∆F ∆F ∆R ∆R N t0 ∆F Pavg fs SNR F ∆f L da η θa Gt

9.3 GHz 1.0 ms 0.81 ms 15 MHz 12.2 MHz 10.0m 12.3m 8,192 9,922 Adaptive 10.1 MHz 20 dB 10 1.23 kHz 10 0.3m 0.90 7.9◦ 810

or 7.9 degrees. The gain Gt of a circular aperture antenna at X-band is approximately (9.4) Gt ≈ d2a η where da is in cm and η is the aperture eﬃciency. For a uniform illumination, η = 0.9 considering a 0.5-dB loss in an equal-level feed network. This results in an antenna gain of Gt = 810. Typically, the SNR for a CW emitter must be at least 6 dB (rather than the 13-dB value required for detecting steady targets with pulse emitters; see p. 449 in [8]). However, a more realistic value for ASCM seekers is 20 dB. The emitter’s PCW is adjusted as a function of the range-to-target in order to keep the SNR = 20 dB. That is, the intelligent power management automatically adjusts the transmit power to maintain a constant IF SNRRo = 20 dB. This value, of course, depends on the postdetection integration, which can be calculated per the equations given in Chapter 1. A summary of the LPI emitter parameters is given in Table 9.3 for a ∆F = 15-MHz design (Example 1 in Table 4.1). The corresponding average power transmitted by the emitter as a function of range-to-target is shown in Figure 9.7 for RCS values of 50, 100, and 500 m2 . Note that the transmitted power is adaptive, and calculated to keep

312

Detecting and Classifying LPI Radar

Figure 9.7: Average power transmitted by LPI emitter as a function of range to the target and target RCS value. the total echo power from the target a constant. Also note that only for the 50 and 100 m2 case does the transmit power exceed 100W. From (1.34) the targets echo power from the CW emitter (with L2 = 1 and LRT = LRR = 1) is PCW G2t λ2 σT W (9.5) PRT = (4π)3 RT4 L and is a constant (PRT = −140 dBW). In summary, the seeker uses the FMCW waveform and adaptive power management to achieve the LPI characteristics. With higher RCS targets, the transmitted power can be reduced even further.

9.4.4

Target-to-Clutter Ratio

Since the primary purpose of the FMCW emitter is to detect and track ship targets in the presence of sea clutter, the target-to-sea clutter ratio within a range bin is examined for sea states 0 to 4 and ship RCS values 50, 100, and 500 m2 . Using the backscatter coeﬃcients σ0i , the power of the clutter within the target’s range bin can be estimated as PRC =

PCW G2t λ2 σ0i RT θa ∆R (4π)3 RT4 L

W

(9.6)

Case Study: Antiship LPI Missile Seeker

313

Figure 9.8: Target-to-clutter ratio for ∆R = 10.09m and σT = 50 m2 . Using (9.5) and (9.6), the target-to-clutter ratio (TCR) is W w 1 σT PRT = TCR = PRC σ0i ∆R θa RT

(9.7)

and is shown in Figure 9.8 for ∆R =10.09m, and a target RCS of σT = 50 m2 . Note that the TCR curve for sea state 1 is not quite accurate. If the required TCR for detection and tracking is 20 dB, Figure 9.8 shows that the target can be tracked throughout the flight of the missile in sea states 0 to 2 (TCR >20 dB). Detection becomes more diﬃcult for higher sea states. Detection is possible at R < 4 km for sea state 3, with no detection capability in sea state 4. Figure 9.9 shows the target-to-clutter ratio for ∆R = 10.09m and σT = 100m2 . Note that the detection capability is now possible in sea state 3 when R < 15 km and sea state 4 when R < 6 km. Figure 9.10 shows the target-to-clutter ratio for ∆R = 10.09m and σT = 500m2 . Here it is shown that detection is possible in all sea states at all ranges with a required TCR > 20 dB. The detection capability for the FMCW emitter is summarized in Table 9.4. Note that only for sea state 4 and RCS = 50 m2 is the target not detectable. Also, it is assumed that the target’s RCS is totally contained within the range bin. The maximum value of PCW required throughout the flight is also summarized. Note that the inclusion of propagation loss standard and nonstandard

314

Detecting and Classifying LPI Radar

Figure 9.9: Target-to-clutter ratio for ∆R = 10.09m and σT = 100 m2 .

Figure 9.10: Target-to-clutter ratio for ∆R = 10.09m and σT = 500 m2 .

Case Study: Antiship LPI Missile Seeker

315

Table 9.4: Summary of Detection Results for Power-Managed FMCW Emitter TCR > 20 dB Sea State 0 1 2 3 4 Max Pavg

RCS = 50 m2 Yes Yes Yes Yes (R < 4 km) No 110 W

RCS = 100 m2 Yes Yes Yes Yes (R < 15 km) Yes (R < 6 km) 100 W

RCS = 500 m2 Yes Yes Yes Yes Yes 90 W

mechanisms will aﬀect these first-order results. Inclusion of these eﬀects must also be included for an accurate prediction of the weapons system performance. Assessment programs such as the advanced refractive eﬀects prediction system (AREPS) [12] can easily provide such results.

9.5

ASCM Ship Target Model

Recall that the two MATLAB programs from Chapter 4: • lpi fmcw design.m • receiver design.m can be used to design and simulate the FFT processing of the FMCW radar, to extract the range and range rate of a target. The results shown in this chapter use the design parameters generated by lpi fmcw design.m and the sea clutter backscatter coeﬃcients generated by clutter polynomial x.m. The missile-to-target scenario results are derived by ascm.m. The variable inputs are: (1) ship RCS, (2) sea state (0, 1, 2, 3, or 4), (3) missile velocity, and (4) initial range of the missile. Variable inputs for the seeker include (1) the required TCR for detection, (2) the diameter of the seeker antenna, (3) the seeker noise factor, and (4) the seeker losses. All other input values for the emitter come from lpi fmcw design.m as global variables.

References [1] Pace, P. E., and Burton, G. D., “Antiship cruise missiles: Technology, simulation and ship self-defense,” Journal of Electronic Defense, Vol. 21, No. 11, Nov. 1998. [2] Lennox, D. “Cruise missile technologies and performance analysis,” Jane’s Strategic Weapons Systems 38, Nov. 2002. [3] Jane’s International Defence Digest, Sept. 2002.

316

Detecting and Classifying LPI Radar

[4] Jurcheck, J., “Visualizing the littoral battlespace,” Surface Warfare, Vol. 22, pp. 10—15 Aug. 1997. [5] Zinger, W. H., and Krill, J. A., “Mountain top: Beyond-the-horizon cruise missile defense,” Johns Hopkins APL Technical Digest, Vol. 18, No. 4, pp. 501—520, 1997. [6] Hitney, H. V., “Refractive Eﬀects from VHF to EHF Part A: Propagation Mechanisms,” Propagation Modeling and Decision Aids for Communications, Radar and Navigation Systems, NATO AGARD Lecture Series 196, Ottawa, Canada, Oct. 1994. [7] Hitney, H. V., “Refractive Eﬀects from VHF to EHF Part B: Propagation Models,” Propagation Modeling and Decision Aids for Communications, Radar and Navigation Systems, NATO AGARD Lecture Series 196, Ottawa, Canada, Oct. 1994. [8] Nathanson, F. E., Radar Design Principles, Second Edition, McGraw-Hill Inc., New York, 1991. [9] Paulus, R. A., “Evaporation duct eﬀects on sea clutter,” IEEE Trans. on Antennas and Propagation, Vol. 38, No. 11, pp. 1765—1771, Nov. 1990. [10] Chan, H. C., Radar sea-clutter at low grazing angles,” IEE Proc. Part F, Vol. 137, No. 2, pp. 102—112, April 1990. [11] Barton, D. K., Modern Radar Systems Analysis, Artech House, Inc., Norwood, MA, pp. 155, 1988. [12] “Defense information and infrastructure common operating environment— User’s manual for advanced refractive eﬀects prediction system,” SPAWAR Systems Command, METOC Systems Program Oﬃce, Jan. 9, 2003.

Problems 1. It is an easy matter to modify the second-order polynomial describing the normalized mean sea backscatter σ0i as a function of grazing angle for the five sea states (useful when better empirical data might be obtained). Recall that these coeﬃcients were derived by curve fitting the values given by Nathanson [8]. The polynomial coeﬃcients (p0—p4) are used in ascm.m and can be regenerated by adjusting the backscatter coeﬃcients in clutter polynomial x.m (y0bs through y4bs). (a) Run lpi fmcw design.m to design the ∆F = 15 MHz LPI seeker discussed in Section 7.4. (b) Edit the file clutter polynomial x.m and change the sea state three normalized mean sea backscatter values to y3bs = [53

46

40

39

37]

(9.8)

Case Study: Antiship LPI Missile Seeker

317

(horizontal polarization). (c) Run the scenario discussed above using ascm.m and compare the detection performance against the vertical polarization results given in the text (plot the results from both designs on the same graph). (d) Summarize the detection range for this horizontally polarized seeker. 2. Using the programs lpi fmcw design.m, clutter polynomial x.m and ascm.m, (a) summarize the detection capability of the 9.3-GHz seeker discussed in Section 9.4 if the modulation bandwidth is changed to ∆F = 25 MHz. (b) summarize the detection capability if the seeker in (a) keeps the SNR = 13 dB (instead of 20 dB).

Chapter 10

Network-Centric Warfare and Netted LPI Radar Systems LPI radar systems can be networked together into a system of systems to covertly gather and share surveillance and targeting data as part of a networkcentric warfare architecture. In this chapter, network-centric warfare concepts are introduced including the information grid (network), the sensor grid, and the weapons grid. A set of metrics is presented to quantify the value added to an operation by the network. Electronic attack on the network is also considered. Advantages of netted LPI radar systems (part of the sensor grid) are discussed, including the improvement in emitter sensitivity that is gained, and a multiple-input multiple-output (MIMO) signal model is presented. Network analysis and netted radar system analysis are presented. Simulation results using LPIsimNet are shown. LPIsimNet is a MATLAB program included with the CD that allows the user to evaluate any general netted radar configuration and the operational performance of a sensor network. Orthogonal PSK, FSK, and noise waveforms for netted LPI radar applications are also presented. Use of MIMO techniques for OTHR is discussed.

10.1

Network-Centric Warfare

In a platform-centric naval architecture the aircraft carrier is the “epicenter” of power. Each weapon has its own sensor and if that sensor is remote there is a stovepipe communication system transmitting the data back to the shooter. Ultimately, this makes necessary many platforms to eﬀectively project the 319

320

Detecting and Classifying LPI Radar

power needed on the battlespace. Platform-centric command and control (C2) also suﬀers limitations in its ability to coordinate operations. For example, in suppression of enemy air defense (SEAD) operations, the standoﬀ jammer suﬀers significant geometrical problems in alignment, making it diﬃcult to detect and jam coherent threats. The geometrical limitations result in an extended standoﬀ range being necessary and consequently an ineﬀective jammer management. Over the past several years there has been a major shift away from platform-centric warfare concepts. Currently we no longer have access to masses of ships and large numbers of weapons. Also, the weapons today are precise and must be employed at exactly the right time and place. No single sensor has the precision to target these advanced technology eﬀectors. They require a dynamic knowledge of the target set and the integration of many sensors and databases. Evolving from platform-centric warfare, network-centric warfare (NCW) integrates a distributed system of C2, sensors and weapons called a grid. NCW can extend the capabilities of sensors and weapons across all the platforms on the network to pursue the maximum eﬃciency in mission execution. The grid provides the capability to collect, process and disseminate an uninterrupted flow of C2, sensors and weapons information between nodes while exploiting and denying the adversary’s ability to do the same (information superiority)[1]. In contrast to platform-centric warfare, which has an additive eﬀect on combat power (N nodes, total force value = N ), NCW has an exponential eﬀect (N nodes, total force value = N 2 ). The exponential advantage in total force value also gives a maneuver and time-critical strike advantage to the NCW nodes. A more formal definition of NCW is given below. Definition 10.1 Network-centric warfare is military operations that exploit stateof-the-art sensor information and networking technologies to integrate widely dispersed human decision makers, weapons, situational and targeting sensors and forces into a highly adaptive comprehensive system to achieve unprecedented mission eﬀectiveness. The NCW grid is composed of three subgrids; the global information grid, the sensor grid and the shooter grid as shown in Figure 10.1 [1]. The global information grid is a deployed tactical sensor and weapons network that provides the infrastructure for plug-and-play of sensors and shooters. It exists in space, low- and high-Earth orbit, and at all altitudes on land and undersea. It is a physical, permanent and fault-tolerant network that receives, processes, transports, stores and protects the information. It makes available communications and sensor data to the war fighter and is self-organizing, self-monitoring and continuously available. Also provided are adaptive and

Network-Centric Warfare and Netted LPI Radar Systems

321

Figure 10.1: Network-centric architecture employing an information grid, shooter grid, and a sensor grid. The sensor grid is composed of a netted LPI radar system of systems. automated decision aids. The number of nodes directly reflects a volume of force on the network and the information processing capability required. The network topology represents the configuration of the links to integrate the sensor and weapons nodes. The sensor grid is composed of air-, sea-, ground-, space-, and cyberspacebased sensor nodes. Netted LPI radar systems play an important part to provide “at all levels” a covert surveillance capability and high degree of situational awareness. In this type of netted radar systems, a number of transmitters and receivers are spatially distributed with each receiver being capable of processing signals scattered by the target from every transmitter. In addition, weapons can also be targeted using the netted LPI emitters. An increase in a radar’s target processing capability (local node processing) benefits the speed of relaying the targeting information. The sensor grid is a transient grid and exists only for the task at hand. It is reformed for every mission with the collaborative C2 performing dynamic sensor tasking and data fusion. With the benefits of new network assurance technology, topologies are now capable of providing a more robust network for information fusion. Sensor network

322

Detecting and Classifying LPI Radar

protocols are described in [2] and secure routing techniques in the presence of electronic attack are described in [3]. The shooter grid consists of both weapons and jammers. It enables the joint war fighter to plan and execute operations in a manner that achieves power projection at a precise time and place. By exploiting the battlespace awareness, new operational capabilities are realized including the execution of time-critical missions, and the rapid acquisition and execution of targets in a timely manner. The shooter grid is also a transient grid where the piece parts are physical. The grid exists for the task only and is reformed for every mission. In Figure 10.1, the NCW architecture is used to track a low RCS target using a netted LPI sensor grid (advantages of netting the distributed radar systems together are discussed in Section 10.5). The target is disabled with a missile from the weapons grid.

10.1.1

NCW Requirements

There are several requirements for NCW operations. To achieve a force that is network-centric, a wideband RF transmit/receive capability is required to compress and transport large amounts of data. Also required is a wideband local area network which can process and transmit information locally between the sensors and/or weapons. Eﬀective information management or the ability to eﬃciently use, process and apply information is also required. Finally, a critical mass of platforms, sensors, and weapons that have the information processing capability is required. When forming the NCW architecture, questions to be answered include: How do diﬀerent degrees of networking impact the strategic, operational and tactical outcomes? What is the optimal network topology (physical, virtual, arrangement of nodes)? How will the network impact the C2? What is the correct balance of sensors, shooters and network technology? Can we quantify how the network processing sustains degradation from events such as an electronic attack? The answer to these questions is diﬃcult since there are complex relationships between the network space and the battlespace. For example, from the information standpoint, the overall information processing capability is mainly determined by the number of nodes, the individual node capability, and the topology of the network as shown in Figure 10.2. Note that this figure does not show information flow but shows an overall relationship dependence. For example, the number and distribution of LPI emitters on a network must be suﬃcient to build a precise and timely picture of the battlespace taking into account the limited detection ranges available. The data distribution and data association between nodes must correlate the data accurately avoiding any misidentification. The increase in information processing capability sequentially results in an enhancement in the situational awareness and operational tempo that aﬀect the maneuverability, decision speed, lethality, and agility on the battlefield.

Network-Centric Warfare and Netted LPI Radar Systems

323

Figure 10.2: Relationship between network space and battlespace

10.1.2

Situational Awareness

Situational awareness is defined by the U.S. Army’s Training and Doctrine Command as “the ability to have accurate real-time information of friendly, enemy, neutral, and noncombatant locations; a common, relevant picture of the battlefield scaled to specific levels of interest and special needs” [4]. The LPI radar sensor can provide a critical role in maintaining the required situational awareness since it is able to gather the information without injecting an influence. That is, the radar sensor used to gather the information should be required to have a low probability of intercept. If detection by enemy noncooperative intercept receivers occurs, an enemy response will ensue increasing the characteristic tempo λT uncontrollably. The characteristic tempo is defined as the speed in which the situational awareness is processed in order to orient (or adjust) the force to the current situation. In practice, situational awareness is built by continuous snapshots that are gathered from the battlefield and transferred to the commander. A larger information gathering ability (e.g., more nodes) results in a larger information volume enabling for example, beyond line-of-sight targeting. Better information exchange ability results in a quick refreshing of the snapshot. Consequently, the situational awareness is mainly determined by the information processing capability [5].

10.1.3

Maneuverability

A far-reaching netted radar system of systems can also improve force maneuverability, which is the capability to perform a strategic or tactical movement. To evaluate the maneuverability performance, we consider three of its prop-

324

Detecting and Classifying LPI Radar

Figure 10.3: Improvement in maneuverability. erties: speed, safety, and cost. Maneuverability can be promoted through the support of situational awareness. Figure 10.3 shows the improvement in maneuverability when a network-enabled situational awareness is eﬀective [6]. For example, better terrain awareness results in optimal route design. The route design not only increases the speed of the maneuver, but it can also reduce the probability of risk and possibly result in a lower cost. Another example is better threat awareness which helps the preparation of a proper oﬀense and contributes to improvements in maneuverability. Furthermore, better integration of coalition war fighters into battlespace actions can also increase force maneuverability.

10.1.4

Decision Speed and Operational Tempo

The observation-orientation-decision-action (OODA) loop is important for operations and has become a critical concept in military strategy. John Boyd originally developed the concept to explain how to direct one’s energies to defeat an enemy and survive [7]. The OODA loop concept is shown in Figure 10.4. A war-fighting enterprise that can process the entire OODA cycle quickly, observing and reacting to unfolding events more rapidly than an opponent, can “get inside” the opponent’s decision cycle and gain a military advantage. The LPI radar nodes and the characteristic tempo λT play a significant part in the observation-to-orientation phase of the OODA loop. The decision tempo λC2 is defined as the speed to make a decision to act. After the decision to act is made, the speed at which action is taken is the sum of the characteristic tempo and a deployment tempo λd . After deployment, the speed at which the situational response (or fighting) is made is the sum of the characteristic tempo and a fighting tempo λf . These individual tempos can be used to quantify the maximum operational tempo of the network-an

Network-Centric Warfare and Netted LPI Radar Systems

325

Figure 10.4: Observation-orientation-decision-action (OODA) loop.

Figure 10.5: Operational tempo determined by the agility of a force. important attribute when considering the fusion of netted radar data. The maximum operational tempo ΛOODA is the inverse of the maximum frequency to complete the OODA cycle. In the experiments and exercises of the Army Battlefield Command System, it has been verified that due to the promotion of information processing capability, operational planning could be improved as the speed of order preparation and the operational tempo is increased. The commander’s intent is then clarified more quickly [1, 8]. Note also that the OODA loop can be scaled to diﬀerent levels of an operation. For example, it could be used to represent the operation of targeting a missile or the operation of force movement on a battlefield. We will come back to the OODA concept in our discussions later.

10.1.5

Agility

Agility is defined as the ability of an organization to sense and respond to advancement opportunities in order to stay ahead and competitive on a turbulent battlefield quickly. The operational tempo is highly dependent on the agility. Figure 10.5 shows the comparison of fast and slow operational tempo. In a given time period, the upper force with low operational tempo (less agile) can only respond to environment events a maximum of three times. The fast operational tempo can react five times and represents better agility.

326

10.1.6

Detecting and Classifying LPI Radar

Lethality

Lethality is the ability to damage an enemy. Only with the suﬃcient situational awareness and eﬃcient operational tempo can the forces perform with the best lethality. The radar sensor network plays a key role in the measure of lethality. For example, the artillery can perform with high lethality with accurate targeting information and timely approval of attack. Infantry attacks also do well with enough intelligence and under quick and timely command. It is important to note that if the enemy is aware of the targeting information being gathered, the characteristic tempo is slowed due to the further reconnaissance that is necessary. The lethality of the action is also severely degraded emphasizing the need for the battlefield sensors to be LPI.

10.2

Metrics for Information Grid Analysis

A military sensor and weapons grid is sometimes assumed to have an infinite number of nodes each with a similar capability. In the analysis, this often leads to misleading results, especially when a small number of dissimilar nodes are used [8]. This section examines the network theory and metrics that are designed to quantify the general value inherent in the information network topology. These include the connectivity measure, the network reach, and the network richness. Combining these metrics with the operational tempos previously discussed, we can quantify the maximum operational tempo of the network. The presence of an electronic attack is also addressed.

10.2.1

Generalized Connectivity Measure

A time-dependent, generalized connectivity measure (CM ) of a network of sensors and weapons is defined as the sum of the value of all the nodes and their connections scaled by the lengths of the routes and their directionality. The connectivity measure can be expressed as [8] Nμ Nμ,ν

NT

CM (t) =

Lγμ,ν (d, t)

Kμ (t) μ=1

(10.1)

ν=1 γ=1

where NT is the number of nodes in the network, Nμ is the total number of nodes connected to the node μ, Nμ,ν is the total number of possible routes connecting the pair of nodes μ and ν, Kμ (t) is the capability value of node μ, and relates to the ability of the node to process and transfer information quickly. Lγμ,ν is the information flow parameter of the route γ connecting nodes μ and ν and depends on the length of the route d and is also a function of time t. The capability and information flow parameters have the range 0 ≤ Kμ (t), Lγμ,ν ≤ 1. For the examples below, we use a normalized value for the route length d. That is, d = 1 from one node to another.

Network-Centric Warfare and Netted LPI Radar Systems

327

Figure 10.6: Three node example to demonstrate generalized connectivity link calculations. Table 10.1: List of All Available Links in Figure 10.6 Links 1→3 2→1 2→3 3→1 3→2

The term “route” is the possible connection from one node to another node. The term “link” represents the direct connection between any two nodes. One route contains at least one or more links. Figure 10.6 shows three information nodes deployed with diﬀerent capability values Kμ . The link from node μ = 1 to node μ = 2 is not available. A list of all available links and routes are shown in Tables 10.1 and 10.2, respectively. The functional dependence of Lγμ,ν on the length of the route d (number of links) and time t can be simplified by separating it into a time-independent component Lμ,ν and a time dependent flow coeﬃcient Fγμ,ν (t), which is scaled by the route length d raised to the power ξ. The expression for CM (t) then becomes [8] CM (t) =

μ,ν

Kν (t) μ=1

Nμ,ν

Nμ

NT

L ν=1

γ=1

Fγμ,ν (t) (dγ )ξ

(10.2)

The value of Fγμ,ν (t) is a minimum of zero and reaches a maximum of one when the route γ is capable of supporting all information exchanges. Note the

328

Detecting and Classifying LPI Radar

Table 10.2: List of All Possible Routes Start Node 1 1 2

End Node 2 3 1

2

3

3

1

3

2

Routes 1→3→2 1→3 2→1 2→3→1 2→3 2→1→3 3→1 3→2→1 3→2

Figure 10.7: Two nodes with a unidirectional link. order of the node superscripts matters. For example, consider the two nodes shown in Figure 10.7. The flow coeﬃcient 0 ≤ Fγμ,ν ≤ 1 however, Fγν,μ = 0. To illustrate these ideas, assume Kμ (t) is time independent and that any two nodes are either connected or not (Fγμ,ν (t) = 0 or 1). The directionality of the information is also included. Also assume that the scaling exponent ξ = 1, and the time independent information flow parameter Lμ,ν = 1 for every route are identical. As a result, (10.2) can be simplified to Nμ Nμ,ν

NT

CM (t) =

Kμ μ=1

ν=1 γ=1

Fγμ,ν (t) dγ

(10.3)

In summary, the following assumptions are held. First, the connectivity is time-independent. That is, Kμ (t) = Kμ and Fγμ,ν (t) = Fγμ,ν . Also, ξ = 1 and any two nodes are either connected (or not). Table 10.3 demonstrates the generalized connectivity CM calculation for Figure 10.6.

10.2.2

Reference Connectivity Measure

R The reference connectivity measure (CM ) is defined to represent a fully connected network configuration. The reference network has all nodes fully connected with bidirectional links [8]. In addition, each node has a capability value of Kμ = 1. For example, Figure 10.8 shows a realistic four-node information transfer network deployed with diﬀerent capability values Kμ . There

Network-Centric Warfare and Netted LPI Radar Systems

329

Table 10.3: Calculation of Connectivity Measure Route 1→3→2 1→3 2→1 2→3→1 2→3 2→1→3 3→1 3→2→1 3→2

Kμ 1 1 0.75 0.75 0.75 0.75 0.25 0.25 0.25

dγ 2 1 1 2 1 2 1 2 1

CM Contribution 0.500 1.000 0.750 0.375 0.750 0.375 0.250 0.125 0.250 CM = 4.375

is a unidirectional link from node 1 to node 2 and from node 3 to node 2. There are also two bidirectional links from node 3 to node 1 and from node 3 to node 4. Figure 10.9 shows the corresponding reference network for Figure 10.8. Note that all the nodes are homogeneous and connected to one another (fully connected) and that all capability values are Kμ = 1 and Fγμ,ν = 1 for all γ, μ and ν. The reference connectivity measure only depends on the total number of nodes NT and is calculated as R CM = NT (NT −1)× 1 +

(NT − 2)(NT − 3) · · · 2 · 1 NT − 2 +··· + 2 NT − 1

(10.4)

The term outside the square brackets in (10.4), NT (NT − 1), represents the number of possible connections in a given network with NT nodes. The numerator in each term inside the square brackets is the number of possible routes of the length given in the denominator. The reference network has the highest connectivity measure of any network with same number of nodes. R for 3 ≤ NT ≤ 8 and shows the exponential Table 10.4 shows the value of CM R increase in CM with a linear increase in the number of nodes.

10.2.3

Network Reach

R The reference connectivity measure CM provides a means to normalize the connectivity measure (10.3) resulting in the network reach IR as [8]

IR =

CM R CM

(10.5)

which is a dimensionless quantity. Normalization by the reference network allows us to investigate varying degrees of network connection, nonidentical

330

Detecting and Classifying LPI Radar

Figure 10.8: Realistic four-node sensor network configuration.

Figure 10.9: Reference network for the radar information network shown in Figure 10.8. Table 10.4: List of Reference Connectivity Measures Node Number 3 4 5 6 7 8

R CM 9 32 120 534 2,905 18,976

Network-Centric Warfare and Netted LPI Radar Systems

331

nodes/links and the eﬀect of broken symmetries due for example, to electronic attack of the network.

10.2.4

Suppression Example

A network-enabled SEAD example with NT = 5 is considered in Figure 10.10. In this scenario, we are concerned with the capability of the network to transfer sensor data eﬃciently. To suppress the Eagle (Ka-band battlefield surveillance and missile control radar), an EA-6B is networked with an RQ-1 Predator, an AC-130 Gunship and an EA-18G. The EA-6B, the gunship and the EA-18G are all data linked to the special operations forces on the ground (note the unidirectional flow of information). The capability value Kμ is assigned as shown for each asset. The capability value depends on the platform’s level of networking and ability to participate in the data and information exchange needed. For the example, both the EA-6B and the EA-18G have a value K = 1.0 since they are in control of the suppression mission and are fully network capable. The RQ-1 Predator is assigned a value of K = 0.5 since it cannot relay directly to the special operation forces, any of its images and data that are gathered. The AC130 gunship is assigned K = 0.85 since it is somewhat less capable than the EA-18G and EA-6B due to its multimission characteristics. Note that the special operation forces are assigned K = 0.3 and is a low value since they only receive images and data and do not transmit (otherwise they would give their position away). The reference connectivity measure is calculated first. For NT = 5, R = 5(4) × 1 + CM

3 3·2 3·2·1 + + 2 3 4

(10.6)

R or CM = 120. Note that this value only depends on the number of nodes participating in the network. Using this value, the expression for the network reach is ⎛ ⎞ Nμ,ν Nμ NT =5 μ,ν F 1 γ ⎠ Kμ Lμ,ν ⎝ (10.7) IR = 120 μ=1 d γ ν=1 γ=1

The values for Nμ = {N1 = 4, N2 = 3, N3 = 4, N4 = 4, N5 = 3}. Also, N11 = 0. The value of N12 = 5 can be verified from Figure 10.10. That is, there are five routes from node 1 to node two. The five routes are shown in Table 10.5. With L12 = 1, the summation of the flow coeﬃcients scaled by the route lengths is 1 1 1 1 1 F 1,2 = + + + + = 2.67 d 1 2 2 3 3

(10.8)

Continuing on, the other node to node flow coeﬃcients scaled by the route

332

Detecting and Classifying LPI Radar

Figure 10.10: Eagle radar suppression using NT = 5 nodes. lengths can be calculated. The network reach is then IR =

1 120 (1.0 [3(2.67)

+ 4.33] + 0.5 [3(2.67) + 5] + (10.9)

0.85 [3(2.67) + 4.33] + 1.0 [3(2.67) + 4.33] + 0) = 0.3473 The first four terms in brackets are the EA-6B, RQ-1A, AC-130 and the EA-18G respectively. The zero term (last term) is due to the fact that this node contributes nothing to the overall information transfer capability of the network. The low value of network reach is due to the reduction in node capability values and the loss of sensor information rerouting options. Note that if the capability value K = 1.0 for all nodes in the above example, then

Table 10.5: Five Routes Identified from Node 1 to Node 2 1 1 2

2 1 3 2

3 1 4 2

4 1 4 3 2

5 1 3 4 2

Network-Centric Warfare and Netted LPI Radar Systems

333

IR = 0.4167.

10.2.5

Extended Generalized Connectivity Measure

We can generalize (10.3) by considering the case where 0 < Fγμ,ν < 1 exists (partial eﬃciency of route). For instance, if a traversed node on one route 1), this route will not be able to maintain full has a low capability (Kμ capability in the flow of sensor information [6]. Consider for example the network shown in Figure 10.6. The route node 1 → node 3 → node 2 is evaluated as K1 /dγ = 1/2 = 0.5. However, the traversed node K3 = 0.25 gives indication that the sensor information flow from node 1 to node 3 cannot be eﬃciently exchanged via node 3. Taking the limitation of the traversed intermediate nodes into account, from (10.3) we get an extended definition of connectivity measure as NT Nμ Nμ,ν

CMe (t) = μ=1 ν=1 γ=1

Kγ Fγμ,ν dγ

(10.10)

where Kγ represents the Kμ with the lowest capability value (bottleneck) in route γ. Note the fact that Kγ in the route only considers the starting node and exchangers; the receiving node is not included. This consideration is due to the fact that many nodes in military networks only accept the information without an equivalent information processing capability in transmitting. For instance, in route node 1 → node 3 → node 2, only the transmitter (node 1) and exchanger (node 3) are available for assignment to Kγ to reflect the bottleneck of the information flow. For the same route, shown in Figure 10.6, the extended CM is recalculated as shown in Table 10.6. Comparing to Table 10.3, notice the value of CM decreases from 4.375 to 3.75 due to the consideration of the bottlenecks in route 1 → 3 → 2 and 2 → 3 → 1 reflecting a more realistic capability. In summary, the robustness of the network can be quantified by comparing R , and by disabling nodes in the reference and the real network CM to CM R . By comparing these values, a representation and recalculating CM and CM appears of the real network behavior while under attack. In fact, the rate of change (degradation) in the value of the connectivity measure as a function of the number of links severed and nodes being attacked can provide good insight into the robustness of the sensor network.

10.2.6

Entropy and Network Richness

At each node or source, the rate at which information is sent has a direct impact on the operational tempo of the grid. Consider the set of J possible sample values (or source symbols) by S = {x1 , . . . , xJ }. We assume the

334

Detecting and Classifying LPI Radar

Table 10.6: Extended Connectivity Measure Calculation Route 1→3→2 1→3 2→1 2→3→1 2→3 2→1→3 3→1 3→2→1 3→2

Bottleneck Node 3 1 2 3 2 2 3 3 3

CM dγ 2 1 1 2 1 2 1 2 1

Kμ 0.25 1 0.75 0.25 0.75 0.75 0.25 0.25 0.25

Contribution 0.125 1.000 0.750 0.125 0.750 0.375 0.250 0.125 0.250 CM = 3.750

probability of the source output xj is known as pj . The amount of information sent from a digital source when the jth message is transmitted is I(j) = − log2 (pj )

(10.11)

where pj is the probability of transmitting the jth message. Shannon defined the primary information-related measure of each message H as a function of the probability of transmission of each message [9]. This entropy (or uncertainty) of the source is J

H(S) = E{I(j)} = −

pj log2 (pj )

(10.12)

j=1

and is measured in information bits per source symbol.1 The information rate of the source is then H bits/s (10.13) λ= T where T is the time required to send the message. A related measure is the channel capacity or C = B log2 (1 + SNR) bits/s

(10.14)

where B is the channel bandwidth (in Hertz) and SNR is the signal-to-noise power ratio (not in decibels) at the receiver input [9]. The channel capacity can be used as a unifying principle for EA and EP actions in EW. Every EA measure (except exploitation) is an attempt to reduce the bandwidth of an adversary signal and/or to reduce the SNR. Every 1 Since

the entropy is measured in bits per sample, the binary logarithm must be used.

Network-Centric Warfare and Netted LPI Radar Systems

335

EP action (except protection against exploitation) is an attempt to increase bandwidth and/or increase SNR. Example 1: The LPI emitter uses frequency hopping as an EP measure and uses a large total bandwidth to protect against jamming, but a small instantaneous bandwidth to protect against interception and exploitation. The large total bandwidth in this case makes it diﬃcult for the jammer to set on the transmission frequency, thus limiting the reduction in SNR to that provided by barrage jamming. Example 2: Repeater or gate stealing EA techniques must achieve a certain reduction of SNR within the bandwidth of the victim’s receiver to be eﬀective. The corresponding EP technique might utilize a combination of guards and filters to recognize and eliminate the unwanted jamming signal, thereby protecting the SNR. Example 3: Against exploitation, a LPI emitter uses a very large bandwidth with low average power density. The low average power reduces the probability of intercept, but the energy over the bandwidth can be summed to extract the information from the signal. Therefore, the transmitter compensates for the low SNR with increased bandwidth to transmit the information at a fast enough rate. The jammer can only achieve high SNRs over small portions of the bandwidth. Each node within the sensor network is able to process the information at a certain rate. The information processing rates of each node can be combined to quantify the network’s richness. The information rate, λμ , of a node μ, is the rate at which the network information is processed by the node (in Hz). The minimum information rate, λmin μ , of the node is the minimum rate that information must be processed for generating decision-level knowledge from the sensor network data. From Shannon’s information entropy theory, the knowledge function is defined as [8] ⎧ 0, if λμ < λmin ⎪ μ ⎪ ⎨ λμ min ln < λμ < e · λmin , if λ min μ μ (10.15) Q (λμ ) = λμ ⎪ min ⎪ e·λ μ min ⎩ ln ≥ e · λ = 1, if λ min μ μ

λμ

Using the knowledge function, the network richness RQ is defined to represent the average rate at which information entropy (or knowledge) is generated from the sensor data shared through the network or [8] RQ =

NT μ=1

λμ Q(λμ ) NT

s−1

(10.16)

336

Detecting and Classifying LPI Radar

Figure 10.11: Time spent in each phase in OODA cycle. (After [8].) From this equation, if a node cannot provide the knowledge at a rate above its minimum value, the node’s contribution λμ Q(λμ ) degrades the overall value RQ . In addition, there is little advantage to generating sensor data faster than knowledge can be generated and absorbed.

10.2.7

Maximum Operation Tempo

A network has a maximum information exchange rate that is determined by the number of nodes, the communication and sensor technologies employed, the information data transfer rates, and the network topology. To quantify this rate within an OODA, a characteristic tempo (λT ) is defined and relates the network topology and its ability to gather the situational awareness. The characteristic tempo for the network is the product of the network reach IR and the network richness RQ λT = IR RQ Hz

(10.17)

and relates the information exchange capability of the sensor network. In addition, for every command and control structure (and associated doctrine), there is a characteristic decision-making rate (λC2 ) or speed at which decisions are made using the transferred sensor data being processed [10]. Figure 10.11 shows the tempo parameters of the sensor network OODA loop. The variable ∆t1 represents the time from observation to orientation and is limited by the information exchange time, ∆t2 is the time from orientation to decision and is dominated by the decision speed, ∆t3 is the time from decision to action and must be greater than the information exchange time (command time) and deployment time, and ∆t4 is the time from action to observation and is always greater than the sum of information exchange time and fighting time.

Network-Centric Warfare and Netted LPI Radar Systems

337

Using the OODA tempo parameters, the maximum operation tempo of the network (ΛOODA ) is of interest and represents the maximum tempo of the network to perform an entire OODA including responding to events as 1 1 1 1 1 1 + + + + + λT λC2 λT λd λT λf

ΛOODA ≤

−1

(10.18)

or after some algebra ΛOODA ≤

λC2 1+

1 λd

+

1 λf

λC2 +

(10.19)

3λC2 λT

Note that λC2 in the numerator emphasizes that the fact that while technology can help increase the network and action tempos, the C2 tempo plays a limiting role not helped by technology alone [8]. Also note that in practice the operational tempo is not a fixed value. The operational tempo calculated here represents the maximum value due to the limitation of the network topology and nodes capabilities. It provides a direct link between the internal metrics of the network and the operational outcome of a sensor and weapons network through a single equation. It is also significant in that it enables direct evaluation of the networks capability to collect, process and disseminate information (information superiority) to the combat outcome (battlespace superiority).

10.3

Electronic Attack

Jamming of the information grid is a form of electronic attack and can take on many forms such as partial band jamming, and tone jamming [11]. The eﬀectiveness of the jamming waveform depends on the signaling format used to transfer the data and the type of jamming used. When a jammer is taken into consideration, the jam-to-signal ratio (JSR) at the victim node’s receiver causes a link failure to occur if the jam-to-signal ratio is greater than a particular threshold causing the bit error rate to be unacceptable. Figure 10.12 shows a jammer (node 4) added into the previous example shown in Figure 10.6. The JSR is determined by many factors including jamming and signal power, jammer range, jamming strategy, RF waveform bandwidth, and properties of the receiver. To simplify the calculation, considering only power and range, the JSR in a single information link can be written as JSR =

ERPJ ERPJ /4π(RJ )2 = ERPC /4π(RC )2 ERPC

RC RJ

2

(10.20)

where ERPJ is the eﬀective radiated power of the jammer (node 4), ERPC is the eﬀective radiated power of the data/communication signal emitted from

338

Detecting and Classifying LPI Radar

Figure 10.12: Addition of a jammer into the node configuration shown in Figure 10.6. node 3 to node 1, RC is the range from node 3 to node 1, and RJ is the range from the jammer at node 4 to the receiver at node 1. The capability values can be assigned and used within the JSR calculation to quantify the jammer eﬀectiveness. The capability values are defined as follows. The value of Kμ is defined as the information-processing capability of the receiving node μ and its importance to the network. Assuming the importance of the information transferred through each node is not diﬀerent, we see that the Kμ is related to the information exchange capability. Also, KνJ is the jamming capability of the hostile jammer and is defined as the information link jamming capability at node ν. Similar to Kμ , 1 ≥ KνJ ≥ 0 and is determined by factors such as its eﬀective radiated power, jammer waveform type, and jamming strategy. Without a loss in generality, the ratio of KνJ to Kμ is set equal to the ratio of the eﬀective radiated powers. Therefore, (10.20) can be written as JSR =

ERPJ ERPC

RC RJ

2

=

KνJ Kμ

RC RJ

2

(10.21)

The JSR is used to represent the eﬀect of the jamming on an existing information exchange link. When the JSR is higher than a given threshold, the information link is regarded as unavailable.

10.4

Information Network Analysis Using LPIsimNet

The MATLAB folder LPIsimNet (see Appendix D) provides the tools to calculate the metrics discussed above and generates a visual summary of the simulation results for any user-defined global information grid configuration.

Network-Centric Warfare and Netted LPI Radar Systems

339

In this section, several simulations are presented to illustrate the metrics discussed above including the eﬀects of an electronic attack. The label notation used is in the form of (i, j) XYZ. The i represents the node type and can be any one of the following: • N: Friendly information/data transfer communication node; • R: Friendly LPI radar node (discussed in the next section); • NR: Friendly node with both information/data transfer capability and radar capability; • JN: Hostile communication jammer node; • JR: Hostile radar jammer node; • JNR: Hostile communication and radar jammer node. The j indicates the index of the node and ranges from 1 to the number of nodes utilized NT . The XYZ represents the name of the node (e.g., EA-6B, E2C). The first simulation considers a sensor network with three nodes as shown in Figure 10.13. In this simulation, the communication between an E-2C, an F-16 and an AC-130 are being studied. Figure 10.14 shows the scenario setup used to generate the simulation. Note that the user can control the number and characteristics of each node within the scenario (including the placement and movement). Top-level properties are in rows 2 through 5. Rows 6 through 10 show the characteristics of the individual nodes. The last section shows the node connectivity. For the simulation shown in Figure 10.13, there are two bidirectional links and one unidirectional link indicated by the direction arrows. The simulation is run and the results are summarized in Table 10.7. The sensor network simulation results can be generated for any number of nodes and connectivity but can take a significantly longer period of time for simulations with a large number of nodes. The details of the connectivity measure CM and network richness RQ are shown in Tables 10.8 and 10.9, respectively. To quantify the eﬀect of an electronic attack, a jammer onboard a Russian Su-34 is added to the sensor network. The sensor network under attack is shown in Figure 10.15. The Russian Su-34 is located at the bottom right corner and is represented by a hollow circle. The jamming connection is shown by a dashed line to E-2C. The initial scenario configuration is shown in Table 10.16. The total time index row represents the number of time indexes that are calculated in the simulation. This oﬀers the ability to include movement of all assets. For the setup shown in Figure 10.15, total time indexes is set to 3. When the simulation is run, the jammer moves closer to the E-2C at each time index and all metrics are recalculated (total of 3 times). Position

340

Detecting and Classifying LPI Radar

Figure 10.13: Three communication nodes.

Table 10.7: Simulation Results of Scenario Shown in Figure 10.13 Results Reference connectivity measure Connectivity measure Network reach Network richness Characteristic tempo Operational tempo

Values 9 3.75 0.42 271.60 113.16 26.78

Network-Centric Warfare and Netted LPI Radar Systems

341

Table 10.8: Analysis Detail of Connectivity Measure for Simulation Shown in Figure 10.13 Route 1→3→2 1→3 2→1 2→3→1 2→3 2→1→3 3→1 3→2→1 3→2

Bottleneck Node 3 1 2 3 2 2 3 3 3

CM Contribution 0.125 1.000 0.750 0.125 0.750 0.375 0.250 0.125 0.250 CM = 3.750

Table 10.9: Analysis Detail of Network Richness for Simulation Shown in Figure 10.9 Node 1 2 3

λ 200 200 300

Q (λ/λm ) 0.69315 0.69315 1.7918

λQ (λ/λm ) 138.630 138.630 537.540 814.800 RQ = 814.8/3 = 271.600

342

Detecting and Classifying LPI Radar

Figure 10.14: User setup of the scenario shown in Figure 10.13. refers to the initial position of the node and velocity indicates the movement of each node per time index (km/time index). A summary of the simulation results for the three time instances is shown in Figure 10.15 (time index 1), Figure 10.17 (time index 2), and Figure 10.18 (time index 3). Note that for each time instant, the jammer is moving closer to the E-2C. Notice on the second time index, the jammer is close enough to disable one of the links. The node 3 to 1 link is disabled due to the JSR > 1. On the third index, the link from node 2 to 1 is also suppressed. Consequently, several trends in the network metrics can be noted across the three time indexes. As the jammer moves towards the network, the measure of connectivity decreases as does the network reach. Also, a noticeable decrease in the characteristic tempo and maximum operational tempo is shown.

10.5

Netted LPI Radar Systems

Despite recent advances in monostatic radar systems (colocated single transmitter and receiver), two major disadvantages are inherent. They oﬀer little

Network-Centric Warfare and Netted LPI Radar Systems

343

Figure 10.15: Simulation of network jammer at time index 1. to counter stealth technology and they only oﬀer a single perspective for each radar [12]. The development of stealth technology has primarily been aimed at defeating the monostatic radar by the use of absorbing materials and nonreflective structural designs that minimize the scattered energy reflected into the hemisphere from which the signal arrives. The limited energy that is returned to the emitter from the stealth target, makes it very diﬃcult to detect the target. In addition, due to terrain obscuration, ground-based or low-flying monostatic radar systems often do not have a line of sight to the target and therefore cannot provide detections. Due to this single perspective, the information contained in the multiple perspectives is missed. Consequently, if a number of cooperative radar systems are distributed spatially and networked together, they can provide the opportunity to view the target from a number of diﬀerent aspect angles. In multifrequency radar networks each radar performs a significant amount of local preprocessing. Outcomes of the local preprocessing can then be delivered to a central processor through a communication link. The preprocessing limits the amount of information that needs to be passed on to make a final detection decision. These systems use diﬀerent frequencies to cope with interference rejection but each receiver is unable to process the information from all transmitters.

344

Detecting and Classifying LPI Radar

Figure 10.16: User setup of the scenario shown in Figure 10.15. Netted radar systems sometimes referred to as spatial multiple-input multiple-output (MIMO) radar systems, consist of a number of distributed radar systems (transmit and receive sensors) each having the ability to transmit independent orthogonal waveforms (to avoid interference) and the ability to receive and process synchronously all waveforms that are transmitted. Figure 10.19 shows an example of a netted radar system with three radar nodes connected by a network. All three radars have already acquired and are tracking the target with their antenna beams. The radar systems R1, R2, and R3 each transmit a diﬀerent waveform but receive and process all three waveforms that are collected from the target. The use of the network allows each system to share its target information noncoherently (using orthogonal waveforms) or coherently where each radar has a common precise knowledge of space and time. The implementation of networked radar systems has become feasible due to recent advances in large bandwidth wireless networks, high-capacity transmission lines, multichannel electronically scanned antennas, high-speed low-cost digital processors and precise synchronization systems [13].

Network-Centric Warfare and Netted LPI Radar Systems

Figure 10.17: Simulation of network jammer at time index 2.

Figure 10.18: Simulation of network jammer at time index 3.

345

346

Detecting and Classifying LPI Radar

Figure 10.19: Example of a sensor network connecting three LPI emitters (R1, R2, R3).

10.5.1

Advantages of the Netted LPI Radar Systems

There are two important characteristics of a netted radar system; the spatial dispersion of the nodes (i.e., transmitter and receiver locations) and the data fusion processing (i.e., processing performed in the receiver at a node to combine multiple receiver outputs). These characteristics lead to several advantages of a netted LPI radar system. The spatial distribution (or geometry) of the nodes enable the surveillance area to be tailored according to the specific mission objective [14]. The multisite emitters can be used to form a specially designed surveillance area to more eﬃciently detect targets based on known patterns of military behavior. The network also allows a multiperspective SAR or ISAR image to be generated. By using a number of distributed transmitters and receivers to collect the echos from the target at diﬀerent aspects or directions, the independent angular samples provide spatial diversity of the target’s RCS. With widely separated antennas, netted radar systems also have the ability to handle slow moving targets by exploiting Doppler estimates from multiple directions. If coherent processing is used, high-resolution target localization can be achieved with a resolution that far exceeds that supported by the radar’s waveform [15]. This however, comes with a price. The receiving and processing requirement for such a coherent summation is highly demanding. For example, if each waveform produces 1,000 resolvable range cells and 10 Doppler cells, integration would be required simultaneously in 10, 000N 2 cells (possibly reduced by excluding regions not mutually covered). Given the high-resolution in both range and Doppler, the numbers used here may in-

Network-Centric Warfare and Netted LPI Radar Systems

347

crease by orders of magnitude, straining the capability of most modern signal processors. One of the inherent properties of the netted radar system is the increase in the number of degrees of freedom due to the spatial diversity [14, 16]. The scattered reflections can be captured to take advantage of the target scintillation providing a gain in detection performance. The spatial diversity can be used to separate scattering centers from one another that otherwise cause a glint signature. In addition, targets can be more easily separated from the clutter in clutter-limited detection scenarios [17]. The target’s RCS spatial variations can also be exploited to obtain a diversity gain for estimation of various parameters (e.g., angle of arrival, Doppler). Target classification and recognition can be improved as a result of the extra information retrieved from the diﬀerent perspectives [18]. With more degrees of freedom, flexible time-energy management modes can be utilized to minimize the amount of energy that is radiated. Since more of the scattered energy from the target is collected (from diﬀerent directions), the sum of the ERP from all the radar systems can be made approximately equivalent to that of a single monostatic radar [19]. As a result, the detection performance of the system is superior while also utilizing a minimum ERP. A better system sensitivity results due to the additional transmitters and receivers which augment the total received signal power leading to an increase in overall SNR. Further, every node is less vulnerable to physical and electronic attack—increased survivability. That is, the destruction of the sensor network by an ARM is less likely. The probability of being coherently jammed is also less likely since the probability of intercept is lowered even further. The likelihood of obtaining a line-of-sight to the target is also greatly improved due to the spatial dispersion of the radar nodes [20].2 Having several radar systems will add confusion to the noncooperative intercept receiver that has to cope with the increased number of signals. Another significant advantage is the increase in the reliability of the netted radar system. The loss of one or even several nodes may not destroy the surveillance capability but more of a graceful degradation will take place as there are still other nodes available [14]. There are also technical challenges to be addressed. The most important is the time and frequency synchronization for coherent operation. By using GPS as a reference timing signal, the network can be made coherent. Another important challenge is the data fusion and registration of the various data streams, which requires reliable and high-capacity communication links in the network [14]. 2 One of the disadvantages of bistatic and multistatic radar systems is that more than one line-of-sight path is required. For low-altitude targets, the network of monostatic radars has a much higher probability of having at least one unusable path. The more nodes that require simultaneous line-of-sight paths, the lower the probability of success.

348

10.5.2

Detecting and Classifying LPI Radar

Netted LPI Radar Sensitivity

The spatially distributed and networked LPI radar system of systems can be broken down into a set of M × N transmitter-receiver pairs each with a bistatic component contributing to the entirety of the netted radar sensitivity [13]. Figure 10.19 can be considered as a connected series of bistatic radar systems where the transmitter and receiver are separated. With this, it is necessary to calculate the target-to-transmitter range and target-to-receiver range separately. These range values then replace the single range term in the monostatic radar equation. In addition, a separate bistatic RCS value for each bistatic radar pair must be computed. Thermal noise at each receiver can be assumed to be statistically independent. The overall netted radar SNR can be calculated by summing up the partial SNR of each transmitter-receiver pair as [12, 19] M

N

SNRnet = i=1 j=1

PCWi Gti Grj σT ij λ2i 2 R2 F L (4π)3 kT0ij BRi Rti rj Rj ij

(10.22)

where PCWi is the ith average CW transmitter power, Gti is the ith transmit antenna gain, Grj is the jth receive antenna gain, σT ij is the RCS of the target for the ith transmitter and jth receiver, λi is the ith transmitted wavelength, BRi is the bandwidth of the matched filter for the ith transmitted waveform, k is Boltzmann’s constant, T0ij is the receiving system noise temperature at a particular receiver, FRj is the noise factor for each receiver, Lij is the system loss for the ith transmitter, jth receiver (Lij > 1), Rti is the distance from the ith transmitter to the target and Rrj is the distance from the target to the jth receiver. Note that this assumes that all signals can be separately distinguished at each receiver and that all antenna beams are pointed at the target. Also note that with i = j = 1, (10.22) reverts to the monostatic case. An important characteristic of netted radar systems can be identified when we consider each radar to be identical with every transmitter-receiver combination the same [12]. In this case the netted radar SNR equation can be written as M N 1 PCW Gt Gr σT λ2 (10.23) SNRnet = 2 2 3 (4π )kT0 BFR L i=1 j=1 Rti Rrj Insight is gained if we group all of the range independent parameters together into a constant K, then the netted radar SNR can be expressed as M

N

SNRnet = i=1 j=1

K 2 R2 Rti rj

(10.24)

Network-Centric Warfare and Netted LPI Radar Systems

349

Normalizing (10.24) by the SNR for a single monostatic radar (10.37) we have M

N

SNRnet 1 = R4 2 R2 SNR1 R ti rj i=1 j=1

(10.25)

which shows that the SNR of the system is related to the power received from the contributing transmit and receive paths. Further, if Rti = Rrj and M = N it follows that [19] SNRnet ∝ N2 SNR1

(10.26)

That is, the system SNR is a function of the square of the number of nodes for coherent operation. This represents an N -fold improvement over the noncoherent case (γ = 0.5). For noncoherent netted radar processing, the number of transmit antennas serves as a factor in the number of diversity paths. For coherent processing the number of transmit antennas contributes to reducing the spurious peaks. In either mode, the processing at the receiver scans through all the possible target locations. It must be pointed out that for each of the N radars to receive and process the N diﬀerent waveforms transmitted by those radars all with antenna gains Gt and Gr , achieving SNRnet applies to the sum of N 2 coherently combined signals. Since antenna gain G ≈ 4π/Ψb where Ψb is the solid angle within the half-power beam contour, there are in the hemisphere visible to each radar 2π/Ψ = G/2 beam positions. Unless the target has been acquired and placed in track by a single radar, using the single-radar (monostatic) SNR available to that radar, and used to point the other radars, the probability that all 1. radars illuminate the target simultaneously is extremely small for Gt Gr This implies that near omni-directional antennas must be used to achieve initial detection based on SNRnet . If designation from a monostatic radar is used, then the other radars must each place a transmitting and receiving beam on each target for which SNRnet is to be obtained, implying either near omnidirectional or multiple directional beams that require splitting transmitter energy amongst multiple targets. In summary, for most cases SNRnet will only be available for tracking or identifying a target that is first detected by a single monostatic radar in the network.

10.5.3

Signal Model

To develop the netted radar (spatial MIMO) signal model, a distributed target with Q independent isotropic scatterers is considered. Figure 10.20 shows four such scatterers located in a 2-D plane along with the M LPI transmitters Tk = (xtk , ytk ), k = 1, . . . , M that illuminate the target and the N receivers Rl = (xrl , yrl ), l = 1, . . . , N that collect the scattered energy. We let

350

Detecting and Classifying LPI Radar

E/M sk (t) be the set of transmitted waveforms where E is the total transmitted energy. Normalization by M makes the total energy independent of the number of transmitters used to illuminate the target [18]. The target reflectivity can be expressed in a diagonal Q×Q matrix with = diag(ξ1 , . . . , ξQ ). T The target average RCS is E[tr( )] = 1 and is independent of the number of scatterers. For the netted radar case, spatial diversity is achieved with the distributed antenna positions. The M waveform generators (W Gk ) transmit orthogonal (noncoherent) waveforms in order that the energy from the diﬀerent transmitters may be easily separated at the receiver where each of the receive antennas has M matched filters (M Fi1 . . . M FiM with one corresponding to each orthogonal waveform). Neglecting the path loss and summing over all of the scatterers, the total signal received can be expressed as zlk (t) =

E M

Q

q=1

ξq sk [t − τtk (Xq ) − τrl (Xq )]e−j2πfc [τtk X(q)+τrl (Xq )] (10.27)

where τtk (Xq ) = d(Tk , Xq )/c is the propagation time delay between the kth transmitting sensor and the scatterer at Xq . The distance d(Tk , Xq ) = (xtk − xq )2 + (ytk − yq )2 . The propagation time delay τrl X(q) is defined analogously. The two exponential terms in (10.27) reflect the phase shift due to the propagation from transmitter k to scatterer q and the phase shift due to the propagation from the scatterer q to the receiver l. The channel components of (10.27) are often collected as [18] (q)

hlk = ξq e−j2πfc [τtk (Xq )+τrl (Xq )]

(10.28)

and can be interpreted as the equivalent “channel” between transmitter k, scatter q and receiver l. The channel element (10.28) consists of e−j2πfc τtk (Xq ) which is the phase shift due to the propagation from transmitter k to scatterer q. Similarly, e−j2πfc τrl (Xq ) is the phase shift due to the propagation from the scatterer q to the receiver l. The reflectivity of the scatterer is ξq . With (10.28), (10.27) can be expressed as zlk (t) =

E M

Q (q)

q=1

hlk sk [t − τtk (Xq ) − τrl (Xq )]

(10.29)

If the target has an RCS center of gravity at X0 = (x0 , y0 ) and we assume that sk (t − τtk (Xq ) − τrl (Xq )) ≈ sk (t − τtk (X0 ) − τrl (X0 )) for all q = 1, . . . , Q then E hlk sk [t − τtk (Xq ) − τrl (Xq )] zlk (t) = (10.30) M where Q

(q)

hlk =

hlk q=1

(10.31)

Network-Centric Warfare and Netted LPI Radar Systems

351

Figure 10.20: Netted radar with M transmit antennas each with a separate orthogonal waveform generator. Receive array consists of N antennas each with a parallel set of M matched filters. Target is shown with distributed scatterers located at Xq with reflectivity ξ. Target’s RCS center of gravity is located at X0 .

352

Detecting and Classifying LPI Radar

Accounting for additive noise, the observed waveforms at the receive antenna l can be expressed as rl (t) =

E hlk sk [t − τtk (X0 ) − τrl (X0 )] + wl (t) M

(10.32)

where wl (t) is the additive circularly symmetric, zero mean, complex Gaussian noise that is spatially and temporally white with autocorrelation function 2 δ(τ ). σw Properties of the elements hlk of the channel matrix and the conditions for spatial decorrelation E[hlk h∗li ] ≈ 0 are further addressed in [18, 21]. In essence, the spatial decorrelation means that diﬀerent receive antennas measure a diﬀerent value of the RCS. Also discussed is the relationship of the model to other types of emitters such as phased arrays, adaptive radar STAP and multistatic radar. Properties of the MIMO radar ambiguity functions are given in [22—24]. As a final point, we point out that the maximum number of targets Kmax , that can be uniquely identified simultaneously by a phased array with N receive antenna elements is Kmax =

2N 3

(10.33)

while the maximum number of targets that can be uniquely identified simultaneously by a MIMO radar is [25] Kmax =

2M N 3

(10.34)

That is, the maximum number of targets that can simultaneously be uniquely identified by a MIMO radar is up to M times its phased array counterpart.

10.5.4

Netted Radar Electronic Attack

The JSR as defined by the jamming power and signal (radar echo) power is given by jamming power (10.35) JSR = signal power Unlike communication antennas that often use dipole antennas for omnidirectional communication, radar antennas frequently use highly directional antennas that can identify the target angle in azimuth and elevation. The shape of the radar antenna pattern (pencil beam) results in degradation of the jamming signal when the jamming signal is not incident on the main lobe. The jam-to-signal ratio is ⎞ ⎛ 2 2 ERPJ 4π (RJ ) ⎠ cos θ = ERPJ RT cos θ (10.36) JSR = ⎝ ERPR RJ ERP 4π (R )2 R

T

Network-Centric Warfare and Netted LPI Radar Systems

353

Figure 10.21: Example of jamming with incident angle. where ERPJ = Pj Gj is the eﬀective radiated power of the jammer, ERPR = PCW Gt is the eﬀective radiated power of the LPI radar, RJ is the range from the jammer to the radar, RT is the range from the radar to the target, and θ is the incident angle of jamming. Figure 10.21 provides an example of the jamming signal incident with θ = 60 degrees that results in cos θ = 0.5 degradation in the jamming power.

10.6

Netted Radar Analysis Using LPIsimNet

The LPIsimNet MATLAB tools (see Appendix D) are used in this section to demonstrate the SNR advantages of a netted-radar configuration. Any user-defined netted radar configuration can be analyzed [26]. Results are also shown when a jammer is included in an electronic warfare topology. We start by examining the SNR contour tools for a monostatic LPI emitter.

10.6.1

Monostatic LPI Emitter and the SNR Contour Chart

A contour chart represents an important analysis tool to quickly quantify the advantages of any netted radar sensor network and jammer configuration. We start by examining the monostatic LPI emitter to present the SNR contour chart that is generated by the MATLAB tools LPISimNet. In a monostatic LPI radar system, the transmitter and receiver are co-located and can only intercept a very small portion of the electromagnetic energy scattered from the target. Much of the signal and its information is lost. To introduce the SNR contour analysis, we revisit the monostatic radar configuration. The SNR for a monostatic configuration can be written as SNR1 =

PCW Gt Gr σT λ2 (4π)3 kT0 FR BR RT4 L

(10.37)

354

Detecting and Classifying LPI Radar

To develop a useful analysis tool for an LPI emitter, a contour chart is constructed with the RCS σT = 1m2 . This normalized contour chart can easily be scaled for any RCS. In addition, the SNR is only dependent on the radar properties and target range. By plotting the results in a 2-D geometric map, the SNR of the radar can be read as shown in Figure 10.22.

Figure 10.22: Example of SNR contour chart for a monostatic LPI emitter. This chart illustrates the SNR contour generated by the MATLAB software contained on the CD (LPIsimNet.m). For this simulation, the Pilot radar is used with an ERPR = PCW Gt = 1,000W, Ae = 0.0815 m2 and is the eﬀective receiving aperture area (equal to Gr λ2 /2π), and noise power kT0 FR BRi = 7.5 × 10−13 W. For any target position selected, the value of SNR can be read from the figure.

10.6.2

Three Netted LPI Emitters

To demonstrate the advantages of a netted LPI radar configuration, three radar systems are simulated within a 2,500-km2 region using the MATLAB

Network-Centric Warfare and Netted LPI Radar Systems

355

Figure 10.23: Sensor network containing three LPI emitters. system of systems software (LPIsimNet). The objective of this simulation is to display and compare the SNR contour chart with network synchronization and without network synchronization. The sensor network shown in Figure 10.23 indicates the three radar nodes within an area of 2,500 km2 . The black asterisk at the position (15, 25) indicates the target, which has an RCS = 1m2 . In this normalized presentation, the contour analysis can easily be scaled to any target RCS value. The properties of each LPI emitter used in the simulation are shown in Table 10.10. The detailed analysis report provided by LPIsimNet, is referenced to the user selected target position. For the sensor network displayed in Figure 10.23, the simulation results are shown in a contour map in order to quantify the SNR quickly and evaluate the benefits of the sensor network configuration [26]. Figure 10.24 shows the contour chart of the three emitters when the sensor network is disabled. The SNR values for each emitter are independent and can be read directly on the map. For the no network configuration, the SNR = −48.7 dB at the target (node 4) as shown in Figure 10.24. For the sensor network—enabled configuration, the contour chart is shown in Figure 10.25. The SNR = −43.2 dB. That is, the netted radar configuration increases the SNR 5.71 dB over the no network configuration as shown in Figure 10.24.

356

Detecting and Classifying LPI Radar

Table 10.10: LPI Sensor Network: Parameters for the Three Emitter Nodes Node Index Type Name ERP (W) Ae (m2 ) Noise Power (W) Position (Km)

1 Blue Force Radar1 1000 0.0815 7.5 × 10−13 (15, 40)

2 Blue Force Radar2 100 0.0815 1 × 10−12 (15, 15)

3 Blue Force Radar3 10 0.0815 1.5 × 10−12 (30, 25)

Figure 10.24: SNR contour chart for three emitters without sensor network.

Network-Centric Warfare and Netted LPI Radar Systems

357

Figure 10.25: SNR contour chart for three emitters with sensor network.

358

Detecting and Classifying LPI Radar

Figure 10.26: Jammer attack on a sensor network containing two LPI emitters. Target is 1 m2 at position (15, 25) km.

10.6.3

Two Netted LPI Emitters with Jammer

To quantify the eﬀects of an electronic attack on a netted radar system, two LPI emitters are placed in a topology with the 1-m2 target. A jammer to attack both emitters is added as shown in Figure 10.26. The parameters for the two LPI emitters and the jammer (onboard an Su-34) are shown in Table 10.11. By comparing the signal-to-jam ratio (SJR) contour chart, with and without networking, the advantages of a sensor network in an electronic warfare configuration can be identified. The contour results for the SJR when no network is used are shown in Figure 10.27. The contour results for the SJR when the LPI emitters use a sensor network are shown in Figure 10.28. The SJR improvement in the sensor network case is 5.75 dB.

10.7

Orthogonal Waveforms for Netted Radar

The increased area of coverage using a system of netted radar systems, each diverse and independent, make netted radar sensing and the development of appropriate waveforms an important area of investigation. Multiradar systems can operate in both monostatic and multistatic modes simultaneously

Network-Centric Warfare and Netted LPI Radar Systems

359

Table 10.11: LPI Sensor Network: Parameters for the Two Emitters and One Jammer Node Index Type Name ERP (W) Ae (m2 ) Noise Power (W) Position (Km)

1 Blue Force Radar1 1000 0.0815 7.5 × 10−13 (15, 40)

2 Blue Force Radar2 100 0.0815 1 × 10−12 (15, 15)

3 Hostile Jammer Su-34 10 (30, 25)

Figure 10.27: SJR for jammer attack on two LPI emitters. Target is 1 m2 at position (15, 25) km.

360

Detecting and Classifying LPI Radar

Figure 10.28: Jammer attack on a sensor network containing two LPI emitters. Target is 1m2 at position (15, 25) km.

Network-Centric Warfare and Netted LPI Radar Systems

361

and can retain the favorable features of both a monostatic radar system and a multistatic radar system if each system transmits a distinct signal from a set of orthogonal signals in which any two signals are not cross-correlated and each receiver uses multiple matched filters. As discussed in Chapter 5, in order to achieve high range resolution and multiple target resolution, the periodic autocorrelation function of any transmitted code sequence should have a low peak side lobe level (PSL). For moving targets, Doppler loss occurs at the matched filter output of the correlation receiver. For a sequence of length Nc , with Doppler shift fd and signal duration T the excessive phase increments from one sequence to the next is 2πfd T /Nc . Netted LPI radar systems require a code sequence with low PSL, resistance to Doppler loss and the use of orthogonal waveforms that have a low cross-correlation between them. This is to avoid interference and to provide independent information about the target at various angles. The concept of orthogonal netted radar systems is diﬀerent than the traditional netted radar systems. Consider the multiradar system shown in Figure 10.19 consisting of L LPI radar systems where each system transmits a distinct low power CW signal using an orthogonal code set {sl (t), l = 1, 2, 3, . . . , L}. Any two signals in the set are uncorrelated or C≈

sp (t)s∗q (t + τ )dt = 0

(10.38)

t

for p = q and p, q = 1, 2, . . . , L. For high-range resolution, the aperiodic autocorrelation function of any code sl (t) in the code set should be close to an impulse function or A=

1 E

sl (t)s∗l (t + τ ) = 1

(10.39)

t

for τ = 0 and A = 0 otherwise. If the radar stations in the multiradar system transmit signal {sl (t), l = 1, 2, 3, . . . , L}, respectively, any radar station can choose to receive and process any of the L signals by including a matched filter that correlates to the transmitted signal only. The target echoes from the other signals generate nearzero outputs at the matched filter because it does not correlate with any of them. If a radar system is equipped with only a matched filter that correlates to its own transmitted signal, then the system will only operate in the monostatic mode. If there are multiple parallel matched filters at a receiver that correlate to the signals that are transmitted by other radar stations, multiple detection results of targets are available for integration processing (coherently or noncoherently). The waveforms used by netted radar systems must be carefully designed to avoid the self-interference and detection confusion. An orthogonal waveform set is a group of waveforms in which each of the waveforms has the nearly ideal

362

Detecting and Classifying LPI Radar

noise-like aperiodic autocorrelation property and any two of them have no cross-correlation. If the emitter transmits the waveforms from an orthogonal coding waveform set, it can adaptively operate based on the environments and real-time needs in regular monostatic mode or in a multistatic mode with the same carrier frequency.

10.7.1

Orthogonal Polyphase Codes

Orthogonal netted radar systems require a set of orthogonal transmit signals with properties as outlined in (10.38) and (10.39) [27]. Orthogonal polyphase codes have several advantages for the emitter over the use of binary phase codes. The orthogonal polyphase codes have a larger main lobe-to-side lobe ratio than binary signals with the same code length Nc . They also have a more complicated signal structure making the signal harder to detect and analyze by a noncooperative intercept receiver. The orthogonal polyphase code set consists of L signals with each signal containing Nc subcodes and can be represented by the complex number sequence (10.40) sl (n) = ejφl (n) where n = 1, 2, . . . , Nc and l = 1, 2, . . . , L where φl (n), (0 ≤ φl (n) < 2π) is the phase of subcode n of signal l in the signal set. If the number of distinct phases available to be chosen for each subcode in a code sequence is Mc , the phase for a subcode can only be selected from the following admissible values [27] 2π 2π 2π (10.41) ,2 · , . . . , (Mc − 1) · φl (n) ∈ 0, Mc Mc Mc or (10.42) φl (n) = {ψ1 , ψ2 , . . . , ψMc } Considering a polyphase code set S with code length Nc , set size of L and distinct phase number Mc , the phase samples of S can be represented with the L × Nc phase matrix

S(L, Nc , Mc ) =

φ1 (1) φ2 (1) .. .

φ2 (2) φ2 (2) .. .

··· ··· .. .

φ1 (Nc ) φ2 (Nc ) .. .

(10.43)

φL (1) φL (2) · · · φL (Nc ) where the phase sequence in row l is the polyphase sequence of signal l and all the elements in the matrix can only be chosen from the phase set in (10.41), (10.42). From (10.38) and (10.39), it can be shown that the aperiodic autocorrelation of the polyphase sequence sl and cross-correlation properties

Network-Centric Warfare and Netted LPI Radar Systems

363

of orthogonal polyphase codes sp and sq will satisfy or nearly satisfy [27] ⎧ Nc −k ⎪ 1 ⎪ exp j[φl (n) − φl (n + k)] = 0 0 < k < Nc ⎨ Nc n=1 A(φl , k) = Nc ⎪ ⎪ exp j[φl (n) − φl (n + k)] = 0 − Nc < k < 0 ⎩ N1c n=−k+1

(10.44) for l = 1, 2, . . . , L and ⎧ Nc −k ⎪ 1 ⎪ exp j[φq (n) − φp (n + k)] = 0 0 < k < Nc ⎨ Nc n=1 C(φl , k) ≈ Nc ⎪ ⎪ exp j[φq (n) − φp (n + k)] = 0 − Nc < k < 0 ⎩ N1c n=−k+1

(10.45) for p = q and p, q = 1, 2, . . . , L where k is the discrete time index. To design the polyphase code set with the properties given in (10.44) and (10.45), the minimization of a cost function that is based on the total autocorrelation side lobe energy and the cross-correlation energy is performed. This minimization then leads to uniformly distributed autocorrelation side lobe and cross-correlation energies among all possible locations thus minimizing the autocorrelation side lobe peaks and cross-correlation peaks. Given values of Nc , Mc and L, the energy-based cost function used is L

E= l=1

Nc −1 k=1

L−1

|A(φl , k)|2 + λ

L

Nc −1

p=1 q=p+1 k=−(Nc −1)

|C(φp , φq , k)|2

(10.46)

where λ is the weighting coeﬃcient between the autocorrelation function and the cross-correlation function in the cost function. Minimization of this function with Nc = 40, L = 4 and Mc = 4 generates a group of polyphase values that are orthogonal as shown in Table 10.12. Minimization of the energy cost function (10.46) was accomplished with a simulated annealing statistical optimization algorithm [27] that was chosen for its ability to avoid becoming trapped in a local optima during the search process. The autocorrelation side lobe peaks (diagonal terms) and cross-correlation peaks (oﬀ diagonal terms) of the polyphase code set are shown in Table 10.13. These results were obtained using λ = 1. A larger value of λ means that the cross-correlation energy is weighted more in the cost function and leads to smaller cross-correlation peaks [27]. The four orthogonal polyphase Nc = 40 sequences were generated with a carrier frequency fc = 1,000 Hz, fs = 7,000 Hz, cpp = 1. The power spectrum magnitude of the signal with Code 1 is shown in Figure 10.29. The polyphase shift for the Nc = 40 orthogonal codes for Code 1 are shown in Figure 10.30. The Nc = 40 orthogonal polyphase shifts for Code 2 are shown in Figure 10.31 and Code 3 are shown in Figure 10.32. The polyphase shift for the

364

Detecting and Classifying LPI Radar

Table 10.12: Phase Sequences of a Polyphase Code Set with Nc = 40, L = 4, and Mc = 4 (from [27]) No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Code 1 π/2 0 0 3π/2 π/2 3π/2 3π/2 π/2 π/2 π π/2 π/2 3π/2 3π/2 π π/2 π/2 3π/2 0 π 0 3π/2 π/2 π/2 π 3π/2 3π/2 3π/2 π/2 3π/2 3π/2 3π/2 π π/2 π π π π 3π/2 π/2

Code 2 3π/2 π π π π/2 0 0 π/2 π/2 3π/2 0 π/2 π π/2 π π π/2 3π/2 0 π/2 3π/2 π/2 π/2 3π/2 π/2 0 0 3π/2 π/2 π/2 π π 3π/2 π/2 3π/2 π/2 3π/2 π/2 π π/2

Code 3 3π/2 0 π/2 π/2 3π/2 π/2 3π/2 π π/2 π/2 π/2 π/2 π/2 π π π/2 0 π/2 3π/2 π π/2 3π/2 0 π π/2 0 0 π 0 π π π/2 π π 3π/2 π/2 0 0 3π/2 0

Code 4 π/2 π/2 0 0 0 π/2 3π/2 π 3π/2 π 0 3π/2 3π/2 0 π 0 0 π/2 3π/2 3π/2 π/2 3π/2 0 π/2 0 3π/2 0 0 π/2 π/2 π 3π/2 π/2 π/2 0 3π/2 π/2 π π π

Network-Centric Warfare and Netted LPI Radar Systems

365

Table 10.13: Autocorrelation Side Lobe Peaks (Diagonal Terms) and CrossCorrelation Peaks (Oﬀ-Diagonal Terms) of Orthogonal Polyphase Code Set with Nc = 40, L = 4 and Mc = 4. (from [27]) Code Code Code Code

1 2 3 4

Code 1 0.1521 0.2062 0.1904 0.2121

Code 2 0.2062 0.1414 0.2064 0.1768

Code 3 0.1904 0.2064 0.1346 0.2016

Code 4 0.2121 0.1768 0.2016 0.1820

Nc = 40 orthogonal codes for Code 4 are shown in Figure 10.33. Note the cross-correlation between any two of these four codes is approximately zero. The ACF and PACF for the Code 1 sequence is shown in Figure 10.34. Note the PSL = −16 dB. The PAF is shown in Figure 10.35. The characteristics of the other three codes are very similar. Note the low Doppler side lobes in PAF. The polyphase code sequences described in the section can be generated using ortho40.m in the LPIT.

10.7.2

Addressing Doppler Shift Degradation

For moving targets, the polyphase sequences above degrade severely in the presence of small Doppler shifts. The Doppler loss results in a degradation of the autocorrelation and cross-correlation properties at the matched filter outputs of the correlation receiver. In [28], an algebraic design method for generating polyphase orthogonal sequences with good Doppler tolerance is presented. The method uses a Hadamard matrix construction technique with circulant matrices3 based on polyphase complementary sequences (sum of their aperiodic autocorrelation functions equals zero except for the zero shift). In [28], Frank complementary sequences are used to create the Hadamard matrix. For their Nc = 36 length sequence, a Doppler tolerance of |fd T | = 1.7 was achieved compared to 0.7 for the Deng sequences above with Nc = 40. Depending on the allowable reduction in output SNR, this implies that the “tolerant” waveform, when detecting a subsonic target (v = ±300m/s) at S-band (λ = 0.1m), for which fd ≈ ±6 kHz, would be limited to T < 1.7/12, 000 = 0.141 ms. Code lengths beyond this value would require multiple Doppler filters (or correlators) to retain sensitivity to subsonic targets of unknown velocity. The mean autocorrelation PSL = −16 dB compared to the Deng sequences with PSL = −16.3 dB. Although the length of the codes that can be developed is constrained, the waveform design methodology addresses all three issues (autocorrelation, cross-correlation and Doppler tolerance). 3 A circulant matrix is a special type of Toeplitz matrix where each row vector is shifted one element to the right relative to the preceding row vector.

366

Detecting and Classifying LPI Radar

Figure 10.29: Power spectrum magnitude of Code 1 with fc = 1,000 Hz.

Figure 10.30: Orthogonal polyphase shifts for Code 1 Nc = 40 phase shifts.

Network-Centric Warfare and Netted LPI Radar Systems

367

Figure 10.31: Orthogonal polyphase shifts for Code 2 Nc = 40 phase shifts.

Figure 10.32: Orthogonal polyphase shifts for Code 3 Nc = 40 phase shifts.

368

Detecting and Classifying LPI Radar

Figure 10.33: Orthogonal polyphase shifts for Code 4 Nc = 40 phase shifts.

Figure 10.34: Orthogonal polyphase Code 1 ACF and PACF.

Network-Centric Warfare and Netted LPI Radar Systems

369

Figure 10.35: Orthogonal polyphase Code 1 PAF. In [29], a new set of polyphase sequences is presented with good correlation properties as well as resilience to Doppler shifts. The sequences are built using a numerical cross entropy optimization based on correlation properties and a structural constraint is also imposed on the optimized polyphase sequences so that Doppler tolerance is maintained. Deng [27] suggested improving Doppler tolerance by using an ambiguity based optimization cost function to include reciprocals for the main lobe peaks, side lobe peaks and the cross-correlation peaks for all possible Doppler frequencies. This method however, is computationally costly for even short code lengths. As another method, recall the polyphase code sets described in Chapter 5 of Frank, P1—P4. For these codes, there is a harmonic relationship of phases from one sequence element to the next that aids in the ability of the code to resist the Doppler loss. In [29], an algorithm is described where this harmonically related structure is applied as a constraint and added to the correlation cross-entropy optimization algorithm to improve the Doppler tolerance. The technique can be used to construct arbitrary length sequences for an arbitrary number of transmitters. Table 10.14 lists three polyphase sequences of length Nc = 40. Table 10.15 shows the autocorrelation PSLs and cross-correlation peaks for these sequences. The mean PSL for these sequences is −17.3 dB and the mean cross-correlation is −14.3 dB; these figures improve on the Deng sequences of the same length discussed above. The op-

370

Detecting and Classifying LPI Radar

timized polyphase code sequences described in the section can be generated using ortho40CE.m in the LPIT.

10.7.3

Orthogonal Frequency Hopping Sequences

Due to the flexible locations of the multitransmitters and multireceivers, the netted radar system of systems has much stronger capability in target detection, tracking, recognition and electronic protection compared with the conventional emitter. In Chapter 6, an algebraic method was presented to derive a single discrete frequency-coding Costas sequence with NF frequencies for use in a monostatic frequency hopping LPI emitter. Although the Costas arrays have nearly an ideal periodic autocorrelation property, for any two or more constructed Costas arrays there is no guarantee that any two sequences will have a nearly zero cross-correlation property. In [30], a set of NF discrete frequency hopping waveforms with good autocorrelation and nearly zero cross-correlation were derived by using a numerical optimization technique. In this technique, the result is achieved through minimizing a cost function that measures the degree to which a result satisfies the design requirements. In frequency hopping waveform design, the cost function is chosen as in the previous section as the sum of the total autocorrelation side lobe energy for each waveform in the set and the total cross-correlation energy for all distinct combinations of two waveforms sp (t), sq (t) in the set. Thus, the cost function to be minimized for the discrete frequency hopping waveform design is L

L−1

E= l=1

τ

|A(sl , τ )|2 +

L

p=1 q=p+1

τ

|C(sp , sq , τ )|2 dτ

(10.47)

Details on the minimization algorithm can be found in [30]. Table 10.16 lists the three frequency hopping sequences of the designed waveform set with NF = 32 and L = 3. The autocorrelation side lobe peaks and cross-correlation peaks of the designed frequency hopping sequence sets in Table 10.16 are given in Table 10.17. The discrete frequency hopping sequence Code 1 was generated with a base frequency multiplier of 1,000 Hz. The NF = 32 codes were sampled with fs = 100 kHz with tp = 0.001 s. The power spectrum magnitude of the discrete frequency hopping sequence Code 1 is shown in Figure 10.36. The ACF and the PACF are shown in Figure 10.37 and the PAF is shown in Figure 10.38. Note the extremely well behaved time and Doppler side lobe levels. The PSL = −20 dB. The discrete frequency coding waveforms can be generated using dfc32.m in the LPIT.

Network-Centric Warfare and Netted LPI Radar Systems

371

Table 10.14: Optimized Cross-Entropy Sequences with Nc = 40 (from [29]) No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Code 1 8π/5 π 6π/5 4π/5 9π/5 2π/5 27π/20 21π/20 3π/10 3π/20 27π/20 27π/20 π/5 0 π/10 4π/5 0 3π/5 π/20 π/5 π/20 π/4 9π/10 9π/10 π/5 7π/10 0 π/5 6π/5 27π/20 0 0 6π/5 3π/10 7π/5 3π/5 π/5 6π/5 6π/5 8π/5

Code 2 3π/5 π/5 π 6π/5 9π/5 9π/5 3π/20 3π/5 27π/20 3π/10 27π/20 6π/5 π/2 4π/5 π/2 0 7π/10 4π/5 0 π/20 π/10 π/20 4π/5 π/10 4π/5 π/10 9π/10 3π/5 6π/5 9π/20 9π/20 0 27π/20 6π/5 2π/5 6π/5 7π/5 3π/5 0 9π/5

Code 3 4π/5 2π/5 0 0 π 9π/5 21π/20 9π/20 6π/5 9π/20 21π/20 27π/20 4π/5 9π/10 π/10 π/5 9π/10 9π/10 0 π/20 π/20 π/4 0 9π/10 0 4π/5 4π/5 π/5 27π/20 3π/20 27π/20 27π/20 3π/10 3π/4 6π/5 3π/5 3π/5 6π/5 7π/5 7π/5

372

Detecting and Classifying LPI Radar

Table 10.15: Autocorrelation Side Lobe Peaks (Diagonal Terms) and CrossCorrelation Peaks (Oﬀ-Diagonal Terms) for the Cross Entropy Sequence Set of Length Nc = 40 (from [29]) Code 1 Code 2 Code 3

Code 1 0.1365 0.1820 0.1799

Code 2 0.1820 0.1303 0.1840

Code 3 0.1799 0.1840 0.1413

Table 10.16: Discrete Frequency Hopping Sequences with NF = 32 and L = 3 (from [30]) No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Code 1 31 28 1 30 3 8 10 12 7 25 11 15 23 13 27 22 26 17 5 21 6 2 29 14 16 19 9 20 18 0 24 4

Code 2 2 11 12 14 29 16 6 1 9 21 24 23 5 26 19 3 7 30 13 8 20 17 18 4 0 28 31 15 27 10 25 22

Code 3 31 13 18 20 11 7 29 27 8 22 0 1 21 14 9 17 5 25 26 10 19 16 30 15 12 23 4 3 6 2 28 24

Network-Centric Warfare and Netted LPI Radar Systems

373

Table 10.17: Autocorrelation Side Lobe Peaks and Cross-Correlation Peaks of the Discrete Frequency Hopping Sequences in Table 10.16 (from [30]) Code 1 Code 2 Code 3

Code 1 0.0764 0.0979 0.1250

Code 2 0.0979 0.0881 0.1068

Code 3 0.1250 0.1068 0.0855

Figure 10.36: Power spectrum magnitude of the orthogonal discrete frequency hopping Code 1 with fs = 100 kHz.

374

Detecting and Classifying LPI Radar

Figure 10.37: ACF and PACF of the orthogonal discrete frequency hopping Code 1 with fs = 100 kHz.

10.7.4

Noise Waveforms

The concept of a multiuser, wireless netted LPI radar system using random noise is proposed in [31]. The proposed system uses noise signals for radar surveillance and a multiradar communication network for transferring the sensor data to a central command center where informed decisions can be made. Due to the spectral characteristics of the UWB random noise waveform, an LPI capability is provided while also eﬃciently sharing the frequency spectrum with other users. A number of UWB random noise radar systems can operate over the same frequency band with minimal cross-interference since each transmitted noise waveform is uncorrelated with the others. It is this property that allows a number of the UWB noise radars to be integrated into a NCW architecture [31]. The bandlimited noise (1—2 GHz) is also notch filtered (1.2—1.3 GHz) to provide room for the intrasensor network communications among the diﬀerent emitters. The spectral fragmentation for the embedded communication causes no distortion if the gap in the noise

Network-Centric Warfare and Netted LPI Radar Systems

375

Figure 10.38: PAF of the orthogonal discrete frequency hopping Code 1 with fs = 100 kHz.

376

Detecting and Classifying LPI Radar

Figure 10.39: Noise radar concept with (a) element-space approach and (b) beam-space approach (after [32]). band is not excessive (≤ 30%). The sensor data to be shared is modulated onto a CW signal whose frequency lies within the notch of the UWB noise signal. Orthogonal frequency division multiple access modulation is used for transporting the target data between sensors. The development of a netted noise radar is also presented in [32]. Two transmission approaches are compared as shown in Figure 10.39. The first approach shown in Figure 10.39(a), is the element space approach where multiple channels (antennas) of independent noise are transmitted. K incoherent noise sources are transmitted. Ignoring the angular variation in the target’s RCS, the received power is independent of the angle of the scatterer from the transmit array. The second approach shown in Figure 10.39(b), is the beam-space approach where each independent noise source is fed into each antenna but is delayed τi (or phase shifted) so as to form a beam illuminating a selected sector of the radar field of view (FOV). This eﬀectively codes each sector in the FOV according to a particular noise source. The direction of each sector is determined by the delay (or phase shift) and the width is determined by the beamwidth of the array. Comparison of element- and beam-space approaches to the netted noise radar indicate that when operating the transmit array at frequencies such that d/λ < 0.5 where d is the receiver spacing, the beam-space approach is a more eﬃcient method of con-

Network-Centric Warfare and Netted LPI Radar Systems

377

centrating the wave number spectrum of the transmit signal in the radiating region and minimizes the problem of nonradiating waves.

10.8

Netted Over-the-Horizon Radar Systems

Future OTHR systems are expected to deliver dramatically improved capability in every performance dimension including LPI. There are three direct benefits to applying MIMO radar concepts to OTHR [33]. First it provides a means to implement radar management trade-oﬀs between radar sensitivity and surveillance footprint coverage allowing a more eﬃcient use of resources (surveillance area requirements, sensitivity, target dynamic behavior, and the interaction of the target characteristics with the data processing algorithms). MIMO radar is also a convenient method to implement adaptive processing algorithms on transmit for clutter mitigation. By changing the illumination source at the transmit array, the clutter is more eﬀectively suppressed. Consequently, orthogonal waveforms have also found application in netted OTHR systems [33]. The use of multiple simultaneously transmitted orthogonal waveforms permit better sensitivity and more flexible trade-oﬀs in footprint coverage. It also allows for adaptive management of the transmitted beam to minimize clutter and simplifies propagation mode selection for improved clutter rejection. In an OTHR, both the transmitter and receiver subsystems can be considered as M and N dimensional digital arrays. The transmit subsystem consists of one waveform generator per transmit power amplifier and transmit antenna element. The receive subsystem consists of one digitizing receiver per array element. Achieving full orthogonality with the CW waveform set over the space-time ambiguity of concern is not possible. Space-time adaptive processing using multiple transmitters and receivers allows using one waveform generator per transmit element and enabling the transmit and receive beamforming to be performed entirely at the receive site [34]. The diversity of target scattering leads to better detection performance using lower power waveforms. Orthogonal waveforms that can be used in OTHR include time-staggered FMCW, Doppler oﬀset FMCW and noise waveforms. The time-staggered FMCW uses a time oﬀset between diﬀerent FMCW waveforms to exploit the fact that the range interval of interest is frequently limited by ionospheric propagation. In surface modes (high Doppler resolution mode), low WRFs are used over extended CITs. It is therefore possible to provide orthogonality between a number of waveforms after range correlation with a single reference waveform. The approach maintains the attractive power eﬃciency and spectral occupancy of the FMCW waveform. For the Doppler oﬀset FMCW a small frequency oﬀset between FMCW waveforms provides orthogonality after slow-time Doppler processing (slow-time MIMO). In this case,

378

Detecting and Classifying LPI Radar

the Doppler extent of the clutter and expected target Doppler shifts limit the number of concurrent orthogonal waveforms that can be supported. This waveform approach is more appropriate to the air-mode for aircraft detection. The band-limited noise waveforms also provide an orthogonal waveform choice despite the large peak to average power ratio and poor Doppler sensitivity. This approach provides a broad class of orthogonal waveforms.

References [1] Cebrowski, A. K., “Implementation of Network-Centric Warfare,” Oﬃce of Force Transformation, 2004. [2] Ahmed, A. A., Hongchi, S., and Shang, Y., “A survey on network protocols for wireless sensor networks,” Proc. of the IEEE International Conf. on Information Technology: Research and Education, pp. 301—305, Aug. 2003. [3] Karlof, C. and Wagner, D., “Secure routing in wireless sensor networks: attacks and countermeasures,” Proc. of the IEEE International Workshop on Sensor Network Protocols and Applications, pp. 113—127, 2003. [4] Stein, F., Garska, J., and McIndoo, P.L., “Network-centric warfare: Impact on Army operations,” EUROCOMM 2000 Information Systems for Enhanced Public Safety and Security, IEEE/AFCEA, pp. 288—295, 2000. [5] Kruse, J., Adkins, M. and Holloman, K. A., “Network centric warfare in the U.S. Navy’s fifth fleet,” Proc. of the IEEE 38th Hawaii International Conf. on Systems Sciences, 2005. [6] Chen, Y-Q, and Pace, P. E., “Simulation of Information Metrics to Assess the Value of Networking in a General Battlespace Topology,” Proc. of the IEEE International Conf. on System of Systems Engineering, June 2008. [7] Boyd, J.R., “A discourse on winning and losing,” Title Boyd gave to his collection of briefings on competitive strategy (widely known as the “Green Book,” with apologies to Wittgenstein), 1987. [8] Ling, F.M., Moon, T., and Kruzins, E., “Proposed network centric warfare metrics: From connectivity to the OODA cycle,” Military Operations Research, vol. 10 No. 1, pp. 5—13, 2005. [9] Shannon, C. E., “A mathematical theory of communication,” Bell Systems Technical Journal, July 1948. [10] Phister, P.W. Jr., and Cherry, J.D., “Command and control concepts within the network-centric operations construct,” Proc. of the IEEE Aerospace Conf., pp. 1—9, Mar. 4—11, 2006. [11] Posiel, R. Modern Communications Jamming Principles and Techniques, Artech House Inc., 2004. [12] Hume, A. L. and Baker, C. J., “Netted radar sensing,” Proc. of the CIE International Conf. on Radar, pp. 110—114, Oct. 2001.

Network-Centric Warfare and Netted LPI Radar Systems

379

[13] Teng, Y., Griﬃths, H. D., Baker, C. J., Woodbridge, K., “Netted radar sensitivity and ambiguity,” IET Radar and Sonar Navig., Vol. 1, No. 6, pp. 479—486, 2007. [14] Derham, T.E., Doughty, S., Woodbridge, K., Baker, C.J., “Design and evaluation of a low-cost multistatic netted radar system,” IET Radar, Sonar & Navigation, Vol. 1, No. 5, pp. 362—368, October 2007. [15] Lehmann N. H., Haimovich, A. M., Blum, R. S., and Cimini, L., “High resolution capabilities of MIMO radar,” Record of the Fortieth Asilomar Conf. on Signals, Systems and Computers, pp. 25—30, 2006. [16] Bliss, D. W., and Forsythe, K. W., “Multiple-input multiple-output (MIMO) radar and imaging: degrees of freedom and resolution,” Record of the ThirtySeventh Asilomar Conf. on Signals, Systems and Computers, Vol. 1, pp. 54—59, Nov., 2003. [17] Sammartino, P.F., Baker, C.J., and Griﬃths, H.D., “Target model eﬀects on MIMO radar performance,” Proc. of the IEEE International Conf. on Acoustics, Speech and Signal Processing, pp. V-1129—V-1132, May, 2006. [18] Haimovich, A. M., Blum, R. S., and Cimini, L. J. Jr., “MIMO radar with widely separated antennas,” IEEE Signal Processing Magazine, pp. 116—129, Jan. 2008. [19] Hume, A. L. and Baker, C. J., “Netted radar sensing,” Proc. of the IEEE Radar Conf., pp. 23—26, 2001. [20] Baker, C. J., and Hume, A. L., “Netted radar sensing,”IEEE Aerospace and Electronic Systems Magazine, Vol. 18, No. 2, pp. 3—6, Feb. 2001. [21] Fishler, E., Haimovich, A., Blum, R., Cimini, L. J., Chizhik, D., and Valenzuela, R. A., “Spatial diversity in radars - models and detection performance,” IEEE Trans. of Signal Processing, Vol. 54, No. 3, pp. 823—838, 2006. [22] Chen, C-Y, and Vaidyanathan, P. P., “Properties of the MIMO radar ambiguity function,” Proc. of the IEEE International Conf. on Acoustics, Speech and Signal Processing, pp. 2309—2312, 2008. [23] Teng, Y., Baker, C. J., and Woodbridge, K., “Netted radar sensitivity and the ambiguity function,” Proc. of the International Conf. on Radar, Vol. 1, No. 6, pp. 1—4, Dec. 2006. [24] Papoutsis, I., Baker, C. J., and Griﬃths, H. D., “Netted radar and the ambiguity function,” Proc. of the IEEE International Radar Conf., pp. 883—888, 2005. [25] Li, J., Stoica, P., Xu, L., and Roberts, W., “On parameter identifiability of MIMO radar,” IEEE Signal Processing Letters, Vol. 14, No. 12, pp. 968—971, Dec. 2007. [26] Chen, Y-Q, and Pace, P. E., “Simulation of Network-Enabled Radar Systems to Assess the Value of Jamming in a General Radar Topology,” Proc. of the IEEE International Conf. on System of Systems Engineering, June 2008. [27] Deng, H., “Polyphase code design for orthogonal netted radar,” IEEE Trans. on Signal Processing, Vol. 52, No. 11, pp. 3126—3135, Nov. 2004.

380

Detecting and Classifying LPI Radar

[28] Khan, H. A., and Edwards, D. J., “Doppler problems in orthogonal MIMO radars,” Proc. of the IEEE Conf. on Radar, pp. 244—247, 2006. [29] Khan, H. A., Zhang, Y., Ji, C. Stevens, C. J., Edwards, D. J., and O’Brien, D., “Optimizing polyphase sequences for orthogonal netted radar,” IEEE Signal Processing Letters, Vol. 13, No. 10, pp. 589—592, 2006. [30] Deng, H., “Discrete frequency-coding waveform design for netted radar systems,” IEEE Signal Processing Letters, Vol. 11, No. 2, pp. 179—182, Feb. 2004. [31] Surender, S. C., and Narayanan, R. M., “Covert netted wireless noise radar sensor: OFDMA-based communication architecture,” Proc. of the Military Communications Conf., pp. 1—7, Oct. 2002. [32] Gray, D. A., and Fry, R., “MIMO noise radar—element and beam space comparisons,” Proc. IEEE Waveform Diversity & Design Conf., pp. 344—347, 2007. [33] Frazer, G. J., Johnson, B. A., Abramovich, Y. I., “Orthogonal waveform support in MIMO HF OTH radars,” Proc. IEEE Waveform Diversity & Design Conf., pp. 423—427, 2007. [34] Frazer, G. J., Abramovich, Y. I., and Johnson, B. A., “Spatially waveform diverse radar: perspectives for high frequency OTHR,” Proc. IEEE Radar Conf., pp. 385—390, April 2007.

Problems 1. A netted LPI radar transmits the target parameters using −1.0 and 0.0V levels with a probability of 0.2 each and 3.0- and 4.0-V levels with a probability of 0.3 each. Determine the average information being sent. 2. A C2 operator uses a numerical keypad that has the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Assume that the probability of sending any one digit is the same as that for sending any of the other digits. Calculate how often the operator must press the buttons in order to send out information at the rate of 2 bits/s. 3. An army field computer has 110 characters on the keyboard and each character is sent using binary words. (a) What is the number of bits required to represent each character? (b) How fast can the characters be sent (characters/s) over a channel if the channel bandwidth is 3.2 kHz and the SNR=20 dB? (c) What is the entropy of each character if each is equally likely to be sent? 4. A 480-by-500 pixel range-Doppler image is to be transmitted from a netted LPI radar where each pixel can have one of 32 intensity values. The emitter sends 30 images/s. If all image elements are assumed to be independent and all 32 intensity levels are assumed to be equally

Network-Centric Warfare and Netted LPI Radar Systems

381

Figure 10.40: Destruction of terrorist weapon system. likely, (a) determine the source rate λ in (bits/s). (b) If the image is to be transmitted over a channel with a 4.5-MHz bandwidth and a 35-dB SNR, find the capacity of the channel (bits/s). 5. The USS Enterprise (capability K = 1.0) has launched a Tomahawk missile to destroy a terrorist weapon system as shown Figure 10.40. To follow up with a damage report, a predator UAV follows the Tomahawk. To provide an intelligence, surveillance and reconnaissance (ISR) component, a Global Hawk (K = 0.8) is also used. The Tomahawk missile capability is given as K = 0.3 due to its limited connectivity and signal rerouting options (note its unidirectional link to the Global Hawk). The Predator also has a limited signal rerouting capability and is given the capability value K = 0.5. Consider each link to have a flow component and value component of either 1 or zero (i.e., F = L = 1, 0). (a) Find R . (b) Determine the network the reference connectivity measure CM reach IR . (c) Determine the network reach if a jammer takes out the link between the USS Enterprise and the Tomahawk. (d) To examine the impact of the rerouting options of the original network configuration (unjammed), let each node capability be K = 1.0 and determine the network reach.

382

Detecting and Classifying LPI Radar

6. Consider problem 5. (a) If the rate that information is processed by node μ = 1 is λ1 = 50 kHz, node μ = 2 is λ2 = 18 kHz, node μ = 3 is λ3 = 260 kHz, and node μ = 4 is λ4 = 3 kHz, determine the network richness RQ (average rate that knowledge is generated through the network). (b) Using the network richness calculated in Problem 5 above, determine the network’s characteristic tempo λT . (c) Consider that the command and control (C2) decision making speed to target the Tomahawk missile is λC2 = 0.5 kHz. After the decision is made, it takes 0.5 ms to send the retargeting command to the missile (η1 = 2 kHz). After the missile receives the retargeting command, the missile guidance takes 0.25 ms to initiate the turn (η2 = 4 kHz). Calculate the OODA operational tempo ΛOODA for this retargeting command. 7. Behavior of the OODA tempo: The action tempos of a force will vary vastly depending on the specific net-centric EW situation; it is not possible to make general statements about their scale. Therefore, the action tempos can be treated as adjustable parameters in ΛOODA . To illustrate the behavior of the OODA tempo with respect to the network tempo, we can normalize both by the C2 tempo. Using MATLAB, plot on the same graph the ΛOODA /λC2 (vertical axis) versus λT /λC2 (horizontal axis) for the three action tempos: (a) η1 = 0.5λC2 and η2 = 0.25λC2 (low-action tempo), (b) η1 = λC2 and η2 = λC2 (mediumaction tempo), and (c) η1 = 2λC2 and η2 = 4λC2 (high-action tempo). What can you conclude about the OODA tempo and the C2 tempo as the network tempo increases? 8. Using the LPIsimNet tools (a) complete the tutorial in Appendix D for the sensor network analysis and the netted radar analysis. (b) Construct a sensor network with four nodes, and a jammer. Movement of one or more nodes should be included with five time index steps. Build an analysis summary of the results. (c) Construct corresponding netted radar scenario with four LPI emitters, a target and a jammer. Build an analysis summary of the results. (d) What insights are you able to gather from your simulation study? 9. (a) Add to the LPIT, four CW orthogonal PSK signals each with one of the polyphase codes shown in Table 10.12. Include five periods of the code set for each signal. (b) Generate the four polyphase signals with fc = 1 kHz, and B = 500 Hz. (c) Compute the ACF, PACF and PAF of each signal with N = 1 and N = 3. (d) How do the PSL levels of the orthogonal PSK waveforms compare with the polyphase codes Frank, P1—P4 ? (e) Compute the cross-correlation of the four PSK signals to verify Table 10.13.

Network-Centric Warfare and Netted LPI Radar Systems

383

10. (a) Repeat the problem above for the cross-entropy orthogonal sequences given in Table 10.14 with correlation properties given in Table 10.15. (b) Repeat for the discrete frequency hopping sequences given in Table 10.16 and correlation properties given in Table 10.17 using a scale factor of 102 Hz.

PART II: INTERCEPT RECEIVER STRATEGIES AND SIGNAL PROCESSING

Chapter 11

Strategies for Intercepting LPI Radar Signals The LPI radar characteristics discussed in the first part of this book (Chapters 1—10) pose a particular challenge to the noncooperative intercept receiver. Modern electronic warfare (EW) intercept receivers must perform the tasks of detection, parameter identification, classification, and exploitation in a complex environment of high noise interference and multiple signals. The wideband nature of the LPI emitter signal can force the intercept receiver to have a significant processing gain by implementing sophisticated receiver architectures and signal processing algorithms (time-frequency, bifrequency) in order to determine the waveform parameters. In this chapter, modern network-centric strategies for EW receiver architectures are discussed, and a contrast is drawn to the traditional platform-centric approach. This includes the use of swarm intelligence. In addition, the look-through problem is discussed in the framework of suppression of enemy defense. Digital receiver architectures are briefly discussed including the direct RF sampling approach. EW intercept receiver problems are also emphasized.

11.1

EW Intercept Receiver Techniques

11.1.1

Traditional Approach

Electronic warfare intercept receivers are used to process threats on the modern electronic battlefield, and consequently, must cover extremely wide bands from 300 MHz to 100 GHz and above, since they do not know the characteristics of the signal that they are attempting to intercept. The wideband nature of LPI threat signals presents a significant challenge to the intercept 387

388

Detecting and Classifying LPI Radar

receiver design. The interception of LPI radar signals has been a topic of investigation for over a decade [1—3]. Traditionally, EW receivers have been divided into three categories: radar warning receivers, electronic support receivers, and electronic intelligence receivers. RWRs are designed to passively intercept enemy radars in time to enable the pilot to react quickly through maneuvering or employing appropriate electronic attack techniques. Their use on the battlefield is time-critical, and combat action is taken directly from their threat information output. Electronic support receivers encompass all actions necessary to provide the information required for immediate decisions involving EW operations, threat avoidance, targeting, and homing. Although not as time-critical as RWRs, information operations rely heavily on ES receivers for intelligence updates and important operational decisions. For electronic intelligence receivers, the information provided is extracted from detailed analysis of radar signals and other noncommunication emitters in a timely manner. Although their operation is the least time critical, their threat identification is used to update national databases. Examples of U.S. collection ELINT assets include the U2 Senior Ruby, the Army’s Guard Rail, and the Air Force’s RC-135 Rivet Joint. These high-value standoﬀ assets typically operate hundreds of kilometers from the emitter and at a high altitude. Together, these receivers provide the underlying intelligence needed for weapon systems deployment. In a platform-centric configuration, each weapon system traditionally had its own receiver system and, if that receiver was remote, there was a stovepipe communication system providing the intercept data back to the shooter. There are limitations to the use of intercept receivers in a platform-centric configuration. Geometrical limitations include extended stand-oﬀ ranges and alignment problems, which make it especially diﬃcult to detect and jam LPI emitters. Also, the intercept receiver is limited by look-through. The lookthrough process allows the jammer to observe its eﬀectiveness on the LPI emitter by stopping the jamming assignment to listen periodically. This results in ineﬃcient jammer management, and limited coordination during a mission.

11.1.2

The Look-Through Problem

To emphasize the look-through problem, consider a frequency-hopping LPI air defense radar used for targeting a surface-to-air missile (SAM) against an incoming strike aircraft. To protect the strike aircraft against these SAM sites, platforms such as the EA-6B Prowler provide standoﬀ (long-range) jamming of the enemy radar, in what is normally called a suppression of enemy air defense operation.1 The aircraft has a fully integrated electronic warfare system combining long-range, all-weather receive and jamming capabilities, mainly 1 The EA-6B is also used to protect ground troops and ships, by jamming enemy electronic data links and communications.

Strategies for Intercepting LPI Radar Signals

389

supplied by the Litton LR-700 intercept receiver, working together with the AN/ALQ-99 tactical jamming system (TJS). The Litton LR-700 is the new intercept receiver system in the Increased Capability III (ICAP III) version of the EA-6B, and gives the Prowler a selective-reactive jamming capability with the TJS. During a SEAD operation, the LR-700 receiver on board the suppression aircraft must detect the threat emitters and manage the TJS in order to prevent the radar from detecting the inbound strike aircraft it is trying to protect. During the jamming process, a certain amount of look-through is required. For example, with an EA-6B reactively jamming a frequency-hopping radar, the jamming must stop in order to sense the radar’s transmit frequency. Of course, the duty cycle of the intercept receiver look-through process must be less than the time necessary for the radar to sense it is being jammed, and switch frequencies. The bottom line is that any amount of look-through is not desired, since this allows the threat radar a window in which to detect the strike aircraft. If however, the EA-6B integrates threat parameters from an electronic order-of-battle database, a reconnaissance aircraft with near real-time onscene intelligence collection, analysis, and dissemination capabilities (e.g., Rivet Joint), and frequency data from an oﬀ-board stand-in sensor (e.g., a UAV) to cue the on-board intercept receiver (tip and tune), a fast reactive electronic attack can be performed that eliminates the need for look-through. For the reactive jamming assignments to be eﬀective, however, the data link used to provide the cueing data must not induce a delay time of any significance to the reactive assignment. That is, if the frequency-hopping radar can switch frequencies faster than the cueing data can arrive from the oﬀ-board intercept receiver, then the eﬀectiveness is significantly degraded.

11.1.3

Modern Network-Centric Concepts Arriving

Due to the complex emitter modulations now available, and the speed with which information is shared, the distinction between the roles of RWRs, ES, and ELINT receivers is fast disappearing, and all capabilities are being integrated within a single EW receiver system, in order to provide a complete situational awareness for ships, helos, and high-value aircraft. In addition, these receivers must now include precision direction finding, countermeasures control, cueing of weapon systems, enhanced radar warning, fusion of oﬀboard sensors and databases, and full integration with the electronic combat system. Other capabilities will include emitter classification and identification, emitter-to-platform correlation, detailed analysis, and signal recording. Eliminating the limitations inherent in a platform-centric configuration comes from a distributed system of systems. A distributed system of systems provides significant geometric flexibility, and can reduce or eliminate the need for look-through. In addition, coordinated jammer responses and improved

390

Detecting and Classifying LPI Radar

Figure 11.1: Disabling an LPI emitter within a network-centric architecture. jammer management can be achieved due to better information being available. The ability for EW receivers to acquire, track, and locate conventional threat emitters and targets, and share this information among stand-oﬀ platforms (e.g., for weapons targeting), is an example of a network-centric architecture, and represents a fundamental shift from a platform-centric approach. As emphasized in Chapter 10, in a network-centric architecture, the network acts as a force multiplier by networking sensors (e.g., EW receivers), decision makers, and shooters (e.g., weapons systems), to achieve shared awareness. The network requires suﬃcient bandwidth for all users to take advantage of data mining in appropriate databases afloat and ashore. The architecture is determined mostly by the mission altitudes, signal densities, reaction times, and modulation analysis that must be performed. Figure 11.1 demonstrates the detection and jamming of an LPI emitter using a networkcentric architecture. See also Figure 10.1 for comparison. The LPI emitter is detected using a number of sensors that relay the information to both a command and control point, and the proper shooter. The command and control then allows the shooter to apply the appropriate electronic attack to disable the LPI emitter. The shooter also relays its information concerning the jammed emitter back to both the sensors and the command and control. That is, instead of each platform making decisions on information received by only its own intercept receiver (the platform-centric approach), modern EW receivers integrate information from many sensors and databases for target-

Strategies for Intercepting LPI Radar Signals

391

Figure 11.2: Predator UAV with a Hellfire missile. ing. Through a superior battlespace awareness, forces can employ the best weapons on the right targets to greatly reduce risk to themselves, and increase the opportunity for a successful LPI emitter engagement.

11.2

Detecting the LPI Radar with UAVs

The network-centric approach to intercept receiver integration is an important trend. This capability requires the platforms to be available in the correct location, and the data links between those platforms to be jam resistant. Unfortunately, LPI emitters are becoming increasingly diﬃcult to detect, locate, and track from stand-oﬀ platforms, due to their low peak power (< 1W), low side lobes (−40 dB down), short on-times (ms), high mobility, and use of terrain masking. As a result, the stand-oﬀ platforms with EW receivers are augmented by specialized receivers that can go to the emitters (stand-in platforms). These specialized receivers are mounted, for example, in unmanned aerial vehicles such as the Predator, shown in Figure 11.2. The use of swarm intelligence technology is fast becoming an important concept in network-centric sensor configurations. Swarm intelligence allows the design of EW receiver networks to detect LPI emitters, and is inspired by the behavior of social insects [4]. In a swarm sensor architecture, the signal collection capability is defined by the group behavior and not the individual behavior. One advantage of using a UAV swarm of EW receivers is the ability to behave autonomously, using digital information pheromones (DIPs; see page 106 in [4]). In what follows we use the analogy of the EW receiver as being an “ant” insect that exists within a swarm. The idea is to use another EW receiver’s (ant’s) experience in prior LPI emitter searches. For example, ants that are looking for particular LPI emitters, access information that has been left in the form of DIPs (ratings) from previous detections by other

392

Detecting and Classifying LPI Radar

colony members. As LPI emitters are detected, an “ant DIP” is published on the network by this “ant server.” This lets other ants know how many previous detections of this emitter were found, and the characteristics of the emitter. Ant DIPs that are continuously detected are continually reinforced, while those that are disabled (see Figure 11.1) evaporate. Only information that is regularly verified and reinforced is conserved. This type of behavior requires only a small number of operators to control many UAVs. Another advantage is the ability of the UAVs to behave cooperatively. Cooperative behavior allows the UAVs to form a robust, self-organizing and self-adapting sensor architecture, while retaining the intercept function even in the presence of a loss. The swarm LPI detection architecture requires only low-cost medium-endurance airframes (expendable), existing wideband intercept receivers (e.g., R-300A, highly integrated microwave receiver), and the use of swarm logic [4] with intraswarm communications, using, for example, an 802.11 link. With the swarm approach, LPI radars run the risk of detection (and classification), especially when the intercept receiver incorporates advanced signal processing techniques that take advantage of timefrequency, bifrequency processing. According to the 2002 Defense Acquisition Board, EA from the UAV platform will become a significant capability.

11.3

Noncooperative Intercept Receivers

The EW community has long debated and ranked many diﬀerent intercept receiver architectures based on their ability to process signals [5, 6]. The comparisons, however, have limited usefulness, since diﬀerent mission scenarios require diﬀerent capabilities. What is certain, however, is that future EW receivers will be digital, and will incorporate various technologies as discussed below.

11.3.1

Comparison of Classic Receiver Architectures for Detecting LPI Waveforms

There are many variations of intercept receivers. These passive receivers can be used to detect the LPI emitter emissions over considerable distances. In this section, three popular intercept receiver architectures are compared in terms of their ability to detect several types of LPI emitter waveforms. The receivers that are compared include the square-law, wideband and channelized receivers [7]. These receivers are relatively inexpensive, readily accessible and are shown in Figure 11.3. The square-law receiver is an energy detector. The parameters of the square-law receiver are given in Table 11.1. The wideband crystal video receiver is characterized by a wide RF bandwidth to account for the uncertainty in the intercepted signal parameters. The specifications of the wideband receiver are given in Table 11.2. The channelized

Strategies for Intercepting LPI Radar Signals

393

Figure 11.3: Block diagram of receiver architectures being compared with (a) square-law, (b) wideband crystal video, and (c) channelized.

Table 11.1: Square-Law Receiver Parameters [7] Receiver Feature Noise figure Instantaneous bandwidth Noise floor System loss Video bandwidth Integration time Detection threshold Local oscillator IF bandwidth

Specification 8 dB 1 GHz −76 dBm 12 dB 60 kHz period matched SNR = 12 dB 12 MHz 12 MHz

394

Detecting and Classifying LPI Radar

Table 11.2: Wideband Crystal Receiver Parameters [7] Receiver Feature Noise figure Instantaneous bandwidth Noise floor System loss Video bandwidth Integration time Detection threshold Local oscillator fLO

Specification 8 dB 4 GHz −70 dBm 10 dB 1 MHz 100 ns SNR = 12 dB 12 MHz

Table 11.3: Channelized Receiver Parameters [7] Receiver Feature Number of channels Noise figure Instantaneous bandwidth Channel bandwidth Noise floor System loss Video bandwidth Integration time Detection threshold

Specification 40 10 dB 2 GHz 50 MHz −92 dBm 5 dB 1.25 MHz 100 ns SNR = 12 dB

receiver contains a large number of parallel narrowband receivers. The RF band is divided into 40 contiguous front-end channels (N = 40). The channel outputs are all folded into a common baseband and passed through 40 IF subchannels (M = 40). The folding is done with the local oscillators at 50 MHz frequency increments. The 40 RF channels span 2 GHz and each channel is 50 MHz wide. The 40 IF subchannels each span 1.25 MHz giving a final 50 MHz coverage of the spectrum. The parameters for the channelized receiver are shown in Table 11.3. LPI Waveforms Used To compare each receiver’s detectability performance, it is important that the emitter waveforms have equal bandwidth and equal energy. This is because many of the compression waveforms oﬀer the same range resolution but not

Strategies for Intercepting LPI Radar Signals

395

all have the same LPI/LPID properties [8]. Six waveforms were compared including a rectangular pulse, an FMCW, P1, P2, P3 and P4 all with a range resolution of 50m. The polyphase codes each have a subcode period of tb = 333 ns (B = 3 MHz) and a code period of T = 64tb = 21.3 μs. The FMCW has a modulation period tm = 64tb or 21.3 μs and the modulation bandwidth is ∆F = 3 MHz (starting at dc). The rectangular pulse has a pulse duration τR = tb = 333 ns with a pulse repetition interval PRI = 64tb = 21.3 μs. The average power transmitted by each emitter is PCW = 100W and λ = 3 × 10−2 m. The emitter transmit antenna gain in the direction of the intercept receiver is Gr = 0 dB [8]. Intercept Range and Sensitivity Comparison A MATLAB simulation was run first to determine the sensitivity. The sensitivity δI is the minimum signal at the back end of the receiver that is detectable given the noise floor associated with that particular receiver. The sensitivity was determined by iteratively adjusting the front-end signal amplitude that achieves the required back-end SNR. Since the noise floor, noise figure, bandwidths and integration times are defined for each receiver, the amplitude was adjusted until detection was achieved [8]. Models were developed in MATLAB for each receiver in order to find the front-end signal strength necessary to satisfy the minimum back-end SNR. A voltage gain of 20 dB was used for each receiver. After determining the sensitivity for each receiver, the intercept range (direct path) was calculated from (1.41) as 5 λ PCW Gt GI (11.1) RI max = 4π δI where LRT = LIR = L1 = 1. Also, the propagation loss was assumed to be zero. Each receiver uses a 12-dB detection threshold. In the case of the channelized receiver, the detection threshold applies to each channel. By keeping the threshold the same across all receivers, the relative detection capability can be quantified. A 1-hour false alarm interval was assumed for each receiver and for each channel of the channelized receiver. The sensitivity and interception range for each intercept receiver is given in Table 11.4. The square-law detector was most eﬀective and detected all signals at essentially the same range (≈ 25 km). The least eﬀective receiver was the wideband receiver. The most detectable waveform in the wideband and channelized receiver was the rectangular pulse. The P1, P2 and P4 perform significantly better than the rectangular pulse, P3 and FMCW in the channelized receiver. The P2 waveform represents a factor of 2.3 reduction in range over the rectangular pulse in the channelized receiver [8].

396

Detecting and Classifying LPI Radar

Table 11.4: Sensitivity and LPI Interception Range for Three Intercept Receivers (After [8])

Waveform Pulse FMCW P1 P2 P3 P4

11.3.2

Square-Law δI (dBm) −80.30 −80.57 −80.38 −80.39 −80.34 −80.36

RI max (km) 24.70 25.49 24.94 24.97 24.83 22.88

Wideband δI (dBm) −59.00 −52.96 −52.20 −52.79 −52.54 −52.54

RI max (km) 2.10 1.06 0.97 1.04 1.01 1.01

Channel δI (dBm) −64.90 −59.98 −56.37 −56.18 −60.36 −57.14

RI max (km) 4.20 2.38 1.57 1.54 2.49 1.72

Digital EW Receivers

Radio receivers that perform the analog-to-digital conversion process close to the antenna and do most of the signal processing in the digital domain are known as digital receivers. Digital receivers, often called software radios, place a high performance burden on the ADC, but allow a good deal of flexibility in postdetection signal processing. EW receiver parameters of interest include sensitivity, dynamic range, resolution, simultaneous signal capability, complexity, and cost. Figure 11.4(a) shows a block diagram of a wideband digital EW receiver. The input signal from the antenna is first amplified by a wideband LNA. Most digital EW receivers use frequency conversion before digitizing the signal. That is, the signal is first downconverted in frequency, and then digitized by an ADC. The digital signal is then processed by a spectrum analyzer that extracts the frequency information. Using this frequency information, the signal is sorted, and a parameter encoder then forms a pulse descriptor word (PDW). For LPI CW emitters, the PDW contains the center frequency fc , the signal coding details such as the modulation period and bandwidth (FMCW), the code period and subcode period details (PSK), and frequency-hopping frequencies (and order), as well as the signal’s angle of arrival. In a network-centric architecture, the PDWs are sent to a fusion processor that integrates other EW receiver information, in order to perform emitter identification (e.g., using a neural network [9]), develop a situational awareness, and form a corresponding response. When the receiver is used to manage a coherent jammer, wideband/narrowband digital RF memories (DRFMs) are also employed. To process all of the emitter information in a timely manner, 100 millions of instructions per second (MIPS) processors must be employed. When downconverting the signal in an EW receiver, two approaches can

Strategies for Intercepting LPI Radar Signals

397

Figure 11.4: Block diagram of (a) a wideband digital EW intercept receiver, (b) two-stage heterodyne down conversion process, and (c) homodyne down conversion process. be used, and are shown in Figure 11.4(b, c). The first (heterodyne) approach (b) downconverts the signal, first to IF and then to baseband, using two or more bandpass filter-local oscillator-mixer stages in series. Since the LPI signals are phase- and frequency-modulated, both in-phase and quadrature components are required at baseband. If the signal bandwidth is B, and I and Q are available with each channel containing an ADC, the sampling frequency fs > B. The advantage of this approach is that by driving the mixer with a frequency-agile LO, the frequency of the desired signal or channel is converted to a fixed frequency. Once converted to a fixed IF, it can be processed by highly selective narrowband filtering (e.g., using surface-acoustic wave devices or high-temperature superconductors). Also, all subsequent frequency translations can be done using fixed-frequency LOs. Also performed is signal amplification using fixed gain LNAs (at RF), and variable gain amplifiers (at IF). The distribution of gain across the IF stage prevents instabilities in the amplifiers, and reduces the chance of saturation. A direct conversion (homodyne) downconversion can also be used, as shown in Figure 11.4(c). This two-channel approach uses only a single local oscillator, and translates the signal of interest to zero frequency (zero-IF). Due to the elimination of the IF stages, all signal conditioning must be performed either at RF or baseband. The direct conversion approach oﬀers a

398

Detecting and Classifying LPI Radar

Figure 11.5: Block diagram of a digital EW receiver with an ADC at the antenna (no downconversion). higher degree of integration at the front end with fewer components, allowing most of them to be monolithically fabricated on a single chip [10]. The direct conversion receiver performance still does not match the IF receiver, due to filter saturation and distortion caused by the dc oﬀsets and self mixing at the mixer inputs. To take advantage of both receiver topologies, a low-IF receiver is now an alternative (a few hundred kilohertz). The low-IF receiver has a high degree of filter integration, and is also insensitive to dc oﬀsets and LO-to-RF crosstalk. In all cases, the signal is downconverted to a baseband frequency that depends on the analog-to-digital converter technology that is available. A direct conversion receiver at Ka-band is described in [11].

11.3.3

Direct RF Sampling

The trend in EW digital receivers is to push the ADC as far towards the antenna as possible, and to eliminate the downconversion stage, as shown in Figure 11.5. The receiver is made up of three sections: the RF front end, which amplifies and bandpass filters the antenna signal before it is sampled; the ADC; and the digital signal processing. That is, the ADC is used directly on the RF signal after appropriate preconditioning by means of amplification and filtering. ADC technology has improved to the point where direct sampling and digital signal processing in the microwave spectrum is possible. Although the development of ADCs have made considerable advancements in the last 10 years, more wideband solutions are required using electro-optics (extremely wideband) and superconductivity (high sensitivity). Bandpass sampling does not use any tuner or mixers to downconvert the antenna signals but instead takes advantage of digital aliasing to down convert a Nyquist band. The advantage here is that the gain fluctuations and noise sources due to the analog mixers and local oscillators that are used in a conventional receiver are eliminated. Other advantages include a simplified hardware approach (fewer components) that allows the integration of the receiver onto a multi-chip module or single chip monolithic microwave integrated circuit. Also, the LPI signal

Strategies for Intercepting LPI Radar Signals

399

Figure 11.6: Block diagram of a reconfigurable direct RF sampling architecture [13]. information is captured prior to significant analog distortion and mixer nonlinearities. Direct RF sampling also allows the receiver to be reconfigurable to support software-defined detection and classification algorithms. If a single fixed clock is used (partially reconfigurable), multiple bands can be covered as long as the bands alias to the same intermediate frequency band. Direct sampling works well for low RF signals but places severe constraints on the ADC for higher analog input frequencies due to the eﬀect of clock jitter or clock uncertainty [12]. To achieve arbitrary tuning over a wide RF range, however, the RF sample clock must be tunable or selectable because of the problems with signal recovery on the boundaries of the Nyquist bands generated by a fixed RF sample clock [13]. A reconfigurable direct RF sampling architecture that oﬀers flexible tuning to cover high RF bands is shown in Figure 11.6. The RF input from the LNA is filtered by the antialiasing filter H(ω) for the band of interest. The filter output signal is then sampled by pulses2 at a rate of fS1 and filtered by a continuous time interpolation filter which also serves as an antialiasing filter for the ADC that is sampling at a rate of fS2 . Sampling is achieved in two stages. In the first stage, the RF signal is bandpass filtered and sampled using an impulse sampling device without quantization. After tunable pulse sampling, the signal is continuous time lowpass or bandpass filtered to generate an IF signal that is then sampled by a conventional ADC. By using continuous time filtering after the first stage sampling, the ADC sample clock may be completely decoupled from the RF sample clock to allow arbitrary tuning without impacting the ADC sample rate. That is, by separating the sampling and quantization processes into multiple stages, the 2 Pulse

sampling is a technique that can be used for direct RF sampling at much higher frequencies than track and hold based sampling. The basic requirements for high RF pulse sampling are narrow pulse width and low pulse amplitude jitter, in addition to the low time jitter required in any direct RF sampling scheme [13].

400

Detecting and Classifying LPI Radar

jitter and clock speed requirements on the ADC can be relaxed. A high degree of reconfigurability in tuning range and bandwidth is achieved by using a tunable (or selectable) antialiasing filter before the first stage of sampling and by using a tunable sample clock in the first stage of sampling. Extension of this receiver architecture to an analog-to-information receiver is described in [14]. Motivated by recent developments in compressed sensing the receiver performs frequency modulated pulsed sampling at sub-Nyquist rates to compress a broadband RF environment into an analog interpolation filter and samples the signal at the information rate rather than using the Shannon bandwidth criteria. The receiver uses structured nonuniform sampling to implement a direct analog-to-information receiver that is eﬀective at recovering signals that have a sparse frequency domain representation [14].

11.4

Demodulation of the LPI Waveform

LPI signals attempt to make the detection and demodulation process impossible. The EW intercept receiver requires a large processing gain to detect the LPI emission, and extract the parameters of the signal. This is followed by the task of classification. Classification requires sorting the signal into groups having similar parameters (clustering). Parameters such as carrier frequency, bandwidth, modulation period, modulation bandwidth, and time of arrival are a few of the parameters that distinguish one signal from another. Correlation with existing signals in a database (identification) can then aid in signal tracking and response management. To identify the emitter parameters, Fourier analysis techniques using the FFT have been used as the basic tool. From this basic tool, more complex signal processing techniques have evolved, such as the short-time Fourier transform, in order to track the signal parameters over time. More sophisticated techniques have also been developed, called time-frequency and bifrequency distributions in order to identify the exotic modulation schemes used by the LPI radar [15]. These techniques include the Wigner distribution, Choi-Williams distribution, quadrature mirror filtering, and cyclostationary processing. The use of these techniques to extract the parameters from some of the well-known LPI modulations is the subject of the remaining chapters.

11.5

EW Receiver Challenges

The steady increase in sophistication of radar systems has resulted in an electromagnetic environment where very few pulses can now be expected. In addition, pulse-to-pulse PRI agility and frequency agility now make it extremely diﬃcult to identify a specific emitter, especially when only a few pulses are intercepted (e.g., from a track-while-scan or LPI radar). LPI CW

Strategies for Intercepting LPI Radar Signals

401

radar, as well as digital-pulsed radar, now transmit with an enormous number of new, complex modulations. These complex modulations can result in many reports for a single diverse emitter, making correct signal identification difficult. Furthermore, these modern radars will essentially blind existing EW designs, resulting in a situation where the warning receivers can no longer handle even those radars they were designed to intercept. For example, an existing EW might be subject to performance degradation, due to possible interference from modern pulse-Doppler radars transmitting from friendly platforms. Other problem situations include the fact that many communication CW signals are now within the radar spectrum. A significant problem can also occur when the intercept receiver processes signals with parameters outside its bounds. This can often cause resets that bring the system oﬀ-line for several minutes. Resets can also occur when the receiver processes signals that are near the internal thresholds. Finally, a significant problem for the receiver is a failure to intercept a threat emitter that is present (including its modulation parameters). This is more likely to happen with LPI emitters. Today’s modern EW receivers must have the ability to intercept both pulse radar signals and CW signals within a wide bandwidth (e.g., 0.5—100 GHz). The trend is to share a common aperture, and combine the communications, the EW, and radar functions requiring less antenna apertures. Another serious problem for the EW receiver is the presence of ultrawideband sources such as spread spectrum communication signals, impulse jammers, and impulse radar. The impact of ultrawideband synthetic aperture radar (SAR), and inverse SAR (or ISAR) imaging radar, and high range resolution profiling sensors, must also be considered. These sources (whether intercepted intentionally or not) can significantly raise the noise floor of the receiver, disabling the ability of the EW receiver to see the important threats of interest. Consequently, the ability to reject unwanted signals is now just as important as the ability to process the signals of interest. Wideband receivers require adaptive notch (band reject) filters at the front end, to exclude these unwanted signals. YIG (yttruim iron garnet) filters are often used. Adaptive thresholds can also be used to increase sensitivity. The EW receiver must also have high power detection and protection circuits at the front end, to protect itself from deliberate destruction by microwave weapons and other directed energy weapons. One high-power microwave pulse at the front end of the intercept receiver can destroy the EW receiver function, causing total failure of the ES/ELINT system onboard the aircraft. The EW receiver and associated EA must also be able to provide the quick reaction mode necessary to counter the new modern range-Doppler imaging missiles. These missiles will use FMCW modes such as SAR, ISAR and high range-Doppler imaging in order to improve target aimpoint accuracy, and to reject decoys that are launched. As we discussed in Chapter 1 and demonstrated in Chapter 9, power-managed seekers adjust the transmitter power

402

Detecting and Classifying LPI Radar

such that the received power at the EW receiver is kept constant (or is decreasing). EW receivers that prioritize incoming threats based on a change of the received signal amplitude will be vulnerable to the power-managed LPI seekers. These power-managed emitters must also be detected and processed correctly. Advanced missiles will also use dual mode seekers (e.g., an antiradiation missile seeker combined with an active millimeter wave LPI seeker) that must also be identified and countered. Finally, the EW receiver must be able to disseminate all onboard detections in real time sometimes referred to as real time out of the cockpit (RTOC). RTOC data is critical in a network-centric architecture in order to provide multiplatform targeting and geolocation. Also the ability to accept real time data in the cockpit (RTIC), and utilize the oﬀboard (multispectral) sensor data, is an important capability in order for the platform to precisely target its weapons or electronic attack. In this way the intercept receiver can be a major player in a multiplatform time diﬀerence of arrival (TDOA)-based geolocation network with, for example, Rivet Joint. The data fusion also exploits any oﬀboard and multispectral signals intelligence (SIGINT) data received. Specific emitter identification (SEI) attempts to fingerprint the emitters that are intercepted. SEI can also be used for improved tracking and deinterleaving. A number of algorithms have been investigated for doing SEI, but their details remain classified. More importantly, however, is the fact that future SEI systems must be standardized for interoperability between platforms and organizations (especially since the dividing line between RWR and ELINT is fast going away). That is, the success in SEI will ultimately lie in the infrastructure (dissemination of databases, correlation of absolutes, organized collection of targets), and not so much in the algorithms that are used.

11.6

Concluding Remarks

The trend in intercept receivers is toward digital receivers and the concept of digital antennas (ADC at the antenna). The future digital receiver will incorporate optical technologies for speed and bandwidth, and will also incorporate high-temperature superconductors for sensitivity. Networking the EW receiver within an information, sensor, and shooter grid will allow the sharing of intercept data. The use of swarm architectures will also become more prevalent. In the following chapters we assume that the signal is digitized in the receiver, and we mainly focus on the signal processing methods used to extract the LPI waveform parameters to classify the signals.

Strategies for Intercepting LPI Radar Signals

403

References [1] Schrick, G., and Wiley, R. G., “Interception of LPI radar signals,” IEEE International Radar Conference, pp. 108—111, 1990. [2] Wiley, R. G., Electronic Intelligence: The Interception of Radar Signals, Artech House Publishers, Dedham, MA, 1985. [3] Lee, J. P. Y., “Interception of LPI radar signals,” Defence Research Establishment Ottawa, Technical Note 91-23, Nov. 1991. [4] Bonabeau, E., Dorigo, M., and Theraulaz, G., Swarm Intelligence From Natural to Artificial Systems, Oxford University Press, New York, 1999. [5] Tsui, J. B. Y., and Stephens, J. P. Sr., “Digital microwave receiver technology,” IEEE Trans. on Microwave Theory and Techniques Vol. 50, No. 3, pp. 699—705, March 2002. [6] Rodrigue, S. M., Bash, J. L., and Haenni, M. G., “Next generation broadband digital receiver technology,” The 15th Annual AESS/IEEE Symposium, pp. 13—20, 14—15 May 2002. [7] Gross, F. B., and Chen, K., “Comparison of detectability of traditional pulsed and spread spectrum radar waveforms in classic passive receivers,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 41, No. 2, pp. 746—751, April 2005. [8] Gross, F. B., and Connor, J., “Comparison of detectability of radar compression waveforms in classic passive receivers,” IEEE Trans. on Aerospace and Electronic Systems, Voltt . 43, No. 2, pp. 789—795, April, 2007. [9] Shieh, C-S, and Lin, C-T., “A vector neural network for emitter identification,” IEEE Trans. on Antennas and Propagation, Vol. 50, No. 8, pp. 1120—1127, Aug. 2002. [10] Pekau, H., and Haslett, J. W., “A comparison of analog front end architectures for digital receivers,” Proc. of the IEEE CCECE/CCGEI, Saskatoon, May 2005. [11] Tatu, S. O., et al., “Ka-band direct digital receiver,” IEEE Trans. on Microwave Theory and Techniques, Vol. 50, No. 11, pp. 2436—2442, Nov. 2002. [12] Chalvatzis, T., Gagnon, E., and Wight, J. S., “On the eﬀect of clock jitter in IF and RF direct sampling systems,” 3rd International IEEE NEWCAS Conference, pp. 63—66, 19—22 June 2005. [13] Fudge, G. L., Chivers, M. A., Ravindran, S., Bland, R. E., and Pace, P. E., “A reconfigurable direct RF receiver architecture,” Proc. of the IEEE International Symposium on Circuits and Systems, May 2008. [14] Fudge, G. L., Bland, R. E., Chivers, M. A., Ravindran, S., Haupt, J. and Pace, P. E., “A Nyquist folding analog-to-information receiver,” Proc. of the Asilomar Conf. on Signals, Computers and Signal Processing, Nov. 2008. [15] Stephens, J. P., “Advances in signal processing for electronic warfare,” IEEE Aerospace and Electronic Systems Magazine, pp. 31—38, Nov. 1996.

Chapter 12

Wigner-Ville Distribution Analysis of LPI Radar Waveforms In Chapter 11, it was shown that tomorrow’s digital intercept receiver must incorporate a time-frequency analysis capability in order to identify the LPI modulation types and also extract the LPI signal’s parametric data. The Wigner-Ville Distribution (WVD), introduced by Wigner in 1932 as a phase representation in quantum statistical mechanics [1] and separately by Ville in 1948 addressing the question of a joint distribution function [2], simultaneously gives the representation of a signal in both time and frequency variables. The WVD has been noted as one of the more useful bilinear timefrequency analysis techniques for signal processing. In this chapter, the WVD is presented and used to analyze the signals discussed in Part I. Extraction of the signal parameters is also emphasized. The main objective is that by studying the results and correlating the signal parameters that are revealed, the user can learn to determine the presence of a particular LPI signal and to recognize the LPI modulation characteristics under various signal-to-noise ratios. We also show how well we can distinguish among several waveforms that have similar time and frequency characteristics. Multiple signal analysis is left as an exercise for the reader. By using the Wigner analysis tools, an intercept receiver can come close to having a processing gain near the LPI radar’s matched filter processing gain. The WIGNER folder on the CD provides the MATLAB tools that can be used to re-create any of the figures presented, as well as generate new and useful results.

405

406

Detecting and Classifying LPI Radar

12.1

Wigner-Ville Distribution

The WVD has been used in many fields of engineering. These include optical implementations of the WVD [3], medical applications [4—6], image analysis [7, 8], target detection [9, 10], and the analysis of nonstationary (LPI) signals [11—14]. The WVD exhibits the highest signal energy concentration in the timefrequency plane for linearly modulated signals, but has drawbacks in the case of nonlinear frequency modulated signals. To improve the concentration where nonlinear modulations are present, various higher-order time frequency representations have been investigated [15]. The WVD also contains interfering cross terms (or ghost terms) between every pair of signal components. As illustrated in the examples that follow, the presence of the cross terms sometimes make it diﬃcult to determine the LPI modulation parameters. A good review of bilinear transforms and their use in signal analysis is given in [16]. The influence that the cross term interference has on the WVD is analyzed in [17, 18]. The extension of the WVD to discrete time signals has been discussed in [19, 20] and a formulation to remove the cross terms has been reported in [21, 22]. Below, we begin with the definition of the WVD, and then present a windowed version of the WVD, the pseudo WVD (PWVD) which is useful in the signal processing of the digital signals within the receiver.

12.1.1

Continuous WVD

The WVD of a continuous one-dimensional function (or input signal) x(t) is given by [23] Wx (t, ω) =

∞

x t+

−∞

τ τ −jωτ dτ x∗ t − e 2 2

(12.1)

where t is the time variable, ω is the angular frequency variable (2πf ), and the ∗ indicates a complex conjugate. The WVD is a three-dimensional function describing the amplitude of the signal as a function of time and frequency. Since the LPI emitter modulations vary the compression of the CW waveform as a function of time, these types of time-frequency distributions give a higher probability of detecting the modulation parameters. The WVD can also be defined from the Fourier transform X(ω) of x(t) by WX (ω, t) =

1 2π

∞ −∞

X ω+

ω0 ω0 −jω0 t dω0 X∗ ω − e 2 2

(12.2)

From (12.1) and (12.2), the following relation is obtained: Wx (t, ω) = WX (ω, t)

(12.3)

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

407

That is, the WVD of the spectra of a signal can be determined simply from that of the time functions by an interchange of the frequency and time variables. This shows the symmetry between space and frequency domain definitions [23]. Equation (12.1) implies that evaluation of the WVD is a noncausal operation. As such, this expression does not lend itself to real-time evaluation. This limitation is overcome by first applying the WVD analysis to a sampled time series x( ), where is a discrete time index from −∞ to ∞. The discrete WVD is defined as W ( , ω) = 2

∞ n=−∞

x( + n)x∗ ( − n)e−j2ωn

(12.4)

Windowing the data results in the pseudo-WVD and is defined by [17] N −1

W ( , ω) = 2

n=−N+1

x( + n)x∗ ( − n)w(n)w(−n)e−j2ωn

(12.5)

where w(n) is a length 2N − 1 real window function with w(0) = 1. Using f (n) to represent the kernel function f (n) = x( + n)x∗ ( − n)w(n)w(−n)

(12.6)

the PWVD becomes W ( , ω) = 2

N −1

f (n)e−j2ωn

(12.7)

n=−N+1

The choice of N (usually a power of 2) greatly aﬀects the computational cost, as well as the time-frequency resolution, of the PWVD output. A large N gives a higher time-frequency resolution since it influences the frequency resolution in (12.7). When the continuous variable ω in (12.7) is sampled to produce a suitable form of the discrete Fourier transform (DFT), a larger N also gives more output samples, yielding a smoother result [24]. The maximum value of N is limited by N≤

M +1 2

(12.8)

where M is the data length. Once N is chosen, the kernel function can be generated. Since f (n) = f ∗ (−n)

(12.9)

only f (n) needs to be computed for n ≥ 0. A block diagram of the PWVD kernel generation for N = 8 is shown in Figure 12.1, where v(n) = w(n)w(−n).

408

Detecting and Classifying LPI Radar

Figure 12.1: The computational structure for an N = 8 PWVD kernel generation [24] ( c 1989 IEEE). Here the input signal enters the buﬀer register from the left and shifts to the right after each kernel generation. The right-most element is disposed after the next shift. The PWVD can detect the presence of LPI signals, as well as extract the signal’s modulation characteristics. For an intercept receiver, it is important that the computation be done in real time or near real time. From the PWVD expression in (12.7), we notice that it is computationally expensive to directly compute the PWVD. Boashash et al. [25] have presented an eﬃcient algorithm to compute the discrete PWVD. The algorithm is presented below. To begin, the continuous frequency variable ω is sampled as ω=

πk 2N

(12.10)

where k = 0, 1, 2, · · · , 2N − 1 (2N samples). The kernel indexes are modified to fit the standard DFT: W

,

πk 2N

N−1

=2 n=−N+1

or W

,

πk 2N

f (n) exp −

2N−1

=2 n=0

f (n) exp −

j2πnk 2N

j2πnk 2N

(12.11)

(12.12)

Wigner-Ville Distribution Analysis of LPI Radar Waveforms where

⎧ ⎨ f (n), 0, f (n) = ⎩ f (n − 2N ),

0≤n≤N −1 n=N N + 1 ≤ n ≤ 2N − 1

409

(12.13)

Since the kernel is a symmetric function, the DFT of the kernel is always real. The resulting PWVD using 2N samples is W ( , k) = 2

2N −1 n=0

f (n) exp −

jπkn N

(12.14)

Equation (12.14) is the algorithm implemented, and several examples are shown in the next section to illustrate the properties of the computation.

12.1.2

Example Calculation: Real Input Signal

Consider an example using a real input signal x( ) = {2, 4, 3, 6, 1, 7}

(12.15)

where N = 3 and the length of the input signal x( ) is 2N = 6. Here = −3, −2, −1, 0, 1, 2 and is the discrete time index in the range −N to N − 1. Note that x = 0 for ≤ −4 or ≥ 3. From (12.13), with N = 3, ⎧ 0≤n≤2 ⎨ f (n), 0, n=3 (12.16) f (n) = ⎩ 4≤n≤5 f (n − 6), From (12.6) f−3 (n) ( = −3), for input signal x( ) is computed as follows: f−3 (n = 0) f−3 (n = 1) f−3 (n = 2) f−3 (n = 3) f−3 (n = 4) f−3 (n = 5)

= = = = = =

x(−3) · x∗ (−3) = 2 · 2 = 4 x(−2) · x∗ (−4) = 4 · 0 = 0 x(−1) · x∗ (−5) = 3 · 0 = 0 0 x(1) · x∗ (−7) = 1 · 0 = 0 x(2) · x∗ (−8) = 7 · 0 = 0

So, from 12.13, f−3 = {4, 0, 0, 0, 0, 0}. Similarly for f0 , ( = 0), f0 (n = 0) f0 (n = 1) f0 (n = 2) f0 (n = 3) f0 (n = 4) f0 (n = 5)

= = = = = =

x(0) · x∗ (0) = 6 · 6 = 36 x(1) · x∗ (−1) = 1 · 3 = 3 x(2) · x∗ (−2) = 7 · 4 = 28 0 x(−2) · x∗ (2) = 4 · 7 = 28 x(−1) · x∗ (1) = 3 · 1 = 3

410

Detecting and Classifying LPI Radar

Figure 12.2: The kernel f (n) matrix for the real six input example. and so, f0 = {36, 3, 28, 0, 28, 3}. Repeating the above procedure, the kernel matrix for all values = −4 to 3, and n = 0 to 5 is as shown in Figure 12.2. The second step after the kernel transformation is to use (12.14) to calculate the Wigner distribution. As an example of the calculation, one can pick any and k to examine the values inside the PWVD matrix. For example, choose = 1, k = 2, with N = 3. The PWVD is 2N−1

W ( = 1, k = 2) = 2 n=0

f (n) exp −j

πkn N

f (n) exp −j

π2n 3

2·3−1

= 2 n=0 5

= 2 n=0

f (n) exp −j

2πn 3

(12.17)

From the kernel matrix in Figure 12.2, the kernel function for = 1 is f1 (n) = {1, 42, 0, 0, 0, 42}. So from (12.17), the PWVD for = 1, k = 2 (6 terms) is W (1, 2) = 2f1 (0) · exp −j

2·π·0 3

+ 2f1 (2) · exp −j

+ 2f1 (1) · exp −j

2·π·2 3

2·π·1 3

+ 2f1 (3) · exp −j

2·π·3 3

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

411

Figure 12.3: The PWVD matrix W ( , k) for the real six input example.

+ 2f1 (4) · exp −j

2·π·4 3

+ 2f1 (5) · exp −j

2·π·5 3

= 2 · 1 · (0) + 2 · 42 · (−0.5000 − 0.8660i) + 2 · 0 + 2 · 0 + 2 · 0 + 2 · 42 · (0.5000 + 0.8660i) W (1, 2) = −82 Repeating the above procedure gives the PWVD matrix at each discrete time index = −4 to 3 for each discrete frequency index k = 0 to 5. The result is a symmetric matrix about k = 3, as shown in Figure 12.3. An important feature of the PWVD is that all the components in the matrix are real. Other important properties of the PWVD are given in [3, 4, 7].

12.1.3

Example Calculation: Complex Input Signal

To demonstrate the PWVD computation for a complex input, consider the signal x = I + jQ (12.18) where = cos(2πfc t)

(12.19)

Q = sin(2πfc t)

(12.20)

I

If the carrier frequency fc = 1 kHz, sampling frequency, fs = 7 kHz, and t ∈ {0, 1/fs , 2/fs , . . . , 7/fs }, then the first eight input points for the discrete

412

Detecting and Classifying LPI Radar

Figure 12.4: The kernel matrix for the complex eight input example. time index

= −4 to 3 is

x( ) = {1 + 0i, 0.62 + 0.78i, −0.22 + 0.97i, −0.90 + 0.43i, −0.90 − 0.43i, −0.22 − 0.97i, 0.62 − 0.78i, 1 + 0i} (12.21) Consider the value when = 0, n = 3. Using (12.13) with an input length 2N = 8 or N = 4. The kernel is ⎧ 0≤n≤3 ⎨ f (n), 0, n=4 (12.22) f = ⎩ 5≤n≤7 f (n − 8), or

f (n) = {f (1), f (2), f (3), 0, f (−3), f (−2), f (−1)}

(12.23)

Since f (n) = x( + n) · x∗ ( − n), the kernel at = 0, n = 3 is f0 (3) = x(3) · x∗ (−3) = 1 · (0.6235 + 0.7818i)∗ = 0.6235 − 0.7818i. Repeating the same procedures as discussed in the real input case, the kernel matrix for the complex eight input example is shown in Figure 12.4. Referring to Figure 12.4, we can calculate the PWVD when = −1. The kernel is f−1 (n) = {1.00, −0.22 + 0.97i, −0.90 − 0.43i, 0.62 − 0.78i, 0, 0.62 + 0.78, −0.90 + 0.43i, −0.22 − 0.97i}

(12.24)

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

413

Figure 12.5: The PWVD matrix for the complex eight input example. Consider the case when is

= −1, k = 4. From (12.14), the PWVD for N = 4

W ( = −1, k = 4) = 2

2N −1 n=0

f (n) exp −j

2·4−1

= 2 n=0

f−1 (n)

πkn N

π4n 4

7

= 2 n=0

f−1 (n) exp(−jnπ)

(12.25)

From (12.24) and (12.25) 7

W ( = −1, k = 4) = 2

n=0

f−1 (n) · exp(−jnπ) = −3.2073

Again, the PWVD matrix of the complex eight input samples is real. The complete PWVD matrix is a symmetric 2N × 2N matrix. Figure 12.5 shows the PWVD matrix of the complex eight input samples. Note this important feature: the PWVD is always real whether the input signal is real or complex. Figure 12.6(a) shows a 3D mesh plot of the PWVD for the complex signal example with eight inputs. This plot shows the magnitude in both the

414

Detecting and Classifying LPI Radar

time domain and the frequency domain. Note that it directly correlates with Figure 12.5. The peak corresponds to the 1-kHz carrier frequency. Figure 12.6(b) shows the corresponding PWVD contour plot. The contour plot is a 2D time-frequency plot that is useful for characterizing the timefrequency behavior of the signal. The magnitude is represented by a diﬀerent gray scale, as shown in the legend bar. To see the marginal details of the PWVD, Figure 12.7(a) shows a plot of the PWVD obtained by rotating the mesh plot in Figure 12.6(a) to show just the time axis with the eight samples. The time resolution is 1/fs . Figure 12.7(b) shows the marginal details in the frequency domain, and is obtained in the same manner as Figure 12.7(a). The carrier frequency is represented by the peak in this plot, and shows up at 900 Hz, very close to the real value 1 kHz. The frequency resolution fs /2/# samples is also indicated. In summary both the real signal example and the complex signal example illustrate the mechanics of the PWVD calculation. The PWVD timefrequency results, when presented in the four diﬀerent plots, give a variety of aspects so that the LPI signal and its modulation characteristics can be determined.

12.1.4

Two-Tone Input Signal Results

Now we consider the PWVD for a two-tone input (two carrier frequencies) with fc1 = 1 kHz and fc2 = 2 kHz. Now I = cos(2πfc1 t) + cos(2πfc2 t) and Q = sin(2πfc1 t) + sin(2πfc2 t). Figure 12.8(a) shows the PWVD results for the two-tone signal in a 3D time-frequency mesh plot. In this plot the cross terms are stronger than the signal terms, and show up with many peaks. Figure 12.8(b) is the 2D PWVD time-frequency contour plot and shows the time dependence of the real signal and the cross terms. Figure 12.9(a) shows the marginal time domain plot obtained by rotating the 3D mesh plot in Figure 12.8(a), to show only the time axis. This reveals the cross terms as a series of positive and negative magnitude components in the time domain. Figure 12.9(b) shows the frequency domain plot obtained in the same manner, and reveals the two-carrier frequencies and the cross term. Note that the shape and magnitude of the cross term is not like the two-carrier frequency components, and can be easily identified.

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

415

Figure 12.6: PWVD for the eight input complex example: (a) 3D mesh plot, and (b) time-frequency domain.

416

Detecting and Classifying LPI Radar

Figure 12.7: PWVD for the eight input complex example: (a) 2D mesh in time domain, and (b) 2D mesh in frequency domain.

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

417

Figure 12.8: PWVD for the two-tone example, showing the (a) 3D timefrequency domain mesh plot, and (b) 2D time-frequency contour.

418

Detecting and Classifying LPI Radar

Figure 12.9: PWVD for the two-tone example, showing the (a) marginal time domain plot, and (b) marginal frequency domain plot.

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

419

Figure 12.10: Diagram of a triangular FMCW waveform.

12.2

FMCW Analysis

In this section, extraction of the signal parameters for two FMCW waveform examples (see Chapter 4) are investigated. When measuring the parameters of the LPI modulations, in all cases the absolute value of the relative error should be reported. That is, if a∗ is a measurement value of a quantity whose exact value is a, then the absolute value of the relative error r is defined by r

=

a∗ − a Error = a True value

(12.26)

The time-frequency diagram of a triangular waveform is shown in Figure 12.10. For the examples, both signals are sampled by the ADC at a rate of fs = 7,000 Hz. The first signal examined is an FMCW waveform with a center frequency of fc = 1,000 Hz, a modulation bandwidth of ∆F = 250 Hz, and a modulation period of tm = 20 ms. Figure 12.11(a) shows the PWVD frequency plot of the FMCW waveform. This graph can also be compared with the PSD of the waveform (see Chapter 4). Note the presence of the additional structure due to the triangular modulation. The carrier frequency can easily be identified and measured. The bandwidth of the signal can also be estimated. Figure 12.11(b) shows the time-frequency distribution. Although cross terms are present in the output image, the modulation bandwidth and the modulation period can be accurately identified, as well as the carrier frequency. Figure 12.12(a) shows the PWVD image for SNR = 0 dB and Figure 12.12(b) shows the PWVD image for SNR = −6 dB. The SNR is defined over fs /2. It is interesting to note that the carrier frequency, the modulation period, and the modulation bandwidth can all be extracted, even with this amount of interference present in the

420

Detecting and Classifying LPI Radar

Figure 12.11: PWVD for an FMCW with ∆F = 250 Hz, tm = 20 ms (signal only), showing the (a) marginal frequency domain plot, and (b) timefrequency plot.

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

421

signal. Also note that this information is not available if only the PSD is calculated in the receiver. In summary, the PWVD technique works extremely well for FMCW waveforms. The results for the ∆F = 500-Hz signal are shown in Appendix E.

12.3

BPSK Analysis

In this section we apply the PWVD and use it to investigate the properties of the BPSK signal discussed in Chapter 5. Parameters varied include the length of the Barker code (Nc = 7 or 11), the number of carrier cycles per Barker subcode (cpp), and the SNR (signal only, 0 dB, and −6 dB). We also investigate how many parameters of the signal can be extracted from the PWVD results. All signals demonstrating the concepts have an fc = 1 kHz carrier frequency, and a sampling frequency of fs = 7 kHz. Both frequency domain and time domain plots are shown for the BPSK signals after the PWVD processing. The time-frequency domain results are the most useful. The first signal, examined in Figure 12.13(a), has a carrier frequency of 1 kHz and can be clearly identified by the location of the highest or lowest peak value. The carrier frequency can also be identified as the center of the symmetric frequency distribution in Figure 12.13(b). Also, the relative peak magnitude in Figure 12.13(a) is about 600, so the 3-dB bandwidth (or subcode rate) B, is the frequency range lying at 300 on both sides, which extends from 500 Hz to 1,500 Hz. Since B = fc /cpp = 1,000 Hz, this correlates well. In Figure 12.13(a), if we look closely within the 3-dB bandwidth, one can find that there are 15 peaks within the bandwidth. That is, there are 14 intervals in the range from 500 Hz to 1,500 Hz. This number is always two times the Barker code length. In Figure 12.14, the 7-bit Barker code is examined with an SNR = 0 dB. Figure 12.14(a) shows the frequency domain where the 15 intervals can be counted within the 3-dB bandwidth. Figure 12.14(b) shows the corresponding time-frequency domain. In this particular case, not much information is revealed. Figure 12.15(a) shows the results for an 11-bit signal. In this case there are 23 peaks within the 3-dB bandwidth (Barker code length Nc = 11). Figure 12.15(b) shows the time-frequency results centered about the carrier frequency of fc = 1,000 Hz.

422

Detecting and Classifying LPI Radar

Figure 12.12: PWVD for an FMCW with ∆F = 250 Hz, tm = 20-ms timefrequency plot for (a) SNR = 0 dB and (b) SNR = −6 dB.

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

423

Figure 12.13: PWVD for BPSK with 7-bit Barker code, cpp = 1, signal only, showing the (a) marginal frequency domain plot and (b) time-frequency plot.

424

Detecting and Classifying LPI Radar

Figure 12.14: PWVD for BPSK with 7-bit Barker code, cpp = 1, SNR = 0 dB, showing the (a) marginal frequency domain plot and (b) time-frequency plot.

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

425

Figure 12.15: PWVD for BPSK with 11-bit Barker code, cpp = 1 (signal only), showing the (a) marginal frequency domain plot and (b) time-frequency plot.

426

12.4

Detecting and Classifying LPI Radar

Polyphase Code Analysis

In this section we begin with two CW signals that are phase coded with a Frank code (see Chapter 5), and examine them using the PWVD. Both signals are sampled in the receiver by an ADC with a sampling frequency fs = 7,000 Hz. The first signal examined has a carrier frequency of fc = 1,000 Hz, 16 phase codes Nc = 16, (M = 4), and a cpp = 1 or one cycle per subcode. That is, each subcode has a length of tb = 1 ms, resulting in a phase-coded signal with a code period of T = Nc tb =

Nc cpp Nc = = 16 ms B fc

(12.27)

Using cpp = 1 results in the maximum bandwidth that can be achieved with any particular carrier frequency. Identifying the signal parameters within the PWVD image is considered again. Figure 12.16(a) shows the PWVD frequency plot and Figure 12.16(b) shows the PWVD time-frequency image. Note that the carrier frequency can be identified by the largest peak value. Also note the presence of the harmonics that appear as modulation spikes every n/T Hz (or 62.5n Hz). The Frank code shows up as a series of unique evenly spaced parallel lines. The bandwidth B can also be identified in the image. When measuring the Frank code B within the PWVD image, it is necessary to skip one of the lines due to the presence of the cross terms. The slope of each line has a magnitude of S=

Bfc fc2 B = = = 62,500 Hz s−1 T Nc cpp Nc cpp2

(12.28)

The code period T is measured through the major cross term, and is also illustrated. This measurement stresses the fact that the PWVD integration period must be at least larger than the signal’s code period, in order to provide an accurate estimate (# samples/fs > T ). Figure 12.17(a) shows the PWVD time-frequency image for SNR = 0 dB. Although the addition of noise is clearly present in the output, the phase code parameters can be easily determined. In Figure 12.17(b) the SNR = −6 dB and it becomes a bit more diﬃcult. Preprocessing the image with a lowpass filter can help reduce the presence of the high frequency noise that hinders the extraction of the important signal parameters. A second Frank signal example with M = 8 (Nc = 64) is given in Appendix F. The PWVD results for the P1, P2, P3, and P4 polyphase codes are similar and given in Appendix G.

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

427

Figure 12.16: PWVD for Frank code with B = 1,000 Hz, T = 16 ms, signal only, showing the (a) marginal frequency domain plot, and (b) time-frequency plot.

428

Detecting and Classifying LPI Radar

Figure 12.17: PWVD for Frank code with B = 1,000 Hz, T = 16 ms, timefrequency plot for (a) SNR = 0 dB, and (b) SNR = −6 dB.

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

12.5

429

Polytime Code Analysis

In this section an analysis of the polytime codes (see Chapter 5) using the PWVD is presented. The structure of the polytime codes (T1 through T4) within the PWVD are significantly diﬀerent, even though they were derived from both step frequency and linear FM waveforms (as are the Frank code and P1—P4). The first signal examined is the T1 code with fc = 1,000 Hz and T = 16 ms. The number of stepped frequency segments used is k = 4 (zero beat at the leading segment), and the number of phase states n = 2, T1(2). The sampling frequency of the ADC is fs = 7,000 Hz. Each segment is 4 ms in duration, resulting in the overall code period of 16 ms. The frequency step between adjacent segments is 1/4 ms = 250 Hz with a total frequency excursion of 1,000 Hz. Figure 12.18(a) shows the PWVD frequency domain. Compared to the Frank and P1 through P4 codes, the T1(2) energy is more evenly distributed within the (approximately) same bandwidth. Also note that the harmonics are not uniformly spaced, due to the time modulation of the binary phase change. Figure 12.18(b) shows the time-frequency distribution of the T1(2) code. The signal shows up as a set of vertical roof tops stacked next to each other, separated by T /2. Note that the carrier is easily identified, as well as the measurement of the bandwidth B and code period T (about the cross term). To understand the bandwidth characteristics shown in Figure 12.18, the phase shift for the T1(2) is shown in Figure 12.19. Here the smallest phase change shown is 4 samples long (0.571 ms). This results in a bandwidth excursion of B = 1,750 Hz, which can be identified in Figure 12.18(b). Figure 12.20(a) shows the signal for an SNR = 0 dB. The signal can still be identified as a T1(2) and the parameters can still be extracted. In Figure 12.20(b) with an SNR = −6 dB, no signal identification can be made and no parameters can be extracted. The T2(2), T3(2), and T4(2) code examples are examined in Appendix H.

430

Detecting and Classifying LPI Radar

Figure 12.18: PWVD for polytime code T1(2) with B = 1,750 Hz, T = 16 ms, signal only showing the (a) marginal frequency domain plot, and (b) time-frequency plot.

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

431

Figure 12.19: T1(2) phase shift showing a minimum subcode width of four samples (0.571 ms), resulting in a bandwidth excursion of B = 1,750 Hz.

12.6

Distinguishing Between Phase Codes

The main objective of the previous sections was to examine the PWVD for each of the important LPI phase modulations discussed in Part I. The intercept receiver running the PWVD must also be able to distinguish between these phase modulations, in addition to extracting the signal parameters (as described above). To illustrate the similarities and diﬀerences, the phase modulations are compared together in Figure 12.21. The Frank code, P1, P3, and P4 have the same slope sign but, although similar, have diﬀerent time-frequency characteristics that can be used to identify the particular phase modulation. The P2 has a diﬀerent slope. The distinguishing features, of course, depend on the sampling period of the ADC, and any receiver nonlinearities that might be present. The T1(2) (as well as T2—T4) are unique, since they contain time-frequency components with both slope signs. Figures 12.22—12.25 show the PWVD time-frequency results, and the corresponding phase states for the T1 through T4, for comparison. Examination of these results shows that it is easy to distinguish between the polytime codes, and also to distinguish them from the Frank, P1, through P4, codes.

432

Detecting and Classifying LPI Radar

Figure 12.20: PWVD for T1(2) code with B = 1,750 Hz, T = 16 ms, timefrequency plot for (a) SNR = 0 dB, and (b) SNR = −6 dB.

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

433

Figure 12.21: PWVD for (a) Frank code, (b) P1, (c) P2, (d) P3, and (e) P4 codes.

434

Detecting and Classifying LPI Radar

Figure 12.22: PWVD for (a) T1(2) code, and (b) phase code showing minimum subcode with 18 samples (2.57 ms).

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

435

Figure 12.23: PWVD for (a) T2(2) code, and (b) phase code showing minimum subcode with 36 samples (5.14 ms).

436

Detecting and Classifying LPI Radar

Figure 12.24: PWVD for (a) T3(2) code, and (b) phase code showing minimum subcode with six samples (0.86 ms).

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

437

Figure 12.25: PWVD for (a) T4(2) code, and (b) phase code showing minimum subcode with seven samples (1 ms).

438

12.7

Detecting and Classifying LPI Radar

FSK and FSK/PSK Analysis

In this section we examine the PWVD results for an FSK Costas signal and a hybrid PSK/FSK signal. The PWVD is used first to investigate the timefrequency characteristics of a Costas sequence {3, 2, 6, 4, 5, 1} kHz. The signal was generated with the costas.m program within the LPIT, using a frequency duration of tp = 0.005s and a sampling frequency of fs = 15,057 Hz. This resulted in single frequency-hopping sequence consisting of 520 samples. The PWVD marginal frequency domain is shown in Figure 12.26(a). Note that the frequencies in the sequence are clearly present, as well as the cross terms. The PWVD time-frequency image is shown in Figure 12.26. The arrows indicate the positions of the Costas frequencies. Note that the time axis is reversed. That is, the frequency order begins at the right side of the figure. The cross terms present tend to make the identification of the frequencies intricate, especially when the cross terms lie about one of the frequencies in the code. In Figure 12.27(a, b), the time-frequency image is displayed for both 0 dB and −6 dB, respectively. As expected, the identification becomes more diﬃcult. With the FSK (Costas)/PSK signal, each frequency selected is phase shifted with a 5-bit Barker code with cpp = 5 (five cycles per phase code). The results are shown in Figure 12.28(a, b) for the signal only, and SNR = 0 dB, respectively. Note that although the cross terms are again significant, the frequencies in the Costas code can be identified. For the FSK/PSK target signal described, the PWVD does not give good results, and no parameters can be determined.

12.8

Summary

The PWVD theory was presented in this chapter and several examples were used to demonstrate generating an eﬃcient kernel function and the subsequent calculation of the PWVD time-frequency results. Whether the signals are real or complex, the kernel and PWVD matrix are always real and symmetric. This is an important feature for the Wigner distribution and a good reason why the PWVD can be used for accurate signal analysis (in spite of the cross terms present). Apart from the parameters listed in the table, other signal characteristics can be measured or estimated. For example, for the FMCW signal, knowing ∆F and tm , the range resolution ∆R and the unambiguous range Ru may be estimated. For the FSK Costas code, the identification of the signal is diﬃcult due to the ghost terms present. This is also the case for the FSK/PSK (binary phase code) signal. For the FSK/PSK (target) signal reported, the PWVD was not able to identify any meaningful signal parameters. This should not be a surprise, considering the PACF, PAF results shown in Chapter 6.

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

439

Figure 12.26: PWVD for Costas code sequence {3, 2, 6, 4, 5, 1} kHz, showing the (a) marginal frequency domain, and (b) time-frequency image.

440

Detecting and Classifying LPI Radar

Figure 12.27: PWVD time-frequency image for Costas code sequence {3, 2, 6, 4, 5, 1} kHz, showing (a) SNR = 0 dB, and (b) SNR = −6 dB.

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

441

Figure 12.28: The PWVD for the FSK/PSK signal, showing the (a) signal only, and (b) SNR = 0 dB.

442

Detecting and Classifying LPI Radar

The presentation of the PWVD results to a trained operator will allow the signal parameters to be extracted, and can enable good classification results in moderate amounts of noise. A modern intercept receiver/analyzer would implement a set of parallel processors; each designed to recognize, within a particular frequency band, a particular class of waveforms that might occupy that band. The outputs would consist of pulse descriptor words containing estimates of the signal parameters. How well the PWVD processing performs this task, as a function of its bandwidth (relative to the actual signal bandwidth) and the SNR in that bandwidth, is of primary concern and must be investigated. Autonomous classification and parameter extraction within an intercept receiver is a significantly harder problem, and is addressed further in Chapters 17 and 18.

References [1] Wigner, E. P., “On the quantum correction for thermodynamic equilibrium,” Physics Review, Vol. 40, pp. 749—759, 1932. [2] Ville, J., “Theorie et applications de la notion de signal analytique,” Cables et Transmission, Vol 2A, pp. 61—74, 1948. [3] Li, Y., Eichmann G., and Conner, M., “Optical Wigner distribution and ambiguity function for complex signals and images,” Optics Communication, Vol. 67, No. 3, pp. 177—179, July 1988. [4] Clayton, R. H., and Murray, A., “Comparison of techniques for time-frequency analysis of the ECG during human ventricular fibrillation,” IEE Proc. on Science and Measurement Technology, Vol. 145, No. 6, pp. 301—306, Nov. 1998. [5] Darvish, N., and Kitney, R. I., “Time-frequency and time-scale methods in the detection and classification of non-stationarities in human physiological data,” Record of the 28th Asilomar Conference on Signals, Systems and Computers, Vol. 2, pp. 1085—1158, Oct. 31—Nov. 2, 1994. [6] Millet-Roig, J., et al., “Time-frequency analysis of a single ECG: to discriminate between ventricular tachycardia and ventricular fibrillation,” Computers in Cardiology, pp. 711—714, 1999. [7] Cristobal, G., Bescos J., and Santamaria, J., “Image analysis through the Wigner distribution,” Applied Optics, Vol. 28, No. 2, pp. 262—271, Jan. 1989. [8] Gonzalo, C., et al., “Space-variant filtering through the Wigner distribution function,” Applied Optics, Vol. 28, No. 4, pp. 730—735, Feb. 1989. [9] Haykin, S., and Bhattacharya, T., “Wigner-Ville distribution: an important functional block for radar target detection in clutter,” Record of the 28th Asilomar Conference on Signals, Systems and Computers, Vol. 1, pp. 68—72, Oct. 31—Nov. 2, 1994. [10] Kumar, P. K., and Prabhu, K. M. M., “Simulation studies of moving targetdetection: a new approach with the Wigner-Ville distribution,” IEE Proc. on Radar, Sonar and Navigation, Vol. 144, No. 5, pp. 259—265, Oct. 1997.

Wigner-Ville Distribution Analysis of LPI Radar Waveforms

443

[11] Milne, P.R., and Pace, P. E., “Wigner distribution detection and analysis of FMCW and P-4 polyphase LPI waveforms,” IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol. 4, pp. 3944—3947, 2002. [12] Taboada, F., et al., “Intercept receiver signal processing techniques to detect low probability of intercept radar signals,” Proc.of the Fifth Nordic Signal Processing Symposium, Hurtigruta Tromso-Trondheim, Norway, 4—7 Oct. 2002. [13] Barbarossa, S., “Parameter estimation of undersampled signals by WignerVille analysis,” IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP-91, Vol. 5, pp. 3253—3256, April 14-17, 1991. [14] Gau, J-Y, “Analysis of low probability of intercept (LPI) radar signals using the Wigner Distribution,” Naval Postgraduate School Master’s Thesis, Sept. 2002. [15] Katkovnik, V., and Stankovic, L., “Instantaneous frequency estimation using the Wigner distribution with varying and data-driven window length,” IEEE Trans. on Signal Processing, Vol. 46, No. 9, pp. 2315—2325, Sept. 1998. [16] Chen, V. C., and Ling, H., Time-Frequency Transforms for Radar Imaging and Signal Analysis, Artech House, Inc., Norwood, MA, 2002. [17] Stankovic, L., and Stankovic, S., “On the Wigner distribution of discrete time noisy signals with application to the study of quantization eﬀects,” IEEE Trans. on Signal Processing, Vol. 42, No. 7, pp. 1863—1867, July 1994. [18] Stankovic, L., “Algorithm for the Wigner distribution of noisy signals realisation,” IEE Electronics Letters, Vol. 34, No. 7, pp. 622—623, April 1998. [19] O’Neill, J. C., Flandrin, P., and Williams, W. J., “On the existence of discrete Wigner distributions,” IEEE Signal Processing Letters, Vol. 6, No. 12, pp. 304—306, Dec. 1999. [20] Claasen, T. A. C. M., and Mecklenbrauker, W. F. G., “The Wigner distribution—a tool for time-frequency signal analysis, Part II: Discrete-time signals,” Phillips Journal of Research, Vol. 35, No. 4/5, pp. 276—300, 1980. [21] Kadambe, S., and Adali, T., “Application of cross term deleted Wigner representation (CDWR) for sonar target detection/classification,” Record of the 32nd Asilomar Conference on Signals, Systems & Computers, Vol. 1, pp. 822—826, Nov. 1—4, 1998. [22] Kadambe, S., and Orr, R., “Comparative study of the cross term deleted Wigner and cross biorthogonal representations,” Record of the 31st Asilomar Conference on Signals, Systems & Computers, Vol. 2, pp. 1484—1488, Nov. 2—5, 1997. [23] Claasen, T. A. C. M., and Mecklenbrauker, W. F. G., “The Wigner distribution— a tool for time-frequency signal analysis, Part I: Continuoustime signals,” Phillips Journal of Research, Vol. 35, No. 3, pp. 217—250, 1980. [24] Sun, M., et al., “A Wigner spectral analyzer for nonstationary signals,” IEEE Trans. on Instrumentation and Measurement, Vol. 38, No. 5, pp. 961—966, Oct. 1989.

444

Detecting and Classifying LPI Radar

[25] Boashash, B. and Black, P. J., “An eﬃcient real-time implementation of the Wigner-Ville distribution,” IEEE Trans. on Acoustics, Speech and Signal Processing, Vol. ASSP-35, No. 11, pp. 1611—1618, Nov. 1987.

Problems 1. (a) Using the LPIT, generate the default FMCW waveform and the default P4 waveform. Load both signals into MATLAB, and truncate such that they both have the same size (be sure to at least include one to two code periods of each signal). (b) Add the two signals together and save as a new signal (e.g., fmcw p4.mat). (c) Using the PWVD, analyze each signal and extract the waveform parameters that are evident. (d) Repeat (b) and (c) for SNR = 0 dB. 2. Using the PWVD, compute the Wigner-Ville distribution for the random noise radar waveform, random noise plus FMCW waveform, random noise FMCW plus sine, and random binary phase modulation discussed in Chapter 7. For each waveform, which modulation parameters can’t be extracted from the Wigner-Ville distribution? 3. Using the PWVD, compute the Wigner-Ville distribution of the (a) polyphase signal that uses one of the orthogonal sequences given in Table 10.12, (b) polyphase signal that uses one of the Doppler tolerant orthogonal sequences in Table 10.14, and (c) frequency hopping signal that uses one of the orthogonal frequency sequences given in Table 10.16. 4. To help identify the capability of the PWVD as a tool for identifying the LPI modulation, extracting the modulation parameters, and to aid in deciding on what signal processing algorithm performs best, construct a table to show the PWVD measurement results for the LPI signals contained in the Test Signals folder. For each parameter of interest, show the actual value, the measured value, and the absolute value of the relative error [see (12.26)]. Although the cross term interference makes things particularly diﬃcult, the measured results should tend to coincide well with the actual values. The relative error depends on how closely the PWVD results are examined. With noise added, the measurement ability degrades slowly as the reader can document and verify. 5. Generate the two orthogonal polyphase codes using ortho40.m and ortho40CE.m and the discrete frequency coding waveforms using dfc32.m with the same signal parameters illustrated in Chapter 10. Use the PWVD tools to examine the waveforms and determine if any coding structure can be extracted from the time-frequency images or their marginal distributions.

Chapter 13

Choi-Williams Distribution Analysis of LPI Radar Waveforms The pseudo Wigner-Ville distribution (PWVD) is useful for identifying the LPI waveform modulation parameters due to the time-frequency characteristics that are calculated. The PWVD time-frequency images however, contain large cross terms, which can sometimes make identification of the modulation, and extraction of the modulation parameters diﬃcult especially in low SNR situations. This chapter examines the Choi-Williams distribution (CWD), which uses an exponential kernel in the generalized class of bilinear time-frequency distributions to minimize the cross term components that are so prevalent in the PWVD. The CWD is used to examine the LPI modulations for comparison to the results in the PWVD chapter. By using the CWD analysis tools, the intercept receiver can increase its processing gain approaching that of the LPI emitter. The absence of strong cross terms in the time-frequency plane allows the modulation type to be more readily determined and also makes the extraction of the modulation parameters easier. The CHOI folder on the CD provides the MATLAB tools that can be used to re-create any of the figures presented, as well as generate new and useful results.

445

446

Detecting and Classifying LPI Radar

13.1

Mathematical Development

The general class of time-frequency distributions introduced by Cohen is given by Cf (t, ω, φ) =

1 2π

ej(ξμ−τ ω−ξt) φ(ξ, τ )A(μ, τ )dμdτ dξ

(13.1)

where φ(ξ, τ ) is a kernel function and A(μ, τ ) = x μ +

τ τ x∗ μ − 2 2

(13.2)

and x(μ) is the time signal, and x∗ (μ) is its complex conjugate. This represents a generalized class of a bilinear transformation that satisfies the marginals and has good resolution in both time and frequency spaces. The Wigner-Ville time-frequency distribution, discussed in Chapter 12, is based on (13.1) where the kernel function φ(ξ, τ ) = 1. For multicomponent signals, the cross terms that are present in the Wigner-Ville distribution were demonstrated to be quite large. The cross terms cause interference that can obscure physically relevant components of the LPI signal’s modulation. Choi and Williams [1] realized that by choosing the kernel in (13.1) carefully, the calculation can minimize the cross terms and still retain the desirable properties of the self-terms. The Choi-Williams distribution (CWD) uses an exponential weighting kernel in order to reduce the cross term components of the distribution. The kernel function that gives the Choi-Williams distribution is 2 2 (13.3) φ(ξ, τ ) = e−ξ τ /σ where σ (σ > 0) is a scaling factor. By substituting this kernel into (13.1) the continuous CWD of the input signal x(t) is given as [1] CWDx (t, ω) =

∞

e−jωτ

τ =−∞

∞ μ=−∞

where

σ G(μ, τ )A(μ, τ )dμ dτ 4πτ 2 2

G(μ, τ ) = eσ(μ−t)

/(4τ 2 )

(13.4)

(13.5)

and t is the time variable, ω is the angular frequency variable (2πf ), and σ is a positive-valued scaling factor. The bracketed term in (13.4) is the estimation of the time-indexed autocorrelation. Just as for the WVD, the CWD can be defined from the Fourier transform X(ω) of x(t) by CWDX (t, ω) =

1 2π

∞

e−jξt

ξ=−∞

X μ+

ξ 2

∞ μ=−∞

X∗ μ −

ξ 2

2 σ (μ−ω) 4ξ2 /σ e 4πξ 2

dμdξ

(13.6)

Choi-Williams Distribution Analysis of LPI Radar Waveforms

447

and in discrete form, the Choi-Williams distribution is ∞

CWDx ( , ω) = 2

e−j2ωτ

τ =−∞

∞ μ=−∞

−σ(μ− )2 /(4τ 2 )

e

1 4πn2 /σ

x(μ + τ )x∗ (μ − τ )

(13.7)

For computational purposes it is necessary to apply the weighting windows WN (τ ) and WM (μ) for the summations in (13.7) before evaluating the distribution at each time index . The windowed Choi-Williams distribution can then be expressed as CWDx ( , ω) = 2

∞

WN (τ )e−j2ωτ

τ =−∞

e

2 − σμ2 4τ

∞

WM (μ)

μ=−∞

σ 4πτ 2

x( + μ + τ )x∗ ( + μ − τ )

(13.8)

where WN (τ ) is a symmetrical window which has nonzero values for the range of −N/2 ≤ τ ≤ N/2, and WM (μ) is a rectangular window which has a value of 1 for the range of −M/2 ≤ μ ≤ M/2. The parameter N , is the length of the window WN (τ ). The length N along with the shape of the window determines the frequency resolution of the distribution. The parameter M , which is the length of the window WM (μ), determines the range from which the time indexed autocorrelation is estimated. The CWDx in (13.8) can also be expressed as L

S( , n)e−j2ωn

CWDx ( , ω) = 2

(13.9)

n=−L

where the kernel is M/2

S( , n) = W (n) μ=−M/2

−σ(μ2 − )2 1 e 4n2 /σ x(μ + n)x∗ (μ − n) 4πn2 /σ

(13.10)

where W (n) is a symmetrical window (such as Hamming), which has nonzero values on the interval −L to L, and W (μ) is a uniform rectangular window that as a value of 1 for the range of −M/2 and M/2. The choices of N and M on these windows, respectively, determine the frequency resolution of the CWD and the range at which the function will be defined. Choi and Williams state that decreasing the size of W (n) reduces the “oscillatory fluctuations of the cross terms,” which at the same time decreases the frequency resolution of the distribution. In other words, there is a trade-oﬀ between the reduction of the cross terms and the frequency resolution obtained from the distribution.

448

Detecting and Classifying LPI Radar

When the above kernel function in (13.10) is compared to the one given for the Wigner-Ville distribution f (n) = x( + n)x∗ ( − n)w(n)w(−n)

(13.11)

the reader will notice that the CWD contains parameters similar to the Wigner-Ville distribution, but includes an exponential term and introduces a new summation. The reader will also notice that the CWD kernel function is a series of Gaussian distributions. Barry points out that these distributions are aligned diagonally and that the mean and variance of each distribution is 1 and 2n2 /σ, respectively [2]. As with the Wigner-Ville distribution, the discrete CWD can be modified to fit the standard DFT by setting ω = πk/2N . Substituting this result into (13.9) and (13.10) above, and adding the window limits, we obtain [3] πk , 2n

2N−1

S ( , n)e−j2πkn/N

(13.12)

where the kernel function S ( , n) is defined as ⎧ S( , n), 0≤n≤N −1 ⎨ 0, n=N S ( , n) = ⎩ S( , n − 2N ), N + 1 ≤ n ≤ 2N − 1

(13.13)

CWDx

13.2

=2 n=0

LPI Signal Analysis

Next we review how the Choi-Williams distribution interprets various LPI signals generated by the LPIT. The greatest advantage to the CWD is the reduction of cross terms such as those in the WVD. Several types of LPI signals will be evaluated to determine the eﬀectiveness of the cross term reduction and the overall suitability of using the CWD detection of the LPI modulations. The MATLAB algorithm for the Choi-Williams distribution uses the same type of kernel transformation as described for the Wigner-Ville distribution. As the utility of these types of algorithms becomes increasingly popular for signal analysis, there is a strong interest to execute the code as fast as possible. Porting the MATLAB algorithms to C++ for execution on a reconfigurable computing architecture can provide significantly faster results than running them on a personal computer. In the reconfigurable computer, the code execution is divided up between the microprocessors and the field programmable gate arrays (FPGAs) [4]. Due to the diﬀerent execution speed of the FPGA processing elements compared to the microprocessor processing elements, significant improvement in run time can result if the code division is done correctly [5].

Choi-Williams Distribution Analysis of LPI Radar Waveforms

13.2.1

449

FMCW Analysis

In this section, extraction of the signal parameters for an FMCW waveform example is investigated. The signal is sampled at a rate of fs = 7,000 Hz. The signal has a center frequency of fc = 1,000 Hz, and a modulation bandwidth of ∆F = 500 Hz, and a modulation period of tm = 20 ms. Figure 13.1(a) shows the CWD marginal frequency results of the FMCW and highlights the carrier frequency. The time-frequency plot in Figure 13.1(b) clearly shows the modulation period (tm ) and the modulation bandwidth (∆F ). The absence of cross terms presents a clear picture of the modulation. Figure 13.2(a) shows the CWD image for SNR = 0 dB and Figure 13.2(b) shows the CWD image for SNR = −6 dB. The signal parameters are clearly visible in the 0 dB and −6 dB SNR. In summary, the CWD technique works well for the FMCW waveforms, and it reduces the cross terms observed by the WVD.

13.2.2

BPSK Analysis

In this section we apply the CWD and use it to investigate the properties of the BPSK CW signal. The parameters varied include the length of the Barker code (number of subcodes Nc = 7 or 11) and the SNR (signal only, 0 dB, −6 dB). All signals have a fc = 1,000 Hz carrier frequency and a sampling frequency of fs = 7,000 Hz. Both frequency domain and time domain plots are shown for the BPSK signals after the CWD processing. With the first signal examined shown in Figure 13.3(a), in the absence of the cross terms, the carrier frequency of 1,000 Hz is suppressed with the CWD. It can, however, be identified as the center of the 3-dB bandwidth. The carrier frequency can also be identified in Figure 13.3(b) as the center of the symmetric frequency distribution. In this case, there are 7 peaks within the 3-dB bandwidth which correspond to the 7 subcodes in the Barker code. Note also, that the Barker subcodes cannot be identified within the WVD. In Figure 13.4, the 7-bit Barker code is examined with an SNR = 0 dB. Figure 13.4(a) shows the frequency domain where the 7-bit code is still visible about the carrier frequency. With the time-frequency plot shown in Figure 13.4(b), the subcodes about the carrier frequency are still clearly visible as well as the bandwidth. These results also indicate that the CWD also appears to suppress the noise better than the WVD. Figure 13.5(a) shows the marginal frequency domain for an Nc = 11-bit Barker code BPSK signal only. All 11 peaks can be identified within the 3-dB bandwidth. In Figure 13.5(b), the bandwidth and the carrier frequency can still be identified.

450

Detecting and Classifying LPI Radar

Figure 13.1: CWD for an FMCW with ∆F = 250 Hz, tm = 20 ms (signal only), showing (a) the marginal frequency domain plot and (b) the timefrequency plot.

Choi-Williams Distribution Analysis of LPI Radar Waveforms

451

Figure 13.2: CWD for an FMCW with a ∆F = 250 Hz, tm = 20 ms timefrequency plot for (a) SNR = 0 dB and (b) SNR = −6 dB.

452

Detecting and Classifying LPI Radar

Figure 13.3: CWD for BPSK with 7-bit Barker code, cpp = 1, signal only, showing (a) the marginal frequency domain plot and (b) the time-frequency plot.

Choi-Williams Distribution Analysis of LPI Radar Waveforms

453

Figure 13.4: CWD for BPSK with 7-bit Barker code, cpp = 1, SNR = 0 dB, showing (a) the marginal frequency domain plot and (b) the time-frequency plot.

454

Detecting and Classifying LPI Radar

Figure 13.5: CWD for BPSK with 11-bit Barker code, cpp = 1, signal only, showing (a) the marginal frequency domain plot and (b) the time-frequency plot.

Choi-Williams Distribution Analysis of LPI Radar Waveforms

13.2.3

455

Polyphase Code Analysis

In this section, we examine two CW polyphase Frank code signals with the CWD. Both signals are sampled in the receiver by an analog-to-digital converter (ADC) with a sampling frequency of fc = 1,000 Hz. The CW signal is generated with Nc = 16 phase codes (M = 4), with a cpp = 1 or one cycle per subcode. Each subcode has a length of tb = 1 ms, resulting in a Frank code signal with a code period of T = Nc tb =

Nc cpp Nc = B fc

(13.14)

or 16 ms. Figure 13.6(a) shows the CWD marginal frequency results. The carrier frequency can be identified by the largest peak value. The harmonic spikes appear every n/T Hz (or 62.5n Hz). Figure 13.6(b) shows the CWD time-frequency image. Unlike the WVD, the Frank code shows the exact number of code periods intercepted. The bandwidth B can also be identified in the image. When measuring the Frank code bandwidth B within the WVD image, it was necessary to skip one of the modulation lines due to the presence of cross terms. With the CWD there are no cross terms and the bandwidth can be measured directly. The slope of each line has a magnitude of S=

f2 T = 2 c 2 = 62,500 Hz s−1 B Nc cpp

(13.15)

The code period T is also measured directly as illustrated. This measurement stresses the fact that the CWD integration period must be at least larger than the signal’s code period in order to provide an accurate estimate of the modulation parameters (# samples/fs > T ). Figure 13.7(a) shows the CWD time-frequency image for SNR = 0 dB. Although the addition of noise is present in the image, the phase code parameters can be easily determined. In Figure 13.7(b), the SNR = −6 dB. The presence of the signal can be identified but the parameter extraction is becoming more diﬃcult.

13.2.4

Polytime Code Analysis

The structures of the polytime codes (T1 through T4) within the CWD are significantly diﬀerent than the polyphase codes such as the Frank code. For the T1 code examined, fc = 1,000 Hz and T = 16 ms. The number of frequency segments used is k = 4 and the number of phase states is n = 2. This signal is referred to as T1(2). The sampling frequency of the ADC is fs = 7,000 Hz. With a code period of 16 ms and 4 frequency segments, each segment must be 4 ms in duration. The frequency step between adjacent segments is 1/4 ms = 250 Hz with a total frequency excursion of 1,000 Hz. Figure 13.8(a) shows the CWD marginal frequency domain. Note that the

456

Detecting and Classifying LPI Radar

Figure 13.6: CWD for Frank code with B = 1,000 Hz, T = 16 ms, signal only, showing (a) the marginal frequency domain plot and (b) the time-frequency plot.

Choi-Williams Distribution Analysis of LPI Radar Waveforms

Figure 13.7: CWD for Frank code with B = 1,000 Hz, T = 16 ms, time-frequency plot for (a) SNR = 0 dB and (b) SNR = −6 dB.

457

458

Detecting and Classifying LPI Radar

harmonics are uniformly spaced due to the time modulation of the binary phase change. Figure 13.8(b) shows the time-frequency distribution of the T1(2) code. The signal shows up as a set of vertical triangles stacked next to each other. They are separated by the code period T . Figure 13.9(a) shows the signal for an SNR = 0 dB. The signal can still be identified as a T1(2) and the parameters can still be extracted. In Figure 13.9(b), with an SNR = −6 dB, no signal identification can be made and no parameters can be extracted.

13.2.5

FSK and FSK/PSK Analysis

In this section, we examine the CWD results for the FSK Costas signal and a hybrid FSK/PSK signal. The CWD is used first to investigate the timefrequency characteristics of the Costas frequency hopping sequence {3, 2, 6, 4, 5, 1} kHz. The signal was generated with the LPIT using a frequency duration of tp = 0.005 seconds and a sampling frequency of fs = 15,057 Hz. The CWD marginal frequency domain is shown in Figure 13.10(a). Note that the frequencies in the sequence are present and there are no cross terms, as were present in the WVD. The CWD time-frequency image is shown in Figure 13.10(b). The positions of the six Costas frequencies are shown clearly. In Figure 13.11, the time-frequency image is displayed for both the 0-dB and −6-dB SNR signals, respectively. As expected, the identification becomes more diﬃcult with increasing noise levels but the presence of the signals can still be identified. With the FSK (Costas)/PSK signal, each frequency is overlayed with a 5-bit narrowband Barker phase code with cpp = 5 (five cycles per phase code). The results are shown in Figure 13.12(a, b) for the signal only, and SNR = 0 dB, respectively. The frequencies in the Costas code can be identified along with the phase code overlay. For the FSK/PSK target signal described, the CWD generates excellent results and gives a clear picture without cross terms.

13.3

Summary

The CWD theory was presented in this chapter. Several examples were used to demonstrate generating an eﬃcient kernel function and the subsequent calculation of the CWD time-frequency results. The CWD was compared to the WVD and the usefulness of the CWD to reduce the cross terms was demonstrated for key LPI signals. The MATLAB folder CHOI contains the file choi.m, which can be used to generate the results in this chapter or any other LPI waveform results.

Choi-Williams Distribution Analysis of LPI Radar Waveforms

459

Figure 13.8: CWD for polytime code T1(2) with B = 1,750 Hz, T = 16 ms, signal only, showing (a) the marginal frequency domain plot and (b) the time-frequency plot.

460

Detecting and Classifying LPI Radar

Figure 13.9: CWD for T1(2) code with B = 1,750 Hz, T = 16 ms, timefrequency plot for (a) SNR = 0 dB and (b) SNR = −6 dB.

Choi-Williams Distribution Analysis of LPI Radar Waveforms

461

Figure 13.10: CWD for Costas code sequence {3, 2, 6, 4, 5, 1} kHz, showing (a) the marginal frequency domain and (b) the time-frequency image.

462

Detecting and Classifying LPI Radar

Figure 13.11: CWD for time-frequency image for Costas code sequence {3, 2, 6, 4, 5, 1} kHz, showing (a) SNR = 0 dB and (b) SNR = −6 dB.

Choi-Williams Distribution Analysis of LPI Radar Waveforms

463

Figure 13.12: CWD for the FSK/PSK signal, showing (a) signal only and (b) SNR = 0 dB.

464

Detecting and Classifying LPI Radar

References [1] Choi, H.I. and Williams W. J., ”Improved Time-Frequency Representation of Multicomponent Signals Using Exponential Kernels,” IEEE Trans. on Acoustics, Speech, and Signal Processing, Vol. 37, No. 6, pp. 862—871, June 1989. [2] D. T. Barry, “Fast calculation of the Choi-Williams time-frequency distribution,” IEEE Trans. on Signal Processing, Vol. 40, No. 2 pp. 450—455, Feb. 1992. [3] Cardoso, J.C., Fish, P. J., and Ruano M. C., ”Parallel Implementation of a Choi-Williams TFD for Doppler Signal Analysis,” Proceedings of the 20th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vol. 20, No. 3, 1998. [4] Harkins, J., El-Ghazawi, T., El-Araby, E., and Huang, M., “Performance of sorting algorithms on the SRC 6 reconfigurable computer,” Proceedings of the IEEE International Conference on Field-Programmable Technology, pp. 295 - 296, 11—14 Dec. 2005. [5] Upperman, G. J., Upperman, T. L. O., Fouts, D. J., and Pace, P. E., “ Eﬃcient time-frequency and bi-frequency signal processing on a reconfigurable computer,” Proceedings of the IEEE Asilomar Conference on Signals, Systems & Computers, 26—29 Oct. 2008.

Problems 1. Using the Choi-Williams distribution, (a) generate the time-frequency results for the random noise radar waveform, the random noise plus FMCW, random noise FMCW plus sine, and random binary phase modulations discussed in Chapter 7. For each waveform, which modulation parameters can be extracted from the Choi-Williams distribution? 2. Using the Choi-Williams distribution, calculate the time-frequency distribution of the (a) polyphase signal that uses one of the orthogonal sequences given in Table 10.12 (ortho40.m), (b) the polyphase signal that uses one of the Doppler-tolerant orthogonal sequences in Table 10.14 (ortho40CE.m), and (c) the frequency hopping signal that uses one of the orthogonal frequency sequences given in Table 10.16 (dfc32.m).

Choi-Williams Distribution Analysis of LPI Radar Waveforms

465

3. To help identify the capability of the Choi-Williams distribution as a tool for identifying the LPI modulation, extracting the modulation parameters, and to aid in deciding on what signal processing algorithm performs best, construct a table to show the Choi-Williams measurement results for the LPI signals contained in the test signals folder. For each parameter of interest, show the actual value, the measured value, and the absolute value of the relative error [see (12.26)]. Compared with Wigner-Ville distribution, the absence of the cross terms should help considerably in identifying the LPI modulation and extracting the modulation parameters.

Chapter 14

LPI Radar Analysis Using Quadrature Mirror Filtering In Chapter 13, it was shown that the Choi-Williams distribution’s timefrequency characteristics are useful for identifying LPI waveform parameters and oﬀered an improvement over the Wigner-Ville analysis due to the suppression of the cross-terms which sometimes gave misleading results. In this chapter, we investigate an LPI intercept receiver, based on a linear decomposition of the received waveform through a quadrature mirror filter bank (QMFB) tree, using wavelet filters. In this approach, the input signal is broken down into a series of time-frequency layers, with each subsequent layer providing a trade-oﬀ in time and frequency resolution. By examining the correct layers, the QMFB time-frequency receiver approach provides good estimates of the LPI signal parameters, making it easy to distinguish between the diﬀerent modulations, and extract the parameter values. Parameters such as bandwidth, center frequency, energy distribution within a tile (region in the time-frequency plane that contains most of the wavelet basis function’s energy), phase modulation, signal duration, and location in the time-frequency plane can be determined. In addition, the number of transmitters present and the types of LPI emitters can be determined. In this chapter, the QMFB theory is presented first, followed by a discussion of the mathematical waveform decomposition using wavelets. The QMFB is then used to analyze and extract the parameters for the LPI signals discussed in Part I. The QMFB folder on the CD provides the MATLAB tools that can be used to re-create any of the figures presented, as well as generate new and useful results. 467

468

14.1

Detecting and Classifying LPI Radar

Time-Frequency Wavelet Decomposition

Various methods of decomposing a waveform on the time-frequency plane have recently been investigated. The most common methods use orthogonal basis functions, and can be divided into linear and bilinear transforms. The short-time Fourier transform (STFT) and the wavelet transform (WT) are examples of linear transforms. The Wigner transform discussed in the previous chapter is an example of a bilinear transform.1 After a discussion of basis functions, the STFT and the WT are discussed, along with their advantages and limitations.

14.1.1

Basis Functions

Linear transforms of a continuous time signal f (t) have the following form ak =

f (t)Φk (t)dt

(14.1)

where Φ(t) is the basis set, t is the time index, and k is the function index. The Fourier transform, for example, has a basis set consisting of sines and cosines of frequency 2πk that oscillate forever. The basis functions are said to be orthogonal if Φ(t)Φ(t − k) = Eδ(k) =

E 0

if k = 0 otherwise

(14.2)

where E stands for the energy of√Φ(t) [1]. If Φ(t) is normalized by dividing by the square root of the energy E, then the basis functions are said to be orthonormal defined by [2] Φ(t)Φ(t − k)dt = δ(k) =

1 if k = 0 0 otherwise

(14.3)

If the basis functions are orthonormal, there is no redundancy in the representation of the signal f (t). If the signal is sampled at or above the Nyquist rate, all of the signal’s information is retained. In this case, the time variable t in (14.1) and (14.3) can be considered to be discrete t = nT where T is the sampling period and the integral should be replaced with summations. 1 Wigner transforms are called bilinear because the input waveform appears twice in the development of the transform. Better resolution occurs in the time-frequency plane than with linear techniques; however, the computational burden is greatly increased and the cross terms can be bothersome for some applications.

LPI Radar Analysis Using Quadrature Mirror Filtering

14.1.2

469

Short-Time Fourier Transform Decomposition

The Fourier transform uses complex sinusoids as basis functions to perform the analysis of signals. This approach is diﬃcult, due to the infinite extent of the basis functions as any time-local information (such as an abrupt change in the signal) is spread out over the entire frequency axis [3]. This problem was addressed by Gabor by introducing windowed complex sinusoids as basis functions. This leads to the doubly indexed windowed Fourier transform: XW F (ω, τ ) =

∞ −∞

e−jωt w(t − τ )x(t)dt

(14.4)

where w(t − τ ) constitutes an appropriate window, and XW F (ω, τ ) is the Fourier transform of x(t) windowed with w(·) shifted by τ . The function of the window is to extract a finite-length portion of the signal x(t) such that the spectral characteristics of the section extracted are approximately stationary over the duration of the window. Also, if w(t) = 1 then the STFT reduces to the conventional Fourier transform of x(t). In most applications, the magnitude of the STFT is of interest, and the display of the STFT magnitude is usually referred to as a spectrogram [4]. The major advantage of the windowed transform or STFT is that if a signal has most of its energy in a given time interval [−T, T ] and frequency interval [−Ω, Ω], then its STFT will be localized in the region [−T, T ]×[−Ω, Ω] and will be close to zero in time and frequency intervals, where the signal has little energy [3]. A limitation of the STFT is that, because a single window is used for all frequencies, the resolution of the analysis is the same at all locations in the time-frequency plane. The possibility of having arbitrarily high resolution in both time and frequency is thus excluded.

14.1.3

Wavelets and the Wavelet Transform

Wavelets are localized basis functions for time-frequency analysis of a signal. That is, the wavelet basis function is eﬀectively nonzero for only a finite time interval, and is designed to satisfy the orthonormality condition (14.3). From a signal processing point of view, a wavelet is a bandpass filter. In the time-frequency analysis, the wavelet filter occurs most often in pairs (a lowpass filter and a highpass filter), and includes a resampling function that is coupled to the filter bandwidth as shown in the two-band analysis bank in Figure 14.1. Here, H0 (z) is the highpass filter and H1 (z) is the lowpass filter. Like the design of conventional digital filters, the design of a wavelet filter can be accomplished by using a number of methods including weighted least squares [5, 6], orthogonal matrix methods [7], nonlinear optimization, optimization of a single parameter (e.g., the passband edge) [8], and a method that minimizes an objective function that bounds the out-of-tile energy [9].

470

Detecting and Classifying LPI Radar

Figure 14.1: Two-band analysis bank. A quadrature mirror filter (QMF) is an iteration of filter pairs with resampling, to generate the wavelets. By varying the window used, resolution in time can be traded for resolution in frequency. To isolate discontinuities in signals, it is possible to use some basis functions, which are very short, while longer ones are required to obtain a fine frequency analysis. One method to achieve this is to have short high-frequency basis functions, and long lowfrequency basis functions [3]. The WT makes this possible by obtaining the basis functions from a single prototype wavelet h(t) using translation, dilation, and contraction as 1 ha,b (t) = √ h a

t−b a

(14.5)

where a is a positive real number and b is a real number. For large a, the basis function becomes a stretched version of the prototype wavelet (low frequency function). For small a, the basis function becomes a contracted wavelet (short high-frequency function). This basis function concept is shown in Figure 14.2(a). The WT is defined as 1 XW (a, b) = √ a

∞ −∞

h∗

t−b a

x(t)dt

(14.6)

The WT divides the time-frequency plane into tiles as shown in Figure 14.2(b). Here, the area of each tile represents (approximately) the energy within the function (rectangular regions of the frequency plane). Note that not all of the signal’s energy can be located in a single tile because it is impossible to concentrate the function’s energy simultaneously in frequency and time. The WT can be interpreted as constant-Q filtering with a pair of subband filters (a lowpass filter and a highpass filter), followed by a sampling at the respective Nyquist frequencies corresponding to the bandwidth of the particular subband of interest.

LPI Radar Analysis Using Quadrature Mirror Filtering

471

Figure 14.2: Basis functions and time-frequency resolution of the wavelet transform: (a) basis functions and (b) coverage of time-frequency plane [3] ( c IEEE 1992).

472

Detecting and Classifying LPI Radar

Figure 14.3: Haar lowpass FIR filter.

14.1.4

Wavelet Filters

Finite impulse response (FIR) filters are the popular choice for the wavelet filter. To meet the requirements for a wavelet filter, the coeﬃcients must ensure an orthogonal decomposition of the input signal, such that the energy at the input will equal the energy at the output from each filter pair [10]. The filter pairs are designed to divide the input signal energy into two orthogonal components based on the frequency. The filter should also pass as much energy within its tile with a flat passband, and reject as much energy outside the tile as possible. Haar Filter A classic example of a wavelet filter is the Haar basis function, which is not continuous but is of interest because of its simplicity. The Haar basis function is ⎧ for 0 ≤ t < 1/2 ⎨ 1 −1 for 1/2 ≤ t < 1 h(t) = (14.7) ⎩ 0 otherwise

and is shown in Figure 14.3. The Haar basis function can serve as a wavelet lowpass FIR filter and has two coeﬃcients, both with values of 1/2. The Haar filter meets the wavelet requirements with the orthonormality being easily verified since, at a given scale, the translations are nonoverlapping [3]. Because of the scale change by 2, the basis functions are orthonormal across scale. Unfortunately, the Haar function is discontinuous. Although the filter meets the wavelet requirements and perfectly tiles the input energy in time, it does not tile well in frequency, and is not appropriate for signal processing. Consequently, a continuous set of basis functions (or filters) is needed that

LPI Radar Analysis Using Quadrature Mirror Filtering

473

Figure 14.4: Sampled sinc filter impulse response. best approximates the perfect time-frequency tiling, by minimizing the outof-time and out-of-frequency energy. Sinc and Modified Sinc Filter A function that tiles the energy perfectly in frequency would have a flat magnitude response across the passband, an infinitely narrow passband-tostopband transition, and a zero across the stopband. From the time-domain description (inverse Fourier transform), the function is called a sinc filter. While it has an infinite number of coeﬃcients, this condition can be modified by windowing [11]. The sinc filter can be expressed as sinc(k) =

sin(πk) πk

1

k=0 k=0

(14.8)

Since the passband ranges from −π/2 < ω < π/2 or −0.25 < f < 0.25, the nulls of the sinc function will be at 2T for a sampling period of T [12]. To obtain the filter coeﬃcients, the sinc function is sampled at the normalized sampling period of T = 1 for a situation similar to that shown in Figure 14.4. One way to sample the function would be to let the main tap sample occur at the center of the main lobe. However, two main taps are needed, and their sum needs to be as large as possible. This occurs for the sinc function if both main tap samples are equally spaced about the center of the main lobe [10]. The sum of the square of √ the coeﬃcients must be unity also, which is achieved by scaling the sinc by 1/ 2, giving 1 h(n) = √ sinc 2 where n is an integer.

n + 0.5 2

(14.9)

474

Detecting and Classifying LPI Radar

This filter meets the criteria of wavelet filters. The only problem is that there is an infinite number of coeﬃcients. A small amount of nonorthogonality will occur when this filter is truncated. Some cross correlation will also take place between both highpass and lowpass filters. If the ends of the filter are simply truncated (a rectangular window in the time domain), some ripples in the passband of the frequency response will appear (Gibb’s phenomena). One solution is to use a nonrectangular window, and one whose Fourier transform has a narrower main lobe and smaller side lobes than the sinc function. The Hamming window is one that is commonly used. Multiplying the coeﬃcients from (14.9) by this window, and using the results in an FIR filter, the frequency response needed is generated. Energy will be lost at the filter transitions, which is primarily the result of the loss of orthogonality from truncating the filter [11]. For detection, instead of losing the energy at those frequencies, a better trade-oﬀ would be a small amount of cross correlation between the filters, so that some energy appears in more than one tile. To achieve this type of prototype filter, the impulse response can be modified to have a passband that is slightly greater than π/2. Thus, the lowpass and highpass filters are squeezed together slightly. This can be achieved by compressing the sinc envelope of (14.9) slightly. At the same time, it is desirable to rescale the coeﬃcients slightly, so the sum of the squares equals one. With these modifications, a modified sinc filter results as [9, 10] h(n) =

S sinc 2

n + 0.5 C

w(n)

(14.10)

where −N/2 ≤ n ≤ (N − 2)/2, C is the compression variable, S is the scaling variable, N is the number of coeﬃcients, and w(n) is the Hamming window to suppress the Gibb’s phenomena. For these filters, the greatest cross correlation occurs between tiles in the same frequency band, and adjacent in time, when N = 512 (the number of coeﬃcients), with values C = 1.99375872328059, S = 1.00618488680080, and a Hamming window with a cross correlation of less than 0.001 results.2 Note the number of coeﬃcients N can be changed using the MATLAB file tsinc su.m.

14.2

Discrete Two-Channel Quadrature Mirror Filter Bank

Digital two-channel QMFB structures have found applications in many areas, including modems, data transmission, image, and video coding. Figure 14.5 2 Personal

communication between P. Jarpa and T. Farrell, March 20, 2002.

LPI Radar Analysis Using Quadrature Mirror Filtering

475

Figure 14.5: Two-channel quadrature mirror filter bank [5] ( c IEEE 2000).

Figure 14.6: Typical frequency response of the analysis filters. shows the basic two-channel QMFB structure consisting of an analysis filter bank and a synthesis filter bank. In the two-channel analysis filter bank, a discrete time signal x[n] is first split into two subbands {vk [n]} by means of the wavelet or analysis filters H0 (z) and H1 (z). The two-band analysis filter bank containing the filters H0 (z) and H1 (z) typically have lowpass and mirrorimage highpass frequency responses, respectively, with a cutoﬀ frequency at π/2 [5, 13]. The typical frequency response of the analysis filters is shown in Figure 14.6. After filtering, each subband signal is downsampled by 2, to form the outputs of the analysis stage. These signals can then be analyzed or processed in various ways, depending on the application. The signals are then transmitted to the “signal synthesis section,” where the signals are upsampled by a factor of 2, and passed through a two-band synthesis filter bank composed of the filters G0 (z) and G1 (z), whose outputs are then added yielding y[n]. The purpose of the synthesis filters is to eliminate the images that are formed in the analysis stage. It follows from the figure that the sampling rates of the input signal x[n] and output signal y[n] are the same. The reconstructed signal y(n) diﬀers, however, from the input x(n) due to aliasing, amplitude distortion, and phase distortion [5, 13]. Consequently, the analysis and the synthesis filters in the QMFB are chosen so as to ensure that the reconstructed output y[n] is a

476

Detecting and Classifying LPI Radar

Figure 14.7: Wavelet filter bank tree filtering the lowpass component (wavelet tiling) [9, 12]. reasonable replica of the input x[n]. Moreover, they are also designed to provide good frequency selectivity, to ensure that the sum of the power of the subband signals is reasonably close to the input signal power.

14.3

Tree Structure to Filter the Lowpass Component

Finite impulse response filters and downsamplers can also be arranged in a tree structure, as shown in Figure 14.7, to eﬀect an orthogonal wavelet decomposition of a signal [9, 12]. This structure filters the lowpass output (H filter) from each stage. The discrete input waveform is denoted as the sequence {c0 } and the output sequences of each branch are as shown in the figure. Since each branch of the tree downsamples by 2, each sequence will have half as many elements as the preceding sequence. A filter tree using the same orthogonal pair of filters throughout and with equal length branches, as in Figure 14.7, yields a rectangular tiling diagram. The time-frequency tiling diagram shown in Figure 14.8 is one method that can be used to describe this decomposition. The time-frequency tile is the region in the plane that contains most of that function’s energy. However, not all of a function’s energy can be located in a tile, because it is impossible to fully concentrate energy simultaneously in time and frequency. The tiles are of diﬀerent shapes, but have a constant area and trade frequency resolution for time resolution, and vice versa.

LPI Radar Analysis Using Quadrature Mirror Filtering

477

Figure 14.8: Time-frequency diagram for the lowpass wavelet filter bank tree [9] ( c IEEE 1999).

Figure 14.9: Wavelet filter bank tree filtering the highpass component.

14.4

Tree Structure to Filter the Highpass Component

The last section demonstrated that by cascading filters and filtering the lowpass component of the previous output, a tiling with finer frequency resolution at lower frequencies was achieved. Now consider the cascading filter diagram in Figure 14.9 where, instead of filtering the lowpass output of each stage, the highpass filter (G filter) output is filtered. Again, the input sequence is split at each stage into high-frequency and low-frequency orthogonal sequences. The tiling diagram is shown in Figure 14.10. Notice that the second and third layers seem to be flipped in Figure 14.9. The figure is drawn so that the output sequence at the top of the drawing contains the highest frequency components of the input sequence. To understand why they are flipped, consider the aliased frequency spectrum of

478

Detecting and Classifying LPI Radar

Figure 14.10: Time-frequency diagram for the highpass wavelet filter bank tree. the filters, shown in Figure 14.11. The output from the G filter in the first layer contains the higher frequency components of the original sequence, but shifted, so that it is actually the dc component of the output of G. The result is that the output of G is frequency reversed, much like the lower sideband of a single sideband communication system. A similar structure farther down the cascade will unflip the signal. It is possible to create another tiling scheme by combining the wavelet filter bank and wavelet tiling, as demonstrated in Figure 14.12. In order to keep the higher frequency outputs of each branch above the lower frequency outputs, the construction rule for this figure is to count the number of G filters up to the branch. If the number is even, the next G filter will output the high frequencies. If odd, the next H filter will output the high frequencies.

14.5

QMFB Tree Receiver

Orthogonal wavelet decomposition of the unknown signal can be implemented using QMFs, by designing filter pairs to divide the input signal energy into two orthogonal components, based on frequency. The tiles are used to refer to the rectangular regions of the time-frequency plane containing the basis function’s energy. By arranging the QMF pairs in a fully developed tree structure, it is possible to decompose the waveform in such a way that the tiles have the same dimensions within each layer. Thus, every filter output is connected to a QMF pair in the next layer, as shown in Figure 14.13 [10]. Each QMF pair divides the digital input waveform into its high-frequency and low-frequency components, with a transition centered at π. A normalized input of one sample per second is assumed, with a signal bandwidth of [0, π]. Since each filter output signal has half the bandwidth, only half the samples are required

LPI Radar Analysis Using Quadrature Mirror Filtering

479

Figure 14.11: Frequency response of filters H and G. to meet the Nyquist criteria; therefore, these sequences are downsampled by two. The same number of output samples is returned. For example, if 100 samples appear at the input of the first QMF pair, 100 samples appear at the output. Each of the two resulting sequences is then fed into QMF pairs, forming the next layer, where the process is repeated, and so on down the tree. Within the time-frequency plane, the WT is sharper in time at high frequencies. At low frequencies, the WT is sharper in frequency. That is, the tiles become shorter in time and occupy a larger frequency band, as the frequency is increased. Since the WT is linear, there is a fundamental limit on the minimum area of these tiles. However, the nature of the QMFB configuration is such that each layer outputs a matrix of coeﬃcients for tiles that are twice as long (in time) and half as tall (in frequency) as the tile in the previous layer. The outputs from each layer of the tree in Figure 14.13 form a matrix whose elements, when squared, approximately represent the energy contained in the tiles of the corresponding time-frequency diagrams shown in the figure. The block diagram of a receiver that uses the QMFB structure is shown in Figure 14.14. A received waveform is bandpass filtered and sampled at the Nyquist rate. The digital sequence is then fed to the QMFB tree where it is decomposed. Matrices of values are output from each layer, and are then squared to produce numbers representing the energy in each tile. Wavelet decomposition has been investigated as a tool for pattern recogni-

480

Detecting and Classifying LPI Radar

Figure 14.12: Combining the wavelet filter bank and wavelet tiling. (Downsampling by 2 is included in each filter box.)

LPI Radar Analysis Using Quadrature Mirror Filtering

481

Figure 14.13: Quadrature mirror filter bank tree [10] ( c IEEE 1996).

Figure 14.14: Quadrature mirror filter bank tree receiver [10] ( c IEEE 1996).

482

Detecting and Classifying LPI Radar

tion and target detection [14], and also as a means for identifying signal modulations [15]. The architecture discussed above has been used to investigate the detection of LPI signals in [16—19], and is used below to investigate the parameters of the signals in Part I. We start with two example calculations, to become familiar with the QMFB processing and its output waveforms.

14.6

Example Calculations

In this section two example calculations are shown for a complex input. A complex single-tone example is shown first, followed by a two-tone signal. These examples serve to demonstrate the diﬀerent QMFB output layers, and show the trade-oﬀ in time-frequency resolution as a function of the layer number being examined. The lower the layer number, the smaller (better) the resolution in time, and consequently the larger (poorer) the resolution in frequency. As the layer number gets larger, the resolution in time gets larger, and the resolution in frequency gets smaller.

14.6.1

Complex Single-Tone Signal

To demonstrate the results available from the QMFB signal processing, we again consider a complex, single-tone signal as in Chapter 9. The signal has a carrier frequency fc = 1 kHz and is sampled by the ADC at a rate of 7 kHz. The results, shown in Figure 14.15 show layers 2, 3, and 4, respectively, in the time-frequency domain using gray scale plots. Figure 14.16(a, b), show layers 5 and 6. One of the important objectives of showing the five layers of the QMFB is to demonstrate how each layer results in a matrix of energy values, and the fact that the tiles are twice as long (in time) and half as tall (in frequency) as the tile in the previous layer. That is, as the layer number increases, the frequency resolution gets smaller, and the time resolution gets larger. This adds quite a bit of flexibility to the analysis of nonstationary signals. Several diﬀerent layers can be examined and compared, and the parameters of the signals can be extracted with high fidelity. Also, since the first and last layer in the QMFB are a single row of data, it is not useful to display them in a time-frequency format. The input signal is zero padded with z zeros, such that the resulting number of data points is a power of 2. This resulting power of 2 is the number of layers L within the QMFB that result. That is, Np = 2L . The QMFB output resolution depends on the layer number. The frequency resolution of a layer l is [19] fs fs = (14.11) ∆f = l 2(2 − 1) 2(NF )

where NF is the number of tiles displayed in frequency. For example, for layer 2 in Figure 14.15, ∆f = 7,000/2(3) = 1,166.67 Hz. The resolution in time is

LPI Radar Analysis Using Quadrature Mirror Filtering

483

Figure 14.15: Time-frequency layers for the 1-kHz single-tone signal, showing (a) layer 2, (b) layer 3, and (c) layer 4.

484

Detecting and Classifying LPI Radar

Figure 14.16: Time-frequency layers for the 1-kHz single-tone signal, showing (a) layer 5, and (b) layer 6.

LPI Radar Analysis Using Quadrature Mirror Filtering

485

determined by how many samples are integrated within the QMFB. For layer l < L, Np Np = (14.12) ∆t = L−l fs (2 − 1) fs NT

where L is the total number of layers, and NT is the number of tiles in time. Also, Np = 2L . For example, for layer 2 in Figure 14.15, ∆t = 128 (1/7,000)/31 = 590 μs. Also note that the lower layers (e.g., layers 2 and 3) can be used to identify how many samples of the signal were collected (excluding zero padding). Since the sampling period for this example is T = 0.143 ms, from layer 2 we see that 105 samples were collected, and that 23 zeros were used to pad the signal. Referring to layer l = 6 in Figure 14.16(b), the tiles have a frequency resolution of ∆f = 55.5556 Hz and a resolution in time of ∆t = 18.286 ms. Layer 6 shows the signal between 944.445 Hz and 1055.56 Hz, and from 0 to 18.286 ms. That is, we can say that fc ≈ 1,000 Hz with the accuracy limited by the tile resolution. Note that if more detailed time information is required, a lower layer could be examined.

14.6.2

Complex Two-Tone Signal

The second example consists of a signal with two frequencies fc1 = 1 kHz and fc2 = 2 kHz, with a sampling frequency fs = 7 kHz. In this example, a contour plot is used. Although the gray scale plot illustrated above quantifies the energy within each tile, the contour plot is useful for other types of information (such as time-domain characteristics), as illustrated in the results below. The number of signal samples collected, the time resolution ∆t, and frequency resolution ∆f for each layer within the QMFB are the same as for the single-tone example above. Figure 14.17 shows the contour plot for layers 2 through 4. Figure 14.18 shows the contour plot for layers 5 and 6. As before, layers 1 and 7 are not displayed, since they have only a single row vector of data. This example illustrates the important concepts that are evident using a contour image. First, for lower layers such as layer 2 and layer 3, the time domain characteristics of the signals can be clearly identified. In layer 2, the complex phase interaction in time, of the two signals within a single filter, can also be identified. The high-frequency resolution layers [such as layer 6 shown in Figure 14.18(b)] reveal the frequencies contained in the input signal with a good amount of accuracy (∆f = 55 Hz).

486

Detecting and Classifying LPI Radar

Figure 14.17: Time-frequency layers for the two-tone signal (1 kHz, 2 kHz), showing (a) layer 2, (b) layer 3, and (c) layer 4.

LPI Radar Analysis Using Quadrature Mirror Filtering

487

Figure 14.18: Time-frequency layers for the two-tone signal (1 kHz, 2 kHz), showing (a) layer 5, and (b) layer 6.

14.7

FMCW Analysis

In this section, the extraction of FMCW signal parameters (discussed in Chapter 4) is demonstrated using the QMFB, and the appropriate layers for parameter extraction are identified. The first example is shown in Figure 14.19. In Figure 14.19(a), the l = 2 layer is shown. For the number of signal samples collected, L = 11 (Np = 2, 048). For layer l = 2, ∆f = 1,166.67 Hz and ∆t = 572.5 μs. For this signal, it appears that four periods of the triangular FMCW waveform were captured. The waveforms also have the general appearance of a linear FM modulation. The modulation period tm can be measured as tm = 20 ms, for a total signal length of 160 ms. Notice that the concentrations of energy within each period of the FMCW waveform are not centered on the carrier frequency fc = 1,000 Hz, but contain a 300-Hz bias. This is due to the fact that there are only three filters in this layer being used to calculate the results. In Figure 14.19(b), layer l = 6 is shown with ∆f = 55.55 Hz and ∆t = 8.866 ms. This layer is appropriate, since the time resolution ∆t < tm /2. Note that the modulation period can be easily identified and measured. Since this layer also has 63 filters, each with a narrow filter width, the bandwidth ∆F can be measured with good accuracy, as ∆F = 250 Hz. Figure 14.20 shows the QMFB layer 5 performance against the FMCW

488

Detecting and Classifying LPI Radar

Figure 14.19: QMFB contour images for FMCW ∆F = 250 MHz, tm = 20 ms (signal only), showing (a) layer 2, and (b) layer 6.

LPI Radar Analysis Using Quadrature Mirror Filtering

489

Figure 14.20: QMFB contour image for FMCW ∆F = 250 MHz, tm = 20 ms (signal only), showing layer 5 with SNR = 0 dB. signal with SNR = 0 dB. Note that the parameters of the signal can still be measured satisfactorily. Appendix I presents the results for an FMCW signal with ∆F = 500 Hz.

14.8

BPSK Analysis

In this section, the QMFB is used to investigate the properties of the binary phase shift keying signal discussed in Chapter 5, and also investigated in Chapter 9 with the PVWD. The signal parameters that were changed include the length of the Barker code (7 or 11), and the SNR (signal only, SNR = 0 dB, SNR = −6 dB). In the first example, fc = 1 kHz, fs = 7 kHz, and cpp = 1, and a 7-bit Barker code is used. The total number of layers is L = 11 (Np = 2,048), and the layers investigated for this signal are l = 3 and l = 6. Figure 14.21(a) shows the l = 3 layer (∆f = 500 Hz, ∆t = 1.15 ms), and the 25 BPSK code periods captured. The number of subcodes within a code period T cannot, however, be distinguished with this particular QMFB layer and scaling. A closer look however is illustrated in Figure 14.21(b). In this figure (∆f = 500 Hz, ∆t = 286 μs), a concentration of energy can be located near the beginning of each code period (along the carrier frequency fc = 1 kHz). This is due to the three contiguous subcodes, all with the same phase. The

490

Detecting and Classifying LPI Radar

code period can be measured between these energy concentrations as T = 7 ms. Note that care must be exercised in this measurement, since a secondary feature could be used, resulting in T ≈ 14 ms. The total length of the signal is 25 times 7 ms = 0.175s and can also be identified in Figure 14.21(a). Figure 14.22(a) examines the l = 6 layer (∆f = 55 Hz, ∆t = 9.44 ms) to further evaluate the frequency content of the signal at a higher resolution. The first important feature is the frequency bands, due to the various lengths of subcode groups within the code period. The overall bandwidth of the signal B = fc /cpp is also shown, and depends on the length of a single subcode. Figure 14.22(b) shows the same layer 6, except that the SNR = 0 dB, and demonstrates the eﬀects of noise on the QMFB output. To further illustrate the QMFB capability to analyze the microstructure of the phase-modulated signal, cpp is increased from 1 to 5. That is, the bandwidth of the signal is narrowed from 1 kHz to B = fc /cpp = 0.2 kHz (code period of T = cpp/fc = 35 ms). Figure 14.23(a) shows the QMFB layer 2 for two code periods of the 7-bit signal. The important feature illustrated here is the presence of a null at each BPSK phase shift. After the total code period T is determined, the measurement of the smallest subphase code is performed (time is measured between the two closest nulls). After this, the number of subphase codes contained within each section of the code is determined, which then uniquely identifies which BPSK code has been intercepted. Figure 14.23(b) shows the QMFB layer 6. Note that the code period T is clearly identified, as well as the bandwidth. The QMFB results for an 11-bit code are shown in Appendix J. Figure 14.24 shows the QMFB layer 6 performance against the BPSK signal, with SNR = 0 dB and cpp = 5. The parameters of the signal such as the code period, carrier frequency, and bandwidth, can still be measured satisfactorily. For layer 2, however, the noise severely distorts the time-frequency results, and identification of the phase nulls is not possible, making it difficult to identify the exact binary phase code used, without further image processing.

LPI Radar Analysis Using Quadrature Mirror Filtering

491

Figure 14.21: QMFB layer 3 contour plot for BPSK with 7-bit Barker code, cpp = 1 (signal only), showing (a) the complete captured signal, and (b) a close-up view showing the code period T = 7 ms.

492

Detecting and Classifying LPI Radar

Figure 14.22: QMFB layer 6 for BPSK with 7-bit Barker code with cpp = 1, showing the (a) contour image (signal only), and (b) contour image with SNR = 0 dB.

LPI Radar Analysis Using Quadrature Mirror Filtering

493

Figure 14.23: QMFB contour images for BPSK with 7-bit Barker code, cpp = 5 (signal only), showing (a) layer 2, and (b) layer 6.

494

Detecting and Classifying LPI Radar

Figure 14.24: QMFB layer 6 contour image for BPSK cpp = 5 signal, with SNR = 0 dB.

14.9

Polyphase Code Analysis

In this section we examine the polyphase codes with the QMFB, beginning with the Frank code. In Chapter 5 we saw that the Frank code is derived from a linear FM waveform. The phase modulation is applied both to the I and Q signals, which are 90 degrees out of phase. In this and the following sections, it is shown that the QMFB can be used to not only identify a particular type of phase modulation, but also to extract the important parameters of the signal. The Frank phase code signal is generated with Nc = 64 (M = 8). The phase codes for M = 8 are shown in Figure 14.25. This is demonstrated in the QMFB l = 2 layer shown in Figure 14.26. The number of layers in this example is L = 12 (Np = 4,096). For this layer ∆f = 1,166.67 Hz, and ∆t = 571.99 μs (small diﬀerence). In Figure 14.26(a), the additional 48 subcodes within a code period results in a longer duration signal. The five code periods have a total length of 320 ms. Figure 14.26(b) shows a close-up of the frequency characteristics within a code period. The linear frequency modulation characteristics are viewed in the QMFB l = 5 layer in Figure 14.27(a, b). Here, the bandwidth can be clearly identified, as well as the code period T = 64 ms. Note the wraparound characteristic within the bandwidth, similar to the 16-subcode example above. Correlation of the

LPI Radar Analysis Using Quadrature Mirror Filtering

495

Figure 14.25: Frank code phase values for M = 8. occurrence in time of the eight major energy concentrations within T , with the M = 8 Frank phase modulation waveform sections, can be easily made. The distribution of the signal energy within the nine frequency tiles within B helps in identifying the phase code, and in distinguishing between the modulation characteristics. The frequency characteristics for the M = 8 Frank code is shown in Figure 14.28. The energy is distributed about the carrier frequency in a Gaussian-type distribution, with the carrier frequency fc centered about tile nine (the tile with the largest energy content). In fact, from Figure 14.28 the five largest energy tiles (in order from largest to smallest) are 9, 10, 7, 11, and 8. Figure 14.29 shows the l = 6 layer results for the M = 8 Frank code with the SNR = 0 dB. Note that the parameters can still be measured quite accurately. The QMFB results for the Nc = 16 Frank signal (M = 4) are given in Appendix K and the results for the P1, P2, P3, and P4 are given in Appendix L.

14.10

Polytime Code Analysis

In this section the T1(2) polytime code is analyzed using the QMFB. Figure 14.30 shows the QMFB contour images for the polytime T1(2) code with a resulting B = 1,750 Hz, T = 16 ms (signal only). The QMFB for this signal has l = 10 layers. Figure 14.30(a) shows the layer 2 output, and Figure 14.30(b) shows a close-up of layer 2, showing the frequency changes due to binary phase code that varies as a function of time. Figure 14.31(a) shows the fourth layer QMFB contour images for the polytime T1(2) code. Figure 14.31(b) shows a close-up of layer 4, showing the resulting linear fre-

496

Detecting and Classifying LPI Radar

Figure 14.26: QMFB contour images for M = 8 Frank code with B = 1,000 Hz, T = 64 ms (signal only), showing (a) layer 2 output, and (b) close-up of layer 2, showing detailed frequency changes due to phase codes.

LPI Radar Analysis Using Quadrature Mirror Filtering

497

Figure 14.27: QMFB contour images for M = 8 Frank code with B = 1,000 Hz, T = 64 ms (signal only), showing (a) layer 5 output, and (b) close-up of layer 5, showing resulting linear frequency modulation.

498

Detecting and Classifying LPI Radar

Figure 14.28: QMFB layer 5 frequency profile for Nc = 64 Frank code.

Figure 14.29: QMFB layer 6 contour image for Frank Nc = 64 signal with SNR = 0 dB.

LPI Radar Analysis Using Quadrature Mirror Filtering

499

quency modulation. Note that the resulting bandwidth is easily identified. The QMFB results for the T2(2) to T4(2) are shown in Appendix M.

14.11

Costas Frequency Hopping Analysis

In this section, five code periods of a Costas frequency hopping signal are examined. The Costas code within each period is 4, 7, 1, 6, 5, 2, and 3 kHz. In Figure 14.32(a), the QMFB layer 4 shows that the frequencies can easily be identified. The close-up in Figure 14.32(b) reveals that no modulation is present on the frequency. Figure 14.33 shows layer 6 with a finer frequency resolution. Note the spread in time, demonstrating the trade-oﬀ in resolution from one layer to the next.

14.12

FSK/PSK Signal Analysis

When a binary phase code modulation is added to the frequency hopping signal, the bandwidth about the carrier is increased. The QMFB layer 4 results for the FH code above, with a binary 5-bit Barker code added, is shown in Figure 14.34. Note that in the close-up figure, the phase modulation is clearly present. In Figure 14.35, the QMFB layer 6 is shown. Due to the decrease in time resolution, the phase modulation is not as distinct as in layer 4.

14.13

Noise Waveform Analysis

The random noise waveforms discussed in Chapter 7 can also be examined with the QMFB. In Figure 14.36, a random noise waveform that has a bandwidth of B = 300 MHz, carrier frequency of fc = 350 MHz and a code period of T = 4 μs is examined with the QMFB layer 6 (out of 13). Note that the bandwidth can be easily identified as well as the carrier frequency and code period. The random noise plus triangular FMCW waveform with tm = 1 μs, ∆F = 300 MHz, B = 300 MHz, and fc = 350 MHz is shown in Figure 14.37. Note in layer 6 the noise bandwidth and the FMCW modulation are easily identified. The use of the QMFB to examine the random noise FMCW plus sine waveform is left as an exercise for the reader. The random binary phase modulation waveform is shown in Figure 14.38 using layer 7. For this waveform, fc = 300 MHz, cpp = 3, and tb = 10 ns. With Nc = 64 and 5 code periods included, T = 3.2 μs. These signal parameters can be easily identified from layer 7. For the signal only, layer 2 is examined in Figure 14.39 and shows the direct correlation of the phase modulation parameters used.

500

Detecting and Classifying LPI Radar

Figure 14.30: QMFB contour images for polytime T1(2) code with resulting B = 1,750 Hz, T = 16 ms (signal only), showing (a) layer 2 output, and (b) close-up layer 2, showing detailed frequency changes due to phase codes.

LPI Radar Analysis Using Quadrature Mirror Filtering

501

Figure 14.31: QMFB contour images for polytime T1(2) code with resulting B = 1,750 Hz, T = 16 ms (signal only), showing (a) layer 4 output, and (b) close-up of layer 4 showing resulting linear frequency modulation.

502

Detecting and Classifying LPI Radar

Figure 14.32: QMFB contour images for layer 4 for FSK code using Costas sequence, showing (a) layer 4 output, and (b) close-up of layer 4 showing frequency resolution.

LPI Radar Analysis Using Quadrature Mirror Filtering

503

Figure 14.33: QMFB contour images for layer 6 for FSK code using Costas sequence, showing (a) layer 6 output, and (b) close-up of layer 6 showing frequency resolution.

504

Detecting and Classifying LPI Radar

Figure 14.34: QMFB contour images for layer 4 for FSK/PSK code using Costas sequence plus 5-bit Barker code cpp = 5 (signal only), showing (a) layer 4 output, and (b) close-up of layer 4 showing Barker phase modulation.

LPI Radar Analysis Using Quadrature Mirror Filtering

505

Figure 14.35: QMFB contour images for layer 6 for FSK/PSK code using Costas sequence plus 5-bit Barker code cpp = 5 (signal only), showing (a) layer 6 output, and (b) close-up layer 6 showing Barker phase modulation.

506

Detecting and Classifying LPI Radar

Figure 14.36: QMFB contour image for the random noise waveform showing the extraction of the bandwidth and carrier frequency from l = 6.

14.14

Summary

The QMFB theory was presented in this chapter and several examples were used to demonstrate the time-frequency results. To extract the unknown signal parameters, several layers must be examined to determine those that provide the best information. The phase changes can be identified from the lower layers, while the frequency information is best obtained from the higher layers. Contrary to the Wigner-Ville distribution, and Choi-Williams distribution, the QMFB performs remarkably well for the FSK Costas code and FSK/PSK (binary phase code) signal. Not only were the frequency hops identified, but the frequency duration could also be indentified, as well as the binary phase modulation if present. For the FSK/PSK target signal reported, the QMFB was not able to identify any meaningful signal parameters for the same reason that the PWVD could not. The use of the QMFB was also demonstrated to work remarkably well with the random noise modulations. The main drawback is the fact that even if the most useful results are from, for example, layer 7, all of the other layers prior to layer 7 must still be computed. The presentation of the QMFB results to a trained operator will allow the signal parameters to be extracted, and can enable good classification results

LPI Radar Analysis Using Quadrature Mirror Filtering

507

Figure 14.37: QMFB contour image for the random noise plus FMCW waveform showing the extraction of the noise bandwidth, FMCW modulation, and carrier frequency.

Figure 14.38: QMFB contour image layer 7 for the random binary phase modulation showing the extraction of the bandwidth, and carrier frequency.

508

Detecting and Classifying LPI Radar

Figure 14.39: QMFB contour image layer 2 for random binary phase modulation showing the direct correlation of the phase modulation used to create one code period.

LPI Radar Analysis Using Quadrature Mirror Filtering

509

when the information from several layers is combined. The use of the QMFB in noisy environments, however, gives problems in parameter identification, and further image processing is necessary.

References [1] Burrus, C. S., Gopinath R. A., and Guo, H., Introduction to Wavelets and Wavelet Transforms, A Primer, Prentice Hall, Upper Saddle River, NJ, 1998. [2] Chui, C. K., Wavelets: A Mathematical Tool for Signal Analysis, First Edition, SIAM, Philadelphi, PA, 1997. [3] Vetterli, M., and Herley, C., “Wavelets and filter banks: Theory and design,” IEEE Trans. on Signal Processing, Vol. 40, No. 9, pp. 2207—2232, Sept. 1992. [4] Mitra, S., Digital Signal Processing, A Computer-Based Approach, Second Edition, McGraw-Hill, Boston, MA, 2001. [5] Al-Namiy, F., and Nigam, M. J., “On the design of 2-band FIR QMF filter banks using WLS techniques,” Proc. of the Fourth IEEE International Conference on High Performance Computing in the Asia-Pacific Region, Vol. 2, pp. 772—776, May 2000. [6] Goh, C. K., and Lim, Y. C., “A WLS algorithm for the design of low-delay quadrature mirror filter banks,” Proceedings of the IEEE International Symposium on Circuits and Systems, Vol. 1, pp. 615—618, May 2000. [7] Zahhad, A., and M. A. Sabah, “Design of selective M-channel perfect reconstruction FIR filter banks,” IEE Electronics Letters, Vol. 35, No. 15, pp. 1223—1225, 1999. [8] Zhang, Z., and L. Jiao, “A simple method for designing pseudo QMF banks,” Proceedings of the IEEE International Conference on Communication Technology, Vol. 2, pp. 1538—1541, Aug. 2000. [9] Farrell, T., and Prescott, G., “A Method for Finding Orthogonal Wavelet Filters with Good Energy Tiling Characteristics,” IEEE Trans. on Signal Processing, Vol. 47, No. 1, pp. 220—223, Jan. 1999. [10] Farrell, T., and Prescott, G., “A Nine-Tile Algorithm for LPI Signal Detection Using QMF Filter Bank Trees,” Proceedings of the IEEE Conference on Military Communications MILCOM ’96, Vol. 3, pp. 974—978, 1996. [11] Proakis, J., and Manolakis, D., Digital Signal Processing. Principles, Algorithms, and Applications, Third Edition, Prentice Hall, Upper Saddle River, NJ, 1996. [12] Herley, C., et. al., “Tilings of the time-frequency plane: Construction of arbitrary orthogonal bases and fast tiling algorithms,” IEEE Transactions on Signal Processing, Vol. 41, No. 12, pp. 3341—3359, Dec. 1993. [13] Shang, Y., Longzhuang, L., and Ho, K. C., “Optimization design of filter banks for wavelet denoising,” Proceedings of the 5th International Conference on Signal Processing, Vol. 1, pp. 306—310, Aug. 2000.

510

Detecting and Classifying LPI Radar

[14] Chan, L. A., and Nasrabadi, N. M., “An application of wavelet-based vector quantization in target recognition,” Proceedings of the IEEE International Joint Symposium on Intelligence and Systems, pp. 274—281, Nov. 1996. [15] Ho, K. C., Prokopiw W., and Chan, Y. T., “Modulation identification of digital signals by the wavelet transform,” IEE Proceedings Radar, Sonar and Navigation, Vol. 147, No. 4, pp. 169—175, Aug. 2000. [16] Farrell, T., and Prescott, G., “A Low Probability of Intercept Signal Detection Receiver Using Quadrature Mirror Filter Bank Trees,” IEEE International Conference on Acoustics, Speech and Signal Processing, Vol. 3, pp. 1558— 1561, March 1996. [17] Copeland, D. B., and Pace, P. E., “Detection and analysis of FMCW and P-4 polyphase LPI waveforms using quadrature mirror filter trees,” Proceedings of the IEEE International Conference on Acoustics Speech and Signal Processing, Vol. 1, May 2002. [18] Taboada, F., et al., “Intercept receiver signal processing techniques to detect low probability of intercept radar signals,” Proceedings of the 5th Nordic Signal Processing Symposium, Hurtigruta Tromso, Norway, Oct. 2002. [19] Jarpa, P., “Quantifying the diﬀerences in low probability of intercept radar waveforms using quadrature mirror filtering,” Naval Postgraduate School Master’s Thesis, Sept. 2002.

Problems 1. (a) Using the LPIT, generate the FMCW waveform (signal only, SNR = 0 dB, and SNR = −6 dB) with a carrier frequency of 2 kHz, tm = 5 ms, and ∆F = 500 Hz. (b) Process the signals with the QMFB algorithm. (c) For each useful layer, diagram your estimates of all the signal parameters for signal only, SNR = 0 dB and SNR = −6 dB. 2. (a) Using the LPIT, generate a P4 waveform (signal only, SNR = 0 dB, and SNR = −6 dB) with a carrier frequency of 2 kHz, Nc = 128, tb = 1 ms, and fs = 7,000 Hz. (b) Process the signals with the QMFB algorithm. (c) For each useful layer, diagram your estimates of all the signal parameters for signal only, SNR = 0 dB, and SNR = −6 dB. 3. (a) Using the LPIT, generate the default FMCW waveform and the default P4 waveform. Load both signals into MATLAB, and truncate such that they both have the same size (be sure to at least include 1 to 2 code periods of each signal). (b) Add the two signals together and save as a new signal (e.g., fmcw p4.mat). (c) Using the QMFB processing, analyze the signal and extract the waveform parameters for each signal that is evident. (d) Repeat (b) and (c) for SNR = 0 dB. (e) Repeat (b) and (c) for SNR = −6 dB.

LPI Radar Analysis Using Quadrature Mirror Filtering

511

4. Using the QMFB tools, (a) add a tic and tock command to the program and then (b) examine the random noise, random noise plus FMCW, random noise FMCW plus sine, and random binary phase modulations discussed in Chapter 7. Be sure to record the amount of time it takes to compute the results. 5. The MATLAB program tsinc su.m, allows you to change the number of filter coeﬃcients used in the wavelet pairs. Use the program to change the number of filter coeﬃcients from 512 to 128. Work the problem above with this new filter configuration and note the amount of time needed. 6. (a) For the 512 filter coeﬃcients, calculate the group delay of the filter. (b) Since the number of filter coeﬃcients is the same for all wavelet pairs, the group delay of each layer is also the same. If the ADC sampling rate is fs = 7,000 Hz calculate how many layers can be computed if the results must be calculated in real time (time to gather the input signal record equals the time to process the signal record). 7. To help identify the capability of the quadrature mirror filter bank analysis as a tool for identifying the LPI modulation, extracting the modulation parameters, and to aid in deciding on what signal processing algorithm performs best, construct a table to show the quadrature mirror filter bank measurement results for the LPI signals contained in the test signals folder. For each parameter of interest, show the actual value, the measured value, and the absolute value of the relative error [see (12.26)]. Be sure to include the layer that is used for identifying the diﬀerent parameter values being measured.

Chapter 15

Cyclostationary Spectral Analysis for Detection of LPI Radar Parameters The Wigner-Ville distribution (Chapter 12), the Choi-Williams distribution (Chapter 13) and the quadrature mirror filter bank processing (Chapter 14) together give time-frequency results that allow the LPI parameters to be determined with good accuracy. This chapter presents an additional bifrequency spectral analysis technique, known as cyclostationary processing, that oﬀers some additional capability in the detection and classification of LPI modulations. Instead of examining the LPI signals in the time-frequency domain, cyclostationary processing transforms the signal into the frequency-cycle frequency domain. Two eﬃcient methods for computing the cyclostationary spectrum are presented: the time-smoothing FFT accumulation method, and the direct frequency-smoothing method. The cyclostationary signal processing is then used to extract the parameters from the LPI radar waveforms discussed in Part I. The folder titled CYCLO contains the signal processing MATLAB files that allow the user to re-create any of the results presented, as well as new results of interest.

15.1

Introduction

Since the development of the theoretical concepts by Gardner in the early 1980s, much work has been carried out to investigate the potential of cyclostationary spectral analysis for many signal processing tasks. Cyclostationary processing has been investigated for use in the detection and identification of 513

514

Detecting and Classifying LPI Radar

weak spread-spectrum communication signals [1—3] and SATCOM signals [4]. Cyclostationary signal models have also been used in array signal processing for estimating the direction of arrival of multiple narrowband signals [5], as well as building adaptive arrays [6, 7]. The estimation and detection of radar signal parameters have been investigated [8—10]. In this chapter, a thorough treatment of this application is presented. Cyclostationary spectral analysis is based on modeling the signal as a cyclostationary process rather than a stationary process. A signal is cyclostationary of order n if and only if one can find some nth order nonlinear transformation of the signal that will generate finite-strength additive sine wave components that result in spectral lines [11]. For example, an n = 2 or quadratic transformation (like the product of the signal with a delayed version of itself, often used to detect BPSK signals) will generate spectral lines. That is, a signal x(t) is cyclostationary with cycle frequency α, if and only if at least some of its delay product waveforms, z(t) = x(t − τ )x∗ (t) for some delays τ , exhibit a spectral line at frequency α, and if and only if the time fluctuations in at least some pairs of spectral bands of x(t), whose two center frequencies sum to α, are correlated. In contrast, for stationary signals, only a spectral line at frequency zero can be generated. For signals with periodic features (e.g., LPI radar signals), the advantage of using a cyclostationary model is that nonzero correlation is exhibited between certain frequency components when their frequency separation is related to the periodicity of interest. Applications that use cyclostationary spectral analysis include time diﬀerence of arrival estimation, signal detection, identification, and parameter estimation. Many useful characteristics of LPI radar signals can be determined, and are reflected in the cyclic autocorrelation function and the spectral correlation density, which form the basis for cyclic spectral analysis. These concepts are discussed below.

15.1.1

Cyclic Autocorrelation

To discuss the cyclic autocorrelation, we begin with the definition of the correlation integral. The correlation integral is defined as 8 ∞ f (u)g(x + u)du (15.1) Rc (x) = −∞

Applying the FFT to both sides gives F {Rc (x)} = F (s)G∗ (s)

(15.2)

If f (x) and g(x) are the same function, the integral above is called the autocorrelation function and cross correlation if they diﬀer. The autocorrelation function is a quadratic transformation of the signal, and may be interpreted as a measure of the predictability of the signal at time t + τ based on knowledge of the signal at time t. When considering a time series of length T , the

Cyclostationary Spectral Analysis for Detection of LPI Parameters

515

autocorrelation function becomes the time-average autocorrelation function given by 8 τQ ∗p τQ 1 T /2 p Rx (τ )= ˆ lim x t+ x t− dt (15.3) T →∞ T −T /2 2 2

The cyclic autocorrelation of a complex-valued time series x(t) is then defined by [12] 1 T →∞ T

ˆ lim Rxα (τ )=

8

p τQ ∗p τ Q −j2παt x t+ dt x t− e 2 2 −T /2 T /2

(15.4)

and can be interpreted as the Fourier coeﬃcient of any additive sine wave component with frequency α that might be contained in the delay product (quadratic transformation) of x(t). The nonzero correlation (second-order periodicity) characteristic of a time series x(t) exists in the time domain, if the cyclic autocorrelation function is not identically zero. That is, the signal x(t) is said to be cyclostationary if Rxα (τ ) does not equal zero at some time delay τ (any real number) and cycle frequency α = 0.

15.1.2

Spectral Correlation Density

Recall that the power spectral density is defined as the Fourier transform of the autocorrelation function 8 ∞ Rx (τ )e−j2πf τ dτ (15.5) Sx (f ) = −∞

In the same manner, the spectral correlation density (SCD), or cyclic spectral density, is obtained from the Fourier transform of the cyclic autocorrelation function (15.4) as [12] 8 ∞ p αQ ∗ p αQ 1 XT f + ˆ Rxα (τ )e−i2πf τ dτ = lim XT f − (15.6) Sxα (f )= T →∞ T 2 2 −∞ where α is the cycle frequency and ˆ XT (f )=

8

T /2

x(u)e−j2πf u du

(15.7)

−T /2

which is the Fourier transform of the time domain signal x(u). The additional variable α (cycle frequency) leads to a two-dimensional representation Sxα (f ); namely, the bifrequency plane (f , α) [12]. Measurement of (15.4) and (15.6) in signal analysis constitutes what is referred to as cyclic spectral analysis. Good insight is gained if we examine a second-order cyclostationary process and compare the time-domain implementation and the frequency-domain implementation. In Figure 15.1 it is shown that the time-domain implementa-

516

Detecting and Classifying LPI Radar

Figure 15.1: Time-domain implementation of a second-order cyclostationary process. tion consists of a delay (τi ) and multiply operation followed by the multiplication by the exponential cycle frequency term. The expected value then gives ˆ xα (τ ) and the subsequent FFT gives the the cyclic autocorrelation function R α ˆ spectral correlation density Sx (f ). With this perspective, it is easy to see that if the signal x(t) contains a periodic component and the delay is chosen properly, a strong sinusoid will be present at the output. A frequency-domain implementation of a second-order cyclostationary process is shown in Figure 15.2. The input signal x(t) with spectral representation X(ν), is split into two channels and multiplied by the two exponential factors that are a function of the cycle frequency and are complex conjugates of each other. The time-domain output signals are u(t) and s(t) which have spectral representations of U (ν) and S(ν) respectively. This time-domain multiplication results in a spectral shift of u(t) by −α/2 and a spectral shift of s(t) by α/2. Figure 15.3 shows the spectral representations X(ν), U (ν), and S(ν) and illustrates the narrowband spectral components of x(t) being aligned at ν = f . Both u(t) and s(t) are filtered with a bandpass filter with bandwidth B and center frequency f . Note that this captures the narrowband spectral components of x(t) centered at f + α/2 and f − α/2. The Fourier transform is taken of both filter outputs and then the correlation of the two spectrums is computed. The expected value of the correlation output is then the spectral correlation density function Sˆxα (f ).

15.2

Spectral Correlation Density Estimation

Estimates of the cyclic spectral density or SCD can be obtained via time or frequency-smoothing techniques. Since the signals being analyzed are defined over a finite time interval ∆t, the cyclic spectral density is only an estimate. An estimate of the SCD can be obtained by the time-smoothed cyclic periodogram given by 8 t+(∆t/2) 1 SxTW (u, f )du (15.8) Sxα (f ) ≈ SxαT (t, f )∆t = W ∆t t−(∆t/2)

Cyclostationary Spectral Analysis for Detection of LPI Parameters

517

Figure 15.2: Frequency-domain implementation of a second-order cyclostationary process.

Figure 15.3: Frequency-domain representation of (a) x(t) [X(ν)], (b) modulation of x(t) by −α/2 [U (ν)], and (c) modulation of x(t) by α/2 [S(ν)].

518

Detecting and Classifying LPI Radar

Figure 15.4: Cyclic spectral density estimation using short-time FFTs. where SxTW (u, f ) =

p 1 αQ ∗ p αQ XTW u, f + XTW u, f − TW 2 2

(15.9)

with ∆t being the total observation time of the signal, TW is the short-time FFT window length, and XTW (t, f ) =

8

t+(TW /2)

x(u)e−j2πf u du

(15.10)

t−(TW /2)

is the sliding short-time Fourier transform. Figure 15.4 shows the SCD estimation graphically for a signal x(t). Here the frequency components are evaluated over a small time window TW (sliding FFT time length), along the entire observation time interval ∆t. The spectral components generated by each short-time Fourier transform have a resolution, ∆f = 1/TW . In Figure 15.4, L is the overlap (sliding) factor between each short-time FFT. In order to avoid aliasing and cycle leakage on the estimates, the value of L is defined as L ≤ TW /4 [13]. Figure 15.5 shows the spectral components of each short-time FFT being multiplied according to (15.9), providing the same resolution capability ∆f = 1/TW , for the cyclic spectrum estimates [4, 14]. Note that the dummy variable t has been replaced by the specific time instances t1 . . . tp . Within each window (TW ), two frequency components centered about some f0 and separated by some α0 are multiplied together, and the resulting sequence of products is then integrated over the total time (∆t), as shown in (15.8).

Cyclostationary Spectral Analysis for Detection of LPI Parameters

519

Figure 15.5: Sequence of frequency products for each short-time Fourier transform. The estimation Sxα (f ) ≈ SxαT (t, f )∆t can be made as reliable and accuW rate as desired for any given t and ∆f , and for all f by making ∆t suﬃciently large, provided that (15.4) exists within the interval ∆t and that a substantial amount of smoothing is carried out over ∆t. This leads to the Grenander’s uncertainty condition ∆t∆f 1 [14]. This uncertainty condition means that the observation time (∆t) must greatly exceed the time window (TW ) that is used to compute the spectral components. A data taper window is also used to minimize the eﬀects of cycle and spectral leakage (estimation noise), introduced by frequency component side lobes [14]. The spectral components obtained from the short-time FFT have a resolution of ∆f =

1 TW

(15.11)

The cycle frequency resolution of the estimate is related to the total observation time by 1 (15.12) ∆α = ∆t The estimation of some (f0 , α0 ) represents a very small area on the bifrequency plane, as shown in Figure 15.6, and, since one needs a significant number of estimates to represent the cyclic spectrum adequately, it follows that obtaining estimates becomes very computationally demanding, and eﬃcient algorithms are required [15].

520

Detecting and Classifying LPI Radar

Figure 15.6: Frequency and cycle frequency resolutions on the bifrequency plane (adapted from [3, 15]).

15.3

Discrete Time Cyclostationary Algorithms

Cyclostationary signal processing can be used to extract the parameters from the sampled LPI signals in an intercept receiver, when moderate to large amounts of additive noise are present. With the signal displayed on the bifrequency plane (frequency-cycle frequency) the intercept receiver or operator can examine and compare the modulation characteristics, using several algorithms that estimate the SCD. Computationally eﬃcient algorithms for implementation of time- and frequency-smoothing techniques are discussed in [16]. These are the FFT accumulation method (FAM), a time-smoothing algorithm, and the direct frequency-smoothing method (DFSM), a frequencysmoothing algorithm, as described below. The temporal and spectral smoothing equivalence is also addressed in [9].

15.3.1

The Time-Smoothing FFT Accumulation Method

The time-smoothing FFT accumulation method was developed to reduce the number of computations required to estimate the cyclic spectrum [3]. This technique divides the bifrequency plane into smaller regions called channel pair regions, and computes the estimates one block at a time using the fast Fourier transform. Describing the estimated time-smoothed periodogram

Cyclostationary Spectral Analysis for Detection of LPI Parameters

521

Figure 15.7: Block diagram of the FAM (adapted from [3, 11]). from (15.8) and (15.9), in discrete terms, yields γ (n, k) SX NI

] N −1 } p 1 3 1 γQ ∗ p γQ = XN I n, k + XN I n, k − N n=0 N 2 2

where ˆ XN I (n, k) =

I N −1 3

w(n)x(n)e−(j2πkn)/N

I

(15.13)

(15.14)

n=0

is the discrete Fourier transform of x(n), w(n) is the data taper window (e.g., Hamming window), and the discrete equivalents of f and α are k and γ, respectively. A block diagram of the FFT accumulation method is shown in Figure 15.7. The algorithm consists of three basic stages: computation of the complex demodulates (divided into data tapering, sliding N point Fourier transform, and baseband frequency translation sections), computation of the product sequences, and smoothing of the product sequences. Table 15.1 shows the relationship between the variables in (15.8), (15.9), and (15.13). The parameter N represents the total number of discrete samples within the observation time, and N represents the number of points within the discrete short-time (sliding) FFT. In the FAM algorithm, spectral components of a sequence, x(n), are computed using (15.14). Two components are multiplied (15.13) to provide a sample of a cyclic spectrum estimate representing the finite channel pair region on the bifrequency plane, as shown in Figure 15.8. There are N 2

522

Detecting and Classifying LPI Radar

Table 15.1: Comparison of the Estimated Time-Smoothed Periodogram Expressed in Continuous and Discrete Time Name SCD

Continuous Time α SX (t, f )∆t

Short FFT size Observation time Time Frequency Cycle frequency Grenander’s Uncertainty Condition

TW ∆t t f α M = (∆f /∆α) ( 1

TW

Discrete Time γ SX (n, k)N I N

NI N n k γ M = (N/N I ) ( 1

channel pair regions in the bifrequency plane. Note the 16 small channel pair regions corresponding to a value of M = 4 in Figure 15.8. A sequence of samples for any particular area may be obtained by multiplying the same two components of a series of consecutive short-time sliding FFTs along the entire length of the input sequence. After the channelization performed by an N -point FFT sliding over the data with an overlap of L samples, the outputs of the FFTs are shifted in frequency in order to obtain the complex demodulate sequences (see Figure 15.7) [4]. Instead of computing an average of the product of sequences between the complex demodulates, as in (15.8), they are Fourier-transformed with a P -point (second) FFT. The computational eﬃciency of the algorithm is improved by a factor of L, since only N/L samples are processed for each point estimate. With fs the sampling frequency, the cycle frequency resolution of the decimated algorithm is defined as γres = fs /N (compare to ∆α = 1/∆t), the frequency resolution is kres = fs /N (compare to ∆f = 1/TW ), and the Grenander’s Uncertainty 1 (compare to ∆t∆f 1). Condition is M = N/N Figure 15.9 reveals that the estimates toward the top and the bottom (shaded areas) of the channel pair region do not satisfy the Uncertainty Condition. In order to minimize the variability of these point estimates, we can retain only those cyclic spectrum components that are within γ = ±kres /2 from the center of the channel pair region [15]. A solution to resolve the entire area of the channel pair region without leaving gaps is to apply a data taper window on the frequency axis (such as a Hamming window), to obtain better coverage.

15.3.2

Direct Frequency-Smoothing Method

Direct frequency-smoothing algorithms first compute the spectral components of the data, and then execute spectral-correlation operations directly on the spectral components. Generally, the direct frequency-smoothing method is

Cyclostationary Spectral Analysis for Detection of LPI Parameters

523

Figure 15.8: Channel pair regions within the bifrequency plane (Adapted from [3, 15]).

Figure 15.9: Cycle frequency and frequency resolutions of the Grenander’s Uncertainty Condition (adapted from [3, 15]).

524

Detecting and Classifying LPI Radar

Figure 15.10: Block diagram of the direct frequency-smoothing algorithm (adapted from [3, 11]). computationally superior to indirect algorithms that use related quantities such as the Wigner-Ville Distribution, but DFSM is normally less eﬃcient than a time-smoothing approach [13]. The basis for the DFSM is the discrete time frequency-smoothed cyclic periodogram represented by γ (n, k)∆k = SX N

N −1 p 1 3 γQ ∗ p γQ XN n, k + XN n, k − N n=0 2 2

where ˆ XN (n, k) =

N−1 3

w(n)x(n)e−(j2πkn)/N

(15.15)

(15.16)

n=0

is the discrete Fourier transform of x(n), w(n) is the rectangular window of length N that is the total number of points of the FFT related to the total observation time, ∆t, γ is the cycle frequency discrete equivalent, the frequency-smoothed ranges over the interval |m| ≤ M/2, and ∆k ≈ M · fs /N is the frequency resolution discrete equivalent [9]. The block diagram in Figure 15.10 illustrates the implementation of the DFSM. In order to provide full coverage of the bifrequency plane with minimal computational expense, (15.15) is computed along a line of constant cycle frequency, thus spacing the point estimates by ∆k = M · fs /N . This method is easier to implement, and is generally used to validate the time-smoothing

Cyclostationary Spectral Analysis for Detection of LPI Parameters

525

approach, but may become more computationally demanding. This is especially true in the last block in which the complex demodulate product sequences are summed. Considerations on the parallel processing of both time and frequency algorithms are discussed in [11]. Finally, we note that combinations of both time-smoothing and frequency-smoothing methods may also be advantageous for certain applications.

15.4

Test Signals

In order to grasp a good understanding of how the signals appear on the bifrequency plane, this section examines several test signals used in previous chapters. The first test signal examined is a tone composed of a single carrier frequency with fc =1 kHz, and is sampled with sampling frequency fs = 7 kHz. The time-smoothing technique to estimate the SCD is demonstrated first using the real part of the input signal. Figure 15.11 shows the time-smoothing SCD results. Figure 15.11(a) shows the bifrequency plane, and reveals that the signal’s frequency shows up at four separate locations. The (γ, k) frequency pairs are (−2fc , 0), (0, fc ), (0, −fc ), and (2fc , 0). Figure 15.11(b) details a close-up of the time-smoothing estimation characteristics for the signal outlined in the box in Figure 15.11(a). For these results the frequency resolution is ∆k = 128 Hz. With the Grenander’s uncertainty value of M = 2, the cycle frequency ∆γ = 64 Hz. The overlap parameter is fixed at L = 4. The number of points in the first FFT N is the next largest power of 2 value of fs /∆k or N = 64. The number of points in the second FFT P is the next largest power of 2 value of 4fs /∆N or P = 8. The total number of signal samples integrated into the SCD are N = P L = 128. Note that in Figure 15.11(b), the γ = 2fc cycle frequency position lies at the resolved signal’s centroid. The frequency-smoothing SCD results for the single-tone signal are shown in Figure 15.12. Figure 15.12(a) shows the bifrequency plane, and Figure 15.12(b) details a close-up of the frequency-smoothing estimation characteristics. The results serve to demonstrate the diﬀerences between the timesmoothing and frequency-smoothing techniques for estimating the SCD. For the frequency-smoothing results, ∆k = 128 Hz. The number of samples integrated into the FFT is the next largest power of 2 value of fs M/∆f = 109 or N = 128. Note in Figure 15.12(b), the γ = 2fc cycle frequency position does not lie at the resolved signal’s centroid. Next, the time-smoothing technique is used to estimate the SCD of a two-tone signal (fc1 = 1 kHz and fc2 = 2 kHz). Figure 15.13 shows the time-smoothing SCD results. Figure 15.13(a) shows the bifrequency plane, and reveals that the two tones show up in the four separate quadrants, along with the cross terms. Figure 15.13(b) details a close-up of the time-smoothing estimation characteristics for the signal outlined in the box in Figure 15.13(a).

526

Detecting and Classifying LPI Radar

Figure 15.11: Time-smoothing SCD for a single frequency fc = 1 kHz tone, showing the (a) bifrequency plane, and (b) close-up of the time-smoothing estimation characteristics.

Cyclostationary Spectral Analysis for Detection of LPI Parameters

527

Figure 15.12: Frequency-smoothing SCD for a single frequency fc = 1 kHz tone, showing the (a) bifrequency plane, and (b) close-up of the frequencysmoothing estimation characteristics.

528

Detecting and Classifying LPI Radar

For these results, the frequency resolution ∆k = 128 Hz, the Grenander’s uncertainty value M = 2, and the cycle frequency ∆γ = 64 Hz. Also, N , N , and P are the same as for the single-tone signal. The frequency-smoothing SCD results for the two-tone signal are shown in Figure 15.14. Figure 15.14(a) shows the bifrequency plane, and Figure 15.14(b) details a close-up of the frequency-smoothing estimation characteristics, including the cross terms. As for the single-tone results, ∆k = 128 Hz and N = 128. Note that in Figure 15.14(b), the γ = 2fci cycle frequency positions do not lie at the signal centroids.

15.5

BPSK Analysis

In this section, two Nc = 7-bit binary phase shift (BPSK) signals are used to present the method of measuring and determining the BPSK signal parameters in the bifrequency plane. Both a wideband modulation (cycles per subcode period cpp = 1) and a narrowband modulation (cpp = 5) are used to illustrate the technique. The ability to extract the BPSK parameters under various SNR conditions is also quantified. For these results, the frequency resolution ∆k = X and the Grenander’s uncertainty value M = 2 (cycle frequency ∆γ = X Hz). Figure 15.15 shows the narrowband BPSK signal. In Figure 15.15(a), the complete SCD bifrequency plane is shown. Note that the cycle frequency extends from −fs to fs and the frequency extends from −fs /2 to fs /2 (see also Figure 15.6). The BPSK modulation shows up in the four quadrants centered on γ = 2fc = 2 kHz. A closer look at the boxed section in Figure 15.15(a) is shown in Figure 15.15(b). The most important parameters of the BPSK signal can be identified clearly. These are the bandwidth B = 1/tb , the code rate Rc = 1/tb Nc , the subcode period tb , and the number of bits N used in the Barker code. The bandwidth can be measured in both the frequency dimension and the cycle frequency dimension. The measurement in the cycle frequency dimension is the width from the centroid (C) to the edge of the pattern, where the SCD peaks on the bifrequency plane start to fall oﬀ in amplitude. The spots to exclude in the calculation have a lower intensity. This is especially noticeable in the k dimension. The bandwidth is measured as B = 1 kHz, giving a subcode period of 1 ms. The code rate Rc is measured in the cycle frequency domain, and is the width between any two spots within the BPSK modulation pattern. Here, Rc = 142.8 Hz. The number of Barker bits is then Nc = B/Rc =7 bits. At first, the sensitivity of the extracted parameter values to the measurement of the bandwidth might seem critical. This is not true, however, since the number of bits N for a BPSK signal can only take on a select set of values. For example, if the next set of spots was included in the calculation, and the bandwidth was measured to be B = 1,142.8, then N ≈ 8, which we know is

Cyclostationary Spectral Analysis for Detection of LPI Parameters

529

Figure 15.13: Time-smoothing SCD for a two-tone signal (fc1 = 1 kHz, fc2 = 2 kHz), showing (a) the bifrequency plane, and (b) a close-up of the timesmoothing estimation characteristics.

530

Detecting and Classifying LPI Radar

Figure 15.14: Frequency-smoothing SCD for a two-tone signal (fc1 = 1 kHz, fc2 = 2 kHz) showing (a) the bifrequency plane, and (b) a close-up of the frequency-smoothing estimation characteristics.

Cyclostationary Spectral Analysis for Detection of LPI Parameters

531

not correct. Therefore, too many spots were included in the measurement. Figure 15.16 shows a contour plot that illustrates the BPSK pattern and measurement technique when the SNR = 0 dB. The white Gaussian noise added to the signal is distributed over a bandwidth equal to fs /2. The complete bifrequency plane is shown in Figure 15.16(a), and the boxed region is examined closer in Figure 15.16(b). Note that the noise is suppressed significantly. This is due to the noise being uncorrelated. The centroid (C) is identified, and the bandwidth is measured out to the row of spots just before the crosshatch ends. The bandwidth in the frequency k dimension is also shown. The bandwidth is measured as shown, and extends between the highest and lowest corners of the crosshatch region. Note that since the noise has enhanced the details of the crosshatch, the measurement is easier to take in the k dimension. The code rate is also easily measured between adjacent spots as shown in Figure 15.17. The next signal examined is the narrowband 7-bit BPSK (cpp = 5). Since the carrier frequency is fc = 1 kHz, the subcode period tb = 5 ms, resulting in a bandwidth of B = 200 Hz. The frequency-smoothing SCD is shown in Figure 15.18. Figure 15.19 illustrates the extraction of the narrowband BPSK signal parameters when noise is present. The bandwidth B is measured in the same manner as is the code rate Rc . This important example shows that significant amounts of noise in the bifrequency plane can still give good results.

15.6

FMCW Analysis

In this section, a method is presented for extracting the parameters from a triangular FMCW radar signal. The signal shows up at four positions within the bifrequency plane, as illustrated in Figure 15.20 and Figure 15.21. We first examine a ∆F = 250 Hz, fc = 1 kHz FMCW signal using frequencysmoothing. For these results, the frequency resolution ∆k = 16 Hz and the Grenander’s uncertainty value M = 4 (cycle frequency ∆γ = 4 Hz). The frequency-smoothing SCD for one of the four positions is illustrated in Figure 15.20, and is a unique pattern for the FMCW modulation. For this result, N = 1,024 and ∆k = 16 Hz. The modulation centroid lies at a cycle frequency of γ = 2 kHz, indicating that the fc = 1 kHz. Note that the centroid lies to the right of the spot (as is the case for the frequency-smoothing SCD results). To determine the modulation bandwidth ∆F from the SCD, the width from the centroid out to the last large set of spots is measured on the cycle frequency axis. Note also that ∆F can also be determined from the frequency axis by measuring the total extent of the modulation as shown. The modulation period tm is determined by measuring Rc in the cycle frequency domain. In the SCD, Rc = 1/2tm for the FMCW signal. From Figure 15.20, Rc = 25 Hz, giving

532

Detecting and Classifying LPI Radar

Figure 15.15: Frequency-smoothing SCD patterns for an Nc = 7-bit BPSK signal, with fc = 1 kHz and cpp = 1, showing (a) the complete bifrequency plane, and (b) a close-up illustrating the method of parameter measurements.

Cyclostationary Spectral Analysis for Detection of LPI Parameters

533

Figure 15.16: Frequency-smoothing SCD patterns for an Nc = 7-bit BPSK signal with fc = 1 kHz, cpp = 1, and SNR = 0 dB, showing (a) the complete bifrequency plane, and (b) a close-up illustrating the method of parameter measurements.

534

Detecting and Classifying LPI Radar

Figure 15.17: Frequency-smoothing SCD patterns for an Nc = 7-bit BPSK signal with fc = 1 kHz, cpp = 1, and SNR = −6 dB, showing (a) a partial bifrequency plane, and (b) a close-up illustrating the method of parameter measurements.

Cyclostationary Spectral Analysis for Detection of LPI Parameters

535

Figure 15.18: Frequency-smoothing SCD patterns for an Nc = 7-bit narrowband BPSK signal with fc = 1 kHz and cpp = 5, showing the bifrequency plane illustrating the method of parameter measurements. tm = 20 ms. Figure 15.21 illustrates the extraction of the FMCW parameters when noise is present. In Figure 15.21(a) the SNR = 0 dB. Note that the pattern is still recognizable as being unique to the FMCW waveform. The noise present actually aids in identifying the centroid of the modulation. The modulation bandwidth ∆F is measured in the same manner as shown in Figure 15.20 also with good fidelity. The measurement of Rc is also easily made. In Figure 15.21(b) the SNR = −6 dB. With this level of noise, a significant degradation in the contour image results, and makes the modulation bandwidth diﬃcult to measure in the cycle frequency dimension. However, the ∆F measurement can still be easily made, with only a slight bit of error. Here ∆F = 240 Hz. The Rc value, however, can still be made with a good degree of accuracy. The extraction of the FMCW parameters from a wideband signal ∆F = 500 is given in Appendix N.

15.7

Polyphase Code Analysis

In this section we look at the bifrequency plane results for the polyphase codes, and demonstrate the bifrequency extraction techniques. We begin with the Frank code example. The analysis of the wideband Frank signal

536

Detecting and Classifying LPI Radar

Figure 15.19: Frequency-smoothing SCD patterns for an Nc = 7-bit narrowband BPSK signal with fc = 1 kHz and cpp = 5, showing (a) the bifrequency plane with SNR = 0 dB, and (b) SNR = −6 dB.

Cyclostationary Spectral Analysis for Detection of LPI Parameters

537

Figure 15.20: Frequency-smoothing SCD patterns for a ∆F = 250 Hz, tm = 20-ms triangular FMCW signal with fc = 1 kHz. with a long code period using the time-smoothing SCD is presented. For these results, the frequency resolution, ∆k = 16 Hz, and Grenander’s uncertainty M = 4. With a longer code period T = 64 ms (Nc = 64 subcodes, and cpp = 1), the Frank code signal converges to a more well-defined insect shape on the bifrequency plane as shown in Figure 15.22(a). Interestingly enough, all the longer phase codes derived from linear FM waveforms have this type of shape, using the time-smoothing SCD technique. Figure 15.22(b) shows a close-up of one of the four modulation patterns. Note the position of the head, abdomen, and wings that provide a convenient reference for measurements of the signal parameters. Also note that the insect points to the right. The direction of the insect is important to help distinguish between the diﬀerent phase codes. The centroid (c) is symmetrically located within the pattern characteristic of the time-smoothing SCD. The bandwidth can be measured as the width from the centroid to the head, on the cycle frequency axis. A correlation can also be made using the bandwidth measurement on the frequency axis and is the width between the wing tips. Also indicated in Figure 15.22(b) is a box that is examined in closer detail to illustrate the Rc measurement. Figures 15.23(a, b) illustrate the measurement of Rc = 1/T . Figure 15.23(b) indicates Rc = 15.5 Hz, giving a modulation period of 64 ms. Since the number of subcodes used by LPI radar are most often a power of 2 (e.g., 64 = 26 ), an accurate result

538

Detecting and Classifying LPI Radar

Figure 15.21: Frequency-smoothing SCD patterns for a ∆F = 250 Hz, tm = 20-ms triangular FMCW signal with fc = 1 kHz, showing (a) the bifrequency plane SNR = 0 dB, and (b) SNR = −6 dB.

Cyclostationary Spectral Analysis for Detection of LPI Parameters

539

Figure 15.22: Time-smoothing SCD insect patterns for the Frank code with Nc = 64, fc = 1 kHz, and cpp = 1, with (a) the complete bifrequency plane, and (b) a closer examination of one of the four modulation patterns illustrating the bandwidth measurements.

540

Detecting and Classifying LPI Radar

can be obtained, even from bifrequency planes with small SNR with Nc = B/Rc = 64. Appendix O examines the Frank code with a shorter code period. The cyclostationary results for the P1, P2, P3, and P4 codes are given in Appendix P.

15.8

Polytime Code Analysis

In this section the frequency-smoothing SCD is used to examine the polytime codes. We begin with the T1(2) code. The T1(2) code has an fc = 1 kHz, and has a time-modulated binary phase shift (of various widths). Figure 15.24(a) shows the bifrequency plane and the four modulation patterns. Figure 15.24(b) shows one of the four unique patterns, and illustrates how the bandwidth of the signal can be measured. Recall that the bandwidth B is measuring the largest excursion in frequency, due to the shortest time phase code. For the case shown in Figure 15.24(b), B = 1,750 Hz, which agrees with the results as measured by the time-frequency tools earlier. Note that this value is not the modulation bandwidth ∆F of the linear FM signal used to derive the polytime phase modulation. Figure 15.25 shows a closer examination of the bifrequency plane, and the measurement of Rc = 1/T = 62.5 Hz. This gives the estimate for the code period as T = 16 ms. Note also that an SCD spot exists at (γ = 2fc , k = 0). The results for the T2(2), T3(2), and T4(2) codes are given in Appendix Q.

15.9

Costas Frequency Hopping Results

In this section the time-smoothing SCD is used to determine what SCD properties a Costas frequency hopping signal takes on. The time-smoothing SCD was created using ∆γ = 16 and N = 2,048. The Costas sequence in this example is S = {4, 7, 1, 6, 5, 2, 3} and is used since this sequence is discussed in Chapter 6. The sampling frequency of the ADC is 15 kHz, and each Costas frequency is generated with 20 cycles per frequency. That is, the time spent at each frequency is not a constant. Figure 15.26(a) shows the complete bifrequency results. One of the four quadrants is shown in Figure 15.26(b). The frequencies within the sequence fci show up at 2fci and are outlined along the k = 0 axis. Also note the presence of the cross terms k = |fci − fcj |/2. Although the SCD analysis does not let us determine the time sequence of information, we can, however, see that frequencies γ = 6 kHz and γ = 5 kHz are fired next to each other, as is the case for frequencies γ = 2 kHz and γ = 3 kHz, but we cannot determine the order.

Cyclostationary Spectral Analysis for Detection of LPI Parameters

541

Figure 15.23: Close examination of the time-smoothing SCD for the Frank code with Nc = 64, fc = 1 kHz, and cpp = 1, with (a) modulation cycles and (b) the measurement of Rc .

542

Detecting and Classifying LPI Radar

Figure 15.24: Frequency-smoothing SCD patterns for the polytime T1(2) code with fc = 1 kHz, showing (a) the complete bifrequency plane, and (b) a closer examination of one of the four modulation patterns illustrating the bandwidth measurement.

Cyclostationary Spectral Analysis for Detection of LPI Parameters

543

Figure 15.25: Close examination of the frequency-smoothing SCD pattern for the polytime T1(2) code illustrating the Rc measurement.

15.10

Random Noise Analysis

In the first example, a random noise waveform with a bandwidth of B = 300 MHz and carrier frequency of fc = 350 MHz was examined with the time-smoothing SCD. Figure 15.27 shows that the bandwidth and carrier frequency can easily be identified as expected. In the second example, a random noise plus FMCW waveform is examined. The FMCW waveform parameters used to modulate the noise are ∆F = 300 MHz (from 200 to 500 MHz) and the carrier frequency is fc = 350 MHz. The noise bandwidth being modulated is B = 300 MHz. Since in this case the noise bandwidth and the modulation bandwidth overlap, the total noise FMCW bandwidth transmitted is B = 300 MHz. The time-smoothing technique was chosen to estimate the SCD. From Figure 15.28, the diamond is centered at 1,200 MHz, which is twice the center frequency of the modulated signal. It might be expected that the center frequency would appear at 1,400 MHz, or twice the center frequency of the two modulated signals (350 MHz for the noise and 350 MHz for the FMCW signal). The diﬀerence of 200 MHz is observed as an oﬀset. Several noise plus FMCW waveforms were examined with diﬀerent modulation bandwidths as summarized in Table 15.2. The relationship of the observed center

544

Detecting and Classifying LPI Radar

Figure 15.26: Time smoothing SCD patterns for the Costas sequence S = {4, 7, 1, 6, 5, 2, 3} showing (a) the complete bifrequency plane, and (b) a closer examination of one of the four modulation patterns illustrating the frequency cross terms (k).

Cyclostationary Spectral Analysis for Detection of LPI Parameters

545

Figure 15.27: Time smoothing SCD for the random noise waveform showing the carrier frequency and the bandwidth measurements. frequency oﬀset as a function of the FMCW modulation bandwidth is left as an exercise for the reader. Other signal characteristics, such as the signal bandwidth of 300 MHz, can be measured along the cycle frequency axis, as expected. The bandwidth can also be measured along the frequency axis as well. This sweep bandwidth shows nicely in the QMFB results.

15.11

Summary

The cyclostationary signal processing was presented in this chapter, and several examples were used to demonstrate the bifrequency results. To extract the unknown signal parameters, the bifrequency plane (frequency-cycle frequency) is examined to determine directly (and indirectly) parameters such as the carrier frequency, code rate, bandwidth, and modulation period. Information not available includes any parameters that change as a function of time (such as the signal’s phase). These phase changes, however, can be identified from the other signal processing tools that are included (such as the PWVD, CHOI, and QMFB). Measurement of the LPI signal parameters agree well with the actual values. With moderate amounts of noise added, however, the measurement ability using the bifrequency analysis, does not degrade significantly but remains fairly robust since symmetrical

546

Detecting and Classifying LPI Radar

Figure 15.28: Time smoothing SCD for the random noise plus FMCW waveform showing the bandwidth measurement and the carrier frequency oﬀset that appears in the bifrequency domain.

Table 15.2: Summary of Time Smoothing SCD for the Random Noise Plus FMCW Waveform Showing the Bandwidth Measurement and the Carrier Frequency Oﬀset That Appears in the Bifrequency Domain ∆F (MHz) 500 300 200 100 1

Oﬀset (MHz) 250 200 100 50 0

Center Frequency Observed 1,150 1,200 1,300 1,350 1,400

Cyclostationary Spectral Analysis for Detection of LPI Parameters

547

white Gaussian noise is not correlated and is suppressed in this spectral correlation technique. The cyclostationary processing, however, does not perform well with the FSK Costas code and FSK/PSK (binary phase code) signal. This is mainly due to a lack of temporal information needed, in order to identify the code sequence in time. The presentation of the cyclostationary results to a trained operator will allow the signal parameters to be extracted, and can enable good classification results for the signals that are appropriate. The use of the cyclostationary processing in noisy environments is particularly good.

References [1] Spooner, C. M., and Gardner, W. A., “Robust feature detection of signal interception,” IEEE Trans. on Communications, Vol. 42, No. 5, pp. 2165— 2173, May 1994. [2] Gardner, W. A., “Signal interception: A unifying theoretical framework for feature detection,” IEEE Trans. on Communications, Vol. 36, No. 8, pp. 897—906, Aug. 1988. [3] Gardner, W. A., and Spooner, C. M., “Signal interception: Performance advantages of cyclic feature detectors,” IEEE Trans. on Communications, Vol. 40, No. 1, pp. 149—159, Jan. 1992. [4] Tom, C., “Cyclostationary spectral analysis of typical SATCOM signals using the FFT accumulation method,” Defence Research Establishment Report No. 1280, Ottawa, Canada, Dec. 1995. [5] Xin, J., and Sano, A., “Linear prediction approach to direction estimation of cyclostationary signals in multipath environment,” IEEE Trans. on Signal Processing, Vol. 49, No. 4, pp. 710—720, April 2001. [6] Yu, S-J., and Ueng, F-B., “Implementation of cyclostationary signal-based adaptive arrays,” Elsevier Signal Processing, Vol. 80, pp. 2249—2254, 2000. [7] Lee, J-H., and Lee, Y-T., “A novel direction-finding method for cyclostationary signals,” Elsevier Signal Processing, Vol. 81 pp. 1317—1323, 2001. [8] Gini, F., Montanari, M., and Verrazzani, L., “Estimation of chirp radar signals in compound-Gaussian clutter: A cyclostationary approach,” IEEE Trans. on Signal Processing, Vol. 48, No. 4 pp. 1029—1039, April 2000. [9] Skinner, B. J., Ingels, F. M., and Donohoe, J. P., “The eﬀect of radar signal construction on detectability,” Proc. of the 26th Southeastern Symposium on System Theory, pp. 147—150, March 1994. [10] Gillman, A. M., “Non-cooperative detection of LPI/LPD signals via cyclic spectral analysis,” Air Force Institute of Technology, Master’s thesis, March 1999. [11] Gardner, W. A., Statistical Spectral Analysis: A Nonprobabilistic Theory, Prentice-Hall, Englewood Cliﬀs, NJ, 1987.

548

Detecting and Classifying LPI Radar

[12] Gardner, W. A., “Exploitation of spectral redundancy in cyclostationary signals,” IEEE Signal Processing Magazine, pp. 14—36, April 1991. [13] Lima, A. F., Jr., “Analysis of low probability of intercept radar signals using cyclostationary processing,” Naval Postgraduate School Master’s thesis, Sept. 2002. [14] Roberts, R. S., Brown, W. A., and Loomis, H. H., Jr., “A review of digital spectral correlation analysis: Theory and implementation,” Cyclostationarity in Communications and Signal Processing, IEEE Press, 1994. [15] Roberts, R. S., Brown, W. A., and Loomis, H. H., Jr., “Computationally efficient algorithms for cyclic spectral analysis,” IEEE Signal Processing Magazine, pp. 38—49, April 1991. [16] Brown, W. A., III, and Loomis H. H., Jr., “Digital implementations of spectral correlation analyzers,” IEEE Trans. on Signal Processing, Vol. 41, No. 2, pp. 703—720, Feb. 1993.

Problems 1. (a) Using the LPIT, generate the FMCW waveform (signal only, SNR = 0 dB, and SNR = −6 dB) with a carrier frequency of 2 kHz, tm = 5 ms, and ∆F = 500 Hz. (b) Process the signals with both the time-smoothing and frequency-smoothing algorithm. (c) For each useful algorithm, diagram your estimates of all the signal parameters for signal only, SNR = 0 dB, and SNR = −6 dB. 2. (a) Using the LPIT, generate a P4 waveform (signal only, SNR = 0 dB, and SNR = −6 dB) with a carrier frequency of 2 kHz, Nc = 128, tb = 1 ms, and fs = 7,000 Hz. (b) Process the signals with both the time-smoothing and frequency-smoothing algorithm. (c) For each useful algorithm, diagram your estimates of all the signal parameters for signal only, SNR = 0 dB, and SNR = −6 dB. 3. (a) Using the LPIT, generate the default FMCW waveform and the default P4 waveform. Load both signals into MATLAB, and truncate such that they both have the same size (be sure to at least include 1 to 2 code periods of each signal). (b) Add the two signals together and save as a new signal (e.g., fmcw p4.mat). (c) For each signal, use the cyclostationary processing to analyze and extract the waveform parameters that are evident. (d) Repeat (b) and (c) for SNR = 0 dB. (e) Repeat (b) and (c) for SNR = −6 dB.

Cyclostationary Spectral Analysis for Detection of LPI Parameters

549

4. To help identify the capability of the cyclostationary signal processing as a tool for identifying the LPI modulation, extracting the modulation parameters, and to aid in deciding on what signal processing algorithm performs best, construct a table to show the bifrequency measurement results for the LPI signals contained in the test signals folder. For each parameter of interest, show the actual value, the measured value, and the absolute value of the relative error [see (12.26)]. Be sure to include which frequency axis (frequency, cycle frequency) is used for identifying the diﬀerent parameter values being measured.

Chapter 16

Antiradiation Missiles A Wild Weasel provides a Warsaw Pact SAM operator the maximum opportunity to give his life for his country — “Relic quote of the Wild Weasel”

This chapter gives a brief account of the concept of suppression of enemy air defenses. The beginnings of SEAD and the development of antiradiation missiles (ARMs) are presented. The use of ARMs in Vietnam and postVietnam is also presented. The design of ARM seekers is addressed and the concept of dual-mode ARMs is discussed including ARM performance metrics. The important ARMs from around the world are then reviewed and their performance given. Anti-ARM techniques that can be employed other than the use of LPI emitters are also presented.

16.1

Suppression of Enemy Air Defense

Suppression of enemy air defense (SEAD) is defined by the U.S. Department of Defense as “that activity that neutralizes, destroys or temporarily degrades surface-based enemy air defenses by destructive and/or disruptive means” [1]. SEAD includes the use of air-to-ground missiles against an enemy’s integrated air defense system (IADS). An IADS is an integration of airand ground-based sensors and the communication that links them together 551

552

Detecting and Classifying LPI Radar

with the weapons and command and control. SEAD capabilities fall within the traditional discipline of electronic warfare (EW), which includes electronic attack (EA), electronic protection (EP), and electronic warfare support (ES). SEAD is also an interdisciplinary construct that integrates EW as an activity of information operations with the use of EA capabilities such as antiradiation missiles (ARMs) against the enemy’s IADS in an eﬀort to obtain information superiority. In suppression, the ARMs are fired and home in on the enemy’s surface-based radar systems that are used to target their surface-to-air missiles (SAMs) against any incoming strike aircraft. In modern network-enabled warfare, there is a dedicated aircraft assigned that specializes in the hard-kill of enemy guidance radars by deploying ARMs [2]. The ARM relies on passive detection of the radiation emitted from the radar. The ARM mission or sortie is an aircraft strike capability against radar directed/radar controlled missile and gun system sites–the greatest threat to eﬀective air operations. ARMs can also be fired preemptively in order to prevent the SAM radar from coming up. The use of ARMs contributes to information superiority by preventing and reducing the enemys use of the electromagnetic spectrum while protecting our own spectrum vulnerabilities. That is, SEAD actions increase an air force’s ability to conduct air operations by reducing their vulnerability to air defense missiles and guns. Below, the U.S. Army’s description of the various forms of SEAD are given highlighting their potential use in suppression of an enemy’s IADS [3]. • Campaign SEAD: SEAD operations that are preplanned, theaterwide eﬀorts conducted concurrently over an extended period against air defense systems normally located well behind enemy lines. • Complementary SEAD: Those operations that involve continuously seeking enemy air defense system targets to destroy them. • Localized SEAD: Those operations that support tactical air operations, Army aviation operations, reconnaissance, and the establishment of corridors for ingress and egress routing for air force and army assets. • Joint SEAD: Broad term that includes all suppression of enemy air defense activities provided by one component of the joint force in support of another. • Nonlethal SEAD: Aims to neutralize or degrade enemy IADS rather than destroy them. While nonlethal SEAD is most commonly associated with the electronic jamming of IADS sensors and command, control and communications (C3) links, this is not the only form of nonlethal SEAD. Other forms of nonlethal SEAD include the use of specialized tactics to exploit known air defense system limitations and the use of stealth technology, or false targets, to deceive enemy air defenses. Note

Antiradiation Missiles

553

that: the threat of destruction alone may degrade an air defense systems eﬀectiveness by forcing its operators to employ defensive measures that would result in suboptimal system performance. • Lethal SEAD: Measures taken to physically destroy one or more components of an IADS. Most hard-kill SEAD options involve specialized weapons such as ARMs, precision guided munitions (PGMs), and standoﬀ weapons (SOWs); the successful use of which will damage the enemys IADS and possibly inflict casualties among their crews. Lethal SEAD can suppress enemy air defenses for a potentially longer period than can nonlethal measures. However, the success of lethal SEAD missions depends on adequate EW support to provide both accurate targeting and protection of the SEAD platform. • Preemptive SEAD: This concept diﬀers from lethal-SEAD practices by preemptively disrupting enemy air defenses before they can engage friendly aircraft. This is typically done by firing an ARM in the air in the direction of a SAM that is suspected to exist but which has not turned on its radar in the aim of preventing the SAM radar from coming up. Although an eﬀective and necessary tactic, it is not eﬃcient.

16.1.1

The Beginning of SEAD

Since the introduction of radar in World War II (WWII), radar was used by both sides to alert ground-based air defenses and fighters of an impending raid. The SEAD role originated in WWII when the German Luftwaﬀe bombed elements of the British CHAIN HOME early warning radar net during the Battle of Britain. This first SEAD attempt heralded a series of Allied SEAD developments made in response to the very eﬀective German radar-based air defenses encountered during the Allied bombing oﬀensive of Germany [4]. One of the first SEAD measures employed by the Allies was to drop chaﬀ, consisting of small strips of metal foil, from lead bombers or pathfinder aircraft to disrupt the German radar picture by creating thousands of false targets. If the location of the radars were discovered, they could be attacked, generally by bombing from a large formation. The British developed a radar homing device (dubbed “Abdullah”) that would locate the enemy radar. The aircraft that were equipped with the Abdullah were not armed and flew only with escort fighters. In addition, Ferret aircraft were used to detect the operating frequencies of German radars and radios so they could be jammed by EA equipment or physically attacked by the Ferret or other aircraft. Similar SEAD measures were used in the Pacific theater during WWII and again during the Korean conflict [4].

554

Detecting and Classifying LPI Radar

Figure 16.1: The Corvus antiradiation missile.

Figure 16.2: The Corvus antiradiation missile being loaded.

16.1.2

Early ARM Developments

In 1955, the U.S. Navy had a requirement for a long-range nuclear-armed heavy standoﬀ air-to-surface missile to be employed by carrier-based attack bombers. In April 1955, the ASM-N-8 Raven project was initiated to develop such a missile [5]. In the same year, a parallel project for an anti-radar missile was redefined to cover the Raven requirements, and therefore the Raven project was canceled and the ASM-N-8 designation transferred to the Corvus. A development contract for the ASM-N-8 Corvus shown in Figure 16.1 was awarded to Temco in January 1957, and the first flight test of an XASM-N-8 prototype occurred in July 1959. Figure 16.2 shows the Corvus missile being loaded with a special purpose cart. The Corvus was designed

Antiradiation Missiles

555

as an ARM, and had a passive radar seeker to home in on the emission of enemy radars at a speed of Mach 0.8 [6]. The Corvus seeker could also home on nonradiating targets when they were illuminated by a compatible radar in the launching aircraft. In this mode there was also a data-link between the missile and the launching aircraft, which could provide mid-course command guidance until the missile’s seeker could detect the radar reflections from the target [7]. The missile could be launched from high or low altitudes, and maximum ranges for high-altitude (15 km) launches were 315 km in ARM mode and 185 km in semiactive homing mode. Corvus was to be armed with a light-weight W-40 nuclear fission warhead (10 kT yield) [5]. By March 1960, the XASM-N-8 test program had progressed to fully guided flights, but in July that year the Corvus program was terminated. The reason was that overall responsibility for long-range nuclear air-to-surface missiles had been transferred to the U.S. Air Force, which regarded the Corvus as unnecessary [6].

16.1.3

Vietnam

The greatest SEAD advances were made during the Vietnam War in 1965 when the eﬀectiveness of the North Vietnamese IADS caused significant losses. The initial U.S. response of launching conventional air strikes against the SAM sites resulted in heavy friendly losses [8]. The Soviet SA-2 SAMs killed at least 83 aircraft and forced the USAF to increase its SEAD capability by building the F-100 Super Sabre Wild Weasel (an evolution of the Ferret aircraft) in 90 days pairing experienced fighter pilots with electronic warfare oﬃcers from the Strategic Air Command. The F-100 was followed by the F-105G Wild Weasel and the F-4G Wild Weasel [9]. The Wild Weasels were free-roving hunters that baited SAM sites at point blank range. The Wild Weasel mission was developed by the U.S. Air Force in 1965, during the Vietnam War era. Its primary concept was the use of two-seat aircraft, to counter hostile radar-controlled surface-to-air weapons. They were able to detect and locate the SAM radars and attack them with bombs, napalm or rockets. However, attacking air defense systems with shortrange weapons proved to be very hazardous. In 1966, the Weasels received a stand-oﬀ attack capability in the form of the AGM-45 Shrike ARM. With early ARM technology, when the enemy air defenses shut oﬀ their emitters, the already launched ARM could only fly about without guidance for a short time until it ran out of fuel and crashed. Shutting down a radar to evade detection protected the radar from destruction but it did not do much good for the radar operator. Although suppression was achieved the most preferred solution in most cases is the destruction of enemy air defense (DEAD) and the destruction of their command and control in order to reduce the number of SAM shooters. For DEAD, a precise knowledge of the enemy location is required.

556

Detecting and Classifying LPI Radar

Other significant SEAD developments of the Vietnam War included the use of compact EA pods that allowed fighter aircraft to conduct self-defense, support jamming and escort jamming of enemy radars [9]. Self-defense jammers are relatively low powered jammers that are primarily designed to counter missiles targeted at the jamming aircraft. Support and escort jammers are somewhat more powerful systems that can also provide protection to aircraft in the immediate vicinity of the jamming aircraft. This type of jamming helps reduce the number of SAM shots that are taken. Most combat aircraft were also fitted with radar warning receivers (RWRs) that allowed the timely employment of defensive EA and evasive maneuvers to avoid enemy missiles. A stand-oﬀ jamming capability was also developed that allowed specialist aircraft to suppress enemy air defenses at long range while electronic reconnaissance aircraft were used to determine the enemys electronic order of battle and to locate the enemy air defense radars and radios [4]. Note that stand-oﬀ jamming does not make the jammer or other aircraft invisible.

16.1.4

Post Vietnam

SEAD developments continued after the Vietnam War, notably during the Israeli Operation Peace for Galilee during which remotely piloted vehicles (RPVs) were used to detect, locate and decoy the Syrian IADSs [8]. The USAF also established the Wild Weasel School. Developments also continued during Operation Desert Storm, with the coalition not losing a single strike aircraft to a radar threat while an armed Wild Weasel was on station [9]. Army AH-64 Apache helicopters were also used in the lethal-SEAD role and EC-130H Compass Call aircraft were used to jam air defense communications. The F-4G units were disbanded after 1996 and the USAF retired the last of its EF-111 radar and communications jamming aircraft in May 1999. This left a critical hole in USAF capabilities. The USAF then replaced its F-4G Wild Weasel fleet with the combination of the F-16CJ Falcon and HARM targeting system (HTS) using multirole squadrons to partially fill the gap. The EF-111s mission was transferred to the United States Navy’s EA-6B which requires one pilot and three electronic warfare oﬃcers (EWOs). The U.S. General Accounting Oﬃce (GAO) believed the success of air operations during Operation Desert Storm depended heavily on SEAD aircraft [10]. Moreover, the GAO predicted SEAD would continue to be important to air operations, even those involving stealth aircraft, and criticized the U.S. Department of Defense (DoD) for reducing its traditional SEAD capability. In 2001 the DoD released the Joint Airborne Electronic Attack (AEA) Analysis of Alternative (AOA) that examined the options available for replacing the aging EA-6B including the F-22, the F/A-18, and the Joint Strike Fighter [11]. The decision was to eventually replace the EA-6B by the carrier-based EA-18G (or Growler)–a multirole two-seat aircraft for jamming (AN/ALQ-99), SEAD and preemptive SEAD.

Antiradiation Missiles

557

Table 16.1: Estimates of Combat Aircraft Losses (from [1]) Conflict World War II Korea Vietnam (AF only) Desert Storm (Iraq) Bosnia Kosovo N./S. Watch Iraqi Freedom

Combat Sorties 2,498,283 591,693 219,407 68,150 (Coalition) 30,000 21,111 268,000 20,733

Combat Losses 19,030 1,253 1,437 33 3 2 0 1

Attrition Rate 0.76% 0.2% 0.65% 0.04% 0.01% 0.009% 0.0% 0.004%

Today the Army has the primary responsibility for suppressing groundbased enemy air defense weapons to the limits of observed fire. The USAF has responsibility from beyond the limits of observed fire out to the range limits of the Army weapons systems; the Army has secondary responsibility. Even if the USAF can target or observe, the Army may still have to attack the target. Beyond the range limits of Army weapons, the USAF is responsible. Although the U.S. DOD is pursuing a new approach to SEAD, the United States continues to recognize the important requirement for SEAD [11—13]. It should also be noted that ARMs are not only used for suppression of air defense SAM networks. Other targets include airborne early warning systems, shipboard radar systems, battlefield surveillance systems and any other radiating RF sensor that can be intercepted. Although some military experts question the need for ARMs, countries continue to develop and build ARMs, including countries new to developing ARMs such as Germany, Taiwan, China, and Brazil. This is in response to the double-digit SAM radars such as the SA-10, SA-11, SA-12, SA-15 and SA-17 that can be integrated into a formidable IADS [14]. To address future SEAD/ARM requirements, three measures of eﬀectiveness have been proposed: combat attrition, eﬀort expended, and eﬃciency [1]. The combat attrition measures how many aircraft have been shot down in recent conflicts. Table 16.1 shows that the loss of U.S. combat aircraft has steadily declined both in absolute terms and relative to the number of combat sorties flown. This identifies that SEAD is an important contributor to aircraft survivability. The amount of eﬀort that is expended to protect U.S. aircraft can be used to assess SEAD capabilities. As shown in Table 16.2, 20—30% percent of all combat sorties in recent conflicts were devoted to SEAD. That is, SEAD continues to be a growing mission area of concern. While suppressing enemy air defenses through EW or intimidation can eﬀectively protect U.S. aircraft, destroying enemy air defenses is generally preferred to suppressing them because of the enduring eﬀect that destruction has on the enemy’s air defense. Table 16.3 shows that the USAF has had mixed results

558

Detecting and Classifying LPI Radar

Table 16.2: Estimates of Combat Aircraft Losses (from [1]) Conflict Vietnam Desert Storm (Iraq) Bosnia Kosovo N./S. Watch

Combat Sorties 219,407 68,150 2,451 21,111 268,000

SEAD Sorties 11,389 4,326 785 4,538 67,000

% 5.2 6.3 32.0 21.5 25.0

Table 16.3: Destructive SEAD: Some Estimated Results (from [1]) Conflict Desert Storm Bosnia Kosovo N./S. Watch

Estimated Results 35 of 120 fixed SAM batteries destroyed 52 of 70 air defense targets destroyed 3 of 25 SA-6 batteries destroyed, 10 of 41 SAM radars destroyed 33 of 35 air defense targets damaged, but many rebuilt and improved

in recent conflicts destroying enemy air defense targets. In cases like Iraq, DEAD eﬀorts have been somewhat successful. In Kosovo however, the SAM threat to NATO’s aircrew proved far more pronounced and harrowing than originally depicted [14, 15]. Even though only two aircraft were shot down (one of them a stealth F-117 by an SA-3), SEAD eﬀorts were comparatively less successful.

16.1.5

Miniature Air-Launched Decoys

The SAM always has the first shot and they start the fight knowing where the target is. That is, the target is always attacked from ambush. Even if a reactive ARM times out, it is, at best a revenge weapon [9]. Consequently, ARM shooters are always looking for a way to stimulate the threat and force it to reveal its position. The best way to do this is to stimulate the threat with jamming or decoys such as the miniature air-launched decoy (MALD) as shown in Figure 16.3. The second best way is to stimulate the threat with the SEAD aircraft. The “not so good” option is to let the strike aircraft stimulate the threat. The MALD is an expendable air launched vehicle that serves as a decoy for fighter aircraft and bombers mimicking their radar signatures and flight characteristics to distract the attention of enemy air defense systems. The MALD is a turbojet-powered decoy, configured as a swing-wing missile that can be launched from an F-16 or B-52 bomber. After launching, MALD flies a preprogrammed flight path into hostile air space to stimulate enemy air defenses, presenting itself to enemy radar as a real aircraft. Once radars and

Antiradiation Missiles

559

Figure 16.3: Miniature air-launched decoy. air defenses are activated they are intercepted by high speed antiradiation weapons

16.2

Antiradiation Missile Seeker Design

The ARM seeker competes with the warhead for valuable finance, weight and volume and presents a significant trade-oﬀ to the ARM designer. After all, in the endgame, it’s the warhead that counts [16]. However, if the seeker does not guide correctly to the target, more serious fratricide problems can occur. Protected by a wideband RF transparent radome, ARM seekers use passive RF homing with an antenna and microwave receiver. The antenna and receiver are tuned to the frequency of the threat radar to acquire and provide location data that can be processed to derive guidance commands. The guidance commands are passed to the missile’s autopilot that filters the signals to produce guidance and control commands that are sent to the control surfaces. Stability and control of the flight path are then provided by the control surfaces. An ARM may have a mid-course as well as a terminal phase of the flight.

16.2.1

Antenna Design

The ARM must detect and track the radar radiation over a very broad bandwidth. It must also have a wide beamwidth in order to detect the emitters at large angles oﬀ boresight. Spiral antennas are frequency independent antennas that can be used to obtain dual-polarized, rotationally symmetric, multiple-mode patterns over a very broad frequency range [17]. Frequency independent antennas are antennas whose geometries are specified by angles and their radiation pattern, impedance and polarization remain virtually unchanged over a large bandwidth. These features make antennas such as the logarithmic and conical spirals a good choice for the ARM seeker. They can

560

Detecting and Classifying LPI Radar

also be implemented with printed circuit technology with a simple microstrip feed network topology that facilitates ease of fabrication [18]. Being conformal with the skin of the airframe and not consuming the internal volume of the nose cone can also be an asset when dual-mode seekers are considered. They can also be fixed in place within the nose, do not require a high-precision gimbal and provide a low cost approach [16]. The antenna performance is not constant for all frequencies. There are physical bounds that limit the band over which the performance can be held almost constant [19]. The performance varies over the bandwidth in a manner that is periodic with the logarithm of the frequency. Consequently, they are called logarithmically periodic or log-periodic antennas. The most popular of those have shapes prescribed by logarithmic spiral curves or log-spirals. As an example, a logarithmic uniplanar spiral antenna that covers a 9:1 bandwidth with a return loss better than 10 dB from 0.4 GHz to 3.8 GHz is described in [20]. The logarithmic spiral antenna has N arms interleaved in a spiral pattern about the center. Their electrical dimensions however scale with frequency. The feed network at the center of the antenna acts as a beamformer and splits the power into the arms with a linear progression in phases and equal amplitudes to produce the various modes of radiation. Radiation occurs from the points on the spiral which have a half-wavelength in transmission line between them. Therefore higher frequencies radiate from the antenna near the central feed point and lower frequencies from the edges. The mutual coupling between arms relates the excitations at the feed ports to the eﬀective pattern radiated by each arm. An N = 2-arm spiral consists of two interleaved arms wound in a spiral, each terminated in a resistance. N arm spiral antennas are rotationally symmetric such that the rotation of an arm about its axis by 2π/N does not change the spiral structure [17]. An N arm spiral can radiate or receive N − 1 independent (characteristic) modes. The shape of right-handed planar log-spiral antenna is shown in Figure 16.4 and is based upon the logarithmic spiral curve defined by the generating equation [21] (16.1) ρ = ρ0 ea(φ−φ0 ) where ρ is the radial distance from the origin in the direction given by the angle φ, and ρ0 is the radius for φ = φ0 . For a logarithmic spiral, a is a constant that controls the flare rate of the spiral (1/a is the spiral rate or rate of expansion of the spiral). We note that the spiral constant a=

1 dρ = cot ψ ρ dφ

(16.2)

where ψ is the angle between a tangent to the curve at any point and a line to the origin at that point. Since ψ is constant for a given logarithmic spiral, an alternative name is equiangular spiral [22].

Antiradiation Missiles

561

Figure 16.4: Equiangular spiral curve with ρ = ρ0 ea(φ−φ0 ) . In wavelengths, (16.1) can be written as ρ0 ea(φ−φ0 ) ρ = λ λ

ρλ =

(16.3)

which shows that changing the wavelength is equivalent to varying φ0 , which is just a rotation of the infinite structure pattern and thus results in a frequency independent antenna. The total length L of the spiral can be calculated as [22] L=

8

ρ1

ρ0

^

2

ρ

w

dφ dρ

W2

1/2

+1

dρ

(16.4)

which can be reduced to 5

L = (ρ1 − ρ0 ) 1 +

1 a2

(16.5)

where ρ0 and ρ1 represent the inner and outer radii of the spiral shown in Figure 16.4. The design of a planar logarithmic (equiangular) spiral antenna can be accomplished using (16.6) ρ1 = ρ0 eaφ

562

Detecting and Classifying LPI Radar

Figure 16.5: Two-arm equiangular spiral plate (adapted from [21]). as edge number 1 (see Figure 16.4). Edge number 2 has the same spiral curve but is rotated through a rotation angle δ as ρ2 = ρ0 ea(θ−δ)

(16.7)

The other half of the antenna has edges that make the structure symmetric (opposite configuration) [21]. Rotating one spiral arm by one-half turn brings it into congruence with the other arm. This assures the antenna can receive signals of either right-hand polarization or left-hand polarization. A two-arm spiral has φ0 = 0, π. The generating equations for the congruent spiral are ρ3 = ρ0 ea(φ−π)

(16.8)

ρ4 = ρ0 ea(φ−π−δ)

(16.9)

and The structure is shown in Figure 16.5 and is self-complementary containing a good degree of pattern symmetry with δ = π/2. The frequency of the spiral antenna at the upper end of the operating band fu is determined by the feed structure [21]. For a = 0.221, the minimum radius ρ0 ≈ λ/4 at fu . A nearly equivalent criterion is that the circumference in the feed region Cu = 2πρ0 = c/fu . The circumference of a circle just

Antiradiation Missiles

563

Figure 16.6: Archimedean spiral antenna with left hand circular polarization (radiation out of the page) [21] ( c John Wiley & Sons, Inc. 1997). enclosing the spiral can be used to set the low frequency limit fl as Cl = 2πρ = c/fl . The low frequency limit set by the overall radius is approximately a quarter wavelength at fl . For example, consider a spiral with one and one half turns with a = 0.221. Here the maximum radius R = ρ(φ = 3π) = 8.03ρ0 which is c/4fl . At the feed point R = ρ(φ0 ) = ρ0 = c/4fu . The bandwidth is then fu /fl = 8 which indicates an 8:1 bandwidth (a typical value). To maintain a large bandwidth, the antenna must also be fed by an electrically and geometrically balanced line. This feed is often referred to as an infinite balun and has an impedance of Z ≈ 120Ω [21]. The radiation pattern of the self-complementary planar equiangular spiral antenna is bidirectional with two wide beams broadside to the plane of the spiral. The filed pattern is approximately cos θ when the z-axis is normal to the plane of the spiral. The half-power beamwidth is thus approximately 90o and the polarization is near circular over wide angles. Spiral antenna gain values range between 2 and 4 dB. The frequency limit is typically 500 MHz to 18 GHz. In the Archimedean spiral antenna, named after the third-century B.C. Greek mathematician Archimedes, the radial distance ρ is linearly proportional to the polar angle φ in the generating equation (rather than exponentially related). It flares more slowly as shown in Figure 16.6. The generating

564

Detecting and Classifying LPI Radar

Figure 16.7: Cutaway view of the programmable wideband British alarm showing the seeker and spiral antennas. equations for the Archimedean spiral antenna are ρ = ρ0 φ

(16.10)

ρ = ρ0 (φ − π)

(16.11)

and The successive turnings of the spiral have a constant separation distance (equal to 2πρ0 if φ is measured in radians). The arms are fed 180o out-ofphase at F1 and F2 giving the antenna circular polarized radiation which is frequency independent. The radiated fields created by the currents are orthogonal, equal in magnitude and 90o out of phase. A unidirectional beam can be created by backing the spiral with a metallic cavity behind the spiral. The pattern of the cavity-backed Archimedean spiral can be modeled empirically by [21] (16.12) F (θ) = cos5.8 (0.53θ) and has a half power beamwidth of 74o . Figure 16.7 shows a schematic cutaway drawing of the British alarm ARM and shows the use of four planar Archimedean spirals to cover the quadrants of interest. Conical equiangular spirals are also often used in ARM seekers since they generate a unidirectional pattern. Figure 16.8 shows the schematic of a conical equiangular spiral. The edges of one conical spiral surface are defined as

Antiradiation Missiles

565

Figure 16.8: The conical equiangular spiral antenna [21] ( c John Wiley & Sons, Inc. 1997). ρ = e(a sin θh )φ

(16.13)

of which the planar spiral is a special case with θh = 90o . Larger values of θh in 0 ≤ θh ≤ π/2 represent less tightly wound spirals [22]. The generating equations for the conical equiangular spiral are ρ1 = e(a sin θh )φ (a sin θh )(φ−δ)

ρ2 = e

(16.14) (16.15)

and δ = π/2 for the self-complementary configuration. The edges of the arms maintain a constant angle α with a radial line for any cone half-angle θh a = cot α

(16.16)

The advantage to the conical spiral is that it provides a unidirectional radiation (single lobe) toward the apex of the cone with the maximum along the axis. It also preserves the circular polarization and relatively constant impedances over the large bandwidths required [22]. Typical patterns for θh ≤ 15o and α ≈ 70o have half-power beamwidths of 80o . For the band design, the apex diameter determines the upper frequency d = c/4fu . The lower frequency of the antenna is determined by the base diameter B = 3c/(8fl ) [21]. As an example of a conical spiral, the Russian Kh-31 ARM uses an array of seven conical elements as shown in Figure 16.9.

566

Detecting and Classifying LPI Radar

Figure 16.9: Photo of the Kh-31 seeker that uses a series of seven conical spiral elements. Several patents have been issued that address the shortcomings of spiral antenna designs for ARM seekers. Methods to counteract the threat of the radar shutting down and to also improve the boresight error of the antenna system and also reduce the radome error slope are reported in [23, 24]. Here the antenna system includes a parabolic reflector dish having a dielectric substrate and a conductive material coating on the substrate in order to provide a narrowbeam high-gain radiation pattern. The parabolic dish also has a conductive material coating on the reflector substrate defining the spiral antenna for a low-gain, wideband radiation pattern. To address coupling between the antenna and the missile body in the VHF band, a broadband polarization diverse monopulse spiral antenna with a body cancelled current array and radial arm-coupled log periodic loop antenna is described in [25]. To provide a novel nonobvious solution to the problem of fitting a number of spiral antennas having diﬀerent configuration senses into the space of a single spiral, the spirals can be symmetrically arranged about a point at the center of a circle. Each spiral antenna is deformed to occupy substantially all of the area within a sector of the circle [26].

16.2.2

Receiver and Signal Processing

A block diagram of an ARM including its seeker is shown in Figure 16.10 [27]. In this example, the receiver (RX) accepts signals from four antennas

Antiradiation Missiles

567

that are used to intercept and direction find the RF emission from the radar. Many designs include both a high-band and low-band antenna to improve the direction finding accuracy (smaller beamwidth). The frequency synthesizer is used to scan the instantaneous bandwidth through the operating bandwidth in order to search for the target radiation. The intercepted emissions are down-converted, and filtered with a passband filter. Logarithmic amplification is used in the RX and applied to the passband filter output. Logarithmic amplifiers are used widely in antiradiation seekers and can be classified into two primary families, the logarithmic IR/RF amplifiers and the detector logarithmic video amplifiers (DLVA) [28]. The logarithmic IF/RF amplifier obtains the logarithmic transfer function at the IF (or RF) frequencies, while the DLVA obtains the logarithmic transfer function in the video frequency domain. Advantages of the logarithmic IF amplifiers over the DLVA include an easily obtainable CW response (important in ARMs attacking LPI emitters), excellent pulse recovery time, fast rise time and wide instantaneous dynamic range. The DLVA, however, generally has a smaller logarithmic error over the temperature range and frequencies of interest. The DLVA has superior dual-channel tracking characteristics and is usually the choice for ARM monopulse direction finding. This is because it is easier to produce matched nonlinear circuits at video frequencies than at IF/RF frequencies [28]. The amplifier output is lowpass-filtered and the monopulse azimuth (AZ) and elevation (EL) error signals are digitized. Also digitized are the RF frequency, the pulse time of arrival (TOA), the pulse width (PW), and the amplitude of the pulse. The signal processing then gates these error signals and uses pulse discriminant logic, deinterleaving, and a PRF correlator in order to sort the various radar signals being intercepted including their angular location. A Kalman filter is then used to derive the command acceleration from the seeker line of sight rate on the selected target signal. The autopilot then filters these commanded accelerations, which are then applied perpendicular to the airframe velocity vector to guide the missile to the target.

16.2.3

Dual-Mode Design

There are two major problems that aﬀect ARM performance. The first consideration is that air defense radars, when anticipating an ARM attack, usually operate in a blink mode turning on just long enough to obtain tactical information then shutting down to avoid attracting ARMs. The second problem is that if the radar stays active allowing the ARM to be launched against it, some attacks will fail because some of the radar energy bounces oﬀ the ground creating a false (multipath) target [29]. If the multipath is not too severe, the problem can be addressed using leading-edge track. To address more significant multipath situations and also counter the blink mode the concept of the dual-mode ARM seeker has been explored.

568

Detecting and Classifying LPI Radar

Figure 16.10: Block diagram of an antiradiation missile seeker (from [27]).

Antiradiation Missiles

569

Dual-mode ARM seekers can increase the capability of the missile when the RF radiation source shuts down. A unique dual-mode guidance scheme devised by the U.S. Army researchers was key to developing a more eﬀective ARM with a minimal increase in cost and weight. The dual-mode seeker would retain the traditional passive mode RF homing capability but would also have either an imaging infrared or active millimeter wave (MMW) radar mode. These latter modes do not require radar emissions from the target and can deal with blink tactics. They can also give higher accuracy when used in the final stage of the attack. The addition of a second guidance mode involves additional hardware increasing the manufacturing costs of the missile. Note that the design and production of ARMs represent a balance between the technology that is incorporated into the missile and the ability of the manufacturer to sell the weapon system. The solution proposed by the U.S. Army is based on an active MMW seeker, but adds to that seeker antiradiation homing antennas and down conversion elements as shown in Figure 16.11. The antiradiation homing antennas intercept signals emitted by enemy air defense radar but instead of passing these signals to a dedicated receiver and guidance system, the antennas pass them to the conversion elements. The task of these conversion elements is to convert the intercepted signals to the IF that is also used by the active MMW processing. This IF could then be handled by the signal processor that already exists as part of the MMW seeker. Use of the same processor to handle both passive and active-mode radar signals greatly reduces the cost penalties of providing the second guidance mode. At least three or four passive detector channels should be used. The associated antennas would be mounted on the exterior of the missile at regular intervals around the circumference of the fuselage. With proper phase relationships between detector channels the azimuth and elevation direction finding (DF) information can be provided. The antennas should have a broad beamwidth so phase comparison monopulse techniques can be used rather than the alternative amplitude comparison DF technique. The angle of arrival of the enemy radar signal would be determined by comparing the phase of the emission signals from the individual antennas. During the initial and mid-course portions of flight the dual-mode missile would use its passive-radar mode to home in on the emissions from the hostile radar. During the terminal phase of the attack, it would switch to the active MMW mode, acquire the hostile radar and conduct an accurate attack that does not depend on the target remaining active. The distance from the target at which the missile switches modes is a function of its speed and maneuverability and is typically 2—4 km. Another example of a dual-mode ARM seeker is Alliant Techsystem’s advanced antiradiation guided missile (AARGM) shown in Figure 16.12. Developed under the Navy’s Quick Bolt program, the passive conformal array antenna provides high accuracy wideband DF capability [30]. Autonomous

570

Detecting and Classifying LPI Radar

Figure 16.11: MMW/Passive detector channels diagram. target detection, identification, tracking and location ranging of the target are provided. The large field of view, sensitivity, frequency and DF accuracy and processing enable the weapon to be successful without an independent targeting system. In addition to homing in on the signal emitted by the hostile radar, the AARGM’s dual-mode guidance includes an active MMW radar. This section of the seeker provides terminal target acquisition, tracking, guidance and fusing to find its target even if the hostile radar is no longer radiating (antiARM tactics). If the radar shuts down, the MMW will go into a search mode. Since the seeker is in the MMW band it can detect RF scattering from the radar antenna, radar platform and missile launcher [30]. An integrated GPS/INS navigation suite is also included in the seeker to provide mid-course guidance and supply the rough coordinates to fly to after the radar shuts down. This prevents the ARM from missing the target in the terminal phase and most importantly, keeps the weapon from landing in the wrong country (preventing fratricide) [13]. It also enables a sensor fusion and autonomous ranging capability. These features extend the AARGM capability providing a long-range, time-critical strike weapon against other than the traditional ARM radar targets. That is, the warfighter survivability is increased with the additional speed, range and targeting capability. The AARGM weapon also has a network-enabled capability with a receiver that links the weapon to na-

Antiradiation Missiles

571

Figure 16.12: Advanced Anti-Radiation Guided Missile (AARGM) seeker. tional systems targeting data. A burst transmitter that transmits critical target data into the warfighter’s information warfare network prior to missile impact on the target is also provided [30].

16.2.4

Signal Processing

To learn and recognize the diﬀerent threat radar emissions being intercepted, traditional if-then-else constructs have been traditionally applied when the radar parameters being sorted (e.g., pulse width and time of arrival) are known. If a new radar emission is intercepted, the deinterleaving process for example may have problems. Artificial neural networks have also been applied with some success due to their ability to learn [31]. To understand this, consider that the threat radar signal features can be quantified. Signal angles of arrival (AZ, EL) and SNR are examples of extrinsic features having to do with where the emitter is located. Carrier frequency, pulse width, pulse repetition pattern and sophisticated RF modulation are intrinsic features having to do with what particular radar is active. These features can be used eﬃciently in a neural network application. An adaptive network sensor processor was designed and implemented in an ARM software application in [31]. They demonstrate that noisy binary inputs could be characterized with respect to noise amplitude and shape by a recall procedure that was tuned to enhance the analog output feature shapes. They also demonstrate that analog input shapes could be stored and recalled and that unstored states could be discriminated against without an output nonlinearity.

572

Detecting and Classifying LPI Radar

In summary, modern microelectronic technology has made it possible to put immensely sophisticated detection and analysis systems into the ARM. Each missile carries its own radar seeker, signal analysis equipment and a threat file, which enables it to identify virtually any radar by its signal structure—frequency, pulse length, modulation and pulse repetition frequency. The ARM can leave the launch aircraft and search for radar signals, comparing received pulses with a comprehensive threat file, in order to find and then home onto the greatest hostile threat. With the loiter capability (e.g., HARM and Alarm), the ARM can climb to altitude, deploy a parachute and then search for target signals as it descends slowly. Once a target has been identified, a high-speed attack phase is initiated, which enables the missile to get to the target in a very short time. Both types have inertial navigation systems which can store positions from which signals have been detected, and then guide the missile to the selected target without further signal inputs. Switching oﬀ the radar provides little protection against this sort of capability. In any case, radar is a fundamental part of many air defense systems, often providing direct control of anti-aircraft missiles in addition to detecting and tracking targets. Such radar systems must have a high priority in the threat file carried by any antiradiation missile and switching oﬀ the radar for self-protection will render the complete missile system ineﬀective. Partly as a result of this, there is a steadily increasing emphasis on highly mobile radar systems although mobility is unlikely to provide a defense against an imminent attack. If an ARM has already been launched from an aircraft, the amount of warning will be measured in seconds. If the launch aircraft pops up over the radar horizon, detects a hostile radar emission and then launches an ARM, the radar will have its first warning of the attack when it is only about 15 km away. This would probably give it between 10 and 20 seconds to reorganize. As shown in Figure 16.13 the F-4G Wild Weasel can carry an air-to-ground missile (AGM)–AGM-88 highspeed ARM (HARM); the AGM-65 Maverick, which has an infrared seeker; the ALQ-119 electronic attack pod; the AGM-78 Standard ARM; and the AGM-45 Shrike ARM.

16.2.5

Future ARMs–Addressing the LPI Emitter

Until recently, almost all radars were designed to transmit short-duration pulses with a high peak power. This type of signal is easy to detect using relatively simple, traditional ARM seeker receivers as shown in Figure 16.10 making the radar source vulnerable to an ARM attack. With the arrival of the LPI requirements, the ARM seeker and signal processing methodology must be revisited. The use of very low peak power (e.g., PCW = 1 mW) requires the ARM seeker to have a much higher sensitivity in order to detect these types of signals. With the increasing number of radars using LPI techniques, the ARM is now required to measure and characterize conventional pulsed

Antiradiation Missiles

573

Figure 16.13: F-4G Wild Weasel carrying an AGM-88 HARM, AGM-65 Maverick, ALQ-119 electronic attack pod, AGM-78 Standard ARM, and an AGM45 Shrike ARM. radar signals as well as detect and characterize the LPI signals. Detection of LPI signals can be accomplished using a number of diﬀerent receiver architectures. The signal processing functions can be quite intensive if all of the received data (pulsed waveforms and LPI waveforms) is digitized at the IF band and analyzed using signal processing. Figure 16.14 shows an example of an LPI signal, a pulsed emitter signal and the presense of thermal noise within the ARM seeker. A solution to the problem of overloading the signal processor when LPI signals are present along with pulsed waveforms can be addressed with an LPI signal discriminator. A block diagram of the discriminator is shown in Figure 16.15. The LPI signal discriminator is operatively coupled to the down converter and produces a trigger signal that is used when the incoming signal is above a predetermined threshold, to thereby transfer the digitized signal to a special digital signal processor for analyzing the incoming LPI signal. The architecture suppresses the high-peak power, short duration signals and triggers a data buﬀer for gating the digitized LPI data to the digital signal processor [32]. The LPI signal discriminator in an analog processor uses a cascade of IF amplifiers with a pad between the amplifiers to distribute the signal power evenly throughout the chain and soft-limit the strong pulsed signals that are received. The amplified signal is detected by a large dynamic

574

Detecting and Classifying LPI Radar

Figure 16.14: LPI and pulsed signal amplitudes within an ARM seeker as a function of time (from [32]). range, successive detector log video amplifier. The logarithmic video output is further compressed using a follow-on video logarithmic amplifier before the signal is time-integrated by one or more integrators. A threshold comparator receives the output from the integrators to provide a trigger pulse output when the input crosses a predetermined threshold value set by the signal processor [32]. The LPI emitter can also be detected with a suﬃcient amount of integration of the intercepted energy. For each direction of arrival, an optimal detector is able to integrate the energy of the emitted signal of which the parameters are unknown. Using a multichannel detector, the diﬀerent channels can be tuned onto diﬀerent durations and passbands for the noncoherent integration. The output of each channel depends on the time of arrival and the starting spectrum frequency. Searching for the emitter in time and frequency is most conveniently done in the time-frequency domain which is easily calculated as shown in the previous chapters. A multichannel detection algorithm recently suggested for time-frequency domain LPI detection is given as [33] ξ(p, q) =

t3 0 +B 0 +T f3 t=t0 f =f0

|G(t, f )|2

(16.17)

which uses the Gabor time-frequency distribution G where t0 is the signal’s time of arrival, f0 is the initial spectrum frequency, T is the signal duration and B is the signal bandwidth. This noncoherent integration is done using two-dimensional sliding windows as shown in Figure 16.16 [34]. In Figure 16.16(a) a model of the time domain signals within the receiver are shown

Antiradiation Missiles

575

Figure 16.15: Block diagram of an analog LPI signal discriminator (adapted from [32]).

Figure 16.16: (a) Time domain and frequency domain model of the thermal noise and LPI emitter signal and (b) two examples of a noncoherent integration sliding window for detection of the LPI signal (adapted from [34]).

576

Detecting and Classifying LPI Radar

Figure 16.17: Block diagram of a digital FMCW signal discriminator (adapted from [35]). and include the LPI signal x(t) and the receiver’s thermal noise n(t) in the time domain and the magnitude spectrum |X(f )| and |N (f )| in the frequency domain. Another architecture for detecting FMCW LPI waveforms employs a technique described as “deramping” which forms an adaptive matched filter to the linear FMCW signal in order to achieve the processing gain that is equal to the LPI signal’s time-bandwidth product [35]. A block diagram of this technique is shown in Figure 16.17. The deramping process mixes the input signal with a locally generated linear FM signal to produce an output signal with a reduced FM slope in comparison with the input signal. To construct a matched filter, the carrier frequency, modulation period and the modulation bandwidth must be known. To determine these parameters, the matched filter must be adaptively formed. A multichannel arrangement is proposed by examining the output of an FFT filter bank using a CFAR scheme that sets the threshold for determining the channel hit. The channel that yields the first detection has its matched filter parameters adaptively changed to achieve optimal processing gain.

Antiradiation Missiles

16.3

577

ARM Performance Metrics

There are 10 metrics that may be used to determine the capability of an ARM missile. These are presented below from [36]. • Maximum Range: Measure of how distant a radar can be successfully engaged by an aircraft at a given altitude. • Speed: Measure of how quickly the missile can reach its target. Slow missiles provide the radar operator time to react and shut down. • Frequency coverage: Measure of how many diﬀerent types of radar can be identified, tracked, and engaged by the missile. Low band coverage is important since it allows engagement of Early Warning (EW) and Ground Control Intercept radar. High band coverage is also important since it allows engagement of SAM fire control radar and illuminators. • Pulse density, CW limitations: Measure of seeker’s ability to identify specific radar in a high pulse density threat environment. The seeker must be capable of de-interleaving pulse trains from many radars in order to select a specific target. This also includes the ability to identify the LPI emitters that are present. • Electronic protection capability: Measure of weapon’s ability to resist seduction by dummy emitters and decoys. This also includes the ability of the ARM to withstand a directed energy attack on the seeker. • Lethality: Determined by accuracy and warhead eﬀectiveness, a measure of what kill probability can be achieved. If the ARM has poor lethality, more rounds must be fired on average per killed radar. • Deliverable Payload: Measure of the delivering aircraft’s payload of ARMs. • Flexibility: Measure of how many diﬀerent modes exist for the weapon. The more delivery modes, the more diﬃcult it is for the opponent to devise defensive measures. • Cost: Measure of how many weapons can be delivered per dollar expended. • Integration with the launch aircraft: Measure of how weapons can exploit the launch aircraft’s onboard RWRs, radar homing and warning system, or emitter locating system. As pointed out in [36], the decision to select a particular type of ARM is not trivial and the ultimate system level metric of usefulness is that of how many hostile radars can you take down for what dollar investment in ARMs, ARM support costs, and aircraft integration is required.

578

Detecting and Classifying LPI Radar

16.4

Former Soviet Union and Warsaw Pact Allies

The former Soviet Union and the current Russian Federated States have been developing ARMs since the 1960s. Unlike the United States, the Soviet Union did not develop aircraft specialized for SEAD missions. That is, they didnt treat SEAD as independent air operations [37]. The Soviet’s development of its ARMs was driven by doctrine of a massive frontal air assault on the most common threat at the time, Western Europe. Since this assault would have numerous aircraft, these ARMs did not have to be sophisticated and no dedicated SEAD aircraft were fielded. SEAD missions were flown to support air-ops on a tactical level (by nonspecialists). They relied on signals intelligence (SIGINT) and other recon assets and preferred preplanned strikes on known enemy IADS rather than targets of opportunity [37]. With the theater of war in western Europe, the western SAM threats (late 1950s, early 1960s) consisted of the U.S. Nike Ajax, Nike Hercules, U.K. Thunderbird, and the Bloodhound systems. With the Ilyushin Il-28 Beagle (nuclear weapon platform) having a cruising speed of only 500 mph, no low-level penetration was attempted. Following this, the Yakovlev Yak-28 (Brewer) supersonic (1960) and Sukhoi Su-7 (Fitter-A) supersonic (1960) also provided no solution to the SAM problem. Instead, the Soviet Union relied on mass nuclear weapons employment. Not until 1963 did work begin on the first tactical ARM. Table 16.4 lists the ARM weapons developed along with their NATO name and year the ARM entered service. Table 16.4: Russian ARM Development Missile AA-10 AS-4 AS-5 AS-6 AS-9 AS-11 AS-12 AS-16 AS-17

16.4.1

NATO code Alamo Kitchen Kelt Kingfish Kyle Kilter Kegler Kickback Krypton

Russian name R-27P Kh-22MP KSR-2P Kh-26MP Kh-28, Kh-28E Kh-58 Kh-25MP, Kh-25MPU Kh-15P Kh-31P

Entered Service 1989 1974 1962 1969 1973 1977 1981 1988 1991

AA-10 Alamo

The AA-10 Alamo is an air-to-air missile fitted with a passive seeker that homes in on the emissions from a threat fighter’s radar. It was fielded in 1989

Antiradiation Missiles

579

Figure 16.18: AA-10 Alamo (from [39]). and is now being possibly exported to India and China [38]. The missile can be used in two modes. One mode is in conjunction with the launch aircraft’s radar. The other mode is one in which the launch aircraft does not use its fire control radar at all. Instead the passive seeker 9B-1032 is used to detect the most powerful radar emission which is then reported to the pilot. A photo of the AA-10 is shown in Figure 16.18 [39]. The Alamo is intended for use against enemy fighters at long range, when the launch aircraft may still be beyond the maximum range of the target’s radar. Since the weapon uses passive homing, it will give the target no warning that a launch has been made. Radars that are fielded on F-15 and F-16 aircraft along with other western fighter radars are the R-27P’s primary targets with the main aim being to stop the threat aircraft radar from emitting. The ARM seeker is capable of detecting emissions from a threat radar at ranges up to 120 km. The homing head is however, capable of detecting a target from a range of more than 200 km, but the R-27EP cannot carry out an interception at such distances. 1 The flight time would exceed the operating duration of the missile’s onboard power supply. Vympel is working on ways of increasing the operating time of the power supply in order to allow R-27EP engagements at up to 200 km. The deployment is believed to have an eﬀect on NATO tactics spurring radar upgrades to more LPI emitters and the use of towed radar decoys. There is also thought of producing a passive-seeker variant of the R-77 AA-12 Adder as a successor to the R-27P [38].

16.4.2

AS-4 Kitchen

The Kh-22MP with NATO code name AS-4b Kitchen was built by Raduga is launched from the Tu-22M “Backfire B,” Tu-20 “Bear G,” and Tu-22 “Blinder B” aircraft. The missile entered service in 1974 and is shown in Figure 16.19 1 Vympel oﬀers two versions of the missile: the standard R-27P with a maximum range of 72km and the R-27EP version with a bigger rocket motor which gives a maximum range of 110km.

580

Detecting and Classifying LPI Radar

Figure 16.19: Kh-22 Kitchen (from [40]). [40]. It is used against ship- or ground-based radars and has a 930-kg HE blast fragmentation warhead with an active laser fuse. Guidance is inertial with a passive radar terminal seeker. The passive guidance (PG) radar seeker can lock on to a target from a distance of 250—270 km. The inertial guided versions use the PSI Doppler radar to compute distance covered. The passive radar homing missiles have the PGP passive radar seeker with a range of 380—350 km [41]. After launch the missile climbs to an altitude of 22,500m for cruise flight stabilized by the APK-22A autopilot and then dives into the target at an angle of 30 degrees. Maximum launch range depends on the speed and altitude of the launching aircraft: from a speed of 950 km/h and an altitude of 10 km it is 400 km and from a speed of 1,720 km/h and an altitude of 14 km it is 550 km. The initial versions of the Kh-22 had a maximum speed of 3,600 km/h, which was increased to 4,000 km/h with the Kh-22M series that entered service in 1974 and 1976. The Kh-22B experimental version reached a speed of Mach 6 and an altitude of 70 km during tests in the 1970s [41].

16.4.3

AS-5 Kelt

The KSR-2P with NATO code name AS-5 Kelt was built by OKB MiG and could be launched from the Tu-16 “Badger C mod,” “Badger G” and had a maximum range of 220 km and a maximum speed of Mach 1.2. The Kelt shown in Figure 16.20 entered service in 1962, but was phased out by the late

Antiradiation Missiles

581

Figure 16.20: An AS-5 Kelt air to surface missile loaded on the wing pylon of an Egyptian Air Force Tu-16 Badger aircraft [42] ( c 2007 Jane’s Information Group). 1980s [42]. The operational ceiling of the missile was 9.1 km. About 25 Kelts were used by the Egyptian Air Force in 1973 against Israeli forces, and five are reported to have been successful. It is believed that 12 of these missiles were anti-radar versions of the AS-5.

16.4.4

AS-6 Kingfish

The KSR-5P with NATO code name AS-6 Kingfish was built by Raduga and was launched from the Tu-16 “Badger G mod.” It had a maximum range of 400 km with maximum speed of Mach 3.0 [43]. The AS-6 missile as shown in Figure 16.21 entered service in 1969, with a second version in 1973 for carriage on the Tu-95 “Bear,” and a third version in 1976 for carriage on the Tu-95M. There were reported to be around 100 missiles in service in Russia in 1990, but modified missiles were oﬀered for export as air targets and it is believed that all AS-6s had been removed from operational service by the end of 1994. Some AS-6 missiles were retained by Ukraine, but by 2002 it is believed that these missiles had been destroyed. The missile is launched from an altitude of 0.5—11 km after which it climbs to an altitude of 20 km for cruise flight. The missile starts its terminal dive 60 km from the target. The most recent version, the KSR-5NM also included the ability to loiter which added more flexibility to attack SAMs that shut down once the missile was in the air.

582

Detecting and Classifying LPI Radar

Figure 16.21: AS-6 Kingfish [37] ( c 2001 Horizon House).

16.4.5

AS-9 Kyle

Along with the Yak-28N supersonic bomber, the Kh-28 missile with NATO designation AS-9 Kyle, and the radar target and acquisition system, the K28P was their sole attempt to build a dedicated SEAD weapon system complex. The P comes from Russian word protivradiolokatsyonny meaning “antiradar.” At the same time the aircraft also became an EW jamming platform, the Yak-28PP Brewer-E. The jammer was taken from the Tupolev Tu-16PP and split among three of the Yak-28PP. Their most eﬀective suppression was when each with a diﬀerent jammer component, operated in one formation on each side of the ingress, egress corridor [37]. The development of the Kh-28 ARM with NATO code name AS-9 Kyle (built by MKB Raduga) began in January 1963 and was based on the Kh22 and KSR-5 missile technology. It entered service in 1973 and is shown in Figure 16.22 being loaded onto an Su-22M3. The Kh-28 seeker had a conically scanning antenna. Its range was 110 km with a speed of 800 m/s with launch altitude of 200—11,000m. From low altitude the launch range is reduced to 45 km. For guidance the missile originally used the APR-28 passive radar seeker developed by NPO Avtomatika. The seeker was later carried on the Su-24 Fencer-A (tactical bomber) and the Su-17M Fitter-C (tactical fighterbomber). It was tuned to the frequencies of the Nike Hercules shown in Figure 16.23, the Thunderbird, and the Bloodhound which is shown in Figure 16.24. Later the Kh-28M missile received a new passive radar guidance PRG-28M seeker that could be used also against the radars of the HAWK SAM system. After cancellation of the K-28P complex in 1967, NATO adopted a new

Antiradiation Missiles

583

Figure 16.22: Ground crews prepare to load a AS-9 Kyle (Kh-28) on an Su-22M3 Fitter-F [37] ( c 2001 Horizon House).

Figure 16.23: Nike Hercules SAM.

Figure 16.24: Bloodhound Mk 2 SAM deployed on its Type 202 launcher.

584

Detecting and Classifying LPI Radar

defense doctrine: “No Nukes.” In changing their SEAD doctrine, for air defense targets 300—400 km deep, the Tu-22K (Blinder-B), Su-24M (FencerD), and Tu-22M (Backfire) were employed to lay down chaﬀ corridors 40—50 km wide using two to three strike groups. The corridors were separated by 10 km and 2 minutes; two corridors were often oﬀset. One corridor was also used to suppress SAMs that had been located by SIGINT. Still there were no dedicated SEAD aircraft with the corridor task groups having 2 to 4 aircraft armed with Kh-28s. The Kh-28 has now been withdrawn from service in Russia. However, a small number may remain in operational use in other countries. It is believed that it was exported to Afghanistan, Azerbaijan, Belarus, Bulgaria, Georgia, Hungary, Iraq, Kazakhstan, Libya, Poland, Syria, Ukraine, and Vietnam [44].

16.4.6

AS-11 Kilter

The Kh-58 with NATO code name AS-11 Kilter uses a new seeker to engage surveillance pulse-radar systems such as the AN/TPS-43 and the AN/TPS44 used for ground controlled fighter intercept and the AN/MPQ-53 radar of the Patriot. Aircraft platforms include the Su-24M Fencer-D, MiG-25BM and Su-17M4. The missile shown in Figure 16.25, has a range of 120 km from a height of 10,000m and 160 km when fired at 15,000m. The missile entered service in 1977 and had a speed of 900 m/s. An upgrade to the missile (Kh58U) extended the range to 250 km [45]. The missile also has an improved seeker allowing lock-on after launch mode. The MiG-25BM Foxbat-F or Su24M with an upgraded Kh-58U missile under the wings is the closest thing the Russians have to a dedicated SEAD aircraft. They are concentrated at the 98th Reconnaissance Wing on the Kola Peninsula [37]. The passive radar seeker of the Kh-58 itself can target various surveillance radars in addition to the Nike-Hercules, HAWK, I-HAWK, and Patriot SAM systems. The missile performs a pop-up maneuver in the terminal phase to hit the target at a 20—30 degree angle which improves the eﬀectiveness of the warhead. The kill probability of the antiradiation version is claimed to be 80% within a 20m radius of the target radar. The Kh-58U was designed primarily for the MiG-25BM SEAD aircraft. It has extended range, improved aerodynamic characteristics and a guidance system allowing lock-on after launch mode, and a new rocket engine. The Kh-58E is an export version of the Kh-58U without the lock-on after launch feature. The missile can be launched at speeds of Mach 0.47 to 1.5 from altitudes of 0.1—22 km, but from low altitude the launch range of the Kh-58 is reduced to 36 km, and that of the Kh-58U to 80 km. The Kh-58 was exported to Bulgaria, Czechoslovakia, East Germany, and Poland [46].

Antiradiation Missiles

585

Figure 16.25: AS-11 Kilter (from [45]).

16.4.7

Kh-27

The Kh-27 antiradiation missile (no NATO designation) has a speed of 850 m/s and was conceived as a replacement for the heavy Kh-28. Conceived as an ARM variant of the earlier Kh-23 (AS-7 Kerry), the Kh-27 entered service in 1977 targeting the Nike Hercules, Thunderbird, Bloodhound and HAWK SAM systems. The missile was carried on aircraft platforms MiG-27 and Su-17M3 and had a range of 60 km when launched from 15,000m and 40 km from 5,000m. The new seeker was developed with a highly sensitive receiver with five antennas in the PRGS-1 type guidance version and with six antennas in the PRGS-2 version. Direction finding to the target was based on phase diﬀerence interferometry and was much more accurate than the conical scanning antenna in the Kh-28. The weapon saw limited service in the late 1970s and early 1980s, and was replaced by the ARM member of the “modular” Kh-25M AS-12 Kegler family.

16.4.8

AS-12 Kegler

The Kh-25MP and improved Kh-25MPU with NATO code name AS-12 Kegler (built by Zvezda) are dedicated antiradiation variants of the Kh-25 (AS-10) air-to-surface missile. The missile was given a new NATO code name because of its specific defense suppression role. The Kh-25MP eﬀectively replaced the Kh-28 (AS-9 Kyle) in Russian service. The missile entered service in 1981 [47]. The missile shown in Figure 16.26 had two interchangeable seeker heads with antennas tuned to the radar frequencies of the HAWK and Nike Hercules SAM systems respectively [48]. Targeting was done with the Vyoga ES

586

Detecting and Classifying LPI Radar

Figure 16.26: AS-12 Kegler (from [48]). pod. The missile was programmed to perform a “hump” maneuver in the terminal phase to hit the target at a 20—30 degree angle and thus improve the eﬀectiveness of the warhead. The seeker had tracking rates of 6 to 8o /s, azimuth coverage of 30o , and elevation cover from +20 to −40o . Most aircraft are reported to carry an APK-8 radar emitter locator pod with the KH-25MP missiles. The concept was also new since it had an interchangeable guidance system in the nose and tail modules attached to a common missile core [37]. It was carried on aircraft platforms MiG-27, Su-17M3 and M4. The missile has a range of 60 km and had a speed of 850 m/s at a launch altitude of 100—15,000m. It is reported as still being used in the Russian Air Force although in limited numbers. The Kh-25MP has a maximum range of 60 km when launched from medium altitude (30,000 ft), and a range of 25 km when launched from low altitude. The minimum range is 3 km [47]. The improved Kh-25MPU version is optimized for use against X-band surface-to-air missile engagement radars, and has a weight increased to 320 kg. The minimum range is 3 km, and the maximum range is reduced to 40 km. A successor antiradiation weapon to replace the Kh-25MP/MPU is under long-term development by Zvezda Strela now the Tactical Missiles Corporation.2 Very little is known about the status of this weapon, the Kh-38 [47]. The new missile is likely to be fitted with a dual-mode passive radar and imaging infrared seeker. Maximum speed: 3,100 km/h. The Kh-25MP is a later version based on the universal Kh-25M design. For threats in the A-waveband a PRGS-1VP seeker is used, whereas for A1-waveband threats a PRGS-2VP seeker is utilized. The Kh-25MPU is a modernized version designed to defeat also the Roland and Crotale SAM systems. The missile can be launched at altitudes of 50m to 10 km and has speeds of 600 to 1,250 km/h. The Kh-25MP was exported to East Germany, Czechoslovakia and 2 In March 2003 the Zvezda-Strela State Research and Production Centre transformed itself into the Tactical Missiles Corporation JSC (Joint Stock Company) following the incorporation of the various engine, seeker, electronics and other equipment concerns that were associated with its missile development programs.

Antiradiation Missiles

587

Figure 16.27: AS-16 Kickback [49] ( c 2007 Jane’s Information Group). Poland [47].

16.4.9

AS-16 Kickback

Little was known about the existence of this antiradar missile until the visit in 1988 by the U.S. Secretary of Defense to Kubinka airbase to see the Tu-160 Blackjack bomber. NATO has given this missile shown in Figure 16.27 the designator AS-16 Kickback and it has the Russian designator Kh-15. AS-16 is reported to be able to cruise at altitudes between 30m and 22 km. There is also a report that states that the missile can have a ballistic trajectory, reaching a maximum altitude of 40 km [49]. The missile has a range of 150 km when released from medium altitude (30,000 ft) against a large ship target, and about 100 km when released from low level. The AS-16 has a minimum range of 40 km. The missile can be released at altitudes between 300m and 22 km. Maximum speed is Mach 5.0. After launch from a speed of 1,000 to 2,100 km/h and an altitude of 0.3 to 22 km, the missile climbs to a height of about 40 km. After having acquired its target, the missile dives, reaching a speed of Mach 5 [49].

16.4.10

AS-17 Krypton

The Kh-31P with NATO name AS-17 Krypton entered service in 1991 and is shown in Figure 16.28. The development program began in the late 1970s, as a follow-on to the Kh-25MP (AS-12 Kegler). Guidance for the Kh-31P is by passive radar homing, with an inertial system to enable homing to continue even if the target radar is switched oﬀ. Three interchangeable seeker head options are available for the Kh-31P, each one tailored to a specific range of radar frequencies (Avtomatika L-111, L-112, and L-113) [50]. These seekers were tailored for use against the Nike Hercules/Improved Hawk and Patriot SAM systems plus the maritime SPY-1 Aegis phase array radar system.

588

Detecting and Classifying LPI Radar

Figure 16.28: AS-17 Krypton (from [51]). The Kh-31PM upgrade, now in development, will produce a single integrated wideband seeker (L-130, developed by the Avtomatika CKBA plant at Omsk) to replace the L-111, L-112 and the L-113. The MiG-27 Flogger usually carries an APK-8 radar emitter locator pod if equipped with the Kh-31P [50]. The missile has a cruise speed of 700 m/sec and a maximum speed of 1,000 m/sec. The Kh-31 can fly high- or low-level cruise profiles and can be launched at altitudes of between 100 and 15,000m. Launch speeds range from 600 km/h (Mach 0.65) to 1 m 250 km/h (Mach 1.5). The high-level cruise can be made at up to 15 km (50,000 ft), with a speed of M3.0. It is reported that the Kh-31 missiles can fly at low level, down to 200 m altitude, cruising at M 2.5 and can maneuver at 10g. The missiles can be programmed to climb at a distance of 2 km from the target, and to dive down onto the target. The missile is designed to be fired in salvos by one or several launch platforms. Due to the threat represented by the Kh-31, a unique U.S.-Russian accord was struck, for the acquisition of missiles by the U.S. Navy for test and trial purposes. Beginning in 1994, under a joint program with McDonnell Douglas (now Boeing), 13 MA-31 test vehicles were supplied for flight trials. The U.S. has launched its MA-31 targets from QF-4 Phantoms. Follow-on batches of MA-31 targets have since been delivered but U.S. access to the missile has now been suspended. In 1998, it was reported that Zvezda-Strela had developed an improved antiradar missile, using the export designation KR1, with a range increased to 400 km. This missile has been strongly linked

Antiradiation Missiles

589

with China. Several photographs have now emerged of Kh-31s in Chinese hands. These weapons have appeared in Chinese research facilities and have also been mounted on a full-scale engineering mock up of the Xian JH-7 strike fighter. Chinese sources report that a small numbers of Kh-31Ps have been purchased and used as the basis for an indigenously produced variant, the YJ-91. It remains unclear how many Russian-built Kh-31s have been supplied to China and how many (if any) have been assembled in China. Some sources believe that China has now established its own Kh-31 (YJ-91) production capability [50]. During the 1990s there were reports that an airto-air version of the Kh-31, designated Kh-31PD, was under development. This was thought to be an antiradiation missile, for use against important targets such as AWACS and JSTARS aircraft and others that use airborne early warning radar. The Kh-31 has been cleared for carriage on MiG-27 “Flogger,” MiG-29K and MiG-29SMT “Fulcrum,” Su-17 “Fitter,” Su-24M “Fencer,” Su-25TM “Frogfoot,” and the Su-30/Su-34 “Flanker” family aircraft. In June 2005 a new upgrade program for the Su-27 to make it compatible with all versions of the Kh-31 (and other advanced weapons) was revealed and is known as the Su-27M1. The Kh-31 is also being integrated on Russian air force Su-27s under the Su-27SM multirole upgrade program [50]. In 2006 an improved version of the Kh-31P was under test at Russia’s Akhtubinsk weapons test center (the Valery Chkalov State Fight Test Center, or 929 GLITs). This weapon was identified as the Kh-31PMK. The designation of the Kh-31PMK marks it as an export-dedicated program (K, Kommercheskaya, commercial). In practice the K in export programs also stands for China (K, Kitai). The Kh-31PMK is longer than a standard Kh-31P and its range is extended to approximately 200 km, indicating the incorporation of additional fuel for the ramjet. Integration of the Kh-31PMK on the Su-27SM would inevitably make it available for China, and China’s Su-30MKKs are already operating with the Kh-31P [50]. Special versions to attack AWACS aircraft such as the E-3A Sentry and an antiship version are also available.

16.5

United States

16.5.1

Shrike

After the time of the Korean conflict, the development of radar-guided surfaceto-air missiles (SAMs) added a new and lethal threat to U.S. aircraft. To combat these new threats, the U.S. Navy started development of an ARM in 1958, with the designation ASM-N-10. This missile program would become the AGM-45A Shrike, named for the predatory songbird Butcher Bird. The Shrike was based on the airframe of the AIM-7 Sparrow and had a top speed of Mach 2. The Shrike first saw combat in Vietnam in 1966 [4, 8].

590

Detecting and Classifying LPI Radar

Figure 16.29: Shrike missile AGM-45A (from [52]). The concept behind the Shrike missile, shown in Figure 16.29 was that the host aircraft’s radar warning receiver was used to activate the AGM-45’s seeker head that, in turn, notified the pilot (by an audio tone in his headset) that it had achieved a positive lock on the target signal. Following launch, the weapon’s guidance section continuously monitored the threat signal’s direction of arrival and generated the appropriate steering commands for the missile’s four mid-body steering surfaces [52]. This enabled the missile to follow the radar beam down to the emitter and destroy it. This would disable the SAM site, making it possible to destroy the SAMs themselves or to allow a strike package to pass through the SAM site’s airspace. The first Shrikes were equipped with seekers optimized for E/F band emitters (2—4 GHz). As other emitters arose, 10 additional seekers were developed to cover the different emitter bands including G-band (4—6 GHz) and I-band (8—10 GHz) [53]. The Shrike first saw combat in Vietnam in 1966. The Shrike was used by the Wild Weasels to suppress enemy air defense (SEAD). The Shrike had better range than the gravity weapons being used and did not require the aircraft to overfly the SAM sites to identify and destroy them. There were however, limitations to employing the Shrike missiles. In order to lock on to the target, the aircraft would have to fly directly at the SAM site. The aircraft must have had the correct AGM-45 loaded. Also, the maximum operational launch range of the AGM-45A was limited to 16 km but progressively increased to 46 km. Also, SAMs such as the SA-2 had a maximum speed of Mach 3.5 compared to the AGM-45 maximum speed of Mach 2. This would allow the SAM site to launch, guide to intercept, and turn oﬀ the emitter before the AGM-45 could strike the site. Furthermore, the AGM-45 needed to track the emitter until impact. If the emitter shut oﬀ, the AGM-45 would not be able to guide to it [37].

Antiradiation Missiles

591

Figure 16.30: Standard antiradiation missile (from [54]).

16.5.2

Standard ARM

The limited range and warhead of the AGM-45 led to the development of a larger AGM-78 standard ARM as shown in Figure 16.30 [54]. The development of AGM-78 combined the standard missile airframe (designed for shipboard use) with the Shrike seeker. The standard missile was a radarguided surface-to-air missile used for ship defense by the Navy. The standard ARM had top speed of Mach 2.5, with a maximum range at an altitude of 56 km. Due to its size, only two standard ARMs could be carried on an EA-6. The Navy then decided to integrate an improved broadband gimbaled seeker that allowed the aircrew to avoid flying directly at the target in order to fire the missile. The standard ARM was also able to remember the elevation and azimuth to the target if the emitter shut down. This did not guarantee the emitter would be destroyed since a small amount of drift in the navigation system would result in a miss. Although the AGM-78 was an improvement over the Shrike, its large size limited it to being carried on large aircraft. In addition, the standard missile airframe was complicated and costly to operate and maintain.

16.5.3

HARM

The U.S. Navy began development of the AGM-88 high speed antiradar missile (HARM) shown in Figure 16.31 which was light weight allowing it to be carried on U.S. fighters [55]. The top speed is described as over Mach 3. The maximum range at altitude is 65 miles. The HARM has only one seeker, which uses a broadband antenna to engage the emitters. The features of the HARM are shown in the cutaway view in Figure 16.32 [54]. The HDAM (HARM destruction of enemy air defense attack module) missile variant was developed partly to address the LPI emitter. It successfully engaged a simulated radar system that was radiating at a low power level. The new HDAM variant adds inertial navigation system/global positioning system (INS/GPS)

592

Detecting and Classifying LPI Radar

Figure 16.31: High speed antiradiation missile (from [55]).

Figure 16.32: Cutaway drawing showing the HARM features (from [54]). capability to the existing HARM.

16.5.4

AARGM

The AGM-88E advanced antiradiation guided missile (AARGM) demonstrates a dual-mode guidance section on a HARM airframe (see Section 16.2.3). The issue of shutdown is a major shortcoming in the SEAD element of the oﬀensive counter-air mission. The AARGM development is to produce an eﬀective and aﬀordable lethal SEAD capability against mobile, relocatable, or fixed air defense threats even in the presence of emitter shutdown or other anti-ARM countermeasures. The AARGM can be employed in the oﬀensive counterair/SEAD role in direct support of strike warfare, amphibious warfare, antisurface ship warfare, command and control warfare, and information warfare. The missile design provides a new multimode guidance section and modified control section mated with existing HARM propulsion and warhead sections. The new

Antiradiation Missiles

593

guidance section is designed to have a passive antiradiation homing receiver and associated antenna, a GPS/INS, and an active millimeter wave radar for terminal guidance capability enabling the missile to engage and destroy enemy air defenses in the event that these systems shutdown or employ other electronic protection. AARGM is projected to have the capability to transmit terminal data via a weapons impact assessment transmitter to national satellites just before AARGM impacts its target. Also incorporated is a provision to receive oﬀ-board targeting information, via the integrated broadcast system. The AARGM acquisition objective is 1,750 missiles [56]. It will provide USN and U.S. Marine Corps F/A 18 Hornet and EA-6B Prowler aircrews with a significantly improved capability to search for, identify, and destroy enemy air defense targets.

16.5.5

Aﬀordable Reactive Strike Missile

The aﬀordable reactive strike missile (ARES) is a derivative of the AGM88E advanced antiradiation guided missile (AARGM) under development for the U.S. Navy and was expected to enter its inventory after 2008 [57]. ARES would have a range greater than 50 nm and a speed of around Mach 3.0, making it the “only supersonic, tactical, GPS-guided strike weapon” available. The ARES concept features the same control section going into AARGM and presents an attractive option for those nations that cannot aﬀord to upgrade their HARMs to the AARGM configuration. Additional options include a semiactive laser seeker for human-in-the-loop control. In missions like pinpoint strikes in an urban setting this could allow parts of buildings to be targeted without bringing down the entire structure and injuring civilians and friendly troops. As with the AARGM, the new control section on ARES will enable pilots to program exclusion zones in which the missile will not strike. Aircraft operating the HARM or the AARGM, like the EA-6B, EA18, F-16, F/A-18, and Tornado, will not require software upgrades to carry ARES. The new missile retains the HARM’s rocket motor, airframe and warhead, but adds the new control section and an all-digital passive seeker and millimeter-wave active terminal seeker to the missile’s front. This allows it to accurately engage fixed-site and mobile air-defense radars that are emitting or have shut down to avoid detection.

16.5.6

Sidearm

The United States has also developed ARM’s for more defensive roles by taking advantage of obsolete AIM-9Cs to develop the AGM-122 Sidearm (Sidewinder ARM) as shown in Figure 16.33. The AIM-9C seeker was adapted to be a broadband passive radar seeker. It also has a gravity bias function added to its autopilot in order to facilitate loft launching from low-altitude, low-speed platforms. The AGM-122A was developed for use on Marine he-

594

Detecting and Classifying LPI Radar

Figure 16.33: Sidearm ARM being loaded onto an aircraft (from [58]). licopters (Bell AH-1W SuperCobra) to suppress air defense threats. The AGM-122 was used as a defensive weapon, rather than in an oﬀensive role and entered service in 1989 [58]. AGM-122A is noted as having a 10.2 kg high explosive and fragmentation warhead that is triggered by active laser and impact fusing. Range is given as being approximately 8 km and functionally, the weapon alerts the pilot of its host aircraft to lock-on via direction of lock-on symbology on his head-up display and an audio tone in his headphones [59]. The AGM-122 has a 10-mile range. Once the stock of AIM-9Cs was depleted, the Navy considered building new AGM-122s, but the program never happened. While Sidearm is less capable than modern antiradiation missiles (like AGM-88 HARM), it is still a cost-eﬀective alternative against low-tech threats [60].

16.5.7

Rolling Airframe Missile

The U.S. Navy has developed the rolling airframe missile (RAM) for ship self defense against incoming antiship cruise missiles (ASCMs). The RAM, designated the RIM-116, was a joint venture between the United States and Germany to develop a low-cost self defense system. The RIM-116 shown in Figure 16.34 uses the 5 inch rocket motor and warhead technology from the AIM-9 Sidewinder. The missile is capable of maneuvers up to 20g in any direction. The RIM-116 seeker is a dual-mode, passive radio frequency/infrared seeker. Initial guidance is provided by the passive RF seeker on the ASCM’s RF emissions. If the ASCM’s IR radiation is acquired, RAM transitions to IR guidance. Originally, the missile was cued by the ship’s ES suite or radar [61]. More recently, the RAM has replaced the 20 mm Gatling gun of the Phalanx system. This new marriage of RAM and the Phalanx system is

Antiradiation Missiles

595

Figure 16.34: Rolling airframe missile launch [61] ( c 2007 Jane’s Information Group). called the SeaRAM and combines RAM’s superior accuracy, extended range, and high maneuverability with the Phalanx high resolution radar systems. SeaRAM shown in Figure 16.35, is essentially a Phalanx Block 1B but with the gun replaced by the 11-cell launcher and is intended to extend ship selfprotection to ranges of 4 km and can enable prosecution of low Doppler targets. In addition to providing an on-mount J-band (12 to 18 GHz), digital MTI search radar and pulse Doppler monopulse tracker radar, there is also the electro-optical sensor used in the latest Phalanx systems for surface target detection.

16.5.8

Army UAVs

The U.S. Army is exploring potential requirements for an antiradiation missile for carriage by its larger unmanned air vehicles (e.g., AAI RQ-7B Shadow 200 UAV) to counter hostile UAV systems [62]. The concept calls for the antiradiation missile to target a hostile UAV system’s ground control station by following its command datalink. The option is one of a number of new weapon concepts being studied by the service as it prepares for the introduction of its new General Atomics Sky Warrior and Northrop Grumman RQ-8B Fire Scout UAVs. The development of an anti-UAV capability anticipates that UAV systems will continue to be an important operational target. Strategies such as targeting unmanned aircraft to take away the intelligence, surveillance and

596

Detecting and Classifying LPI Radar

Figure 16.35: Group).

SeaRAM missile launch [61] ( c 2007 Jane’s Information

reconnaissance capability is a significant tactical response. Other anti-UAV capabilities being studied include the use of electronic warfare techniques such as countertargeting and jamming of the command datalink.

16.6

France

The French introduced the Armat (Anti-Radar Matra) in 1984 which was an evolved variant of the antiradiation version of the French-British BAe-Matra AS-37 Martel missile. By using the AS-37 airframe and replacing the seeker and associated electronics with new and improved versions with added electronic protection, the missile shown in Figure 16.36 was given the capability to overcome decoys and jamming techniques including long radar switch-oﬀ periods. The microprocessor based seeker homes on to a programmed emitter and uses inertial midcourse guidance. Several interchangeable homing heads are used to cover the wide spectrum of target radar frequencies including Lband (500—2,000 MHz), S-band (2—4 GHz), C-band (4—8 GHz) and X-band (8—12 GHz) [63]. The missile can be launched from high or low levels and will home onto the radar or jamming transmissions of the pre-selected target radar. After lock-on of the missile seeker, the location, radar parameters and launch success zones are displayed to the aircrew who can then select the best launch time. With its high launch weight, heavyweight warhead and long range, the Armat is primarily an oﬀensive strategic ARM designed to

Antiradiation Missiles

597

Figure 16.36: AS-37 Martel. destroy early warning and ground control intercept radars. This is where it diﬀers fundamentally from the HARM and the ALARM, which are built to also perform as defensive ARMs carried as part of a mixed weapon load. The missile has been cleared for carriage on Jaguar, Atlantique, Mirage F1, Mirage III and Mirage 2000 aircraft. The missile is believed to have a maximum range of 100 km when launched from high altitude. An improved version has also been produced, the Armat-D, which is fitted with an updated passive homing seeker.

16.7

United Kingdom

In the early 1980s, the British conducted a study to replace their aging AS37s. The British decided on the Alarm for several reasons. The United States developed HARMs for specially equipped aircraft, such as the F-4G Wild Weasel and the EA-6. Both of these aircraft are equipped with sophisticated and complex emitter locating systems. Since the British have a smaller number of aircraft than the U.S., they did not want to limit the role of any aircraft by specially equipping them. With the smaller numbers, the British required that all of their fighters be able to conduct any mission. The British also did not wish to incur the cost and in-service support overheads of deploying and maintaining these sophisticated and complex systems. Additionally, the British thought that adopting the Weasel operational model would expose SEAD aircraft to attack more frequently, thus incurring high loss rates. The Alarm can be carried on all British fighters, such as the Harrier and Tornado, which carry up to nine Alarms. Figure 16.37 shows the launch of an Alarm from a Tornado [63]. The Alarm has a range of 28 miles and has five launch modes: direct, dual, loiter, universal, and area suppression. A unique feature to the Alarm is it parachute system for loitering over the target area. In the dual and loiter modes, the missile climbs to a high altitude above the target area and

598

Detecting and Classifying LPI Radar

Figure 16.37: Alarm missile firing from an RAF Tornado (from [63]). searches for the enemy emitter. If one is detected, the missile dives on the target. If not, it deploys a parachute and listens for the enemy emitter to come up. Once the radiation is detected, the missile jettisons the chute and dives on to the emitter. The parachute system allows the ALARM to loiter for several minutes. With ALARM-equipped aircraft in the area, enemy SAM sites would not know when it was safe to turn on their radars, thus suppressing their ability to deter attacking aircraft. Figure 16.38 shows the modes used by the Alarm. The Alarm’s seeker is similar to that of the HARM with a microprocessor controlled passive homing receiver, designed to locate and identify the characteristic Pulse Repetition Frequencies (PRF) of programmed threat emitters [63]. The Alarm has a wideband RF antenna/receiver and a conventional quartet of cavity backed spiral antennas, forming a fixed two axis interferometer with lower mid-band to hi-band coverage. Like the HARM, the Alarm has logic to select the highest value alternate target, should the primary target go oﬀ the air.

16.8

Taiwan

Taiwan is intensely concerned about China’s growing air power dominance of the Taiwan straits. Having an eﬀective ARM capability hinders China’s ability to conduct air operations from secure bases on the mainland. Since no country will export ARMs to Taiwan, its air force has developed its own ARM, known as the Tien Chien IIA. Tien Chien translates to “sky sword.” The Tien Chien IIA replaces the active radar seeker of the Tien Chien II air-to-air missile with a passive antiradar seeker and guidance section. The seeker is housed in a reprofiled, notched fairing, giving rise to speculation that it may use a dual-mode design, incorporating both passive RF and infrared sensors [64]. The Tien Chien IIA equips the Republic of China’s Air Force’s AIDC FCK-1 Ching Kuos (otherwise known as the IDF, Indigenous Defense Fighter).

Antiradiation Missiles

599

Figure 16.38: Alarm modes of attack (from [63]).

Figure 16.39: Tien Chien 11A being carried by an indigenous defense fighter. According to the Chung-Shan Institute of Science and Technology (CSIST), any Ching Kuo can carry the new ARM, as it requires no modifications to the launch aircraft. The ROCAF does not intend to field a dedicated “Wild Weasel” defense suppression force armed with the Tien Chien IIA. Instead, the capability will be introduced across the front-line fleet. Up to four Tien Chien IIAs can be carried by one aircraft on individual pylons—without losing the existing hardpoints for two Tien Chien IIs plus two wingtip-mounted Tien Chien Is. Tien Chien IIA can be carried on any aircraft equipped to carry the Tien Chien II as shown in Figure 16.39.

600

Detecting and Classifying LPI Radar

Figure 16.40: German ARMIGER [65] ( c 2007 Jane’s Information Group).

16.9

Germany

Germany, a longtime user of the HARM, is developing the ARMIGER (antiradiation missile with intelligent guidance and extended range). The Germans have been participating in the development of the international HARM upgrade program, the AGM-88D. The improvements consist of software and hardware upgrades including replacing the original mechanical gyros with a state-of-the-art GPS/IMU. The addition of GPS to the HARM would correct the long-standing problem of ARMs of what to guide on if the emitter shuts down. GPS allows you to fly to a certain point when the target is not emitting at all. However, the U.S. Navy decided not to proceed with the project. The Germans decided to proceed with the ARMIGER program as a replacement for the HARM. Due to concerns over whether it is wise to develop a single purpose weapon, the German Luftwaﬀe has decided to proceed slowly with the ARMIGER [65]. The ARMIGER is roughly the same weight as the HARM. The ARMIGER will have a GPS/IMU, as would the AGM-88D, to overcome the ARM problem when the emitter shuts down. In addition to the GPS/IMU, the ARMIGER will have a new technology passive radar/high-resolution imaging infrared dual-mode seeker (called ARAS). This dual-mode seeker will also combat the problem of an emitter shutting down while the missile is in flight. Typically, the ARMIGER would be launched using the passive radar and switch over to the infrared for terminal tracking if the targeted emitter shuts down. In addition to the seeker, the ARMIGER will have improved range over the HARM. The GPS will bridge the gap between the time when the passive radar seeker loses track of the radar emitter and the point when the enemy radar is detected by infrared. Combined GPS information collected by multiple aircraft can be used to find the position of enemy radar with the information then passed to the ARM prior to its launch from the aircraft [65].

Antiradiation Missiles

16.10

Israel

16.10.1

Harpy

601

Dedicated for the SEAD mission, Harpy is an operational loitering attack weapon. The current version of Harpy is deployed as a fire and forget weapon. In order to verify the drones operational capability, its seeker head is being tested by a special radar simulator just before launch, to ensure that all systems are working. It patrols the assigned area, and will attack any hostile radar activated in its vicinity. When used in appropriate numbers, Harpy can be launched into a target area to support continuous operations, or time limited strike packages. Unlike antiradar missiles such as HARM, whose speed, range and direction of approach are predictable, the killer-drone deployment is more flexible and unpredictable, and therefore, conventional countermeasure techniques are not useful against it. The Harpy system shown in Figure 16.41 is designed to operate multiple munitions simultaneously over a specific area, to eﬀectively cover the target. Each drone is deployed au-

Figure 16.41: Harpy antiradar UAV being launched from a truck canister [66] ( c 2007 Jane’s Information Group). tonomously, without interference and overlapping the other drones [66]. The Harpy mission is planned and programmed in the ground control center, as an independent mission, or planned in accordance with other manned or unmanned systems. Prior to launch, individual weapons are programmed and tested, to verify their operational readiness. After the rocket-assisted launch, the drone flies autonomously in route to its patrol area, predefined by a set of navigational waypoints. Due to its low speed and economical fuel

602

Detecting and Classifying LPI Radar

consumption, the drone can sustain a mission of several hours over the target area. Its radar seeker head constantly searches for hostile radars. Once an enemy radar is acquired, Harpy compares the signal to the library of hostile emitters, and prioritizes the threat. If the target is verified, the drone enters an attack mode and a near vertical dive homing in on the signal. The attack sequence is shown in Figure 16.42. The drone is set to detonate its warhead

Figure 16.42: Harpy UAV attack sequence against an emitter [66] ( c 2007 Jane’s Information Group). just above the target, to generate the highest damage to the antenna, and surrounding facilities. If the radar is turned oﬀ before Harpy strikes, the drone can abort the attack and continue loitering. If no radar was spotted during the mission, the drone is programmed to self-destruct over a designated area. Follow-on systems are calling for a combination of seeker and killer drones that will enable visual identification and attack of targets even after they turn oﬀ their emitters. Current Harpy canisters are installed on trucks, and can be carried by C130 transport aircraft. Each truck carries 18 weapon launchers. Each battery of Harpy is composed of three trucks, capable of deploying up to 54 drones for simultaneous, coordinated attack. The battery also has a ground control station and logistical support element. The system can also be deployed from the decks of assault landing ships, in support of marine or amphibious operations. Harpy is currently operational with the Turkish, Korean, Chinese and Indian Armies, in addition to the Israel Air Force. In December 2004 China was reported to be interested in an upgrade of its systems to a more advanced version.

Antiradiation Missiles

603

Figure 16.43: STAR-1 antiradiation missile [67] ( c 2005 Jane’s Information Group).

16.10.2

STAR-1

Israel Military Industries (IMI)–formerly TAAS–has developed its Delilah air-launched decoy into a long-range, lightweight cruise missile. Described by its manufacturer as an advanced air-to-ground standoﬀ powered UAV, the Delilah has a range capability that takes it out of the tactical category and into the realms of the cruise missile. Furthermore, the oﬃcial maximum range quoted for the system is 250 km. The original Delilah decoy was derived from the US MQM-74 Chukar aerial target, that entered service in the mid1960s. The first reports that Israel had developed the Delilah air vehicle as an oﬀensive weapons system emerged in 1995 [67]. Since then, the Delilah has evolved into a modular air strike weapon with a range of possible applications. Driving the design of the Delilah system was an emphasis on single-pilot operations. The weapon is programmed on the ground with key parameters such as waypoints and flight altitudes, but a datalink gives the launch aircraft the ability to retask the missile in flight. During the mid-1990s a long-range antiradar defense suppression variant of the Delilah was actively marketed under the designation STAR-1. This program was linked with China in several reports but has since disappeared from view and is no longer included in IMI’s oﬃcial product portfolio. To give the Delilah a SEAD capability, a broadband, 2—18-GHz, passive radar seeker with an INS/GPS mid-course update system was incorporated into its basic design. The STAR-1 shared the same size and weight of the Delilah, and used the standard 30 kg warhead. The STAR-1 as shown in Figure 16.43, would have both a direct attack mode and the ability to loiter over a target area waiting for hostile radars to start transmitting, or to reattack radars if they restart transmissions after an attack. A STAR-1 variant (or equivalent) is believed to be in service in Israel and was oﬀered for export as far back as 1995. In 2004 an IMI representative said that a dual-mode antiradiation seeker was available for the Delilah, but that it was not being oﬀered as a product yet. It is understood that the STAR-1 can be

604

Detecting and Classifying LPI Radar

both air-launched and ground-launched [67]. IMI has now developed several versions of the Delilah, which can be launched from land, sea and air. The standard Delilah missile can be fitted with interchangeable FLIR (forward looking infrared) or electro-optical seekers, in separate seeker assemblies. The seekers have a target auto-tracking capability but not yet an automatic target recognition function. In tests the Delilah has proved its ability to hit a target moving at 50 km/h, and IMI is promoting the system for use against time-critical targets such as mobile SSMs or SAMs. The existing seekers are capable of identifying targets at ranges of up to 10 miles. Operators have found that moving targets are easier to locate and identify than static ones. The missile’s datalink capability allows for man-in-the loop control, to confirm the final target. If this target is not confirmed, or if datalink communications are lost, the missile has a default navigation mode to fly around the target and reengage. The Delilah carries enough onboard fuel to fly for a maximum of 22 minutes, so the weapon is optimized for high-altitude straight line cruise profiles. A 30-kg high explosive warhead is currently fitted, but IMI confirms it is working on a new penetrating warhead option for hardened target attacks [67].

16.11

China

The China National Precision Machinery Import and Export Corporation (CNPMIEC) oﬀers the FT-2000 (Chinese Fei Tung = FT), which is an export variant of the antiradar surface-to-air system specifically for use against airborne early warning, command and control, and EA aircraft. It is believed that the missile is an upgrade of the SA-10 design. The missile system has the Chinese designator Hong-Qi-12 (HQ-12)[68]. The missile contains a wideband surface-to-air passive seeker to engage either single or multiple radiating airborne targets that radiate in the 2—18 GHz band such as the Airborne Early Warning and Command System (AWACS) or Suppression of Enemy Air Defense (SEAD) EA-6B/EA-18G EA aircraft. The missiles are also capable of detecting and locking on to random electronic interference and jamming. With primarily Russian technology and with minimal use of imported components, China has mastered the production of air defense missile systems such as the HQ-15 missile. This missile is shown in Figure 16.44 along with its transporter-erector launcher vehicle. A photograph of the passive radar seeker assembly for the HQ-15 missile is shown in Figure 16.45. A typical HQ-12 battalion has three batteries. Each battery has four ES vehicles, three transporter erector launchers (TELs), one command launch center, and three transporter/loader vehicles. The ARMs are vertically cold launched from the TEL Taian TAS5380 that is also an 8 × 8 transport vehicle as shown in Figure 16.45. The TEL has four missile canisters that are raised to the vertical for launching. The four ES stations are deployed at distances of up to 30 km in a

Antiradiation Missiles

605

Figure 16.44: Outline drawing and launch system for the Chinese HQ-15 missile.

Figure 16.45: Photograph of the passive radar seeker assembly for the Chinese HQ-15 missile.

606

Detecting and Classifying LPI Radar

triangle with a central fourth unit acting as command and control. The four ES receiver vehicles associated with each battery can track up to 50 targets. The complete FT-2000 system includes a wideband passive radar detecting station, the specially developed ARM vertically launched missile and a fourround launcher platform. A first test launch was reported in September 1997. The passive seeker has a memory, for use if the target radar is switched oﬀ, and a home-on-jam capability. The missile has a maximum speed of 1.2 km/s. Targets can be intercepted at altitudes between 3 and 20 km. The proximity fuse is activated 5 km from the target with a range of 35m. The second version, known as FT-2000A in its export version, was reported to have a passive radar seeker covering the 2—6-GHz (S and C-band) range, that has its frequency selected on the ground before launch. This missile has a maximum range of 60 km, and can be used as part of the HQ-2 system but requires separate launchers and fire-control units. This system is still in the developmental stages but is expected to be a static weapon system [69]. The FT-2000B version has been designed for use as an upgrade to the HQ-12 missile system, with the maximum range increased to 120 km and with a new 1—18-GHz passive radar seeker. The system has been oﬀered for export with the potential first customer Pakistan. During discussions between China and Pakistan in February 2004, the oﬀer was made by China to supply the FT-2000/FT-2000A to counter the Indian threat to Pakistan of the Indian Agni missile systems. Batteries have been reported around Beijing and in Fujian province.

16.12

Anti-ARM Techniques

The earliest form used to defeat the ARM (and still the most common method) is radar position flexibility. In most cases the radar position being attacked is provided by an electronic intelligence (ELINT) system prior to aircraft takeoﬀ. The ability of the radar to set up, tear down, and move to a new location within a few minutes can help to hide the radar position. The latest generation of SAMs have put a much higher premium on system mobility. That is, the ability to leave in a hurry is closely linked to survival in modern warfare. Most land-based surveillance, ballistic missile detection and weapon-related radars currently in development claim to have relatively high mobility, including some of the very powerful long range systems such as Marconi’s latest version of Martello, the S 753, and the Israeli Arrow Green Pine antiballistic missile radar. Rapid relocation however, has its limits. If a surveillance radar is attacked by an ARM fired from below the radar horizon, or by an aircraft approaching low over the horizon, the radar has approximately 20 seconds to move to a safe location. Consequently, manufacturers are looking to increase mobility, with multifunction radars using planar-array antennas, mounted on a truck

Antiradiation Missiles

607

(including all of the electronics), and with a microwave link to relay target data back to command and control. They will also use highly sophisticated land navigation systems to provide an accurate position reference. This is important if their target data is to be tied into an overall battlefield awareness. Radar methods include twinkle (or blink) transmission. In this technique, the oﬀ time is much greater than the on time. This makes it diﬃcult for the ARM to keep track of the emitter’s signal (and location). In this method of protecting a pulse radar from an ARM missile attempting to home in on interrogating pulses emitted, a number of decoys at diﬀerent locations are deployed in the vicinity of the pulse radar. Each one of the decoys are adapted, when activated, to emit pulses of a given amplitude and duration; activating, when each one of the interrogating pulses is generated in the pulse radar. A selected decoy is chosen to lead the remaining decoys for a period of time determined by range and range rate measurements of a pulse Doppler missile warning sensor. The decoy selected is changed to lead the remaining decoys at a time determined from the range and range rate measurements of a pulse Doppler missile warning sensor thereby defining a blink rate associated with the decoys, to form a covering pulse overlapping the then emitted one of the interrogating pulses, and adaptively changing the blink rate. Two examples of radar using this transmission control technique for anti-ARM include the AN/APY-1 Cosmic Shield and the AN/MPQ-53 Patriot [70]. Another technique often used is called the snap-and-shoot method. In this technique, a fire control radar is assigned to intercept and track targets. The remaining fire control radar systems receive the target flight path parameters. When the tracked targets enter the fire range, the unit snaps open and makes the response. Other methods that may be used include using other types of radiation to detect and track the targets. This may include using visual television with infrared measurements of the target’s range. Examples of this include the Swedish GLV200 and the Swiss Air Guard. Also, the use of very high frequency (VHF) band or ultra high frequency (UHF) bands can be used to avoid the ARM attack [70]. The reason for this is that the diameter of the ARM body is limited with the aperture of the ARM antenna greater than the wavelength. For example, with a diameter of 40 cm, it is diﬃcult to target radar with frequencies below 1 GHz.

16.12.1

Decoys

Dispensing of active decoys is also an important method for anti-ARM [71]. The ARM decoy has characteristics that are coincident with the radar. For example, the decoy has the same eﬀective radiated power (or ERP) and carrier frequency and the transmission waveform is synchronous with the radar. The decoy also emits a decoy pulse 0.1—0.2 μs ahead of the radar pulse so that the ARM triggers its guidance on the wrong waveform. Typically, the distance between the radar and the decoy is 100—300m with the spatial angle between

608

Detecting and Classifying LPI Radar

Figure 16.46: Flaps technology for decoying an ARM (from [72]). radar and decoy smaller than the ARM track angle resolution. An ARM decoy antenna that uses low-windload FLAPS (flat parabolic surface) technology is shown in Figure 16.46 [72]. Once the incoming ARM is detected, the radar is turned oﬀ and the reflectors are illuminated by a remote feed. Since the frame is staked to the ground, it can survive an ARM blast from any direction. The blast travels through the aperture then the reflector springs back to is operating position. The antenna uses FLAPS technology to enable a geometrically flat surface as shown in Figure 16.47(a) to behave electromagnetically as though it were a parabolic reflector as shown in Figure 16.47(b). The FLAPS reflector is a thin (planar or conformal) surface consisting of an array of dipole scatterers. The elemental dipole scatterer as shown in Figure 16.47(c), consists of a dipole positioned approximately 1/8 wavelength above a ground plane. Here, a crossed shorted dipole configuration is shown with each dipole controlling its corresponding polarization. Incident RF energy causes a standing wave to be set up between the dipole and the ground-plane [72]. The dipole itself possesses an RF reactance which is a function of its length and thickness. This combination of standing-wave and dipole reactance causes the incident RF to be reradiated with a phase shift, which can be controlled by a variation of the dipole’s length [72]. The integrated ARM warning radar and decoy deployment method is shown in Figure 16.48 and consists of an integrated system of advanced ARM detection radar and general purpose distributed decoys to protect the ground air-defense radar [73]. The ARM detection radar is used to detect and iden-

Antiradiation Missiles

609

Figure 16.47: FLAPS antenna technology showing (a) a thin planar surface consisting of an array of radiating and phase shifting elements, (b) a conventional reflector, and (c) the schematic of an elemental dipole scatterer used in the FLAPS antenna technology (from [72]). tify the attacking ARM (RCS = 0.1 m2 ), which triggers a shutdown of the sensors and cues the crew manning the site to leave. Studies also indicate that by using changeable sample ratios within the radar receiver, a higher probability of ARM detection can result [74]. ARM detection radars with multiple antennas using VHF have also been reported [75]. The use of VHF enhances the ARM RCS significantly increasing the probability of detection. Extended coherent integration and dedicated signal processing can also be used. At the same time, the ARM messages are sent to a series of decoys. The signal radiated by the decoys guide the ARM (speed 2 to 4 Mach) to a preset safety area. If the ARM fails to continue the attack, a cancellation of the alarm is made and protected radar triggered to restart. The anti-ARM warning radar’s frequency band selection (UHF, VHF) is to give an antistealth capability, ground clutter and weather suppression and to also control the deployment of the decoys. It must be highly mobile to operate in the sometimes rough terrain and also have good target identification capability. The PRF of the warning radar should be as large as possible with a compressed pulse width as small as possible to decrease the energy in the range-Doppler detection cell. With high-speed ARM detection (>1.5 Mach), the separation of the missile from the launch aircraft can be detected with the warning radar using pulse-Doppler waveforms and frequency agility [73]. For slow ARM targets such as UAV ARMs and cruise ARMs, an accurate radial velocity and unambiguous range of the target must also be reported. To avoid turning the radar oﬀ early and deploying the decoys, two transmitters T1 and T2 can be used that are placed far away from the protected

610

Detecting and Classifying LPI Radar

Figure 16.48: Deployment of the integrated anti-ARM system (adapted from [73]). radar with the receiver placed near the protected target as shown in Figure 16.48. They should be connected by an RF optical fiber communication link. When the ARM approaches, T1 and T2 can work together to protect each other. Their use of polarization and frequency diversity can provide the means to reduce the power of each solid state transmitter by 3—5 dB. The two transmitters are noncoherent and can be placed at diﬀerent heights to prevent lobe splitting [73]. The antenna should be a small foldable, nonrotation antenna array. Because the distance between T1 and T2 and the receiver cannot be too far, the use of othogonal waveforms such as those discussed in Chapter 10 are required. Another type of decoy is the simulated model—in eﬀect, a cardboard cutout that looks like a radar. These can be very eﬀective, and it is possible to metalize them to provide a radar return that looks like a gun, a tank, or a radar station. This type of decoy has been used very eﬀectively against ground attack aircraft threats, and could contribute toward the protection from the active radar homing phase in a dual-mode ARM.

16.12.2

Gazetchik

The Iraqi newspaper Al-Qabas Daily, in July 2000, reported that Iraq had acquired from Russia a jamming device that was capable of neutralizing U.S. ARMs during the enforcement of the no-fly zones, making the missiles miss their targets. The first two systems were reported to be a gift to Baghdad by the Russian ultra-nationalist leader Vladimir Zhirinovsky. The Gazetchik anti-ARM system built by the All-Russian Radio Engineering Research Insti-

Antiradiation Missiles

611

Figure 16.49: Russian Gazetchik anti-ARM system. tute, Moscow, is designed to protect radar emitters such as the GAMMA-DE (67N6E) (a mobile 3-D solid-state phased array surveillance radar) from attack by ARMs. The Gazetchik system shown in Figure 16.49 consists of a stand-alone detector, active radio frequency decoys, a set of passive countermeasure dispersers (not shown), and an interface with the radar or radars being defended. The ARM detector unit alerts the system to the approach of an incoming ARM weapon. Then a warning is initiated that activates a host of responses including interruption of the protected emitter’s transmission, transmission of RF decoy signals on the protected emitters operating frequency and the firing of passive decoys from the equipment’s chaﬀ and aerosol launchers [75]. With coverage of up to 90 degrees elevation and 360 degrees azimuth, the system operates autonomously and draws its power from the radar systems being protected. Gazetchik is reported to be available in a number of variants and has an automatic operating mode if required.

16.12.3

AN/TLQ-32 ARM-D Decoy

AN/TLQ-32 ARM-D is a lightweight, ruggedized, tunable magnetron that imitates the AN/TPS-43E and AN/TPS-75 radar signals. It is designed to protect radars in the field from ARMs that are guided by homing in on the radar’s own transmission signals. The ARM-D built by ITT Gilfillan, provides protection to the radar by emulating the transmission characteristics of the host radar, thereby deceiving and confusing the incoming missile. The decoys are placed on the ground as shown in Figure 16.50 in triangulation to attract enemy antiradiation missiles, and ultimately saving the radar site.

612

Detecting and Classifying LPI Radar

Figure 16.50: AN/TLQ-32 anti-ARM radar transmitter [76] ( c 2004 Jane’s Information Group). Features of ARM-D include its capability to emulate frequency-agile radars; 360o coverage; protection of both the radar and the decoy assets against ARMs; lightweight fiber optic interface between the radar and decoy emitter groups and low prime power operation. It also features rugged, lightweight modular packaging, extensive built-in test capability and rapid set up and tear down. It is claimed that the decoy can be transported by two people with individual decoys being deployable within 15 minutes. In operational use, three decoys are allocated to each radar system. The surveillance decoys are designed to be capable of protecting the radar site from multiple missile launches, whether simultaneous or consecutive [76]. The AN/TLQ-32 ARM-D was selected by the USAF in March 1989, with a contract for two “first article” examples being awarded during the following September. Testing of these began in May 1992 and full-scale production of 14 systems to protect USAF AN/TPS-75 radars began in December 1992. During 1996, additional TLQ-32 systems were delivered to the U.S. Air National Guard.

References [1] Bolkcom, B., “Military suppression of enemy air defenses (SEAD): Assessing future needs,” CRS Report for Congress, RS21141, Sept. 23, 2004. [2] Farroth, A., and Krishnamurthy, V., “Optimal threshold policies for hardkill of enemy radars with high-speed anti-radiation missiles (HARMs),” Proc. of the International Conference on Acoustics, Speech and Signal Processing, 14-19 May, 2006. [3] Department of the Army, Field Manual 101-5: Staﬀ organization and operations, May 1997. [4] Davis, L., Wild Weasel: The SAM Suppression Story—Vietnam, Squadron Signal Publications, July 1993.

Antiradiation Missiles

613

[5] Friedman, N., US Naval Weapons, Conway Maritime Press, 1983. [6] Parsch, A., “Corvus,” Encyclopedia Astronautica, www.astronautix.com/lvs/corvus.htm [7] Gunston, B., The Illustrated Encyclopedia of Rockets and Missiles, Salamander Books Ltd, 1979. [8] Streetly, M., Airborne Electronic Warfare: History, Weapons and Tactics, Jane’s Information Group, 1988. [9] Pietrucha, M., “Starbaby”: “A quick primer on SEAD,” Defense IQ Airborne Electronic Warfare Conference, London, England, Aug. 2006. [10] Levin, R. E., “Electronic Warfare—Comprehensive strategy needed for suppressing enemy air defenses,” United States General Accounting Oﬃce Report to Congressional Requesters, GAO-01-28, Jan. 2001. [11] Kopp, C., “Support jamming and force structure,” The Journal of Electronic Defense, May, 2002. [12] Lum, Z., “Hardcore Hard Kill: Seeds of a New SEAD,” Journal of Electronic Defense, February 1997. [13] McKenna, T., “Poisoned Arrows,” The Journal of Electronic Defense, March 2004. [14] Zaloga, S. J., “The evolving SAM threat: Kosovo and beyond,” The Journal of Electronic Defense, May, 2000. [15] Lambeth, B. S., “Kosovo and the continuing SEAD challenge,” Air Power Journal, Summer 2002. [16] Martin, N. M., Nandagopal, D., Kara, M., Tran, V. N., and Hamilton, S. “Body fixed antenna options for seekers,” Proc. of the IEEE International Conference on Radar, pp. 272—275, Oct. 1992. [17] Cencich, T. and Huﬀman, J., “The analysis of wideband spiral antennas using modal decomposition,” IEEE Antennas and Propagation Magazine, Vol. 46, No. 4, Aug. 2004. [18] Muller, D. J., and Sarabandi, K., “Design and analysis of a 3-arm spiral antenna,” IEEE Trans. on Antennas and Propagation, Vol. 55, No. 2, pp. 258—266, Feb. 2007. [19] Mayes, P. E., “Frequency-independent antennas and broad-band derivatives thereof,” Proc. of the IEEE, Vol. 80, No. 1, pp. 103—112, Jan. 1992. [20] Thaysen, J., Jakobsen, K. B., and Appel-Hansen, J., “A logarithmic spiral antenna for 0.4 to 3.8 GHz,” Applied Microwaves & Wireless pp. 32—45, 2001. [21] Stutzman, W. L., and Thiele, G. A., Antenna Theory and Design, John Wiley & Sons, Inc. New York, 1997. [22] Balanis, C. A., Antenna Theory Analysis and Design, Harper & Row, Publishers, New York, 1982. [23] Salmond, W. E., “High accuracy broadband antenna system,” U.S. Patent 4,095,230, June 13, 1978.

614

Detecting and Classifying LPI Radar

[24] Salmond, W. E., “Common aperture dual mode seeker antenna,” U.S. Patent 4,348,677, Sept. 7, 1982. [25] Corzine, R. G., Bolstad, B. E., and Johantgen, J. S., “Broadband polarization diversity monopulse antenna,” U.S. Patent 5,021,796, June 4, 1991. [26] Bohlman, W. A., and Schuchardt, J. M., “Dual polarized ambidextrous multiple deformed aperture spiral antennas,” U.S. Patent 5,227,807, July 13, 1993. [27] Neri, F., Introduction to Electronic Defense Systems, 2nd ed., Artech House, 2001. [28] Hughes, R. S., “RF detector logarithmic video amplifier,” Microwave Journal, vol. 32, no. 8, pp. 137—148, Aug. 1989. [29] Jane’s Information Group, “Two-for-one guidance could steer future antiradar missiles,” Jane’s Missiles and Rockets, Jan. 2005. [30] Klass, P. J., “New anti-radar missile uses dual-mode seeker,” Aviation Week and Space Technology, pp.60 Oct., 26 1998. [31] Penz, P. A., Katz, A., Gately M. T., Collins, D. R., and Anderson J. A., “Analog capabilities of the BSB model as applied to the anti-radiation homing missile problem,” IEEE Conference, pp. II-7 — II-11. [32] Lee, J. P. Y., “Circuit for LPI signal detection and suppression of conventional pulsed signals,” U.S. Patent 6,388,604, issued May 14, 2002. [33] Shirman, Y. D., Orlenko, V. M., and Seleznev, S. V., “Passive detection of the stealth signals,” Proc. of the European Radar Conf., Amsterdam, pp. 321—324, 2004. [34] Shirman, Y. D., Orlenko, V. M., and Seleznev, S. V., “Present state and ways of passive anti-LPI radar implementation,” Proc. of the International Radar Symposium, pp. 1—4, 24-26 May, 2006. [35] Jie, S., Xiao-ming, T. and You, H., “Multi-channel digital LPI signal detector,” Proc. of the International Conf. on Radar, pp. 1—4, Oct. 2006. [36] Kopp, C. “Texas Instruments (Raytheon) AGM-88 HARM,” Air Power International, Vol. 4, No. 1, Dec. 1998. [37] Fiszer, M. and Gruzczynski, J., ”Crimson SEAD,” The Journal of Electronic Defense, pp. 44 — 56, Oct. 2001. [38] Barrie, D., “Silent Hunter,” Aviation Week and Space Technology, pp. 36, July 26, 2004. [39] http://www.fas.org/man/dod-101/sf/missile/row/aa-10.htm [40] http://www.fas.org/nuke/guide/russia/bomber/as-4.htm [41] Jane’s Strategic Weapon Systems, “Kh-22 (AS-4 ’Kitchen’/Burya)”, Sept. 2007. [42] Jane’s Strategic Weapon Systems, “KSR-2P (AS-5 ’Kelt’),” Sept. 2007. [43] Jane’s Strategic Weapon Systems, “KSR-5P (AS-6 ’Kingfish’),” Sept. 2007. [44] Jane’s Air Launched Weapons “Kh-28 (AS-9 ’Kyle’), May, 2006.

Antiradiation Missiles

615

[45] http://www.testpilot.ru/russia/raduga/kh/58/images/kh58 1.jpg. [46] Jane’s Strategic Weapon Systems, “Kh-58 (AS-11 ’Kilter’),” April, 2006. [47] Jane’s Air Launched Weapons, “Kh-25MP/MPU (AS-12, ’Kegler’),” Aug. 2006. [48] http://www.fas.org/man/dod-101/sys/missile/row/as-12.htm [49] Jane’s Strategic Weapon Systems, “Kh-15 (AS-16 ’Kickback’/RKV-15), Sept. 2007. [50] Jane’s Strategic Weapon Systems, “Kh-31P (AS-17 ’Krypton’), Sept. 2007. [51] http://www.military.cz/russia/air/weapons/rockets/agm/ch31/Ma-31.jpg. [52] http://www.raf.mod.uk/falklands/images/bbmartel.jpg. [53] Jane’s Electronic Mission Aircraft, “Raytheon Systems AGM-45 Shrike AntiRadiation Missile,” Dec. 2002. [54] http://www.fas.org/man/dod-101/sys/missile/agm-78.htm. [55] http://common.wikimedia.org/wiki/image:agm-88 harm on f-4g.jpg. [56] http://www.globalsecurity.org/military/systems/munitions/aargm.htm. [57] Sirak, M., “Aﬀordable Reactive Strike Missile (ARES),” Jane’s Defence Weekly, June 29, 2005. [58] Parsch, A., “Sidearm,” www.astronautix.com/lvs/sidearm.htm. [59] Friedman, N., World Naval Weapons Systems, 1997/98, Naval Institute Press, 1997. [60] Ozu, H., “Missile 2000 - Reference Guide to World Missile Systems,” Shinkigensha, 2000. [61] Jane’s Electro-Optic Systems, “Raytheon/RAM Systems RIM-116 Rolling Airframe Missile,” June, 2007. [62] La Franchi, P., “Army looks to battle unmanned threat,” http://www.flightglobal.com, Sept. 8, 2007. [63] Kopp, C., “Matra/BAe Alarm,” Australian Aviation, June 1997. [64] Jane’s Air Launched Weapons, “Tien Chien IIA Anti-Radiation Missile,” July 2006. [65] Jane’s Air Launched Weapons, “ARMIGER,” Oct. 2007. [66] Jane’s Electronic Mission Aircraft, “Israel Aerospace Industries (IAI) MBDA Raytheon CUTLASS/Harpy/Horop/White Hawk,” Sept. 2007. [67] Jane’s Electronic Mission Aircraft, “Israeli Miltitary Industries (IMI) STAR-1 Anti-Radiation Missile,” Oct. 2005. [68] Jane’s Land Based Air Defense, “HQ-9/FT-2000 surface-to-air anti-radiation missile system,” Sept. 2007. [69] Jane’s Land Based Air Defense, “FT-2000A anti-radiation seeking air defense missile,” Mar. 2004.

616

Detecting and Classifying LPI Radar

[70] Neng-Jing, L., “Radar ECCM new area: anti-stealth and anti-ARM,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 31. No. 3, pp. 1120—1127, July 1995. [71] Fan, W., RuiLong, H. and Xiang, S., “Anti-ARM technique: distributed general purpose decoy series (DGPD)” pp. 306—309, 2001. [72] http://www.maliburesearch.com/technology.htm. [73] Fan, W., RuiLong, H., and Xiang, S., “Anti-ARM technique: Feature analysis of ARM warning radar” Proc. of the International Conference on Radar, pp. 293—296, Bejing, China 2001. [74] Wang, S., and Zhang, Y., “Detecting of anti-radiation missile by applying changeeable-sample ratios technology in the AEW,” Proc. of the International Conference on Radar, pp. 289—292 , 2001. [75] Streetly, M., “Gazetchik Anti-Anti-Radiation Missile (ARM) system,” Jane’s Radar and Electronic Warfare Systems, Jan. 2004. [76] Streetly, M. “AN/TLQ-32 ARM-D anti-radiation missile decoy,” Jane’s Radar and Electronic Warfare Systems, Jan. 2004.

Problems 1. An ARM seeker (fixed) antenna is being considered for use in the AGM88 (missile body diameter of 0.25 m, length of 4 m). It uses four cavitybacked spiral antennas arranged in a phase comparison monopulse configuration (protected by a radome) as shown in Figure 16.51. Assuming that the antennas are on a flat disc and the spirals are nearly touching, (a) what is the equation for the external radius of each spiral in terms of the disc diameter? One of the properties of the spiral antenna is that the longest useable wavelength λL = 4r. (b) Estimate the frequency coverage of the AGM-88 HARM missile if the bandwidth coverage is 10:1. (c) If the gain of each antenna is 3 dB (θaz = θel = 80o ) over the 10:1 frequency band, what is total gain of the ARM antenna? 2. For the ARM seeker above, now assume a pulsed emitter with a carrier frequency fc = 9 GHz whose transmitted peak power is Pt = 1 MW. Its one-way main lobe antenna gain is Gt = 25 dB with a general side lobe level of −30 dB with respect to the main lobe, giving a side lobe gain Gt = −5 dB. The ARM missile is aimed at the radar with the gain of the array as calculated above. Assume the range to the radar is 25 km. Also assume that the receiver front-end uses a superheterodyne configuration with a bandwidth BIR = 250 MHz with a linear detector to feed a bank of 250 video filters each with a bandwidth of 1 MHz. For this wideband receiver, a reasonable value of noise figure is N F = 20 dB. (a) Determine the expression for the single-pulse signalto-noise ratio at the ARM receiver. (b) Do you think the seeker will

Antiradiation Missiles

617

Figure 16.51: Cavity backed spiral antennas. have any problem acquiring the emitter? (c) If the ARM RCS is 0.03 m2 , the noise figure of the emitter is 10 dB, the transmitted pulsewidth is just suﬃcient to enclose the ARM within a range bin and the minimum single pulse SNR required by the emitter to detect a target is 13 dB, calculate the emitter’s maximum detection range for this ARM target. (Assume T0 = 290K.) 3. The expansion ratio for an equiangular spiral antenna can be expressed as ρ0 ea(φ+2π) ρ(φ + 2π) = = ea2π (16.18) = ρ(φ) ρ0 eaφ For = 4 for a two turn spiral (φ = 4π), determine the bandwidth ratio.

Chapter 17

Autonomous Classification of LPI Radar Modulations In this chapter, autonomous (no human operator intervention) feature extraction and classification algorithms that can be used for identifying LPI radar modulations using time-frequency (T-F) detection images are presented. The multilayer perceptron network and the radial basis function network are presented to identify the type of LPI modulation present in the intercepted signal. These nonlinear classification networks use an input feature vector that is generated from the T-F images (preprocessing). In the first feature extraction algorithm, the modulation energy is cropped from the T-F image using the marginal frequency distribution to determine the cropping region. An adaptive binarization algorithm is then used to build the feature vector in order to preserve the high-resolution detail that emphasizes the diﬀerences between modulation classes without overwhelming the classification networks. Initial classification results show that the cropping region is sensitive to highfrequency noise contained in the marginal frequency distribution. In a second feature extraction algorithm, lowpass filtering of the T-F image is used prior to calculation of the marginal frequency distribution. Wiener filtering of the marginal frequency distribution is also added to improve the stability of the cropping region. The use of principal components analysis to construct the feature vector is investigated. An extended database is developed and the classification results for simulated LPI radar modulations are shown as a function of both SNR variations and variations in the modulation parameters (most diﬃcult, but realistic case).

619

620

17.1

Detecting and Classifying LPI Radar

Classification Using Time-Frequency Imaging

Although the automatic recognition of LPI radar modulations is a new area of investigation, the automatic recognition of communication signal modulations has been of interest for many years [1—3]. In general, there are two methods for autonomous classification of signal modulations: decision theoretic techniques and pattern recognition techniques. In particular, research on this topic is typically applicable to military systems. Now with the advent of software radios, research on autonomously recognizing communication signal modulations has resulted in the realization of reconfigurable and adaptive wireless transceivers. The use of neural networks [4], wavelet transforms [5], higher order statistics [6], and hidden Markov models [7] have been explored. In a general sense, the autonomous recognition of communication modulations is an easier problem than the autonomous recognition of LPI radar modulations due to the fact that there are only a finite number of modulation techniques used for communication. On the other hand, there are an infinite number of modulation techniques that can be used for the LPI radar. In fact this is why the noncooperative intercept receiver has such a diﬃcult time! Classification using T-F imaging has received considerable attention in such diverse fields as humpback whale signal recognition [8, 9], biomedical engineering [10, 11], underwater acoustic target detection [12], radar target classification [13], power grid analysis [14], and radar transmitter identification [15]. With the high degree of detail contained in the image, trainable autonomous classifiers can easily be overwhelmed by the complexity of the T-F input representation and many eﬀorts have been examined to reduce this problem. Smoothing the T-F images can be used to reduce the density of the features but will most often remove the class-distinction detail that the representation was intended to resolve. Quantizing the T-F representation in a class- or signal-dependent manner can also preserve the needed high-resolution detail that highlights the diﬀerences between classes. A vector quantization technique that is a modified version of a Kohonen’s self-organizing feature map is applied to the T-F representation in [16]. Class-dependent smoothing can also be accomplished by optimizing the T-F transformation kernel [15]. This approach eliminates the need to make a priori assumptions about the amount and type of smoothing needed and also allows for a direct classification without the need for preprocessing to reduce the dimensionality. Optimizing the T-F kernel parameters based on the Fisher criterion objective function is also examined in [8]. The Fisher criteria however, assume the classes have equal covariance. In [9], the T-F representation is used to construct a quadratic discriminant function, which is evaluated at specific times to form a set of statistics that are then used in a

Autonomous Classification of LPI Radar Modulations

621

multiple hypothesis test. The multiple hypotheses are treated simultaneously using a sequentially rejective Bonferroni test to control the probability of incorrect classification. A method based on T-F projection filtering is presented in [12]. In this approach the decision strategy about which target is present depends on the comparison of a reference target and the filter output signal. In [13], a reduction in the feature vector dimensionality using the geometrical moments of the adaptive spectrogram is investigated. A principal components analysis is then used to further reduce the dimension of the feature space. This involves calculation of the covariance matrix and its eigenvectors. The feature vector is then formed using the eigen vectors associated to the highest eigen values, and then it is applied to a multilayer perceptron for automatic recognition.

17.2

Classification Authority and Automation

The LPI emitter has established itself as the premier tactical and strategic radar in the military spectrum. In addition to surveillance and navigation, the LPI emitter also operates in the time-critical domain for applications such as fire control and missile guidance. In the EW battle, the noncooperative intercept receiver is a significant element in the detection and classification of the LPI radar in a complex environment of multiple emitters and high noise interference. The LPI radar modulations force the intercept receiver to increase its processing gain by implementing T-F signal processing algorithms. With these detection techniques a human operator can examine the resulting T-F image on a human-computer interface (HCI) and identify the type of signal modulation present (classification) as well as quantify (or extract) the modulation parameters. The development of a corresponding jammer response, when required, is almost always a time critical event.

17.2.1

Human-Computer Interface Considerations

In an embedded system, cost, size, power, and complexity are limited, so the HCI must be easy to use without sacrificing accuracy in the analysis capability. Human operators are often one of the biggest sources of error in any embedded system and many operator errors are attributed to a poorly designed HCI [16]. Electronic intelligence (ELINT) receiver designers must insure that the HCI is easy and intuitive for human operators to use, but not so simple that it lulls the operator into a state of complacency and lowers their responsiveness to vital situations. The ELINT receiver HCI must give appropriate feedback to the operator to allow well informed decisions to be made based on the most up-to-date information on the electromagnetic environment. High false alarm rates will make the operator ignore a real alarm condition. If the human operator is out of the control loop in an automated

622

Detecting and Classifying LPI Radar

Table 17.1: Sheridan Levels of Authority (after [18]). Level 1 2 3 4 5 6 7 8

Computer Task No assistance Suggests alternatives Selects way to do task Selects and executes Executes unless vetoed Executes immediately Executes immediately Executes immediately

Human Task Does all Chooses Schedules response Must approve Has limited veto time Informed upon execution Informed if asked Ignored by computer

task, the operator will tend to adapt to the normal operation mode and not pay close attention to the system (operator drop out). When an emergency condition occurs, the operator’s response will be degraded and they will tend to make more mistakes. For example, the operator might unexpectedly have to manage a proper EW response to the intercepted emitter.

17.2.2

Automation and the Human Operator

The need for human analysis of the T-F results limits these techniques to ELINT receivers where the emitter information derived is not time-critical. High-level automation of the classification decision, parameter extraction and response management are however justified in highly time-critical situations in which there is insuﬃcient time for a human operator to respond and take appropriate action [17]. This is the case for ES receivers and RWRs. Human beings are often still needed to be the fail-safe in an otherwise automated system. The Sheridan level shown in Table 17.1 is a system of eight levels to indicate the amount of automation that is incorporated in the response, its level of autonomy and whether the response execution authority is assigned to the system or to the operator [18]. The Sheridan levels or levels of authority (LoA) vary from level 1: “Computer oﬀers no assistance, human does all” to level 8: “Computer selects method, executes task and ignores human.” In levels 1 to 4 the operator has authority over function execution; in levels 6 to 8 authority has moved to the system. In level 5 the authority is shared between the system and the operator. Figure 17.1 shows an example where the intercept receiver calculates the T-F results from an intercepted LPI signal and must then administer a jamming waveform response. The figure shows the EW response management detailing the interaction between automation, autonomy and authority for

Autonomous Classification of LPI Radar Modulations

623

Figure 17.1: Interaction between automation, autonomy, and authority (adapted from [17]). the jamming waveform. Depending on the Sheridan level of the response, the T-F data is presented to the operator (arrow 1a) or used by the system part “Autonomous decision making” to decide what LPI modulation is present and what the modulation parameters are (1b), given these T-F inputs [17]. Then, the system can suggest the particular modulation type to the operator (2a), who then schedules the jamming response execution (4a) or the system can select and schedule an automated response (2b). Whether the execution of the scheduled jamming response must be acknowledged by the operator depends on the LoA assigned to the response (4b). This is realized by the “Authority filter” and the switch below the filter that determines whether the scheduled response is executed (3). Depending on the setting of the “Authority filter,” the operator does or does not receive feedback upon response execution (5). The interaction can be summarized as: Autonomy schedules automated responses, while authority allows or blocks response execution [17].

17.2.3

Autonomous Modulation Classification

Figure 17.2 shows the steps that can be used to autonomously classify the LPI radar signal modulations. The LPI radar signal is intercepted with a digital receiver that digitizes the intercepted signal. The signal is processed by both T-F and B-F detection techniques. After the T-F, B-F detection processing, the resulting image planes are used by the autonomous decision making process to identify the modulation type. The autonomous decision making consists of a feature extraction algorithm that is used to derive the feature vector from the T-F, B-F image plane. A nonlinear classification

624

Detecting and Classifying LPI Radar

Figure 17.2: Noncooperative intercept receiver for autonomous detection and identification of LPI radar modulation. network is then used to recognize the LPI signal modulation type from the feature vector or pattern. The most important segment of this pattern recognition scheme is how the feature vector is formed and how it is presented to the nonlinear classification network. Note that if a high performance reconfigurable computer is used, several T-F and B-F detection/classification algorithms can be executed quickly and in parallel [19]. Below we first discuss the nonlinear classification networks that are used to identify the modulation type. This includes the multilayer perceptron (MLP), and the radial basis function (RBF) network. Feature extraction image processing techniques are then discussed and results are shown.

17.3

Nonlinear Classification Networks

Nonlinear classification networks use a set of processing elements (or nodes) loosely analogous to neurons in the brain (hence the name, artificial neural networks). The nodes are interconnected in a network that can then identify patterns in data as it is exposed to the data. In a sense, the network learns from experience just as people do. This distinguishes neural networks from traditional computing programs that simply follow instructions in a fixed sequential order. The architectures are specified by: (1) the network topology, (2) the node characteristics, and (3) the training or learning rules used to configure the weights on each connection [20]. The classification networks can be either static or dynamic. Static networks are characterized by node equations that are memoryless. That is, their output is a function of only the current input and not of past or future inputs or outputs. Dynamic networks are systems with memory. The

Autonomous Classification of LPI Radar Modulations

625

Figure 17.3: Rosenblatt perceptron (static network).

Figure 17.4: Hard limiting nonlinearity. dynamic neural networks are characterized by diﬀerential equations or diﬀerence equations [21].

17.3.1

Single Perceptron Networks

An example of a static network is the Rosenblatt perceptron as shown in Figure 17.3. Here Xn represents the n-dimensional input vector and Wn represents the n-dimensional weighting vector. The Rosenblatt perceptron forms a weighted sum of n-components of the input vector and adds a bias value, θ. The result y is passed through a nonlinear activation function to give the output value u. The activation function shown in Figure 17.3 is a hard-limiting nonlinearity fHL . An example of a hard-limiting nonlinearity is shown in Figure 17.4 where fHL (y) =

1 y>0 0 y≤0

(17.1)

Another popular activation function is the sigmoid. The sigmoid nonlinearity

626

Detecting and Classifying LPI Radar

is given by the expression fs (y) = 1 + e−βy

−1

=

1 1 + e−βy

(17.2)

and is continuous. The nonlinearity varies monotonically from 0 to 1 as y varies from −∞ to ∞. The β value represents the gain of the sigmoid. One of the key attributes of the sigmoid nonlinearity fs (y) is that it is a diﬀerentiable function. This also makes it well suited to our application of pattern recognition since the output is between 0 and 1. Note that this can be interpreted as a probability distribution. The value of the output y is a weighted sum and is the inner product between the augmented input vector and the weight vector or [21] T

y=W X or

(17.3) ⎡

⎢ ⎢ ⎢ y = [W0 , W1 , · · · , Wn ] ⎢ ⎢ ⎣ 1×n

1 X1 X2 .. . Xn n×1

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(17.4)

and then the output u = fHL (y)

(17.5)

A single Rosenblatt perceptron can be used to build several important logic units. One example is the AND function as shown in Figure 17.5 [21]. With the weights shown the summation output y = 2X1 +2X2 −3. The output u for binary values of X1 and X2 and the value of y are as shown in the truth table. The binary logic unit OR can also be implemented with one perceptron as shown in Figure 17.6. The summation is y = 2X1 +2X2 −1. The complement or NOT function can also be implemented with a single perceptron with one input as shown in Figure 17.7 [21]. The equation for the NOT summation is y = −2X1 + 1. Note that a single perceptron cannot implement an exclusive OR (XOR) or an exclusive NOR (XNOR). To recognize how the perceptron can be used to recognize patterns, we examine the general two input (three weights) perceptron shown in Figure 17.8. A critical threshold occurs when the linear output y = 0 or y = X1 W1 + X2 W2 + W0 = 0

(17.6)

Therefore, in slope intercept form we have X2 = −

W1 W0 X1 − W2 W2

(17.7)

Autonomous Classification of LPI Radar Modulations

Figure 17.5: Binary logic unit: AND [21].

Figure 17.6: Binary logic unit: OR [21].

627

628

Detecting and Classifying LPI Radar

Figure 17.7: Binary logic unit: NOT [21].

Figure 17.8: General two-input perceptron.

Figure 17.9: General two-input perceptron as a linear separable function.

Autonomous Classification of LPI Radar Modulations

629

Figure 17.10: Three-layer perceptron model. which is a linear separable function. That is, a linear line is formed to separate two regions of a plane as shown in Figure 17.9. With each additional weight, a new dimension is added to the separation boundary. That is, with four weights, the separation boundary becomes a plane, and with five weights, the separation boundary becomes a hyper-plane.

17.3.2

Multilayer Perceptron Networks

In an MLP network the perceptrons (neurons or nodes) are the information processing units and they are cascaded in layers to create the complex decision regions. The inputs propagate through the network in a forward direction, on a layer by layer basis. Most often the input set of nodes is not considered a layer. A model of a three-layer perceptron network is shown in Figure 17.10. In this model there are four neurons at the input, two hidden layers with five and four neurons respectively and an output layer with two neurons. Within the MLP is a set of synapses or connecting links, each of which is characterized by a weight of its own. Each neuron has an adder for summing the input signals, weighted by the respective synapses of the neuron. The activation function then limits the amplitude of the output of each neuron. The neuron may also include the externally applied bias which has the eﬀect of increasing or lowering the net input to the activation function, depending on whether it is positive or negative, respectively. The network exhibits a high degree of connectivity, determined by the synapses of the network. Most often the nodes are fully connected with every node in layer i connected to every

630

Detecting and Classifying LPI Radar

node in layer i + 1. In an MLP network the inputs propagate through the network in a forward direction, on a layer by layer basis. Training algorithms include gradient search, backpropagation and temporal diﬀerence. The measure of how well the network performs on the actual problem, once training is complete, is called generalization. It is usually tested by evaluating the performance of the network on new data that is outside the training set. Parameters that can aﬀect the generalization are: (a) the number of data samples and how well they represent the problem at hand, (b) the complicity of the underlying problem, and (c) the network size. In general, a large number of weights adversely aﬀects generalization and the time required to learn the solution. It is also worth noting that the feature vector derived from the T-F and B-F images has a significant impact on both (a) and (b). An MLP with I input nodes, and H hidden layers can be described in general as [22] H

yk ( ) = fs

I

wkh fs h=1

whi xi ( )

(17.8)

i=1

where yk is the output, xi is the input, is the sample number, i is the input node index, h is the number of hidden layers index and k is the output node index. Here wkh and whi represent the weight value from neuron h to k and from neuron i to h respectively and fs represents the sigmoid activation function. All weight values in the MLP are determined at the same time in a single, global (nonlinear) training strategy involving supervised learning. The activation function fs may vary for diﬀerent layers within the network. The activation function can be any type of function that fits the action desired from the respective neuron and is a design choice which depends on the specific problem. Log sigmoid and hyperbolic tangent sigmoid functions are commonly used in multilayer neural networks since they are diﬀerentiable and can form arbitrary nonlinear decision surfaces [23]. The network activation function, fs , that is popular for pattern recognition classification is the log-sigmoid discussed previously defined as fs (y) = 1/(1 + e−βy )

(17.9)

When supervised learning is used, the input-output examples are used to train the network and derive the network weights. Since the network design is statistical in nature we can improve the network generalization during the supervised learning process by minimizing the trade-oﬀ between the reliability of the training data and the goodness of the model. This trade-oﬀ is realized during the supervised learning process through the network regularization R R = gMSE + (1 − g)MSW

(17.10)

Autonomous Classification of LPI Radar Modulations

631

where g is the Tikhonov’s regularization parameter 0 < g < 1 [23]. The term MSE is a performance measure and is the mean sum of squares of the network errors. The performance measure depends on both the network design and the training data. The term MSW is the mean sum of squares of the network weights and biases and is sometimes referred to as the complexity penalty. From (17.10), the regularization parameter g influences directly the trade-oﬀ between the complexity penalty and the performance measure. The optimum values to minimize R are found and the process is carried out for all the training examples on an epoch-by-epoch basis. Note that if g = 1, the network design is unconstrained with the solution depending only on the input-output training examples. For most applications, a three-layer network with H = 2 hidden layers should suﬃcient. Note that when more hidden layers are included, the convergence of the weight values becomes more diﬃcult and significantly more time is required to complete the global training. Further, there is a much larger chance that an overgeneralization will be provided which degrades the ability of the network to identify correctly the modulation type present. The number of output neurons reflects the number of modulation types that are expected. For example, if 12 modulation types were expected in the theater of operations, then the output layer should have 12 neurons each of which corresponds to a modulation type. The output neurons can be hard limiting (0 or 1) or can be sigmoidal which gives more of a modulation type probability. The input feature vector is extracted from the T-F or B-F detection processing image. The feature vector dimension D × 1 is determined by feature extraction signal processing. The supervised training of the feed-forward MLP network uses the gradient of the performance function to determine how to adjust the weights. The gradient is determined using a technique called backpropagation [24]. The backpropagation algorithm is a generalization of the least mean square algorithm used for linear networks, where the performance index is the mean square error. Basically, a training sequence is passed through the multilayer network, the error between the target output and the actual output is computed, and the error is then propagated back through the hidden layers from the output to the input in order to update weights and biases in all layers. Diﬀerent modifications of training algorithms may improve the convergence speed of the network. One of these modifications is the variable learning rate. With the standard steepest descent algorithm, the learning rate is held constant throughout the training. The performance of the algorithm is very sensitive to the proper setting of the learning rate. When a variable learning rate is used and the learning rate is allowed to change during the training process, the performance of the steepest descent algorithm is improved [24].

632

Detecting and Classifying LPI Radar

Figure 17.11: Block diagram of a radial basis function neural network.

17.3.3

Radial Basis Function

The radial basis function (RBF) network is a static feed-forward, two-layer network originally proposed by Broomhead and Lowe [25]. A block diagram of the RBF is shown in Figure 17.11. Each element of the input vector x is applied to the hidden layer which is composed of J basis functions Φ. The N output nodes form a linear weighted (Wnj ) summation of the basis function outputs that are computed [26]. Unlike the MLP, the RBF uses a linear adaptive algorithm in the training of the network coeﬃcients. This makes the RBF network appropriate for real-time applications since it can be designed in a fraction of the time it takes to train an MLP. Since LPI signal modulations are nonstationary, this on-line learning ability allows the classifier to be adaptive to the electromagnetic threat environment. In addition, the RBF network is a universal approximator which has the capability of approximating a decision boundary of any shape providing a major advantage for the noncooperative intercept receiver. Each basis function in the hidden layer produces a nonzero response to the input data when the input falls within the basis function’s small localized region. The RBF determines the similarity between a new input vector and a number of stored vectors representing the basis function centers by using the concept of Euclidean norm or distance. For example if we let xi denote an n-by-1 vector (17.11) xi = [xi1 , xi2 , . . . , xiN ]T all of whose elements are real, the vector xi defines a point in n-dimensional space called Euclidean space. The Euclidean norm between a pair of m-by-1

Autonomous Classification of LPI Radar Modulations

633

vectors xi and xj is defined as 1/2

n

||xi − xj || =

2

(xik − xjk )

(17.12)

k=1

where xik and xjk are the kth elements of the input vectors xi and xj respectively [23]. Correspondingly, the similarity between the inputs represented by xik and xjk is defined as the reciprocal of the Euclidean distance ||xi − xj ||. The output of the RBF can be expressed as J

ypn = Wn0 + j=1

Wnj Φ(||xp − cj ||)

(17.13)

where ypn is the output of the nth modulation node in response to the pth input pattern, Φ(||xp − cn ||) is the output of the hidden node n in response to the pth input vector xp and the vectors cn , n = 1, . . . , N are referred to as the centers of the radially symmetric basis functions Φ. The weighting matrix Wnj represents the synaptic weights from the jth radial basis function to the nth modulation output node and Wn0 is the bias or threshold assigned to the nth modulation output node. One symmetrical choice for the radial basis function Φ is the Gaussian function ⎧ ⎫ J ⎨ 2 (xj − cnj ) ⎬ (17.14) Φ(||xp − cn ||) = exp − 2 ⎩ ⎭ 2σnj j=1

where σnj are the elements of a covariance matrix (or spread), which is taken here to be diagonal. The set of hidden units consist of a set of functions which constitute an arbitrary basis for the feature vector patterns to be classified when expanded into hidden unit space. These are referred to as radial basis functions. The expansion of input vectors into a hidden unit space of relatively high dimension (many radial basis functions) will result in a greater likelihood of the classification problem becoming linearly separable. One approach for an efficient RBF network design is by iteratively creating the RBF one neuron at a time. Neurons are added to the network until either the sum-squared error falls beneath an error goal or a maximum number of neurons has been reached [23]. The two parameters used to optimize the RBF to obtain a better probability of correct classification are the goal and spread σ. The spread constant should be larger than the distance between adjacent input vectors, so as to get a good generalization, but smaller than the distance across the whole input space. The training is accomplished in two stages. The basis functions are determined by unsupervised techniques using the input data while the second layer weights are found by a fast linear supervised method. Hence the training is fast and eﬃcient.

634

17.4

Detecting and Classifying LPI Radar

Feature Extraction Signal Processing

In Figure 17.2, the LPI signal is detected with three T-F signal processing methods. Each T-F image contains features that identify the modulation type (and its parameters). Methods to autonomously extract these features from the T-F distribution have recently received much attention (see for example [27, 28]). Two eﬃcient feature extraction methods that build a feature vector from a T-F image are described below.

17.4.1

Marginal Frequency Adaptive Binarization

An autonomous (no human operator intervention) T-F feature extraction image processing approach that can be used for classification of LPI radar modulations is examined. The feature extraction image processing uses the marginal frequency distribution, or instantaneous energy [29], derived from the T-F representation in order to isolate the location of the modulation autonomously. In order to isolate the modulation, a histogram of the normalized marginal frequency distribution is first computed to choose a threshold for comparison against the mean energy value calculated from the convolution of the normalized marginal frequency distribution with an averaging kernel (sliding window) of length n. This convolution gives the start and stop frequency of the modulation energy. With the location of the modulation energy known it is possible to crop the energy from within the T-F image and compute a feature vector for input into the classification network. In order to preserve the high-resolution detail that emphasizes the diﬀerences between modulation classes without overwhelming the classifier, an adaptive binarization algorithm is used to generate a vector of 1’s and 0’s that represent the modulation [30]. A block diagram of the autonomous feature extraction image processing technique is shown in Figure 17.12. This technique uses the T-F marginal frequency distribution and an adaptive binarization algorithm to form the feature vector. The Choi-Williams detection of a T1(2) signal modulation is used to demonstrate the marginal frequency adaptive binarization (MFAB) feature extraction algorithm. Deleting No-Signal Region One of the characteristics that may be present in the T-F image is when the signal does not extend for the entire distribution. The T-F image will then show the presence of a black column starting where the signal ends and covering all frequencies. Since this no-signal region within the T-F image does not contain useful information for classification, this region must be removed (see the detect & delete no-signal region block in Figure 17.12). Figure 17.13

Autonomous Classification of LPI Radar Modulations

635

Figure 17.12: Autonomous feature extraction using the marginal frequency adaptive binarization (MFAB) algorithm [30]. shows the no-signal region within a Choi-Williams distribution for a T1(2) modulation. Also shown is the image with the no-signal region removed. Marginal Frequency Distribution to Determine Cropping The marginal frequency distribution oﬀers a way to examine a T-F image in intercept situations where there is a low SNR [30]. The marginal frequency distribution gives the instantaneous energy of the signal as a function of frequency. The marginal frequency distribution is generated by CWDx (ω) =

CWDx ( , ω)

(17.15)

or summing the time values for each frequency in the T-F image and then storing the sums in an array. Each marginal frequency distribution is a unique representation of the T-F image it was generated from. The marginal frequency distribution is normalized by dividing the sums by the largest sum in the array. The normalized marginal frequency distribution of the T1(2) modulation is shown in Figure 17.14. The normalized distribution is used to extract a threshold that is used later to isolate and crop the modulation energy within the T-F image. The threshold is determined by generating a histogram of 100 bins of the normalized marginal frequency distribution and then taking the value from the histogram bin which generates the best probability of correct classification (Pcc) results. An example of the T1(2) histogram is shown in Figure 17.15. Once the threshold is determined (n = 9) the convolution of the averaging kernel with the normalized marginal frequency distribution is used to

636

Detecting and Classifying LPI Radar

Figure 17.13: Choi-Williams T-F image for the T1(2) modulation showing (a) presence of the no-signal region and (b) no-signal region removed.

Figure 17.14: Normalized marginal frequency distribution of the T1(2) modulation shown in Figure 17.13.

Autonomous Classification of LPI Radar Modulations

637

Figure 17.15: Histogram of the normalized marginal frequency distribution for T1(2) modulation used to determine threshold autonomously. determine the start and stop cropping locations of the modulation energy. The convolution operation calculates the mean of the corresponding cells in the normalized distribution and compares it to the threshold identified from the histogram. If the average of the convolution is greater than the threshold the start of the modulation energy is found. To find the stop location the same convolution algorithm is used but the kernel is initialized at the end of the normalized distribution. With the location of the modulation energy known it can be cropped from the original image as shown in Figure 17.16. Adaptive Binarization An adaptive binarization algorithm is used to generate a binary image that is then resized to form a feature (column) vector containing ones and zeros. A block diagram of the adaptive binarization process is shown in Figure 17.17 [30]. The intensity image |I(t, ω)| is normalized I (t, ω) with respect to the largest value in the image, where the pixel values 0 ≤ I (t, ω) ≤ 1. A histogram of the intensity level content, h(n), is then generated using N = 50 bins. The cumulative distribution function is computed using this histogram as n h(i) (17.16) cdf (n) = Ni=1 n=1 h(n) A cdf threshold, C, is chosen and the intensity bin n where cdf (n) ≥ C is

638

Detecting and Classifying LPI Radar

Figure 17.16: Autonomous cropping with (a) original resized image and (b) cropped image. then identified. For example, if the cdf threshold is chosen experimentally to be C = 0.8, this means that only 20% of the brightest pixels above the threshold are retained. With this intensity bin, a corresponding normalized intensity threshold, T = n/N , is calculated. This adaptive threshold is then used to convert the intensity image into a binary image. That is, I (t, ω) =

1 (black) I (t, ω) ≥ T 0 (white) I (t, ω) < T

(17.17)

which eﬀectively removes much of the noise and weak interference. The final step is to resize the image. The binarized image is resized to Nr × Nc by lowpass filtering, resampling and then applying a bilinear interpolation. The lowpass filter is used to reduce the eﬀect of Moir´e patterns and ripple patterns that result from aliasing during the resampling operation [31]. The Nr ×Nc image is then converted into a feature vector of size (Nr Nc )× 1 for processing by the multilayer perceptron classification network where Nr = Nc = 50.

17.4.2

Classification Results with Multilayer Perceptron

For testing the MFAB feature extraction, five modulation types are used. The modulation types include BPSK, FMCW, Frank, P4, and T1. To classify the signal modulations, a multilayer perceptron is used with two hidden layers and an output layer. The signals used in the training of the classification

Autonomous Classification of LPI Radar Modulations

639

Figure 17.17: Adaptive threshold binarization process [30]. network contain signal only, SNR = 0 and SNR = −3 dB. Each signal is corrupted with additive white Gaussian noise (WGN) before input to the TF detection transforms. The SNR is defined as SNR = A2 /2σ 2 where A is the amplitude of the signal and σ 2 is the WGN power. WGN is used since this model most generally reflects the thermal noise present in the IF section of an intercept receiver. Two diﬀerent carrier frequencies were also used (fc = 1 kHz and fc = 2 kHz). To test the classification algorithm, noise variations (TestSNR) and modulation variations (TestMod) were used. Note that the TestMod testing is the most diﬃcult case. The database description is given in Table 17.4.2. To optimize classification with the MFAB algorithm it is necessary to pick an accurate threshold using the histogram derived from the marginal frequency distribution in order to find the start and stop frequencies of the modulation energy. In order to do so, a loop that cycles through each of the histogram bins can be used to determine the bin that gives the best threshold for optimum classification. Once the bin that gives the best Pcc is identified, that threshold can be used to generate the classification results.

640

Detecting and Classifying LPI Radar

Table 17.2: Database Description for MFAB Feature Extraction and Classification (fs = 7 kHz) Signal modulation BPSK

FMCW

Frank

P4

T1

Variable cpp Nc fc (kHz) ∆F (Hz) tm (ms) fc (kHz) cpp Nc fc (kHz) cpp Nc fc (kHz) n k fc (kHz)

TestSNR values 1, 4, 7 7, 11 1, 2 250, 500 20, 50 1, 2 1, 4, 7 16 1, 2 1, 4, 7 16 1, 2 2, 6 4 1, 2

TestMod values 2, 3, 5, 6 7, 11 1, 2 350, 450 35, 45 1, 2 2, 3, 5, 6 16 1, 2 2, 3, 5, 6 16 1, 2 3, 4, 5 4 1, 2

Description Cycles per subcode No. of subcodes Carrier frequency Mod. bandwidth Mod. period Carrier frequency Cycles per subcode No. of subcodes Carrier frequency Cycles per subcode No. of subcodes Carrier frequency No. of phase states No. of code segments Carrier frequency

The MLP used to generate the results was executed for a total of 5,000 epochs, with an error goal of 1 × 10−6 . Thirty-five neurons were used in both the first and second hidden layers (S1 = S2 = 35) for the Choi-Williams results and the Wigner-Ville distribution results. For the QMFB, due to the diﬀerent size of the layers, S1 = 20 neurons were used in the first hidden layer and S2 = 35 neurons were used in the second hidden layer. The output layer for all MLP configurations contained 5 neurons which matches the number of modulations that were expected. Optimum classification for the Choi-Williams distribution occurred when bin 16 was used as shown in Figure 17.18 (testing with modulation variation) and Figure 17.19 (testing with noise variation). No classification results were obtained using thresholds from histogram bins greater than 72 because the feature extraction algorithm could not isolate the modulation. Table 17.3 shows the classification results in the form of a confusion matrix for the ChoiWilliams distribution. The diagonal terms represent the Pcc percentage. The oﬀ-diagonal terms are the percentages for the modulation being misclassified. Classifying signals with variations in their modulation (TestMod) is a more diﬃcult case than classifying signals with only variations in noise (TestSNR). This fact is present in all of the classification results. Figures 17.20 and 17.21 are the optimization tables for the Wigner-Ville distribution. Optimum classification occurs when bin 31 (n = 31) is used. No classification results were obtained using thresholds from histogram bins

Autonomous Classification of LPI Radar Modulations

Figure 17.18: Choi-Williams: MLP optimization (TestMod).

Figure 17.19: Choi-Williams: MLP optimization (TestSNR).

641

642

Detecting and Classifying LPI Radar

Table 17.3: Choi-Williams MLP Classification Confusion Matrix (n = 16) TestMod BPSK FMCW Frank P4 T1 TestSNR BPSK FMCW Frank P4 T1

BPSK 0.93 0.00 0.01 0.05 0.01 BPSK 0.96 0.00 0.01 0.03 0.00

FMCW 0.0 1.0 0.0 0.0 0.0 FMCW 0.00 1.0 0.0 0.0 0.0

Frank 0.08 0.01 0.53 0.35 0.04 Frank 0.22 0.00 0.74 0.01 0.03

P4 0.35 0.00 0.05 0.60 0.00 P4 0.11 0.00 0.02 0.85 0.01

T1 0.08 0.00 0.07 0.02 0.83 T1 0.12 0.00 0.03 0.05 0.81

greater than 66 because the feature extraction algorithm could not isolate the modulation. Table 17.4 shows the classification results for the Wigner-Ville distribution when bin 31 is used. Figures 17.22 and 17.23 are the optimization tables for the QMFB detection technique. Optimum classification occurs when bin 9 (n = 9) is used. No classification results were obtained using thresholds from histogram bins greater than 18 because the feature extraction algorithm could not isolate the modulation. Table 17.5 shows the classification results for the QMFB distribution when bin 9 is used.

17.4.3

Classification Results with Radial Basis Function Network

To produce optimum results with the RBF it is necessary to pick an accurate threshold using the histogram derived from the marginal frequency distribution in order to accurately find the start and stop frequencies of the modulation energy similar to what was done for the MLP. The optimum classification occurs when bin 16 (n = 16) is used. Table 17.6 shows the classification using the RBF and the Choi-Williams for n = 16. For the Wigner-Ville distribution, the optimum classification occurs when bin 58 (n = 58) is used. Table 17.7 shows the classification using the RBF and the Wigner-Ville distribution for n = 16. For the quadrature mirror filtering, the optimum classification occurs when bin 14 (n = 14) is used. Table 17.8 shows the classification using the RBF and the Wigner-Ville distribution for n = 16.

Autonomous Classification of LPI Radar Modulations

643

Figure 17.20: Wigner-Ville distribution: MLP optimization (TestMod).

Figure 17.21: Wigner-Ville distribution: MLP optimization (TestSNR).

644

Detecting and Classifying LPI Radar

Table 17.4: Wigner-Ville MLP Classification Confusion Matrix (n = 31) TestMod BPSK FMCW Frank P4 T1 TestSNR BPSK FMCW Frank P4 T1

BPSK 0.96 0.00 0.02 0.02 0.01 BPSK 0.95 0.00 0.02 0.01 0.02

FMCW 0.0 1.0 0.0 0.0 0.0 FMCW 0.00 1.0 0.0 0.0 0.0

Frank 0.08 0.00 0.58 0.33 0.00 Frank 0.19 0.00 0.76 0.03 0.03

P4 0.12 0.00 0.22 0.65 0.01 P4 0.06 0.00 0.01 0.91 0.02

T1 0.20 0.00 0.27 0.04 0.49 T1 0.10 0.01 0.02 0.01 0.86

Figure 17.22: Quadrature mirror filtering: MLP optimization (TestMod).

Autonomous Classification of LPI Radar Modulations

645

Figure 17.23: Quadrature mirror filtering: MLP optimization (TestSNR).

Table 17.5: Quadrature Mirror Filtering MLP Classification Confusion Matrix (n = 9) TestMod BPSK FMCW Frank P4 T1 TestSNR BPSK FMCW Frank P4 T1

BPSK 0.82 0.14 0.01 0.03 0.00 BPSK 0.95 0.01 0.02 0.02 0.00

FMCW 0.40 0.48 0.01 0.11 0.0 FMCW 0.03 0.94 0.02 0.02 0.00

Frank 0.48 0.21 0.13 0.18 0.01 Frank 0.08 0.03 0.81 0.03 0.05

P4 0.35 0.21 0.14 0.30 0.00 P4 0.11 0.01 0.01 0.86 0.01

T1 0.23 0.00 0.05 0.02 0.70 T1 0.09 0.01 0.03 0.04 0.85

646

Detecting and Classifying LPI Radar

Table 17.6: Choi-Williams RBF Classification Confusion Matrix (n = 16) TestMod BPSK FMCW Frank P4 PT1 TestSNR BPSK FMCW Frank P4 PT1

BPSK 1.00 0.00 0.00 0.00 0.00 BPSK 0.95 0.00 0.00 0.02 0.03

FMCW 0.00 1.00 0.00 0.00 0.00 FMCW 0.00 1.00 0.00 0.00 0.00

Frank 0.0 0.00 0.50 0.38 0.13 Frank 0.07 0.00 0.87 0.03 0.03

P4 0.00 0.00 0.14 0.88 0.03 P4 0.07 0.00 0.00 0.90 0.03

T1 0.17 0.00 0.05 0.00 0.83 T1 0.00 0.00 0.00 0.10 0.90

Table 17.7: Wigner-Ville Distribution RBF Classification Confusion Matrix (n = 58) TestMod BPSK FMCW Frank P4 T1 TestSNR BPSK FMCW Frank P4 T1

BPSK 0.75 0.00 0.00 0.00 0.25 BPSK 0.83 0.03 0.00 0.02 0.13

FMCW 0.00 1.00 0.00 0.00 0.00 FMCW 0.00 1.00 0.00 0.00 0.00

Frank 0.00 0.13 0.50 0.25 0.13 Frank 0.07 0.00 0.70 0.07 0.17

P4 0.00 0.00 0.38 0.50 0.13 P4 0.03 0.00 0.10 0.83 0.03

T1 0.00 0.00 0.00 0.00 1.00 T1 0.00 0.00 0.05 0.10 0.95

Autonomous Classification of LPI Radar Modulations

647

Table 17.8: Wigner-Ville Distribution RBF Classification Confusion Matrix (n = 58) TestMod BPSK FMCW Frank P4 T1 TestSNR BPSK FMCW Frank P4 T1

17.4.4

BPSK 0.81 0.19 0.00 0.00 0.00 BPSK 0.97 0.03 0.00 0.02 0.00

FMCW 0.25 0.50 0.00 0.25 0.00 FMCW 0.00 1.00 0.00 0.00 0.00

Frank 0.75 0.13 0.13 0.00 0.00 Frank 0.10 0.17 0.73 0.00 0.00

P4 0.63 0.25 0.00 0.13 0.00 P4 0.10 0.07 0.00 0.83 0.00

T1 0.67 0.00 0.00 0.00 0.80 T1 0.20 0.00 0.00 0.00 0.80

Discussion of Classification Results

The marginal frequency adaptive binarization (MFAB) algorithm was able to be applied to a complex database of LPI signals that closely resembles the types of signals that are found operationally. The ADC sampling frequency (fs = 7, 000 Hz) and LPI signal frequencies and bandwidths are considerably lower than those within the actual intercept receiver hardware due to computational considerations. The classification results however, are representative of the type of results that would be obtained using actual LPI emitters and intercept receiver hardware. The success of the MFAB feature extraction algorithm is due in part to the user’s ability to choose the cropping threshold from an optimization analysis. Choosing the optimum threshold ensures that the algorithm is able to isolate the modulation energy and produce the best possible results for the signal types that are expected. The best classification results were produced with the Choi-Williams distribution. It might be suggested that the success of using the Choi-Williams distribution is attributed to its lack of cross terms (compared to the WignerVille distribution), which can confuse the classification network. That is, the large cross-terms are not conducive to producing unique T-F features that can help the classifier distinguish the diﬀerent signal modulations from one another. The MLP consistently produced better results than the RBF. The MLP was successful because it had more variables that could be configured to produce optimum results. The only variable in the RBF that could be changed was the spread. While the results from the RBF were not as good as those seen coming from the MLP the RBF does have an advantage in terms of its

648

Detecting and Classifying LPI Radar

application to an operational environment. Its training phase is fast and eﬃcient. Because it trains faster than the MLP, in an operational environment a user would not have to wait long before receiving classification results for an LPI signal. This feature of the RBF is important and should be investigated in an attempt to improve the RBF’s results so that it can be applied operationally. In the next section, several signal processing changes are made in order to improve the classification results.

17.5

Modified Feature Extraction Signal Processing

Calculation of the cropping region using the marginal frequency distribution allows the low frequency LPI modulation to be retained and the remaining T-F regions to be discarded. It is important that the size of the cropping region be adaptive and only contain the modulation energy so that the derived feature vector is consistently correlated with the modulation type. In the cropping technique described above, the presence of high frequency noise within the T-F image however, can vary the size of the cropping window. To minimize this eﬀect, the use of a lowpass filter prior to the calculation of the marginal frequency distribution is investigated to help achieve the most consistent cropping of the modulation energy. To make the threshold calculation more robust, the marginal frequency distribution is smoothed using a Wiener filter before normalization. The Wiener filter takes the form of a linear adaptive filter which adjusts its free parameters in response to the statistical variations in the marginal frequency distribution. Also as an alternative to directly using the feature vector as input to the classifier, this section also examines the use of principal components analysis (PCA) in order to develop a lower dimensional feature vector for use by the classifier. A block diagram of the modified autonomous T-F cropping and feature extraction algorithm is shown in Figure 17.24 [32].

17.5.1

Lowpass Filtering for Cropping Consistency

The detect and delete no-signal region is followed by a low pass filter (LPF) applied to the T-F image. This insures that the low frequency LPI modulation energy is preserved and the high frequency noise is removed. The filtering can easily be performed in the frequency domain. Frequency domain filtering using the 2-D Fourier transform is fast and eﬃcient. Let f (k1 , k2 ) for k1 = 0, 1, 2, . . . , M − 1 and k2 = 0, 1, 2, . . . , N − 1 denote the M × N T-F image. The 2-D discrete Fourier transform (DFT) of f denoted by F (u, v) is [33] F (u, v) =

M−1 N −1 k1 =0 k2 =0

f (k1 , k2 )e−j2π(uk1 /M+vk2 /N)

(17.18)

Autonomous Classification of LPI Radar Modulations

649

Figure 17.24: Modified T-F autonomous cropping and feature extraction algorithm. for u = 0, 1, 2, . . . , M − 1 and v = 0, 1, 2, . . . , N − 1. The M × N rectangular region F (u, v), defined by u and v, is often referred to as the frequency rectangle and is the same size as the input image. Note that the frequency rectangle can also be defined by digital frequencies as shown in Figure 17.25 where ω1 = 2πu/M and ω2 = 2πv/N . Given F (u, v), f (k1 , k2 ) can be obtained by means of the inverse DFT. Both DFT and inverse DFT are obtained in practice using a fast 2-D Fourier transform (FFT) algorithm [33]. The convolution theorem, which is the foundation for linear filtering in both spatial and frequency domains, can be written as follows (17.19) f (k1 , k2 ) ∗ h(k1 , k2 ) ⇔ H(u, v)F (u, v) and conversely,

f (k1 , k2 )h(k1 , k2 ) ⇔ H(u, v) ∗ F (u, v)

(17.20)

Filtering in the spatial domain consists of convolving an image f (k1 , k2 ) with a filter mask, h(k1 , k2 ). According to the convolution theorem, the same result can be obtained in the frequency domain by multiplying F (u, v) by H(u, v), which is referred to as the filter transfer function. A block diagram of the frequency domain filtering process is shown in Figure 17.26. The filter transfer function H(u, v) can be obtained in three steps. First, the desired frequency response (ideal lowpass filter) Hd (u, v) is created as a

650

Detecting and Classifying LPI Radar

Figure 17.25: Frequency rectangle for F (u, v).

Figure 17.26: Frequency domain filtering.

Autonomous Classification of LPI Radar Modulations

651

matrix. An ideal lowpass filter has the transfer function [33] Hd (u, v) =

1 if D(u, v) ≤ D0 0 if D(u, v) ≥ D0

(17.21)

where D0 (cutoﬀ parameter) is a specified nonnegative number and D(u, v) is the distance from point (u, v) to the center of the filter. D0 can also be defined as the normalized value of digital frequencies ω1 , ω2 by π. Second, a two-dimensional Gaussian window is created with a standard deviation σ = N × D0 /8 where N is the number of columns in the image. The standard deviation of the window is related to D0 , and the structure becomes adaptive to the changes in the desired frequency responses. For the detection of LPI emitter modulations, both the frequency response matrix and the Gaussian window have dimensions of M × N which is equal to the image dimension f (k1 , k2 ) and the 2-D FFT output dimension F (u, v). The last step is to multiply Hd (u, v) by the Gaussian window. The transfer function of the Gaussian lowpass filter obtained by this multiplication process is then given by [34] H(u, v) = eD

2

(u,v)/2σ 2

(17.22)

These steps are illustrated in Figure 17.27. Figure 17.27(a) shows the desired frequency response with D0 = 0.3 (where |D0 | ∈ [0, 1]) or ω1 = ω2 = 0.3π, Figure 17.27(b) shows the Gaussian window with σ = N × D0 /8 = 33.825. The dimension of both the frequency response matrix and Gaussian window is M = 1,024, N = 902. Figure 17.27(c) shows the resultant Gaussian lowpass filter and Figure 17.27(d) shows the Gaussian lowpass filter as an image. Several values of ω1 , ω2 can be tested during the simulation process to find an optimum value for each distribution. For each trial the digital cutoﬀ frequencies should be set to ω1 = ω2 . After obtaining the lowpass filter, the frequency domain filtering can be implemented by multiplying F (u, v) by H(u, v). This operation is followed by shifting the frequency components back and taking the inverse FFT of the filtered image. The last step is obtaining the real part of the inverse FFT.

17.5.2

Calculating the Marginal Frequency Distribution

After the LPF is used to eliminate the high frequency noise, the marginal frequency distribution of the T-F image is calculated. The marginal frequency distribution gives the instantaneous energy of the signal as a function of frequency. The steps for determining the modulation frequency band from the T-F plane are shown in Figure 17.28. The operations are applied to the MFD of the T-F plane. The MFD gives the instantaneous energy of the signal as a function of frequency. This is obtained by integrating the time values for each frequency in the T-F image resulting in an M × 1 vector A.

652

Detecting and Classifying LPI Radar

Figure 17.27: Implementation of filter function (a) desired frequency response, (b) Gaussian window, (c) Gaussian lowpass filter, and (d) Gaussian lowpass filter as an image [32].

Figure 17.28: Modified method for determining the cropping region [32].

Autonomous Classification of LPI Radar Modulations

653

Figure 17.29: Frank code signal with Nc = 36 (a) MFD and (b) MFD after thresholding [32]. As an example, the marginal frequency distribution of a Frank coded signal with fs = 7 kHz, fc = 1,495 Hz, Nc = 36, and cpp = 1 (B = 1, 495 Hz) with an SNR = 0 dB is shown in Figure 17.29(a). The higher energy interval corresponds to the frequency band of interest and contains the modulation energy. The goal is to isolate and crop the LPI modulation as accurately as possible. This is done by computing the threshold from the histogram as before. As the noise level changes however, the cropping window set by the threshold may change as a function of noise (from one SNR to another). In order to minimize this eﬀect, a smoothing operation is applied on A [32]. The smoothing of the marginal frequency distribution can be applied in a number of diﬀerent ways. One of the most eﬃcient methods is to apply a linear adaptive filter to attenuate the noise followed by a moving average filter to smooth the edges and local peaks. The smoothing operation is then followed by a normalization. An adaptive filter is a filter that changes behavior based on the statistical characteristics of the input signal within the filter. A Wiener filter is a good choice. The Wiener filter is applied to A using the local neighborhood of size m-by-1 to estimate the local image mean and standard deviation. The filter estimates the local mean and variance around each vector element. The local mean is estimated as [34] 1 A(n) (17.23) μ= m n∈η

654

Detecting and Classifying LPI Radar

and the local variance is estimated as σ2 =

1 A2 (n) − μ2 m n∈η

(17.24)

where η is the m-by-1 local neighborhood of each element in the vector A. The processed image within the local neighborhood can be expressed as b(n) = μ +

max(σ 2 − ν 2 , 0) (A(n) − μ) σ2

(17.25)

where v is the noise variance estimated using the average of all the local estimated variances. When the variance is large, the filter performs little smoothing and when the variance is small, it performs more smoothing. For PWVD and CWD images a local neighborhood of η = 10 is used and for the QMFB images η = 4 is used. Figure 17.29(b) shows the output of the adaptive filter for the input MFD of the Frank signal with Nc = 36. Note the considerable noise attenuation. Although the adaptive noise attenuation gives promising results, the threshold determination may be aﬀected by the local noise peaks that could not be reduced by the adaptive filter. To avoid this problem a moving average filter is applied to the output of the adaptive Wiener filter. As a generalization of the average filter, an averaging over N + M + 1 neighboring points can be considered. The moving average filter is represented by the following diﬀerence equation [35] y(n) =

1 N +M +1

M

k=−N

x(n − k)

(17.26)

where x(n) is the input and y(n) is the output. The corresponding impulse response is a rectangular pulse. For PWVD and CWD images a window length of N + M + 1 = 10 is used and for QMFB images N + M + 1 = 4 is used. The moving average filter ˜ avg is then normalized as output, A An =

˜ avg A ˜ avg ) max(A

(17.27)

where An is the normalized smoothed MFD. After normalization a histogram of 100 bins is generated for PWVD and CWD images and a histogram of 30 bins is generated for QMFB images. Using these histogram bins a threshold is determined. Threshold determination is illustrated in Figure 17.30(a) using the histogram of An shown in Figure 17.30(b) for n =30 bin. Note that the corresponding value to the 30th bin Th = 0.2954 is selected as the threshold. For the simulation purposes the histogram bin numbers are optimized using a

Autonomous Classification of LPI Radar Modulations

655

Figure 17.30: Threshold determination showing (a) normalized energy values, (b) histogram of energy values and (c) cropped frequency band of interest using n = 30.

656

Detecting and Classifying LPI Radar

Figure 17.31: (a) LPF output, (b) cropped region, and (c) contour plot of the cropped region showing the Frank modulation. range of values for each detection technique and each network. The bin number that provides the best Pcc is selected. Once the threshold is determined, the values of An below the threshold are set to zero. Then the beginning and ending frequencies of the frequency band of interest are determined as shown in Figure 17.30(c). Using the lowest and highest frequency values from the frequency band of interest the modulation energy can now be cropped from the image. After the determination of the modulation band of interest the energy is autonomously cropped from the LPF output containing the noise filtered image. The cropping was illustrated in Figure 17.31. Figure 17.31(a) shows the LPF output that is obtained previously, Figure 17.31(b) shows the cropped region and Figure 17.31(c) shows the contour plot where the signal energy can easily be seen. Once the LPF output is cropped, the new image is resized to 50 × 400 pixels for the PWVD and CWD images. The QMFB images are resized to 30 × 120 pixels. Resizing is done in order to obtain as much similarity as possible between the same modulation types. Following the resizing operation the columns of the resized image are formed with the feature vector of size 50× 400 = 20, 000 for PWVD and CWD images, and of size 30 × 120 = 3,600 for the QMFB images.

17.5.3

Principal Components Analysis

Principal components analysis (PCA) is mathematically defined as an orthogonal linear transformation that transforms the data to a new coordinate system such that the greatest variance by any projection of the data comes to

Autonomous Classification of LPI Radar Modulations

657

lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on [36]. In other words, PCA is a rotation of the existing axes to new positions in the space defined by the original variables, where there is no correlation between the new variables defined by the rotation. PCA is theoretically the optimum transform for a given data set in least square terms. That is, the method projects the high-dimensional data vectors onto a lower dimensional space by using a projection which best represents the data in a mean square sense. Using PCA the given data vector is represented as a linear combination of the eigenvectors obtained from the data covariance matrix. As a result, lower dimensional data vectors may be obtained by projecting the high-dimensional data vectors onto a number of dominant eigenvectors [37]. PCA can be used for dimensionality reduction of the feature vector by retaining those characteristics of the cropped modulation that contribute most to its variance, by keeping lower-order principal components and ignoring higher-order ones. This assumes of course, that the low-order components contain the most important features of the LPI modulation within the cropped (and resized) T-F data. To facilitate the PCA, we form a training matrix X as shown in Figure 17.32 where N is the length of the feature vector and P is the number of training signals, which is 50 for our results. It is important to note that the mean has been subtracted from the data set. The PCA maps the ensemble of P N-dimensional vectors X = x1 , x2 , · · · , xp onto an ensemble of P D-dimensional vectors Y =

y 1 , y 2 , · · · , y p where D < N using a linear projection. This linear projection can be represented by a rectangular matrix A so that [37] Y = AH X

(17.28)

where A has orthogonal column vectors, i = 1, 2, · · · , P and H is the Hermitian operation. The matrix A is selected as the P ×D matrix containing the D eigenvectors associated with the larger eigenvalues of the data covariance matrix XH X. With this choice of transformation matrix A, the transformed data vectors Y have uncorrelated components. The matrix X is obtained first to form the training data set. The feature extraction algorithm is applied to the images in the “Training” folder for each detection technique. The cropped images are resized and a column vector is formed to represent the signal modulation. These column vectors are stacked together to form the training data set matrix. The mean of the training matrix is calculated column wise and the mean is subtracted from the training data set matrix giving the matrix X. This operation is illustrated in Figure 17.32 where P is the number of training signals which is 50 for this example, and N is the length of the feature vectors. For PWVD and CWD X is of dimension 20,000 ×50 (50 training signals) and for the QMFB X is of dimension 3,600×50.

658

Detecting and Classifying LPI Radar

Figure 17.32: Forming the training matrix X. Figure 17.33 shows a block diagram of the PCA signal processing. In order to obtain the eigenvectors of X, singular value decomposition (SVD) may be performed. SVD states that any N × P matrix X can be decomposed as [37] (17.29) X=U VH where U is the N × N unitary matrix, V is the P × P unitary matrix and is the N × P matrix of nonnegative real singular values. Note that XH X = V

H

(U)H U

VH = V(

H

)VH

Figure 17.33: Principal components analysis.

(17.30)

Autonomous Classification of LPI Radar Modulations

659

indicates that the eigenvectors of XH X are contained in the V matrix and the eigenvalues of XH X are the squared singular values of X, which are the diagonal elements of the matrix H . It can similarly be shown that the eigenvectors of XXH are contained in the U matrix. If p = min(P, N ), both XXH and XH X will have the same p nonzero eigenvalues. The product of X and V gives XV = U

VH V = U

(17.31)

since V is unitary and the eigenvectors associated with nonzero eigenvalues can be extracted by U = XV

−1

(17.32)

As a result, the nonzero eigenvalues of the higher dimensional covariance matrix XXH may be computed by computing the SVD of the smaller dimensional covariance matrix XH X. Following the SVD of the data matrix and determination of the eigenvector matrix U, dimensionality reduction is performed using the projection (transformation) matrix A. The matrix A is composed of D eigenvectors selected from the eigenvector matrix U corresponding to D largest eigenvalues. In order to find the D largest eigenvalues, the biggest eigenvalue is multiplied by a threshold constant and the eigenvalues above the product are taken. Let Thλ be the eigenvalue selection threshold constant. In our example, three values are used as Thλ = [0.001, 0.005, 0.01]. For each case, once the eigenvalues are found, four variations of eigenvector selection are used. Let these variations be ∨i , where i = 0, 1, 2, 3. The variations are defined by the i index as follows: • ∨0 : All the eigenvectors corresponding to the eigenvalues above Thλ are used to form the matrix A. • ∨1 : All the eigenvectors corresponding to the eigenvalues above Thλ are selected initially; all of them except the eigenvector corresponding to the eigenvalue with the highest value are used to form the matrix A. • ∨2 : All the eigenvectors corresponding to the eigenvalues above Thλ are selected initially; all of them except the two eigenvectors corresponding to the two eigenvalues with the highest values are used to form the matrix A. • ∨3 : All the eigenvectors corresponding to the eigenvalues above Thλ are selected initially; all of them except the three eigenvectors corresponding to the three eigenvalues with the highest values are used to form

660

Detecting and Classifying LPI Radar the matrix A.

Once the projection matrix A is generated, both the training matrix X and the test signals are projected onto a smaller dimensional feature space. The dataset is reduced in dimension to D using the projection process. The projected data is then used for classification.

17.5.4

Classification Using Modified Feature Extraction

The classification results in this section use an extended database to determine the performance of the modified feature extraction technique as a function of the SNR. After the database is described, steps to optimize the MLP and RBF are discussed. Classification results are then shown for both the TestSNR signals (same signals used in training but with varying SNR) and the TestMod signals (diﬀerent modulations and varying SNR). Extended Database To investigate the detailed performance of the modified feature extraction and classification process, a more extensive database is developed that consists of 12 LPI modulation techniques each having 21 SNR levels (−10 dB, −9 dB, · · · ,9 dB, 10 dB). The LPI modulation techniques include Costas frequency hopping, Costas frequency hopping plus a Barker phase shift keying, FMCW, PSK and FSK. PSK signals include polyphase (Frank, P1, P2, P3, P4) and polytime (T1, T2, T3, T4) codes. This database allows a detailed look at the Pcc as a function of the SNR. The signals are generated using the LPIT and placed in the “Input” folder within the proper subfolder (TestSNR, TestMod, Training, Signals). Note that the “Signals” folder should contain only one signal from each modulation type being used. This folder is used to correlate the modulation prefix (F for FMCW, FR for Frank and so forth) to build the confusion matrix. The output T-F and B-F images from the detection signal processing (Wigner-Ville, Choi-Williams, quadrature mirror filtering, cyclostationary processing) are automatically placed in the corresponding output folder (e.g., QMFB output). Before the feature extraction and nonlinear classification signal processing algorithms are run, the detection output signals within the “TestMod” and “TestSNR” folders that have the same SNR must be collected and put into a folder that designates the SNR (e.g., TestMod-10, and TestSNR4). The folder structure should be as shown in Figure 17.34. Note that the SNR = 10 dB signals for each modulation are used for training. This is a choice that the user can make. Training the LPI feature extraction and classification networks with only “signal only” waveforms however, is not realistic since any received signal will have a noise component related to the thermal noise present in the intercept receiver and the range of the LPI emitter.

Autonomous Classification of LPI Radar Modulations

661

Figure 17.34: Folder structure for TestSNR, TestMod, and Training (10-dB TestSNR only) [32]. Table 17.9: Costas Frequency Hopping Modulation Parameters for TestSNR (fs = 7,000 Hz) Signal modulation Costas

Frequency sequence (Hz) {3, 2, 6, 4, 5, 1} × 200 {2, 4, 8, 5, 10, 9, 7, 3, 6, 1} × 150

Frequency duration tp (ms) 5 3

Signals Used for TestSNR and TestMod The signals used to test the performance of the feature extraction and classification signal processing for various values of SNR are described below. This database is used to generate the results shown in this section. Supervised training of the autonomous classification process is done with the signal modulations below using SNR = 10 dB. The parameters for the Costas codes and the Costas codes with a Barker PSK used for testing the performance of the classification signal processing as a function of the SNR are shown in Tables 17.9 and 17.10, respectively. The FMCW signal parameters are shown in Table 17.11. The polyphase signals (Frank, P1—P4) used for testing the performance as a function of the SNR are as shown in Table 17.12. Tables 17.13 and 17.14 are the polytime signals T1, T2, T3, and T4 respectively. These signals are used to evaluate the performance of the autonomous classification Pcc when the received signal has the same modulation parameters but diﬀerent SNR. After supervised training of the classification network using the SNR = 10 dB signals from the TestSNR database, the performance using the signals from the TestMod database are evaluated. It is important to

662

Detecting and Classifying LPI Radar

Table 17.10: Costas Plus Barker PSK Frequency Hopping Modulation Parameters for TestSNR (fs = 7,000 Hz) Signal modulation Costas + PSK

Frequency sequence (Hz) {3, 2, 6, 4, 5, 1} × 150 {5, 4, 6, 2, 3, 1} × 300

Barker subcode period tb (ms) 1 (Nc = 5) 0.3 (Nc = 13)

Table 17.11: FMCW Modulation Parameters for TestSNR Signal modulation FMCW

Carrier frequency fc (Hz) 1,495 2,195

Modulation bandwidth ∆F (Hz) 250 800

Modulation period tm (ms) 15 15

point out that this is a more diﬃcult (and realistic) situation. The TestMod signals model the interception of a waveform with a modulation that is not within the training set. The signals in TestMod are also tested as a function of the SNR. The Costas frequency hopping modulation parameters and the Costas frequency hopping plus Barker PSK modulation parameters used for TestMod are shown in Tables 17.15 and 17.16, respectively. The FMCW signals used for testing the performance of the signal processing as a function of the SNR are as shown in Table 17.17. The polyphase signals (Frank, P1—P4) used for testing the performance as a function of the SNR are as shown in Table 17.18. The polytime signals are shown in Tables 17.19 and 17.20. Optimizing the Feature Extraction and Classification Network Using the initial nonlinear network parameters two feature extraction parameters, LPF cutoﬀ frequency and histogram bin, must be optimized. Using the optimum values derived, the PCA network parameters are then optimized. The Pcc results shown are with the final optimum values. The optimization is performed using the test signals with SNR = 10 dB. The optimum parameter selection is based on the highest average Pcc. For each detection technique, the MLP network configuration starts with a default set of values for the epochs, the number of neurons in the first and second hidden layers S1 , S2 , the eigenvalue selection threshold constant T hλ and eigenvector selection variations ∨i . Once the initial values are set, an optimization is performed to determine optimum values for the LPF digital frequencies ω1 = ω2 and histogram bin number. After these two values are

Autonomous Classification of LPI Radar Modulations

Table 17.12: Polyphase Modulation Parameters for TestSNR Signal modulation Frank

Carrier frequency fc (Hz) 1,495

............

................... 2,195

P1

............

P2 ............

P3

............

P4

............

1,495

................... 2,195 1,495 ................... 2,195 1,495

................... 2,195 1,495

................... 2,195

Code length Nc 9 25 36 .......... 16 25 9 25 36 .......... 16 16 16 36 .......... 16 36 9 9 36 .......... 16 25 9 25 36 .......... 16 16

Cycles per subcode cpp 5 2 1 ............. 6 3 5 2 1 ............. 4 5 3 1 ............. 5 3 4 5 1 ............. 6 3 5 2 1 ............. 4 5

663

664

Detecting and Classifying LPI Radar

Table 17.13: Polytime T1, T2 Modulation Parameters for TestSNR Signal modulation T1 ............

T2

Carrier frequency fc (Hz) 1,495 ........... 2,195

1,495

............

........... 2,194

Code period T (ms) 30 30 ....... 30 30 30 30 30 ....... 30 30 30

No. phase states n 2 3 ........... 2 2 4 4 8 ........... 4 4 6

No. code segments k 5 4 .......... 3 4 3 3 4 .......... 3 4 3

Table 17.14: Polytime T3, T4 Modulation Parameters for TestSNR Signal modulation T3 ............

T4

Carrier frequency fc (Hz) 1,495 ........... 2,195

1,495

............

........... 2,194

Modulation period tm (ms) 25 30 ............. 25 30 35 25 30 30 ............. 30 30

Modulation bandwidth ∆F (Hz) 300 900 ............. 400 1000 800 400 550 850 ............. 600 900

No. phase states n 4 9 ........... 2 7 6 2 3 7 ........... 5 9

Table 17.15: Costas Frequency Hopping Modulation Parameters for TestMod (fs = 7,000 Hz) Signal modulation Costas

Frequency sequence (Hz) {5, 4, 6, 2, 3, 1} × 400

Frequency duration tp (ms) 5

Autonomous Classification of LPI Radar Modulations

Table 17.16: Costas Plus Barker PSK Frequency Hopping Modulation Parameters for TestMod (fs = 7,000 Hz) Signal modulation Costas + PSK

Frequency sequence (Hz) {3, 2, 6, 4, 5, 1} × 200 {5, 4, 6, 2, 3, 1} × 250

Barker subcode period tb (ms) 0.4 (Nc = 11) 0.7 (Nc = 7)

Table 17.17: FMCW Modulation Parameters for TestMod Signal modulation FMCW

Carrier frequency fc (Hz) 1,495 2,195

Modulation bandwidth ∆F (Hz) 500 400

Modulation period tm (ms) 20 20

Table 17.18: Polyphase Modulation Parameters for TestMod Signal modulation Frank ............

Carrier frequency fc (Hz) 1, 495 ................... 2, 195

P1 ............

1,495 ................... 2,195

P2 ............

1,495 ................... 2,195 1,495 ................... 2,195

P3 ............

P4 ............

1,495 ................... 2,195

Code length Nc 9 .......... 16 16 9 .......... 16 25 16 .......... 16 25 .......... 16 16 9 .......... 16 25

Cycles per subcode cpp 4 ............. 4 5 4 ............. 6 3 2 ............. 4 2 ............. 4 5 4 ............. 6 3

665

666

Detecting and Classifying LPI Radar

Table 17.19: Polytime T1, T2 Modulation Parameters for TestMod Signal modulation T1 ............ T2 ............

Carrier frequency fc (Hz) 1,495 ........... 2,195 1,495 ........... 2, 194

Code period T (ms) 30 30 ....... 30 30 30 ....... 30

No. phase states n 4 6 ........... 3 6 4 ........... 8

No. code segments k 4 3 .......... 3 4 5 .......... 3

Table 17.20: Polytime T3, T4 Modulation Parameters for TestMod Signal modulation T3 ............ T4 ............

Carrier frequency fc (Hz) 1,495 ........... 2,195 1,495 ........... 2,194

Modulation period tm (ms) 30 35 ............. 30 35 ............. 25 35

Modulation bandwidth ∆F (Hz) 500 700 ............. 600 700 ............. 450 750

No. phase states n 5 8 ........... 3 6 ........... 4 8

Autonomous Classification of LPI Radar Modulations

667

Table 17.21: Optimum Feature Extraction and MLP Parameters Detection Wigner-Ville Choi-Williams Quadrature mirror

ω1 = ω2 0.1π 0.1π 0.4π

Bin 45 15 18

S1 = S2 80 80 60

T hλ 0.001 0.001 0.005

∨i ∨1 ∨0 ∨0

epochs 5,000 6,000 5,000

Table 17.22: Optimum Feature Extraction and RBF Parameters Detection Wigner-Ville Choi-Williams Quadrature mirror

ω1 = ω2 0.2π 0.5π 0.6π

Bin 55 55 4

σ 2000 3500 25

goal 0.9 0.9 0.8

T hλ 0.001 0.001 0.001

∨i ∨0 ∨0 ∨0

found, a second optimization for epochs, S1 , S2 , Thλ and ∨i is performed. Once all the values are found and set the classification network is tested. For the classification of PWVD images the initial values used are epochs = 6,000 S1 = S2 = 50, Thλ = 0.001 and ∨i = ∨0 . After optimization ω1 = ω2 = 0.1π and the histogram bin number is 45. Using these values, the remaining parameters giving optimum Pcc are S1 = S2 = 80, Thλ = 0.001, ∨1 and epochs = 5,000. The optimization is repeated for the Choi-Williams, the quadrature mirror filtering, and the Wigner-Ville distribution detection techniques. Table 17.21 shows the resulting optimum parameters using the MLP. A similar optimization is also run for the RBF. The optimum parameters are shown in Table 17.22 for the RBF.

17.5.5

Classification Results with the Multilayer Perceptron

The classification results are presented for comparison of the three T-F detection techniques including the Choi-Williams distribution (CWD), the pseudo Wigner-Ville distribution (PWVD) and the quadrature mirror filter bank approach (QMFB). The MLP classification results for the Costas frequency hopping code are shown in Figure 17.35 and the results for the Costas plus Barker PSK are shown in Figure 17.36. The MLP classification results for the FMCW are shown in Figure 17.37. The MLP results for the Frank, P1—P4, T1—T4 are shown in Figures 17.38—17.46. All the detection techniques show similar results on the TestSNR case. Most of the modulations are classified with more than 80% classification rate for SNR > 0 dB. There is a considerable stability in classification of signals with SNR > 0 dB. This stability indicates that the autonomous modulation

668

Detecting and Classifying LPI Radar

Figure 17.35: Costas code classification results using the MLP for (a) TestSNR and (b) TestMod.

Figure 17.36: Costas frequency hopping plus PSK classification results using the MLP for (a) TestSNR and (b) TestMod.

Autonomous Classification of LPI Radar Modulations

669

Figure 17.37: FMCW classification results using the MLP for (a) TestSNR and (b) TestMod.

Figure 17.38: Frank classification results using the MLP for (a) TestSNR and (b) TestMod.

670

Detecting and Classifying LPI Radar

Figure 17.39: P1 classification results using the MLP for (a) TestSNR and (b) TestMod.

Figure 17.40: P2 classification results using the MLP for (a) TestSNR and (b) TestMod.

Autonomous Classification of LPI Radar Modulations

671

Figure 17.41: P3 classification results using the MLP for (a) TestSNR and (b) TestMod.

Figure 17.42: P4 classification results using the MLP for (a) TestSNR and (b) TestMod.

672

Detecting and Classifying LPI Radar

Figure 17.43: T1 classification results using the MLP for (a) TestSNR and (b) TestMod.

Figure 17.44: T2 classification results using the MLP for (a) TestSNR and (b) TestMod.

Autonomous Classification of LPI Radar Modulations

673

Figure 17.45: T3 classification results using the MLP for (a) TestSNR and (b) TestMod.

Figure 17.46: T4 classification results using the MLP for (a) TestSNR and (b) TestMod.

674

Detecting and Classifying LPI Radar

energy isolation and cropping becomes more sensitive to noise variations below 0 dB. The Pcc of Frank, FSK/PSK, FMCW, T1, T2, and T4 modulations with PWVD and CWD techniques exhibit 100% for most of the SNR levels above 0 dB. Concerning the TestMod case, the best results are obtained in the classification of FMCW, Costas, FSK/PSK, P2, and T2 modulations while the worst results are obtained in the classification of polyphase codes. Note that most of the results for Frank, P1, P3, and P4 modulations are below Pcc = 0.4. Classification of Costas, FSK/PSK, FMCW, P2, P4, T1, T2, T3, and T4 modulations with PWVD and CWD techniques exhibit similar results. Overall, the classification results with the PWVD technique outperform the other detection techniques. Overall the QMFB technique performs worse than the other techniques but it does well in the classification of T2 and T4 modulations for SNR > 5 dB. Recall that the QMFB images have a very low resolution compared to the PWVD and CWD images, which becomes a disadvantage for modulation discrimination. One interesting result is observed on Costas modulation classification. While the Pcc for TestMod is 100% with all detection techniques, the Pcc for TestSNR is not. This is an unexpected result. It is expected that the TestSNR results would outperform the TestMod results since the signals used in TestSNR have the same parameters as the training signals. In this sense the TestSNR results can be used as a measure of reliability. This shows that, although the Costas results seem very good for TestMod case, they may not be reliable. Further, it is shown that the classification of Costas code is best performed with CWD detection technique for SNR > 4 dB. Note also that it is not necessarily true that the TestMod results perform better if the TestSNR results perform well. The Pcc for TestMod depends on the modulation discriminative power of the feature extraction algorithm implemented.

17.5.6

Classification Results with the Radial Basis Function

The RBF classification results for the Costas frequency hopping signals are shown in Figure 17.47. The RBF classification results for the Costas plus PSK frequency hopping signals are shown in Figure 17.48. The results for the FMCW signals are shown in Figure 17.49. The results for the Frank polyphase signals are shown in Figure 17.50. The RBF classification results for the P1—P4 polyphase signals are shown in Figures 17.51—17.54. The results for the T1 and T2 polytime signals are shown in Figures 17.55—17.58. For the TestSNR classification, the Frank, FMCW, P2, T1, T2, T3 and T4 modulations are classified with greater than Pcc = 80% probability of correct classification for SNR > 2 dB. The autonomous modulation energy isolation and cropping becomes more sensitive to noise variations below SNR = 2 dB.

Autonomous Classification of LPI Radar Modulations

675

Figure 17.47: Costas classification results using the RBF for (a) TestSNR and (b) TestMod. The FMCW modulation is classified with 100% for SNR > 4 dB, and the P2 modulation is classified with 100% for SNR > 4 dB with all detection techniques. Concerning the TestMod case, the best results are obtained in the classification of FMCW, Costas, P1, P2 and T2 modulations while the worst results are obtained in the classification of P4, T1 and T3 modulations. The FMCW modulation is classified 100% with PWVD detection technique for SNR > −10 dB and 100% with CWD detection technique for SNR > −1 dB . The T4 modulation is classified 100% with PWVD detection for SNR > 2 dB and the P2 modulation is classified 100% with CWD detection for SNR > −3 dB. Overall, the classification results with the PWVD technique outperform the other detection techniques. The QMFB technique performs worse than the other two detection techniques. It outperforms however, the other techniques in the classification of the P1 modulation with a Pcc above 66%. MLP and RBF Comparision Both the MLP and RBF networks are examples of nonlinear layered feedforward networks. The important trait that is illustrated in the figures shown is that the RBF classification Pcc results are not as stationary as those for the MLP. This is due in part to the fact that the RBF has a single hidden

676

Detecting and Classifying LPI Radar

Figure 17.48: Costas plus PSK classification results using the RBF for (a) TestSNR and (b) TestMod.

Figure 17.49: FMCW classification results using the RBF for (a) TestSNR and (b) TestMod.

Autonomous Classification of LPI Radar Modulations

677

Figure 17.50: Frank classification results using the RBF for (a) TestSNR and (b) TestMod.

Figure 17.51: P1 classification results using the RBF for (a) TestSNR and (b) TestMod.

678

Detecting and Classifying LPI Radar

Figure 17.52: P2 classification results using the RBF for (a) TestSNR and (b) TestMod.

Figure 17.53: P3 classification results using the RBF for (a) TestSNR and (b) TestMod.

Autonomous Classification of LPI Radar Modulations

679

Figure 17.54: P4 classification results using the RBF for (a) TestSNR and (b) TestMod.

Figure 17.55: T1 classification results using the RBF for (a) TestSNR and (b) TestMod.

680

Detecting and Classifying LPI Radar

Figure 17.56: T2 classification results using the RBF for (a) TestSNR and (b) TestMod.

Figure 17.57: T3 classification results using the RBF for (a) TestSNR and (b) TestMod.

Autonomous Classification of LPI Radar Modulations

681

Figure 17.58: T4 classification results using the RBF for (a) TestSNR and (b) TestMod. layer, whereas the MLP has two hidden layers. Also, the computation nodes of the MLP within a hidden or output layer share a common neuronal model whereas the computation nodes in the hidden layer of the RBF network have a significantly diﬀerent purpose from those in the output layer of the network. The argument of the activation function of each hidden unit in the RBF network computes the Euclidean norm (distance) between the input vector and the center of that unit. For the MLP the activation function of each hidden unit computes the inner product of the input vector and the synaptic weight vector of that unit. Finally, the MLP constructs a global approximation to the nonlinear input-output mapping of the LPI modulations while the RBF network uses exponentially decaying localized nonlinearities (Gaussian functions) to construct local approximations to the nonlinear input-output mappings. For the approximation of a nonlinear input-output mapping, the MLP requires a smaller number of parameters than the RBF network for the same degree of accuracy [23].

682

17.6

Detecting and Classifying LPI Radar

Summary

Autonomous (no human operator intervention) feature extraction and classification algorithms that can be used for identification of LPI radar modulations using time-frequency (T-F) images are presented. The first approach uses a histogram processing of the marginal frequency distribution to identify the modulation within the T-F image. After the modulation is cropped from the image, an adaptive binarization process is used to develop a feature vector for classification of the modulation contained in the signal. Classification techniques evaluated include the multilayer perceptron and the radial basis function neural networks. To evaluate the performance of the feature extraction processing, the classification results for five LPI modulations were investigated. The algorithms were trained using an SNR = 10 dB. To evaluate the classification performance of the algorithms, a database containing the LPI signals with varying SNR was used (TestSNR database). A second database containing the same modulations but with varied parameters (TestMod database) was also used. The percent of correctly classified modulations for this considerably more diﬃcult (but more realistic) database set of signals, were much lower than the TestSNR signals. Due to the poor stability of the cropping region and the large size of the feature vector, a modified feature extraction method was also presented. The modified approach included the addition of a filtering process (to reduce the presence of high frequency noise) and the use of principal components analysis (to reduce the dimensionality). Results showed good improvement and the performance of the modified feature extraction technique was evaluated as a function of SNR. Both the TestSNR and TestMod results were shown. By eliminating the need for a human operator to examine the T-F results, realtime signal analysis is possible, which can allow a faster response management to the intercepted threat signals.

References [1] Azzouz, E., and Nandi, A. K., Automatic Modulation Recognition of Communication Signals, Kluwer Academic Publishers, 1996. [2] Nandi, A. K., and Azzouz, E., “Algorithms for automatic modulation recognition of communication signals,” IEEE Trans. on Communications, Vol. 46, No. 4, pp. 431—436, April 1998. [3] Azzouz, E., and Nandi, A. K., “Automatic identification of digital modulation types,” Signal Processing, Vol. 47, No. 1, pp. 55—69, 1995. [4] Louis, C., and Sehier, P. “Automatic modulation recognition with a hierarchical neural network,” Record of the IEEE Military Communications Conference, MILCOM ’94, Vol. 3, pp. 713—717, October 1994.

Autonomous Classification of LPI Radar Modulations

683

[5] Lin, Y-C., and Kuo, C-C. J., “Modulation classification using wavelet transform,” Proc. of the SPIE, Vol. 2303, pp. 260—271, Wavelet Applications in Signal and Image Processing II, Andrew F. Laine, Michael A. Unser; Eds., Oct. 1994. [6] Reichert, J., “Automatic classification of communication signals using higher order statistics,” Proc. of the IEEE International Conference on Acoustics, Speech and Signal Processing, Vol. 5, pp. 221—224, 23—26 Mar. 1992. [7] Schreyogg, C., Kittel, K., Kressel, U., and Reichert, J., “Robust classification of modulation types using spectral features applied to HMM,” Record of the IEEE Military Communications Conference, MILCOM ’97, Vol. 3, pp. 1377— 1381, Nov. 1997. [8] Breakenridge, C. “Nonstationary signal classification using time-frequency optimization,” Proc. of the 10th IEEE International Conference on Electronics, Circuits and Systems, ICECS, pp. 132—135, 14—17 Dec. 2003, [9] Roberts, G., Zoubir, A. M., and Boashash, B., “Time-frequency classification using a multiple hypothesis test: an application to the classification of humpback whale signals,” Proc. of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol. 1, pp. 563—566, 1997. [10] Breakenridge, C., and Mesbah, M., “Minimum classification error using timefrequency analysis,” Proc. of the 3rd IEEE International Symposium on Signal Processing and Information Technology, ISSPIT, pp. 717—720, 14—17 Dec. 2003. [11] Wang, T. Deng, J., and He, B., “Classification of motor imagery EEG patterns and their topographic representation,” Proc. of the International Conference on Engineering in Medicine and Biology Society, IEMBS ’04, pp. 4359—4362, 1—5 Sept. 2004. [12] Gache, N., Chevret, P., and Zimpfer, V., “Target classification near complex interfaces using time-frequency filters,” Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Vol. 4, pp. 2433— 2436, 12—15 May 1998. [13] Kim, K.-T., Choi, I.-S., and Kim, H.-T., “Eﬃcient radar target classification using adaptive joint time-frequency processing,” IEEE Trans. on Antennas and Propagation, Vol. 48, No. 12, pp. 1789—1801, Dec. 2000. [14] Chilukuri, M. V., Dash, P. K., and Basu, K. P., “Time-frequency based pattern recognition technique for detection and classification of power quality disturbances,” Proc. of the IEEE Region 10 Conference, Vol. 3, pp. 260— 263, 21—24 Nov. 2004. [15] Gillespie, B. W., and Atlas, L. E., “Optimizing time-frequency kernels for classification,” IEEE Trans. on Signal Processing, Vol. 49, No. 3, pp. 485— 496, March 2001. [16] Shelton, C. P., “Human Interface/Human Error,” em Dependable Embedded Systems, Carnegie Mellon University pp. 18—849b Spring 1999.

684

Detecting and Classifying LPI Radar

[17] De vries, M. F. L., Koeners, G. J. M., Roefs, F. D., Van ginkel, H. T. A., and Theunissen, E., “Operator Support for Time-Critical Situations: Design and Evaluation,” Proc. of the IEEE/AIAA 25th Digital Avionics Systems Conference, Delft Univ. of Tech., Netherlands, pp. 1—14, Oct. 2006. [18] Sheridan, T. B., Humans and Automation: System Design and Research Issues, John Wiley & Sons, Inc., 2002. [19] Upperman, G. J., Upperman, T. L., Fouts, D. J., and Pace, P. E., “Eﬃcient time-frequency and bi-frequency signal processing on a reconfigurable computer,” IEEE Asilomar Conference on Signals, Systems and Computers, Nov. 2008. [20] Lippmann, R. P., “An introduction to computing with neural nets,” IEEE ASSP Magazine, pp. 4—22, April 1987. [21] Hush, D. R., and Horne, B. G., “Progress in supervised neural networks,” IEEE Signal Processing Magazine, pp. 8—39, Jan. 1993. [22] Wong, M. L. D., and Nandi, A. K., “Automatic digital modulation recognition using artificial neural network and genetic algorithm,” Signal Processing, Vol. 84, No. 2, pp. 351—365, February 2004. [23] Haykin, S., Neural Networks—A Comprehensive Foundation, Second Ed., Upper Saddle River, New Jersey: Prentice Hall, 1999. [24] Theodoridis, S., and Koutroumbas, K., Pattern Recognition, Third Ed., San Diego, CA: Academic Press, 2006. [25] Broomhead, D. S., and Low, D., “Multi-variate functional interpolation and adaptive networks,” Complex Systems, Vol. 2, pp. 321—355, 1990. [26] Husain, H., Khalid, M., and Yusof, R., “Nonlinear function approximation using radial basis function neural networks,” Student Conference on Research and Development, pp. 326—329, July 2002. [27] Atlas, L., Owsley, L., McLaughlin, J., and Bernard, G., “Automatic featurefinding for time-frequency distributions,” Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, pp. 333— 336, 18—21 June 1996. [28] Zilberman, E. R., and Pace, P. E., “Autonomous time-frequency morphological feature extraction algorithm for LPI radar modulation classification,” Proc. of the IEEE International Conf. on Image Processing, 2006. [29] Cohen, L., “Time-frequency distributions—A review,” Proc. of the IEEE, Vol. 77, No. 7, p. 941—981, 1989. [30] Zilberman, E. R., and Pace, P. E., “Autonomous cropping and feature extraction using time-frequency marginal distributions for LPI radar classification,” Proc. of the IASTED International Conf. on Signal and Image Processing, Aug., 2006. [31] Van De Ville, D.,Van de Walle, R., Philips, W., and Lemahieu, I., “Image resampling between orthogonal and hexagonal lattices,” Proc. International Conf. on Image Processing, Vol. 3, pp. III-389—III-392, 24—28 June 2002.

Autonomous Classification of LPI Radar Modulations

685

[32] Gulum, T. O., “Autonomous Non-Linear Classification of LPI Radar Signal Modulations,” Naval Postgraduate School Master’s Thesis, 2007. [33] Gonzales, R. C., Woods R. E. and Eddins, S. L., Digital Image Processing Using MATLAB, Upper Saddle River, NJ, Prentice Hall, 2004. [33] Lim, J. S., Two-Dimensional Signal and Image Processing, Englewood Cliﬀs, NJ Prentice Hall, 1990. [34] Oppenheim, A. V., Willsky, A. S., and Nawab, S. H., Signals and Systems, Upper Saddle River, NJ: Prentice Hall, 1997. [35] Jolliﬀe, I. T., Principal Component Analysis, Series: Springer Series in Statistics, 2nd ed., Springer, New York, 2002. [36] Fargues, M. P., “Investigation of Feature dimension Reduction Schemes for Classification Applications,” Naval Postgraduate School Technical Report, Monterey, CA, NPS-EC-01-005, June 2001. [37] Therrien, C. W., Discrete Random Signals and Statistical Signal Processing, Prentice Hall, Englewood Cliﬀs, NJ, 1991.

Problems 1. Setting Up the Database: a. Begin by reading the Readme.doc file in the LPI Class folder on the CD. b. Using the LPIT, generate with a sampling frequency of fs = 7,000 Hz, and SNR = 10 dB, a BPSK signal, a polyphase Barker signal, a P1 signal, a P2 signal, a P3 signal, a P4 signal, a Frank code signal, a FMCW signal, T1(2) and a T3(2) signal. Make sure you record the parameters for each of your signals. c. Go to the Input Folder. The Input Folder should have four subfolders. They are the Signals, TestSNR, TestMod and Training folders. Copy the 10 signals into the Training folder and the Signals Folder. d. Copy the 10 signals into the TestSNR folder. e. For each signal generated in b., generate the same signal but with SNR = −10, −9, . . . , 0, . . . , 8, 9 dB. Copy these signals into the TestSNR folder. f. For each signal generated in b., generate the signal with diﬀerent modulation parameters and SNR = −10, −9, . . . , 0, . . . , 10 dB. Be sure to record the modulation parameters for each signal. Copy these signals into the input TestMod folder.

686

Detecting and Classifying LPI Radar

2. Running the Detection Signal Processing: a. Go to the LPI class folder and examine and run the MATLAB script file SCRIPT detection ALL.m. This runs the Wigner-Ville distribution, Choi-Williams distribution, quadrature mirror filtering, and cyclostationary detection signal processing algorithms on all of the files within the Input folder database. Note that these detection algorithms may be run separately by commenting out all but one of the detection processing calls. The output files from the detection processing are put in their respective output folders. Each detection algorithm should be flow diagrammed by the student. b. Collecting the TestSNR, TestMod Output Files: Within each TestSNR folder, collect all of the signals that have the same SNR and put them into a separate folder named as, for example, TestSNR10 (10 dB files), TestSNR-8 (−8 dB files) and so on. Repeat this for the TestMod files. When this is complete, under each output folder you should have folders Signals, Training, TestSNRxx and TestModxx. You should also have a folder named TestSNR and a folder named TestMod that are empty. 3. Running the Feature Extraction and Classification Process In the LPI class folder, examine and flow diagram the MATLAB scripts for computing the feature vector (feature extraction) and running the classification processing. These scripts are named: SCRIPT FE Classification PWVD.m; SCRIPT FE Classification CHOI.m; SCRIPT FE Classification QMFB.m; SCRIPT FE Classification CYCL.m. Note the diary files that are initiated. You should name the diary files so that you can track the results that you generate. From these diary files, the results can be extracted and put into the EXCEL spreadsheet included. This enables the Pcc (probability of correct classification) to be plotted as a function of the SNR. Be sure to normalize your results to one by dividing by the number of times the network runs through the classification algorithm (max test). Include with your classification results, the flow diagrams of the detection, feature extraction and classification algorithms. Note the software architecture is structured to be flexible enabling any new modulations of interest can be included in the analysis.

Chapter 18

Autonomous Extraction of Modulation Parameters In the previous chapter, autonomous classification techniques were investigated to identify the LPI modulations present on the intercepted signal. In this chapter, postclassification signal processing techniques are used to autonomously extract the modulation parameters. Algorithms to autonomously extract the parameters from the time-frequency plane are presented and include extracting the polyphase modulation parameters from the QMFB and Wigner-Ville distribution. Autonomous extraction of parameters from the bifrequency plane (cyclostationary signal processing) is also presented.

18.1

Emitter Clustering

The noncooperative intercept receiver attempts to detect the LPI emitter waveform and determine the angle of arrival. The intercepted waveform is detected most eﬀectively using time-frequency techniques (i.e., WignerVille distribution, quadrature mirror filtering, Choi-Williams distribution) and bifrequency signal processing (cyclostationary processing). Noncooperative intercept receivers must classify the modulation type autonomously across a broad spectrum in the presence of noise and multipath. The detection processing results in a two-dimensional image that is preprocessed in order to produce a feature vector for purposes of classifying the modulation. The detection results are also used for direction finding to determine the angle-of-arrival (AOA) and geodetic location of the emitter. The detection T-F and B-F images can also provide the means for increasing the receiver’s processing gain by autonomously extracting the modulation parameters. Figure 18.1 shows a block diagram of the autonomous detection, 687

688

Detecting and Classifying LPI Radar

Figure 18.1: Block diagram of autonomous classification and parameter extraction processing for a noncooperative intercept receiver. and classification including the parameter extraction process. That is, the images can provide details about the modulation parameters that are unavailable using power spectral density techniques. The need for human interpretation of the T-F and B-F results to determine the parameter values however limits the extraction process to nonreal-time electronic intelligence receivers. The autonomous parameter extraction of the LPI emitter modulations can eliminate the need for a human operator and enable near real-time coherent handling of the threat emitters being intercepted. Parameter extraction followed by correlating the modulation parameters of the intercepted waveform with a database of previously detected emitter parameters or clustering can then aid in signal tracking and coherent EA response management.

18.2

Polyphase Parameters Using Wigner-Ville Distribution–Radon Transform

This section presents an eﬃcient algorithm to autonomously extract the polyphase modulation parameters from an intercepted waveform using a novel Wigner-Ville distribution—Radon transform [1]. The modulation parameters include the bandwidth B, carrier frequency fc , cycles of the carrier frequency

Autonomous Extraction of Modulation Parameters

689

per subcode cpp, code length Nc , and code period T . Results show that the method results in a small relative error in the extracted parameters for signalto-noise ratios as low as −6 dB. The Wigner-Ville distribution—Radon transform approach is particularly useful for this time-frequency signal processing task since the majority of polyphase modulations are developed by approximating a linear frequency modulation waveform. We evaluate the sensitivity of the algorithm using the five polyphase modulations Frank, P1, P2, P3, and P4 for signal-to-noise ratios (SNRs) of 0 dB and −6 dB. To illustrate the algorithm, a Frank code is used with Nc = 36 subcodes, a carrier frequency of fc = 1,495 Hz and an analog-todigital converter (ADC) sampling frequency of fs = 7 kHz with SNR = 0 dB. The number of carrier frequency cycles within a subcode is cpp = 1, giving a transmitted bandwidth B = fc /cpp = 1,495 Hz and a code period of T = 24.1 ms.

18.2.1

Time-Frequency Algorithm Description

A block diagram of the autonomous PWVD-Radon transform algorithm is shown in Figure 18.2. The carrier frequency fc is extracted by finding the location of the maximum intensity level within the PWVD image. In order to extract the code length T and bandwidth B, the Radon transform is computed from the T-F PWVD image. The Radon transform is the projection of the image intensity along a radial line oriented at a specific angle. It transforms the 2-D image with line-trends into a domain of the possible line parameters ρ and θ, where ρ is the smallest distance from the origin and θ is its angle with the x-axis. In this form, a line is defined as [1]. ρ = x cos θ + y sin θ

(18.1)

Using this definition of a line, the Radon transform of a 2-D image f (x, y) can be defined as 8 +∞ f (ρ cos θ − s sin θ, ρ sin θ + s cos θ) ds (18.2) R(ρ, θ) = −∞

where the s-axis lies along the perpendicular to ρ as shown in Figure 18.3. Here s can be calculated as s = y cos θ − x sin θ

(18.3)

Note ρ and s can be calculated from x, y, and θ using (18.1) and (18.3) [2]. In this work the projection of the images are computed as line integrals from multiple sources along parallel paths in a given direction. The beams are spaced 1 pixel unit apart. Figure 18.4 shows the Gray-scale image from

690

Detecting and Classifying LPI Radar

Figure 18.2: Block diagram of the Wigner-Ville distribution—Radon transform technique. the PWVD illustrating the parameters to be extracted (i.e., signal bandwidth B and polyphase code period T ). The algorithm measures B and T by implementing the Radon transform to find θ and d. Here d is the perpendicular distance between consecutive linear energy lines at the modulation angle θs [3, 4]. Once θs and d for the modulation are determined, B and T can be calculated using geometrical relations [3, 4]. The Radon transform is implemented so that the parallel-beam projections of the image are taken between [0◦ , 179◦ ]. Once the transform is completed it is normalized. In some cases the maximum intensity on the transform may occur around θ = 90◦ , which corresponds to the marginal frequency distribution (MFD) and around θ = 0◦ , which corresponds to the time marginal. In order to avoid the detection of the angle corresponding to the MFD and marginal time distribution, it is assumed that the slope of linear energy lines are not between [10◦ , −10◦ ] and between [85◦ , 95◦ ] and the projections on angles between θ = [80◦ , 100◦ ], [0◦ , 5◦ ], [175◦ , 179◦ ] are masked, and set to zero. After masking, the location of the maximum intensity level of the transform is found. The corresponding projection angle at this location gives θs . Once θs is found, the projection at angle θs is cropped from the masked Radon transform and a projection vector is obtained. Figure 18.5 illustrates the cropping of the projection vector A

Autonomous Extraction of Modulation Parameters

Figure 18.3: Geometry of the Radon transform.

Figure 18.4: Radon transform geometry on PWVD image.

691

692

Detecting and Classifying LPI Radar

Figure 18.5: Radon transform and projection cropping on angle θs = 156◦ . at angle θ, from the masked Radon transform of the Frank code. From Figure 18.5 the number of modulation energy lines contained in the PWVD image (number of code periods intercepted) can easily be detected from both the Radon transform and the projection vector at angle θs . The ripples between each modulation energy component correspond to the additive noise and the cross term integration at angle θs . The projection vector is then smoothed with a Wiener filter. b(n) = μ +

max(σ 2 − ν 2 , 0) (A(n) − μ) σ2

(18.4)

where n is an index into the local neighborhood of size η, μ is the estimated local mean, σ2 is the estimated local variance and ν 2 is the estimated noise variance obtained by using the average of all the estimated local variances. A local neighborhood of η = 10 is used in the adaptive filter. Following smoothing, the projection vector is thresholded with a threshold equal to one half of the maximum value of the projection vector. Figure 18.6(a) shows the filtered projection vector and Figure 18.6(b) shows the thresholded projection vector after filtering. After thresholding several distances can be found between the nonzero values in the projection vector which correspond to the consecutive modulation energy components. The final distance d (pixels) can be determined by finding the mean value of these distances. In Figure 18.4, once d is found the modulation code period can now be found using [3, 4]

Autonomous Extraction of Modulation Parameters

693

Figure 18.6: (a) Filtered projection vector and (b) threshold projection vector after filtering.

T =−

] } d 1 fs cos (θs )

and the bandwidth B can be found using the relation } ] d B = ∆f / tan(θs ) cos (θs )

(18.5)

(18.6)

where ∆f is the frequency resolution of the PWVD image. Note that (18.5) is not applied to P2 coded signals since the modulation has an opposite T-F slope. For P2 code modulation, the following relationship applies: ] } d 1 (18.7) T = fs cos (θs )

694

Detecting and Classifying LPI Radar

Figure 18.7: Parameters of polyphase modulation signals. Once fc , T , and B are obtained, the code length Nc can be found using Nc = T × B and the number of carrier frequency cycles per subcode cpp can be obtained using the relation cpp = fc /B.

18.2.2

Testing the Algorithm

The parameter extraction algorithm is tested with 6 LPI polyphase signals as shown in Figure 18.7. The parameters used to generate the polyphase LPI signal modulations are: fs = 7,000 Hz for the noncooperative intercept receiver ADC sampling frequency, fc = 1,495 Hz (signals 1 to 3), 2,495 Hz (signals 4 to 6) for the carrier frequency, Nc = 9, 16, 25, 36 for the number of subcodes, number of cycles of carrier frequency per subcode of cpp = 1, 2, 3, 4, 5, 6 and SNRs of 0 dB and −6 dB. Figure 18.7 also shows the corresponding code periods T and modulation bandwidths B that range from 299 Hz to 1,495 Hz.

Autonomous Extraction of Modulation Parameters

695

Recall that if a∗ is a measurement value of a quantity whose exact value is a, then the absolute value of the relative error r is defined by e e ∗ e a − a e ee error ee e=e e (18.8) e r =e a e truevalue

The relative error is plotted in Figure 18.8 for the carrier frequency fc , code period T , bandwidth B and number of subcodes Nc for each signal number under test. The carrier frequency error is very small for 0 dB but for −6 dB higher errors occur for small values of Nc . If the frequency resolution of the PWVD is increased (integration of more samples from the ADC), the error in estimating fc is expected to decrease and can be easily investigated with the software contained with the textbook. The error in the estimation of Nc is related to algorithm results for T and B since Nc = T B. The overall errors are reasonably small for 0 dB. For SNR = −6 dB the largest errors occur for Nc = 9, 16. That is, the simulation shows the important result that for smaller values of SNR, the error in the extracted parameters are smaller for larger values of Nc . That is, due to the larger processing gain obtained by the intercept receiver (larger numbers of subcodes), a better estimation of the B (18.6) and T (18.7) can be obtained. Note that another important advantage to this approach is that the extraction algorithm is not aﬀected by the cross terms present within the PWVD images. The reason is that integration of the cross term projections is very small compared to the modulation projections obtained.

18.3

Polyphase Parameters from Quadrature Mirror Filtering

In this section the polyphase modulation parameters are extracted using the middle quadrature mirror filter bank (QMFB) time-frequency layer. The parameters to be extracted are carrier frequency (fc ), the code period (T ), number of subcodes within a code period (Nc ), the signal bandwidth (B) and the number of carrier cycles within a subcode (cpp). Polyphase modulations include the Frank, P1, P2, P3, and P4 codes.

18.3.1

Wavelet Decomposition Algorithm Description

This algorithm depends on the quadrature mirror filter bank (QMFB) technique to examine and analyze polyphase signals. The QMFB generates timefrequency layers and the number of layers depends on the signal length. The initial layers oﬀer high time resolution with the final layers oﬀering higher frequency resolution. The middle layer, however, provides the best compromise of both time and frequency, which makes it suitable to extract the parameters

696

Detecting and Classifying LPI Radar

Figure 18.8: Relative error results for polyphase parameter extraction using Wigner-Ville distribution.

Autonomous Extraction of Modulation Parameters

697

of the signals. The accuracy of extracted parameters depends on frequency as well as time resolution of the layer. A flow diagram of the algorithm is shown in Figure 18.9. The algorithm works as follows: a. First qmfb gui.m is executed to input the name of signal (without file extension), directory of signal, sampling frequency (Hz), number of layer and “0” for first time or “1” for another time computation of the layer. b. QMFB is executed by clicking on the “Run” tab on the graphic user interface (GUI) by calling startpoint.m which reads inputs from the GUI and calls the qmfb.m function for formatting and filtering of the signal. This function also computes the total number of time-frequency layers (N ). As mentioned above the center layer provides good compromise of time and frequency resolutions. c. For extraction of the parameters the time-frequency layer is selected (N/(2−1) for N even and (N −1)/2 for N odd) and user is prompted on MATLAB command window to input this layer number in the “choose layer” block of GUI and “1” in “examining another layer” block. After these inputs the “Run” tab is executed on the GUI. d. The data of selected time-frequency layer is saved “QMFB signalfile.mat” for further input to the algorithm.

as

e. The main algorithm file “Ext Para.m” is called within “startpoint.m” to extract the requisite parameters of the poly phase LPI signal. f. The carrier frequency (fc ) is calculated by finding the maximum intensity point of the time-frequency matrix of the selected layer. g. The 3-dB bandwidth is computed by picking the signal intensity points greater than 0.5 in frequency dimension. h. To calculate time period (T ) the time slice is taken on carrier frequency and MATLAB command “movavg” is used to reduce the noise eﬀects along time axis. i. The number of sub codes and number of cycles per sub code are calculated with already computed parameters (carrier frequency, bandwidth and time period).

698

Detecting and Classifying LPI Radar

Figure 18.9: Block diagram of QMFB parameter extraction algorithm.

Autonomous Extraction of Modulation Parameters

18.3.2

699

Testing the Algorithm

The information contained in the time-frequency QMFB layers can be used to extract the parameters with reasonable accuracy using the algorithm described in this section. The middle time-frequency layer that is computed provides a good compromise of time and frequency resolutions. for further analysis of LPI signals. For extracting the carrier frequency and bandwidth of the signal, the signal processing could be restructured to examine the higher layers for more accurate results. Similarly, for time period measurement, the initial layers can yield better results. These accurate results will be at the cost of more computations and processing time. The algorithm should be tested with a number of polyphase signals including Frank, P1, P2, P3, and P4 polyphase codes. We leave this an exercise for the student.

18.4

FMCW Parameters from Cyclostationary Bifrequency Plane

This section demonstrates an algorithm to autonomously extract the modulation parameters of a triangular FMCW signal using the spectral correlation density function. The signal processing uses the DFSM bifrequency plane where the presence of the FMCW modulation has been identified. The parameter extraction process determines the modulation period tm , modulation bandwidth ∆F and the carrier frequency fc . Extraction for low SNR bifrequency images gives reasonable results due to the denoising capability of the spectral correlation processing since noise is not correlated. The DFSM algorithm first computes the spectral components of the signal and then executes the spectral correlation operations directly on the spectral components. One important consideration in obtaining accurate results with the FMCW extraction algorithm is to insure that the DFSM frequency resolution, cycle frequency resolution selected, is small enough to measure the parameters accurately (for example, the code rate Rc ). As an example, an FMCW waveform with ∆F = 500 Hz, tm = 30 ms, fc = 1 kHz and SNR = 0 dB is processed through the DFSM algorithm. The frequency resolution was set to 16 Hz and the value of the Grenander’s uncertainty condition is selected as M = 2 (N = 1,024). Due to the quadrant symmetry of the bifrequency plane, the FMCW modulation shows up at four distinct locations as shown in Figure 18.10. Each of these four positions contains a geometrical shape representative of the modulation from which all the parameters can be extracted. Two of the modulation parameters of interest are shown on the one selected quadrant of the bifrequency plane shown in Figure 18.11. Both the modulation bandwidth and carrier frequency are easily recognized from this result. To extract the modulation period we closely examine the details re-

700

Detecting and Classifying LPI Radar

Figure 18.10: Direct frequency-smoothing method for cyclostationary extraction of FMCW parameters with ∆F = 500 Hz, tm = 30 ms and fc = 1 kHz using a frequency resolution of 16 Hz and M = 2. vealed in any one of the four quadrants. What we can measure easily is the modulation code rate Rc as shown in Figure 18.12. The modulation period for a triangular FMCW waveform is related to the code rate as tm =

1 2Rc

(18.9)

where the factor of 2 in the denominator accounts for the triangular waveform extending for 2tm .

18.4.1

Cyclostationary Algorithm Description

A block diagram of the FMCW extraction processing algorithm that uses the DFSM bifrequency plane results is shown in Figure 18.13. The first step in the algorithm is to crop one of the quadrants within the area of support matrix. A diﬀerent angle of the bifrequency plane is shown in Figure 18.14 and is a contour plot of the bifrequency matrix S from the DFSM processing. The figure shows the area of support that is cropped for parameter extraction processing (left upper corner of the figure). After cropping the area of support, an adaptive threshold operation is performed to reduce the amount of noise present in the image. This is followed by creating windows for detection of local maximums. The local maximums are used to

Autonomous Extraction of Modulation Parameters

701

Figure 18.11: Bifrequency plane showing the measurement of FMCW modulation parameters ∆F = 500 Hz (frequency), and fc = 1 kHz (cycle frequency).

Figure 18.12: Bifrequency measurement of FMCW code rate on the cycle frequency axis showing Rc = 16.6 Hz (=1/2tm ).

702

Detecting and Classifying LPI Radar

Figure 18.13: Block diagram of FMCW extraction processing using DFSM bifrequency plane. calculate the code rate Rc and subsequently the modulation period tm by finding the minimum cycle frequency diﬀerence for the local maximums. Determining the boundaries of the modulation allows the carrier frequency and modulation bandwidth information to be calculated. The boundaries of the signal are defined in Figure 18.14. The modulation bandwidth of the signal is (18.10) ∆F = f2 − f1

and the carrier frequency is

fc =

α1 − α2 2

(18.11)

where the goal is to find the correct values of α1 , α2 , f1 and f2 . To find the appropriate index values corresponding to the correct values for this computation, the image is scanned in two diﬀerent directions as shown in Figure 18.15. An approximation to the pdf is constructed by scanning both the i- and j-axis and finding the magnitude corresponding to each index. The horizontal scan gives the i-index values as xi =

N 3

S(i, j)

(18.12)

j=1

and

xi=(1:N ) pdfi = xj=(1:N )

(18.13)

and the vertical scan similarly the j-index values. This energy distribution enables the location of the signal on the bifrequency plane to be determined. The algorithm scans from the lower index values to the higher index values to look for the signal power above the threshold of −6 dB. The first index with a level above −6 dB gives i1 and j1 . Starting from the higher index values and going toward the lower index values gives i2 and j2 resulting in ∆F = fi2 ,j2 − fi1 ,j1

(18.14)

Autonomous Extraction of Modulation Parameters

703

Figure 18.14: Contour plot of DFSM matrix S showing the region of support being cropped for parameter extraction. and

αi1 ,j2 − αi2 ,j1 (18.15) 2 The same algorithm is used to extract the parameters from a noisy signal. The scan method described above however, will smear the signal’s pdf so the procedure for determining the index values must be modified to avoid possible errors (due to the high energy levels in the skirts of the pdf). An adaptive noise filter is also used here. fc =

18.4.2

Testing the Algorithm

To evaluate the algorithm’s accuracy, the program is run for 12 diﬀerent signals, which are listed below. The algorithm is also run for a set of higher frequency signals. The program checks the signal for the existence of the noise and uses the appropriate method to extract the parameters. The algorithm also checks the extracted parameters and does a closest match with the possible threat signals in a database. This gives the exact parameters of

704

Detecting and Classifying LPI Radar

Figure 18.15: Scan geometry for DFSM matrix S to determine the correct index values i and j. the signal. The signals are analyzed using cyclo gui.m. The signals with no noise and with 0 dB noise are analyzed with 16 Hz of frequency resolution but the signals with −6 dB noise are analyzed with 32 Hz of frequency resolution. The high resolution selected for the −6 dB signals is due to the computational diﬃculties when using a personal computer. Hence the results for −6 dB signals do not have a modulation period solution because the solutions are not reliable for the 32 Hz of resolution that is used. As discussed in Chapter 15, the resolution of the cycle frequency and frequency should be smaller than the largest parameter being measured or extracted. F F F F

1 1 1 1

7 7 7 7

250 250 500 500

20 30 20 30

s.mat s.mat s.mat s.mat

(fc (fc (fc (fc

=1 =1 =1 =1

kHz, kHz, kHz, kHz,

fs fs fs fs

=7 =7 =7 =7

kHz, kHz, kHz, kHz,

∆F ∆F ∆F ∆F

= 250 = 250 = 500 = 500

Hz, Hz, Hz, Hz,

tm tm tm tm

= 20 = 30 = 20 = 30

ms, ms, ms, ms,

signal signal signal signal

only) only) only) only)

F F F F

1 1 1 1

7 7 7 7

250 250 500 500

20 30 20 30

0.mat 0.mat 0.mat 0.mat

(fc (fc (fc (fc

=1 =1 =1 =1

kHz, kHz, kHz, kHz,

fs fs fs fs

=7 =7 =7 =7

kHz, kHz, kHz, kHz,

∆F ∆F ∆F ∆F

= 250 = 250 = 500 = 500

Hz, Hz, Hz, Hz,

tm tm tm tm

= 20 = 30 = 20 = 30

ms, ms, ms, ms,

SNR SNR SNR SNR

= = = =

0 0 0 0

F F F F

1 1 1 1

7 7 7 7

250 250 500 500

20 30 20 30

-6.mat -6.mat -6.mat -6.mat

ms, ms, ms, ms,

SNR SNR SNR SNR

= = = =

−6 −6 −6 −6

(fc (fc (fc (fc

=1 =1 =1 =1

kHz, kHz, kHz, kHz,

fs fs fs fs

=7 =7 =7 =7

kHz, kHz, kHz, kHz,

∆F ∆F ∆F ∆F

= 250 = 250 = 500 = 500

Hz, Hz, Hz, Hz,

tm tm tm tm

= 20 = 30 = 20 = 30

dB) dB) dB) dB) dB) dB) dB) dB)

Autonomous Extraction of Modulation Parameters

18.5

705

Concluding Remarks

In this chapter, we have shown that we can extract the parameters for the signal only measurements very accurately as shown in Figure 18.16. The parameters extracted from the noisy signals are also fairly accurate, but the algorithm for the noisy signals can be improved to get better performance. The threshold set for the noisy measurements were set to a fixed intuitive level, which is somewhat subjective. One may think of adding an adaptive threshold that changes according to the noise level in the signal. Here we took advantage of the cyclostationary analysis to get rid of the noise. Note that the cyclostationary analysis has an inherited noise reducing process within its spectral correlation algorithm. Once the signal is classified correctly, the exact parameters of the intercepted signal can be determined.

References [1] Hejazi, M.R., Shevlyakov, G., and Ho, Y-S., “Modified discrete radon transforms and their application to rotation-invariant image analysis,” IEEE 8th Workshop on Multimedia Signal Processing, pp. 429—434, Oct. 2006. [2] Minsheng, W., Chan, A.K., and Chui, C.K., “Linear frequency modulated signal detection using Radon-ambiguity transform,” IEEE Trans. on Signal Processing, Vol. 26, No. 3, pp. 571—586, March 1998. [3] Gulum, T. O., Pace, P. E. and Cristi, R. “Extraction of Polyphase Radar Modulation Parameters Using a Wigner-Ville Distribution—Radon Transform,” IEEE International Conf. on Acoustics, Speech and Signal Processing, Las Vegas, NV, March 2008. [4] Gulum, T. O., “Autonomous Non-linear Classification of LPI Radar Signal Modulations,” Naval Postgraduate School Master’s Thesis, Sept. 2007.

Problems 1. (QMFB) The files in the Part II folder Extract\POLY FROM QMFB perform the quadrature mirror filtering but have been modified to implement the extraction routines in Section 18.3. (a) Generate a Frank code signal with fc = 1 kHz, fs = 7 kHz, M = 16 and cpp = 2 for SNRs between −10 dB and 10 dB (in steps of 1 dB). (b) Run poly from qmfb.m to extract the parameters for the Frank code. Be sure to follow the instructions on the command line that are displayed. (c) Plot the relative error as a function of the SNR for each of the extracted parameters. (d) Repeat (a)—(c) for the P4 code and compare your results.

706

Detecting and Classifying LPI Radar

Figure 18.16: Extraction results using the cyclostationary signal processing bifrequency plane.

Autonomous Extraction of Modulation Parameters

707

2. (QMFB) Edit the m-files contained in the Part II folder Extract\POLY FROM QMFB folder to analyze a diﬀerent layer (other than the middle layer). Repeat Problem 1 and compare your results. 3. (QMFB) Write a MATLAB procedure similar to Ext Para.m to extract the parameters from an FMCW signal. Use the FMCW files in the Test Signals folder to evaluate your results. 4. (CYCLO) The files in the Part II folder Extract\FMCW FROM CYCLO perform the direct frequency smoothing spectral correlation technique to derive the bifrequency domain results. The file cyclo gui.m calls DFSM.m which has been modified to include the parameter extraction algorithm described in Section 18.4. (a) Generate an FMCW signal with fc = 1 kHz, fs = 7 kHz, ∆F = 500 Hz and tm = 30 ms for SNRs between −10 dB and 10 dB (in steps of 1 dB). (b) Run cyclo gui.m to extract the parameters of the FMCW waveforms. (c) Plot the relative error as a function of the SNR for each of the extracted parameters. (d) Repeat (a)—(c) for an FMCW signal with twice the modulation bandwidth and compare your results. 5. (CYCLO) Copy the FAM.m file contained in the Part II folder CYCLO to the Extract\FMCW FROM CYCLO folder. Edit the file to include the parameter extraction algorithm (see Problem 4). Repeat Problem 4 (a)—(c) and compare your results. 6. (PWVD) The files in the Part II folder Extract\POLY FROM WVD perform the extraction of the polyphase parameters using the PWVD— Radon transform described in Section 18.2.1. The main file poly from WVD.m uses a routine that cycles through the subfolder “polyfiles” to extract the parameters for all of the files contained in the folder. (a) Copy one example of each polyphase modulation for signal only from the TestSignals folder (Part I) to the polyfiles folder. Edit the main file and change the diary file to represent your case under study. Run the parameter extraction algorithm and then compute the relative error for each result. (b) Repeat (a) for a SNR = 0 dB. (c) Repeat (a) for a SNR = −6 dB. (d) How does the noise aﬀect the relative error for the extraction results?

Appendix A

Low Probability of Intercept Toolbox A.1

Introduction to the LPIT

The low probability of intercept toolbox is a collection of MATLAB files that give the user the quick capability to generate a number of LPI complex signals easily. The user can change the parameters of the signal, plot out the signal’s time domain and power spectral density characteristics, and save the time domain signal to the current directory for further analysis, using the timefrequency and bifrequency classification programs discussed in Part II. The LPIT software is contained on the CD provided with this book, in the folder titled LPIT. To install the toolbox, simply copy this folder to your computer. When the LPI signals are generated, they are saved to the same folder where the program files reside. After folder has been copied to your computer, the following steps should then be followed to generate the signals: 1. Start MATLAB and change the current directory to the LPIT folder. 2. Type lpit on the command line to start the toolbox. 3. Choose one of the LPI signals on the menu and enter the parameters requested. 4. Choose whether (or not) to plot the signal. 5. Choose whether (or not) to save the signals to the current directory. Note that if the user chooses to save the signal, two .mat files are created: one for the signal only, and one for the signal-plus-noise for SN R = 0 dB. 709

710

Detecting and Classifying LPI Radar

SNRs other than 0 dB can also be generated when supplying the requested parameters. For each file, the complex signal is saved in a .mat file, with the I and Q variables in two separate column vectors. The number of code periods generated by the LPIT is five (four for FMCW) although that can easily be changed. The 14 signal types available from the LPIT, and the corresponding chapter where they are discussed are shown below:1 1. FMCW (Chapter 4); 2. BPSK (Chapter 5); 3. Polyphase Barker codes (Chapter 5); 4. Polyphase Frank code (Chapter 5); 5. Polyphase code P1 (Chapter 5); 6. Polyphase code P2 (Chapter 5); 7. Polyphase code P3 (Chapter 5); 8. Polyphase code P4 (Chapter 5); 9. Polytime signals (Chapter 5). 10. Costas frequency hopping code (Chapter 6); 11. FSK/PSK (Costas) (Chapter 6); 12. FSK/PSK (Target) (Chapter 6); 13. Noise waveforms (Chapter 7); 14. Test signals (Chapters 9, 10, and 11);

A.2

Naming Convention and Example

For all signals, the name is automatically assigned to the .mat file, and reflects the signal parameters that were supplied by the user. The naming convention is the same for each signal, but varies slighty due to diﬀerent parameters required for diﬀerent types of signals. The first character in the file name 1 Taboada, F. L., “Detection and classification of low probability of intercept radar signals using parallel filter arrays and higher order statistics,” Naval Postgraduate School, Master’s Thesis, Sept. 2002.

Appendix A: Low Probability of Intercept Toolbox

711

Figure A.1: LPIT file naming convention. always indicates the type of signal. The second character indicates the carrier frequency (in kHz). The third character indicates the selected sampling frequency (in kHz). The remaining characters are diﬀerent, depending on the type of signal generated. The file naming convention is summarized in the tree diagram shown in Figure A.1 For example, for an FMCW, the fourth character is the modulation bandwidth (in Hz), and the fifth character is the modulation period (in ms). The sixth character is either an “s” indicating signal only, or a number indicating the SNR for a noisy signal. Consider the signals F 1 7 250 20 s.mat (signal only) and F 1 7 250 20 0.mat (SNR=0 dB). Here the F indicates FMCW. The 1 indicates an fc = 1 kHz carrier frequency, the 7 indicates fs = 7 kHz sampling frequency, the 250 indicates the modulation bandwidth ∆F = 250 Hz, and the 20 represents the modulation period tm = 20 × 10−3 s. The “s” in the first file name indicates that the .mat file contains only the signal. The “0” in the second file name indicates the .mat file with SN R = 0 dB. For example, if the signal is generated with a −6 dB SNR, then this value would be 6. When the signals are saved, the names are always displayed, so the parameters chosen can be recognized.

Appendix B

Generating PAF Plots Using the LPIT Files For CW signals, the Web site by Levanon (www.eng.tau.ac.il/˜ nadav/) includes the files to calculate and display the autocorrelation function, the periodic autocorrelation function, and the periodic ambiguity function.1 These files can be downloaded and used easily with the time domain signals generated by the LPIT. To calculate and display the ACF, PACF, and PAF, download the files into the LPIT folder. After generating the .mat files containing the LPI signal (see Appendix A), follow the steps below: 1. Run ambfn7.m (Levanon’s PAF code from the Web site). 2. Select “User Defined” in the first block at the top. 3. Deselect the Frequency Radio button that follows. 4. Next go to the command line and run the paf preprocess.m file distributed with the LPIT. This file will ask the user to supply: • Name of the signal file (.mat file that resides in the LPIT directory); • Sampling frequency fs (in Hz);

• Carrier frequency fc (in Hz);

1 The MATLAB code to calculate the ambiguity function is described in Mozeson, E., and Levanon, N., “MATLAB code for plotting ambiguity functions,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 38, No. 3, 1064—1068, 2002.

713

714

Detecting and Classifying LPI Radar • Number of code periods to include in PAF calculation N (1) for PSK and (2) for FSK.

5. Return to the ambfn7.m graphical user interface (GUI) and, next to the sliders, enter in the five suggested values for the signal analysis. 6. On the GUI select Cal & Signal Plot first, then ACF and SPEC plot or PAF. Note that the number of code periods N to include in ACF, PAF calculation is independent of the number of periods generated using the LPIT.

Appendix C

Primitive Roots and Costas Sequences In this appendix, a concise description of prime numbers, residues, reduced residues, the Euler function φ(n), and primitive roots is given. The significance of this appendix is to present the concepts in a framework that lends itself to the derivation of Costas frequency-hopping sequences. These concepts are useful for understanding the construction of Costas sequences using the Welch method.1

C.1

Primes

To begin we give the definition of a prime number. Definition 1 An integer p > 1 is called a prime number, or a prime, in case there is no divisor d of p satisfying 1 < d < p. For example, the numbers 2, 3, 5, and 7 are prime numbers and there is an infinite number of primes. Although the numbers 4, 5, and 7 are not all primes, they are all relatively prime with respect to each other, in that none have a common factor.2 1 Note that mathematical concepts such as the division algorithm, the Euclidean algorithm for finding the greatest common divisor (gcd), and the solutions of simultaneous congruencies using the Chinese remainder theorem are not described here, but a complete treatment is presented in Pace, P. E., Advanced Techniques for Digital Receivers, Artech House, Inc., Norwood MA, 2000. 2 Niven, I., Zuckerman, H. S., and Montgomery, H. L., Introduction to the Theory of Numbers, 5th Edition, John Wiley and Sons, New York, 1991.

715

716

C.2

Detecting and Classifying LPI Radar

Complete and Reduced Residue Systems

If a congruence involves only addition, subtraction, and multiplication, we may replace the integers with congruent integers. To help in this, the following definitions describing residue systems are given, followed by an example to illustrate the concept. Definition 2 If h and j are two integers and h ≡ j(mod m), then we say that j is a residue of h modulo m. Definition 3 The set of integers {r1 , r2 , . . . , rs } is called a complete residue system modulo m if ri = rj (mod m) and for each integer n there corresponds an ri such that n ≡ ri (mod m). If s diﬀerent integers r1 , r2 , . . . , rs form a complete residue system modulo m, then s = m. If m is a positive integer, then {0, 1, . . . , m − 1} is a complete residue system modulo m. For example, for m = 7, the smallest positive integer values within the modulus are {0, 1, 2, 3, 4, 5, 6}. Definition 4 The set of integers {r1 , r2 , . . . , rs } is called a reduced residue system modulo m if (a) the gcd(ri , m) = 1 for each i, (b) ri = rj (mod m) whenever i = j, and (c) for each integer n relatively prime to m there corresponds an ri such that n ≡ ri (mod m). For example, the set {0, 1, 2, 3, 4, 5} is a complete residue system modulo 6, but {1, 5} is a reduced residue system modulo 6. That is, we can obtain a reduced residue system from a complete residue system by simply deleting those elements of the complete residue system that are not relatively prime to m. Example 1 The sets {1, 2, 3}, {0, 1, 2}, {−1, 0, 1}, and {1, 5, 9} are all complete residue systems modulo 3. When working with congruences modulo m, we can replace the integers in the congruences by elements of {0, 1, 2, . . . , m − 1}. This can make many complicated problems much easier.3 3 Andrews,

G. E., Number Theory, Dover Publications Inc., New York, 1971.

Appendix C: Primitive Roots and Costas Sequences

717

Example 2 Find an integer n that satisfies the congruence 325n ≡ 11(mod 3)

(C.1)

325 ≡ 1(mod 3)

(C.2)

11 ≡ 2(mod 3)

(C.3)

n ≡ 2(mod 3)

(C.4)

Since and

the problem is reduced to finding an integer n such that [15]

The obvious answer here is the integer 2. Definition 5 The function φ(m) denotes the number of positive integers less than or equal to m that are relatively prime to m. This function φ(m) is called the Euler φ−function, and represents the number of integers that form the reduced residue system modulo m. Example 3 We know φ(6) = 2 and {1, 5} is a reduced residue system modulo 6. Note the set {5, 52 } is also a reduced residue system modulo 6, since 5 ≡ 5(mod 6) and 25 ≡ 1(mod 6).

C.3

Primitive Roots

We have examined the concept of the reduced residue system modulo p where p is a prime number. In this section, we present an integer g such that g, g 2 , . . . , g φ(p) constitutes a reduced residue system modulo p. The integer g is called a primitive root. Primitive roots are fundamental to how Costas frequency sequences can be formed. An algorithm for deriving these types of sequences is presented, along with an example illustrating the method. A few properties of reduced residue systems must now be given. The first is that if h is the smallest positive integer such that ah ≡ 1(mod m)

(C.5)

we say that the order of a is h modulo m. If g is an integer, and the order of g is φ(m) modulo m, then g is called a primitive root modulo m. Further, if g is a primitive root modulo m, then g, g 2 , . . . , g φ(m) makes up a reduced residue system modulo m (sometimes referred to as a cyclic group). Since the goal of this development is to derive a Costas sequence, the first step is to determine a prime number p, remembering that the number of frequencies in the FH sequence will be NF = p − 1. Also, since p is prime, we have the following definition:

718

Detecting and Classifying LPI Radar

Definition 6 If p is prime, then there exist φ{φ{p}} = φ{p − 1}, primitive roots modulo p. This number can be determined by first eliminating those elements in the reduced residue set that are not relatively prime to p − 1, and then counting the remaining entries. Note also that the order of a in (C.5) must be a divisor of φ(p) = p − 1. Example 4 Consider the case for which p = 11, a prime number. The number of frequencies in the Costas array will be N = p − 1 = 10. The complete residue set is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} There are p − 1 = 10 elements in the reduced residue set modulus 11 {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and there are φ{p − 1} = φ{10} = 4 primitive roots. The questions we have now are what are the primitive roots and what are the corresponding Costas sequences? To determine the primitive roots by which we can derive the Costas sequences, we start with g = 1 (the first element in the reduced residue set). For g = 1 we have {11 , 12 , 13 , . . . , 1φ{11} } = {1} and we say the order of 1 is 1. Consequently, 1 is not a primitive root. For 2, {21 , 22 , 23 , . . . , 2φ{11} } or {2, 4, 8, 5, 10, 9, 7, 3, 6, 1} and the order of 2 is 10, indicating that g = 2 is a primitive root. For 3 we have, {3, 9, 5, 4, 1} and the order of 3 is 5. That is, 3 is not a primitive root. Continuing on for the rest of the integers within the reduced residue system for 4 we have, {4, 5, 9, 3, 1} and the order of 4 is 5 (not a primitive root). For 5 we have, {5, 3, 4, 9, 1}

Appendix C: Primitive Roots and Costas Sequences

719

and the order of 5 is 5 (not a primitive root). For 6 we have, {6, 3, 7, 9, 10, 5, 8, 4, 2, 1} so the order of 6 is 10, and consequently, 6 is a primitive root. For 7 we have, {7, 5, 2, 3, 10, 4, 6, 9, 8, 1} so the order of 7 is 10, and 7 is also a primitive root. For 8 we have, {8, 9, 6, 4, 10, 3, 2, 5, 7, 1} so the order of 8 is 10, and therefore 8 is a primitive root. Since we now have our four primitive roots, we know that there are no more. For completeness however, we verify that for 9 we have, {9, 4, 3, 5, 1} and the order of 9 is 5 (not a primitive root), and for 10 we have, {10, 1} therefore the order of 10 is 2, and 10 is not a primitive root. In summary, the four primitive roots are {2, 6, 7, 8}. One question still remains. How do we know, short of multiplying out, if a in (C.5) is a primitive root? That is, is there a way to find the primitive roots and Costas sequences without having to calculate the order of each integer value within the reduced residue set modulo p? Fortunately, the answer is yes, and we can use the following definition Definition 7 If a is a primitive root modulus p then ar is a primitive root modulus p if and only if gcd(r, φ(p))=1 (r is relatively prime to φ(p) = p − 1). In this case we can reduce our work by starting with the smallest value (e.g., a = 2), and first determining if this is a primitive root. Once the smallest primitive root is found, the others may be found easily by using the definition above. In our example, since we have confirmed that a = 2 is a primitive root, we know from the above definition that 2r is a primitive root modulus 11, if and only if gcd(r,10)=1. So for r = 1, 21 = 2, for r = 3, 23 = 8, for r = 7, 27 = 7, and for r = 9, 29 = 6. In summary, the primitive roots are {2, 6, 7, 8} and the corresponding sequences are Costas arrays. Also note that the Costas arrays for a = 2 and a = 6 are reverse ordered (except for the 1 on the end). This is also true for a = 7 and a = 8. This symmetry can be used to further simplify the sequence calculations.

Appendix D

LPIsimNet LPIsimNet is a collection of MATLAB files that let the user easily evaluate the information network metrics and the SNR advantages of general netted LPI radar topologies that were discussed in Chapter 10 including the presence of an electronic attack or jammer. The objective of this tutorial is to have the student work several examples to become familiar with the program set. The program set is organized as shown in Figure D.1. The “ScenarioEditor.m” file lets the student open a Graphical User Interface (GUI) and create a new “Scenario File” or modify an existing one. A “Result File” is generated after the student confirms the “Scenario File” and executes the simulation calculation with the assistance of “Calculator.m.” The “SimulationViewer.m” is used to review the “Result File” by examining the results grid. The “Painter.m” file supports the drawing of the two GUI figures.

D.1

Overview of LPIsimNet Architecture

The LPIsimNet architecture can be used to set up a sensor network with any configuration and number of communication nodes. Evaluation of the information exchange capability and the operational tempo is presented to the user using the sensor network metrics. LPI radar detection performance and the SNR values of a network enabled configuration of emitters across an operational landscape containing targets is also presented to the user including the ability to have the sensor nodes and jammer nodes move in time with any velocity.

721

722

Detecting and Classifying LPI Radar

Figure D.1: Program flow diagram.

D.1.1

Loading the Default Sensor Network

Start MATLAB and change the “Current Directory” to the folder where the LPIsimNet program resides. Run “ScenarioEditor.m” to open up the GUI battlespace grid. You should see the grid as shown in Figure D.2. The right side of the GUI is designed for displaying a schematic of the network topology. Click the “Refresh Figure” to load the default network topology. The default network consists of NT = 3 nodes: NR1 (node-1); NR2 (node2); and NR3 (node-3) which are capable both in information processing and synchronized, coherent target detection. Note the links between these nodes are bidirectional. Click on the “Legend” and see the legend as shown in Figure D.3. The legend describes the symbols on the grid and can be brought up at any time.

D.1.2

Building a Scenario File and Running the Simulation

Go back to the “ScenarioEditor.” In the top left corner is the “Top Level Properties Panel” containing several generic simulation properties that must be set including the number of nodes, total time index(s) for including platform and target movement, decision tempo, deployment tempo, and the fighting tempo. The boundary of the X axis, and the boundary of the Y axis must also be set to model the battlespace landscape. For this tutorial, modify these properties according to the values shown in Table D.1.

Appendix D: LPIsimNet

Figure D.2: ScenarioEditor battlespace grid.

Figure D.3: Symbol legend for LPIsimNet.

723

724

Detecting and Classifying LPI Radar

Table D.1: Top Level Properties For Scenario Properties Number of nodes Total time indexes Decision tempo Deployment tempo Fighting tempo Boundary of X axis (km) Boundary of Y axis (km)

Values 3 1 200 400 300 0, 100 0, 100

Description Total number of nodes in network Number of time steps in simulation C2 decision tempo Tempo of deployment in OODA Tempo of fighting in OODA Left, right battlespace boundary Upper, lower battlespace boundary

The panel below the “Top Level Properties Panel” is the “Node Properties Panel.” The node properties panel contains the following scenario information: • Current node index; • Type; • Name; • Initial position; • Velocity; • Availability of links to each node; • Capability value K of information or jammer; • Information rate λμ ; • Minimum information rate, λmin μ ; • ERP of radar or jammer; • Eﬀective antenna area Ae ; • Noise power. The node properties for the Blue Force E2-C in the default simulation are shown in Figure D.4.

Appendix D: LPIsimNet

Figure D.4: Node properties.

725

726

Detecting and Classifying LPI Radar

Table D.2: Link Condition of 001 Availability of link

Node 1 N

Node 2 N

Node 3 Y

Table D.3: Parameters for Node 2 and Node 3 Properties Type Name Initial position Velocity Links Cap. of info. or jamming Info. rate Min. info. rate ERP (W) Eﬀ. antenna area Noise power

D.2

Node2 Blue Force F-16 20, 70 0, 0 101 0.75 200 100 0 0 0

Node3 Blue Force AC-130 60, 70 0, 0 110 0.25 300 50 0 0 0

Setting the Node Properties

At the bottom of the “Node Properties Panel,” try switching between the properties of the diﬀerent nodes. Note the “Node Index” that indicates the current node. Set the properties of node 1 to the following values shown in Figure D.4. The “Availability of Links to Each Node” represents the link condition to each node. For example, for node 1, 001 represents the link configuration as shown in Table D.2. After setting node 1 availability, set node 2 and node 3 to the values shown in Table D.3. After setting all node properties needed, click “Refresh Figure” to see the layout and the overall connection of this scenario. The topology should look like that shown in Figure D.5. Click “Save Scenario” and save the scenario file as “Sce-3C.mat.” Configure the MATLAB command line analysis to be visible along with the “ScenarioEditor.” Click “Run Simulation” to activate the calculation of the simulation results file. The MATLAB command line shows the tracking message of the four phases in the calculation. Wait until a “Save As” dialog appears and save the simulation results as “Sim-3C.mat.” Now, we have successfully finished creating a scenario file (Sce-3C.mat) and generated the simulation results file (Sim-3C.mat).

Appendix D: LPIsimNet

Figure D.5: Simulation topology.

727

728

D.3

Detecting and Classifying LPI Radar

Viewing the Simulation Results

Go to the MATLAB environment and launch the “SimulationViewer.m.” The SimulationViewer GUI grid appears as shown in Figure D.6. Click “Load” to load the simulation result file, “Sim-T1(3C).m” that was just generated. After loading, the simulation result file is displayed as shown in Figure D.7. The values for the simulation properties are now shown in the top left “Information Network Analysis Panel.” This panel consists of: • Number of links suppressed; • Reference Connectivity Measure; • Connectivity Measure; • Network Reach; • Network Richness; • Decision Tempo; • Deployment Tempo; • Fighting Tempo; • Characteristic Tempo; • Max Operational Tempo. Observe the simulation results in the “Information Network Analysis Panel.” Click the “Detail” after the Reference Connectivity Measure. The detailed analysis data is shown in the MATLAB command line as shown in Figure D.8. Click the “Detail” after the Connectivity Measure. The detailed analysis data is shown in MATLAB command line as shown in Figure D.9. Click the “Detail” after the Reference Network Richness. The detailed analysis data is shown in the MATLAB command line as shown in Figure D.10.

Appendix D: LPIsimNet

Figure D.6: SimulationViewer GUI.

Figure D.7: GUI.

729

730

Detecting and Classifying LPI Radar

R Figure D.8: Reference connectivity measure CM for number of sensor network nodes NT = 3 to 20.

Figure D.9: Detailed results for connectivity measure.

Figure D.10: Detailed results for network richness.

Appendix D: LPIsimNet

731

Table D.4: LPI Radar Network: Scenario Setup for Three Nodes Properties Type

Node1 Blue Force

Node2 Blue Force

Name Initial position Velocity Link configuration Cap. of info. or jamming Info. rate Min. info. rate ERP (W) Eﬀ. antenna area (m2 ) Noise power (W)

E-2C 40,40 0,0 0010 1.0 200 100 0 0 0

F-16 20,70 0,0 1010 0.75 200 100 0 0 0

D.4

Node3 Blue Force AC-130 60,70 0,0 1100 0.25 300 50 0 0 0

Node4 Hostile Jammer Su-34 80,40 -10,0 1000 0.3 0 0 0 0 0

Adding a Moving Jammer to the Scenario

Go back to the “ScenarioEditor.m” (if you have closed it, re-launch it) and load the scenario file Sim-3C.mat. In the “Top Level Properties Panel,” change the number of nodes to 4, and the total time index(s) to 3. That is, the scenario can evolve over time and the platforms within the scenario can have movement. Each platform can also have a diﬀerent velocity (by including larger movements over a time index) in any general direction. Click “Refresh Figure” and see a fourth node, (NR4 ) node 4, that was added into the network. Go to the “Node Properties Panel” and set the properties as in Table D.4. Note the jammer is identified as being onboard an Su-34 “Flanker” fighter-bomber 2-seat strike aircraft. After refreshing, the figure should look like Figure D.11. Save this scenario as “Sce-3C+J.mat” and run the simulation calculation and save the result file as “Sim-3C+J.mat”. Go to “SimulationViewer” and load “Sim-3C+J.mat.” Your figure should look like Figure D.11. Note the two links to E-2C survive even with the Su-34 jammer. All the simulation results in “Information Network Analysis” are identical to those of the previous simulation. Click the double right arrows in the lower right section to switch the time index to 2. Note that the Su-34 jammer moves closer to E-2C and the link from AC-130 to E-2C is now not available (the arrow is missing). At this index the sensor information changes. The number of links suppressed in now one as shown in the “Information Network Analysis” panel. Click “Detail” and review the detailed data in the MATLAB command line as shown in Figure D.12.

732

Detecting and Classifying LPI Radar

Figure D.11: Sensor network with jammer added.

Figure D.12: Command line analysis of sensor network with link suppression.

Appendix D: LPIsimNet

733

Table D.5: LPI Radar Network: Scenario Setup for the Three Nodes Properties Type Name Initial position Velocity Link configuration Cap. of info. or jamming Info. rate Min. info. rate ERP (W) Eﬀ. antenna area (m2 ) Noise power (W)

Node1 Blue Force Force Radar1 15,40 0,0 0000 0 0 0 1000 0.0815 7.5 × 10−13

Node2 Blue Force Force Radar2 15,15 0,0 0000 0 0 0 100 0.0815 1.0 × 10−12

Node3 Hostile Jammer Su-34 30,25 0,0 1100 0 0 0 10 0 0

Node4 Radar Target Target 15,25 0,0 0000 0 0 0 0 0 0

Now click the double right arrows to increment the time index to 3. Note that now two links are not available due to the new closer position of the jammer. The “Trend” buttons provide the ability to review the trend of the results as a function of time.

D.5

Netted Radar with a Jammer

To examine how a jammer influences a netted radar configuration, go to the “ScenarioEditor” and change the Number of nodes to 4, Number of Time Indexes to 1. Set the node properties according to Table D.5. Click “Refresh Figure” to see Figure D.13. Save this scenario as “Sce-2R+J+T.mat” and run the simulation calculation. After the simulation completes save the result file as “Sim-2R+J+T.mat.” After saving the file go to “SimulationViewer” and load “Sim-2R+J+T.mat.” The figure should look like Figure D.14. At the bottom left corner is the “Netted Radar Analysis Panel.” Figure D.15 describes several options that are applied to control the contour chart display. Leave the “Enable Nework Synchronization” box unchecked and select the “SNR(dB)” radial button. Click “Refresh” to see the SNR contour chart. It should look like Figure D.16. Note that this may take a few seconds. Click “Detail” for the SNR and the detailed analysis data is displayed in the MATLAB command line as shown in Figure D.17. For a network-enabled configuration, check the “Enable Network Synchronization” in the “Netted Radar Analysis Panel” and click “Refresh” again. The SNR contour chart with the network synchronization should appear as

734

Detecting and Classifying LPI Radar

Figure D.13: Topology of simulation: two emitters, one target, one jammer.

Figure D.14: Radar network properties with jammer added.

Appendix D: LPIsimNet

735

Figure D.15: Description of netted radar analysis panel. shown as Figure D.18. Click “Detail” for the SNR, and the detailed analysis data is displayed in the MATLAB command line as shown in Figure D.19. To examine the eﬀects of the jammer, uncheck “Enable Network Simulation” and select the “S/N+J” Ratio (dB)” radial button. Then click “Refresh.” The eﬀect of hostile jamming on the netted radar systems and sensor network can be examined by reviewing the SNJR contour chart as shown in Figure D.20. In this figure, the network connecting the radar sensors is disabled. Click the “Detail” of S/N+J and view the detailed analysis as displayed in Figure D.21. The contour chart and the detailed analysis show that without the network, the S/N+J = −70 dB at the target. If the sensor network is enabled however, the S/N+J increases as shown in the contours displayed in Figure D.22. The command line analysis shows the S/N+J = −64 dB when the network is enabled.

736

Detecting and Classifying LPI Radar

Figure D.16: SNR contour chart without network synchronization.

Figure D.17: Command line analysis of SNR—no network.

Appendix D: LPIsimNet

Figure D.18: SNR contour chart with network synchronization.

Figure D.19: Command line analysis of SNR—with network.

737

738

Detecting and Classifying LPI Radar

Figure D.20: S/N+J contour chart: sensor network with jammer and without network synchronization.

Figure D.21: Command line analysis of netted radar systems with jammer and without network synchronization (S/N+J = −70 dB at target).

Appendix D: LPIsimNet

739

Figure D.22: S/N+J contour chart: netted radar systems with jammer and with network synchronization.

Figure D.23: Command line analysis of sensor network with jammer and without network synchronization (S/N+J = −64 dB at target).

Appendix E

PWVD for FMCW with ∆F = 500 Hz In Figures E.1 and E.2, a signal with fc = 1,000 Hz, tm = 20 ms and ∆F = 500 Hz is examined using the PWVD. In Figure E.1(a) the increase in bandwidth is noticeable and in the time-frequency distribution in Figure E.1(b), the important parameters can all be extracted. In Figure E.2(a), the SN R = 0 dB, and the signal is still visible and the parameters can be extracted. In Figure E.2(b) the increase in noise is apparent (SN R = −6 dB), but the parameters can still be extracted.

741

742

Detecting and Classifying LPI Radar

Figure E.1: PWVD for FMCW with ∆F = 500 Hz, tm = 30 ms (signal only), showing the (a) marginal frequency domain, and (b) time-frequency plot.

Appendix E: PWVD for FMCW with ∆F = 500 Hz

743

Figure E.2: PWVD for FMCW with ∆F = 500 Hz, tm = 30 ms, timefrequency plot for (a) SN R = 0 dB, and (b) SN R = −6 dB.

Appendix F

PWVD for Frank Code with T = 64 ms In the second example of a Frank signal using the PWVD, the signal has a carrier frequency of fc = 1,000 Hz, 64 phase codes (M = 8), and a cpp = 1. The signal has a code period of T = N 2 tb = 64 ms. Figure F.1(a) shows the PWVD frequency domain plot. As expected, due to the longer code length (Nc = M 2 = 64), the modulation spikes that were clearly visible in Figure 9.16(a) (Nc = M 2 = 16) are now hard to distinguish. Figure F.1(b) shows the PWVD time-frequency plot, and indicates the bandwidth measurement and code period measurement. Figure F.2(a) shows the time-frequency plot with SN R = 0 dB. All parameters can still be extracted. In Figure F.2(b), however (SN R = −6 dB), identification of the major crossterm and the measurements of the signal parameters become more diﬃcult.

745

746

Detecting and Classifying LPI Radar

Figure F.1: PWVD for Frank code with B = 1,000 Hz, T = 64 ms (signal only), with (a) frequency domain, and (b) time-frequency contour.

Appendix F: PWVD for Frank Code with T = 64 ms

747

Figure F.2: PWVD for Frank code with B = 1,000 Hz, T = 64 ms, timefrequency contour, for (a) SN R = 0 dB, and (b) SN R = −6 dB.

Appendix G

PWVD Results for P1, P2, P3, and P4 Codes G.1

P1 Code Analysis

In this section, the PWVD is used to extract the parameters from a P1 phasecoded CW signal. The intercepted signal shown in the following example has a carrier frequency of fc = 1,000 Hz, a cpp = 1 (B = 1,000 Hz), 64 phase codes (Nc = 64), and is sampled by the ADC at a rate of fs = 7,000 Hz. The marginal frequency domain result is shown in Figure G.1(a). Here the harmonics are not as evident, without zooming in on the signal in the frequency domain. Figure G.1(b) demonstrates the P1 modulation in the time-frequency domain, and reveals that a longer code period makes it easier to identify the major crossterm in order to make the signal measurements. Notice that the slopes of each line are negative. It is interesting to note that if the crossterms were deleted, the parameter measurements might not be easier to extract. Figure G.2(a) shows the SN R = 0 dB results. Extraction is still possible, but in Figure G.2(b) with SN R = −6 dB, this capability again disappears quickly.

G.2

P2 Code Analysis

The P2 code shows up in the PWVD in a similar manner as the P1 and Frank code, except the slope is positive. Since the code period T = Nc2 tb both (12.27) and (12.28) apply. The signal examined has fc = 1,000 Hz, a cpp = 1 and 64 phase codes (Nc = 64). Figure G.3(a) shows the phasecoded signal with a code period of 64 ms. Note the eﬀect the additional code 749

750

Detecting and Classifying LPI Radar

Figure G.1: PWVD for P1 code with B = 1,000 Hz, T = 64 ms (signal only), showing the (a) marginal frequency domain, and (b) time-frequency plot.

Appendix G: PWVD Results for P1, P2, P3, and P4 Codes

751

Figure G.2: PWVD for P1 code with B = 1,000 Hz, T = 64 ms, timefrequency plot, for (a) SN R = 0 dB, and (b) SN R = −6 dB.

752

Detecting and Classifying LPI Radar

length has on the frequency domain modulations. The carrier frequency is also easily identified. In Figure G.3(b), the measurement of the code period and the bandwidth are illustrated. Figure G.4(a) shows the P2 signal with an SN R = 0 dB. The signal parameters can be identified, although the crossterms make this somewhat diﬃcult. Figure G.4(b) shows the signal with an SN R = −6 dB. Without further processing, the identification of the signal parameters is not possible in this case.

G.3

P3 Code Analysis

In this section, a P3 signal with fc = 1,000 Hz, a cpp = 1 (B = 1,000 Hz), and 64 four phase codes Nc = 64 is examined using the PWVD. The characteristics of the P3 code are evident as shown in Figure G.5(a) which shows the frequency domain. Figure G.5(b) shows the time-frequency domain, and clearly shows the slope characteristics previously demonstrated in the Frank and P1 code. Extraction of the signal parameters within these figures can also be compared to Figures G.3(a) and (b). Figure G.6(a) shows the signal with SN R = 0 dB, and Figure G.6(b) shows the signal with SN R = −6 dB. Detection of the signal parameters here can be compared with Figure G.4(a) and (b). Notice that we have not discussed distinguishing between the various phase codes; this is an important consideration that is discussed further below.

G.4

P4 Code Analysis

The P4 code signal is very similar to the P3 code signal in the way it shows up in the PWVD. The P4 signal examined in this section has fc = 1,000 Hz, a cpp = 1, and a code length of 64 (Nc = 64). Note that the equations for the parameter measurements given for the Frank code also apply for the P4 code (as well as for the P1, P2, and P3). Figure G.7(a) shows characteristics of the P4 code in the frequency domain and Figure G.7(b) shows the corresponding time-frequency domain. Extraction of the signal parameters within these figures can be compared to Figure G.5(a) and (b). Figure G.8(a) shows the signal with SN R = 0 dB, and Figure G.8(b) shows the signal with SN R = −6 dB. Detection of the signal parameters here can be compared with Figure G.6(a) and (b).

Appendix G: PWVD Results for P1, P2, P3, and P4 Codes

753

Figure G.3: PWVD for P2 code with B = 1,000 Hz, T = 64 ms (signal only), showing the (a) marginal frequency domain, and (b) time-frequency domain.

754

Detecting and Classifying LPI Radar

Figure G.4: PWVD for P2 code with B = 1,000 Hz, T = 64 ms, timefrequency plot, for (a) SN R = 0 dB, and (b) SN R = −6 dB.

Appendix G: PWVD Results for P1, P2, P3, and P4 Codes

755

Figure G.5: PWVD for P3 code with B = 1,000 Hz, T = 64 ms (signal only), showing the (a) marginal frequency domain, and (b) time-frequency plot.

756

Detecting and Classifying LPI Radar

Figure G.6: PWVD for P3 code with B = 1,000 Hz, T = 64 ms, timefrequency plot, for (a) SN R = 0 dB, and (b) SN R = −6 dB.

Appendix G: PWVD Results for P1, P2, P3, and P4 Codes

757

Figure G.7: PWVD for P4 code with B = 1,000 Hz, T = 64 ms (signal only), showing the (a) marginal frequency domain, and (b) time-frequency plot.

758

Detecting and Classifying LPI Radar

Figure G.8: PWVD for P4 code with B = 1,000 Hz, T = 64 ms, timefrequency plot, for (a) SN R = 0 dB, and (b) SN R = −6 dB.

Appendix H

PWVD Results for Polytime Codes T2, T3, and T4 H.1

T2(2) Polytime Code

The T2(2) signal examined with the PWVD has the same parameters as the T1(2) signal investigated above, except that it has a zero beat at its carrier frequency. Figure H.1(a) shows the PWVD frequency domain for the T2(2). The energy is not as evenly spread out as the T1(2) previously shown, and a strong negative component at the carrier frequency is evident. Figure H.1(b) shows the time-frequency distribution, and shows a unique pattern of X’s centered about the carrier (due to the zero beat at the carrier frequency). The measurement of the bandwidth B and code period T are also shown, although this is somewhat more diﬃcult without any post-PWVD image processing. To understand the bandwidth characteristics shown in Figure H.1, the phase shift for the T2(2) is shown in Figure H.2. Here, the shortest phase change is eight samples long, or 1.143 ms. This results in a bandwidth excursion of 875 Hz, as shown. Figure H.3(a) shows the signal for an SNR = 0 dB. The signal can still be identified as a T2(2), but it is much more diﬃcult to do compared to the T1(2). Errors can also occur when the parameters are extracted. In Figure H.3(b) with a SNR = −6 dB, no signal identification can be made, and no parameters can be extracted without any post-PWVD image processing.

759

760

Detecting and Classifying LPI Radar

Figure H.1: PWVD for polytime code T2(2) with B = 875 Hz, T = 16 ms (signal only), showing the (a) marginal frequency domain, and (b) timefrequency plot.

Appendix H: PWVD Results for Polytime Codes T2, T3, and T4

761

Figure H.2: T2(2) phase shift showing a minimum subcode width of eight samples (1.143 ms), resulting in a bandwidth excursion of 875 Hz.

762

Detecting and Classifying LPI Radar

Figure H.3: PWVD for polytime code T2(2) code with B = 875 Hz, T = 16 ms, showing the time-frequency plot, for (a) SNR = 0 dB, and (b) SNR = −6 dB.

Appendix H: PWVD Results for Polytime Codes T2, T3, and T4

H.2

763

T3(2) Polytime Code

The T3(2) is examined next, and represents an approximation of a linear FM waveform with modulation bandwidth ∆F . As discussed in Chapter 5, the T3(2) is generated from the quadratic linear FM phase trajectory, with a zero beat at its beginning. Figure H.4(a) shows the PWVD frequency domain for the signal-only case, with ∆F = 600 Hz and modulation period tm = T = 16 ms. Figure H.4(b) shows the time-frequency image with the modulation bandwidth and modulation period indicated. Note the similarity to Figure 9.18(a) and (b). To understand the bandwidth characteristics shown in Figure H.4, the phase shift for the T3(2) is shown in Figure H.5. With six samples making up the shortest phase change (0.857 ms), the bandwidth excursion is 1,167 Hz (approximately 2∆F ). The PWVD results for the T3(2) with SNR = 0 and SNR = −6 dB are shown in Figure H.6(a) and (b), respectively.

H.3

T4(2) Polytime Code

The T4(2) code for a ∆F = 600 Hz and tm =16 ms is shown in Figure H.7 To understand the bandwidth characteristics shown in Figure H.7, the phase shift for the T4(2) is shown in Figure H.8. The smallest phase change here is again six samples resulting in a bandwidth excursion of 1,167 Hz. Figure H.9 shows the PWVD for the T4(2) code with Figure H.9(a) showing the SNR = 0 dB case and Figure H.9(b) showing the SNR = −6 dB case (∆F = 600 Hz, B = 1,167 Hz).

764

Detecting and Classifying LPI Radar

Figure H.4: PWVD for polytime code T3(2) with ∆F = 600 Hz, B = 1,167 Hz, and tm = T = 16 ms (signal only), showing the (a) marginal frequency domain and (b) time-frequency plot.

Appendix H: PWVD Results for Polytime Codes T2, T3, and T4

765

Figure H.5: T3(2) phase shift showing a minimum subcode width of six samples (0.857 ms), resulting in a bandwidth excursion of 1,167 Hz.

766

Detecting and Classifying LPI Radar

Figure H.6: PWVD for T3(2) code with ∆F = 600 Hz, B = 1,167 Hz, and tm = T = 16 ms, showing the time-frequency plot for (a) SNR = 0 dB, and (b) SNR = −6 dB.

Appendix H: PWVD Results for Polytime Codes T2, T3, and T4

767

Figure H.7: PWVD for T4(2) code with ∆F = 600 Hz, B = 1,167 Hz, tm = T = 16 ms (signal only), showing the (a) marginal frequency domain, and (b) time-frequency plot.

768

Detecting and Classifying LPI Radar

Figure H.8: T4(2) phase shift showing a minimum subcode width of six samples (0.857 ms) resulting in a bandwidth excursion of 1,167 Hz.

Appendix H: PWVD Results for Polytime Codes T2, T3, and T4

769

Figure H.9: PWVD for T4(2) code with ∆F = 600 Hz, B = 1,167 Hz, and T = 16 ms, time-frequency plot, for (a) SNR = 0 dB, and (b) SNR = −6 dB.

Appendix I

QMFB Results for FMCW with ∆F = 500 Hz In Figure I.1, the tm is increased from tm = 20 ms to tm = 30 ms, and the bandwidth is increased from ∆F = 250 Hz to ∆F = 500 Hz. Figure 10.19(a), shows layer l = 2. The same general characteristics are shown as in Figure I.1(a) except that fewer zeros are needed to pad the signal to Np = 2,048. In Figure I.1(b) the l = 5 layer is shown with ∆F = 112.9 Hz and ∆t = 4.64 ms < tm /6. That is, this layer provides a finer detail in time, and less detail in frequency. The bandwidth of the signal can easily be estimated as shown.

771

772

˚ Detecting and Classifying LPI Radar

Figure I.1: QMFB time-frequency contour images for FMCW ∆F = 500 MHz, tm = 30 ms (signal only), showing (a) layer 2, and (b) layer 5.

Appendix J

QMFB Results for 11-Bit BPSK An 11-bit Barker code (cpp = 1) is examined with the QMFB in Figure J.1. In Figure J.1(a), the full contour QMFB output for layer l = 3 is shown. In Figure J.1(b) a close-up view of the QMFB layer 3 output is shown, illustrating the time changing frequency detail. Note the similarity in the structure of the frequency information when compared to Figure 10.21. Also note the major diﬀerences in the frequency structure. Figure J.2 shows the QMFB output contour of the 11-bit signal for both layers 3 and 6 for an SN R = 0 dB. Note that some of the features such as bandwidth can be estimated but, even with a closer view of the results, information such as the phase is hard to determine. In Figure J.3, the bandwidth of the 11-bit signal is narrowed from 1 kHz to B = 0.2 kHz (code period of T = 55 ms). Figure J.3(a) shows the QMFB layer 2 for two code periods. The presence of a null at each BPSK phase shift is evident. With T = 55 ms, the measurement of the smallest subphase code is performed, to determine the number of subphase codes contained within each section of the code. Figure J.3(b) shows the QMFB layer 6. The code period T and bandwidth B are clearly identified. Comparison with Figure 10.23 indicates a slightly diﬀerent form, due to the additional subphase codes.

773

774

Detecting and Classifying LPI Radar

Figure J.1: QMFB layer 3 for BPSK with 11-bit Barker code, cpp = 1 (signal only), showing (a) the full contour image, and (b) a close-up view showing frequency details of Barker code.

Appendix J: QMFB Results for 11-Bit BPSK

775

Figure J.2: QMFB contour image for BPSK with 11-bit Barker code, cpp = 1 (SN R = 0 dB), showing (a) layer 3, and (b) layer 6.

776

Detecting and Classifying LPI Radar

Figure J.3: QMFB contour images for BPSK 11-bit Barker code, cpp = 5 (signal only), showing (a) layer 2, and (b) layer 6.

Appendix K

QMFB Results for Frank Signal with Nc = 16 The Frank code for M = 4 is shown in Figure K.1. The M = 4 Frank code signal has Nc = 16 subcodes, fc = 1 kHz, and a cpp = 1. The QMFB l = 2 layer for this signal is shown in Figure K.2 (∆f = 1,166.67 Hz, ∆t = 573.67μs). The QMFB has 10 layers (Np = 1,024). Figure K.2(a) shows the entire signal (80 ms) and reveals that five code periods have been captured. Note the unique structure of the phase modulation. A closer examination is shown in Figure K.2(b). The code period (T = 16 ms) is shown, along with the phase modulation characteristics due to the 16 subcodes. Correlation of the frequency characteristics within the code period shown in Figure K.2(b), with the phase modulation waveform shown in Figure K.1, can be made directly (four sections). In Figure K.3(a) and (b), the QMFB l = 4 layer is shown (∆f = 233.33 Hz, ∆t = 2.32 ms), and reveals the linear frequency modulation that results from the Frank phase code. The bandwidth is also indicated. Note that the Frank code phase modulation results in the linear frequency modulation wrapping around for the i = 3 and i = 4 segment, starting at t = 40 ms.

777

778

Detecting and Classifying LPI Radar

Figure K.1: Frank code phase values for M = 4 (Nc = 16).

Appendix K: QMFB Results for Frank Signal with Nc = 16

779

Figure K.2: QMFB contour images for M = 4 (Nc = 16) Frank code with B = 1,000 Hz, T = 16 ms (signal only), showing (a) layer 2 output, and (b) close up of layer 2, showing detailed frequency changes due to phase codes.

780

Detecting and Classifying LPI Radar

Figure K.3: QMFB contour images for M = 4 Frank code with B = 1,000 Hz, T = 16 ms (signal only), showing (a) layer 4 output, and (b) close up of layer 4, showing resulting linear frequency modulation.

Appendix L

QMFB Results for P1, P2, P3, and P4 L.1

P1 Analysis

The P1 signal is also derived from a linear FM waveform. In this section it is shown that the P1 QMFB time-frequency characteristics are diﬀerent from the Frank code, and these diﬀerences can be used for waveform identification. In Figure L.1 the phase code for a P1 Nc = 64 signal is shown for reference. The QMFB l = 2 layer is shown in Figure L.2. The total number of points shown are Np = 4,096 with L = 12 QMFB layers, ∆f = 1,166.67 Hz, and ∆t = 571.99 μs. Since the number of phase codes is Nc = 64, the five code periods extend for 320 ms. In the close-up view of the code period in Figure L.2(b), the variation in phase modulation characteristics can be identified and correlated with the phase waveform given above. This is especially evident for the last four sections given in Figure L.1. In Figure L.3(a) and (b), the l = 5 layer is shown, demonstrating the linear frequency modulation resulting from the P1 phase codes. For this layer, ∆f = 112.9 Hz and ∆t = 4.61 ms. Note the immediate frequency wraparound at the beginning of the code period. Also evident is the nonuniform spacing of the energy concentrations, due to the nonlinear phase modulation. The code period (T = 64 ms) and bandwidth B = 1,000 Hz are also shown. The marginal frequency characteristics for the Nc = 64 P1 code are shown in Figure L.4. Due to the nonlinear phase modulation characteristics, the energy is not symmetrically distributed about filter 9 (the carrier frequency fc = 1 kHz). From Figure L.4 the four largest energy tiles (in order from largest to smallest) are 7, 8, 10, and 9. That is, the carrier has the smallest amount of energy among the four largest components. 781

782

Detecting and Classifying LPI Radar

Figure L.1: P1 code phase values for Nc = 64.

L.2

P2 Analysis

The P2 phase modulation diagram for Nc = 64 phase codes is shown in Figure L.5. This phase diagram has a particularly interesting shape, giving rise to some unique characteristics in the time-frequency domain. The QMFB for the signal shown in this example has L = 12 layers. In Figure L.6, the contour images for QMFB layer 2 are shown with ∆f = 1,166.67 Hz and ∆t = 571.99 μs. The pattern of the frequency characteristics changes form toward the middle of the code period (T = 40 ms). The result is a linear frequency modulation that has a negative slope. This is illustrated in Figure L.7, which shows the l = 5 layer. For this layer, ∆f = 112.9 Hz and ∆t = 4.61 ms. Note from Figure L.7(b), the four energy concentrations are located toward the center of the code period. Diﬀerent signal modulations will have distinct levels of energy concentration. Consequently, the marginal frequency distribution can be used to identify the signal’s modulation type. Figure L.8 shows the QMFB layer 5 marginal frequency profile for the Nc = 64 P2 code. From Figure L.8 the four largest energy tiles (in order from largest to smallest) are 7, 9, 8, and 10. The diﬀerence between the P1 and P2 code can be identified by comparing marginal frequency distributions shown in Figure L.8 and Figure L.4.

L.3

P3 Analysis

The P3 phase modulation for Nc = 64 (64 phase codes) is shown for reference in Figure L.9. The QMFB l = 2 layer for the P3 signal is shown in Figure L.10. The contour images are shown with ∆f = 1,166.67 Hz and ∆t = 571.99

Appendix L: QMFB Results for P1, P2, P3, and P4

783

Figure L.2: QMFB contour images for Nc = 64 P1 code with B = 1,000 Hz, T = 64 ms (signal only), showing (a) layer 2 output and (b) close up of layer 2, showing detailed frequency changes due to phase codes.

784

Detecting and Classifying LPI Radar

Figure L.3: QMFB contour images for Nc = 64 P1 code with B = 1,000 Hz, T = 64 ms (signal only), showing (a) layer 5 output, and (b) close up of layer 5, showing resulting linear frequency modulation.

Appendix L: QMFB Results for P1, P2, P3, and P4

785

Figure L.4: QMFB layer 5 marginal frequency profile for Nc = 64 P1 code.

Figure L.5: P2 code phase values for Nc = 64.

786

Detecting and Classifying LPI Radar

Figure L.6: QMFB contour images for Nc = 64 P2 code with B = 1,000 Hz, T = 64 ms (signal only), showing (a) layer 2 output, and (b) close up of layer 2, showing detailed frequency changes due to phase codes.

Appendix L: QMFB Results for P1, P2, P3, and P4

787

Figure L.7: QMFB contour images for Nc = 64 P2 code with B = 1,000 Hz, T = 64 ms (signal only), showing (a) layer 5 output, and (b) close up of layer 5, showing resulting linear frequency modulation.

788

Detecting and Classifying LPI Radar

Figure L.8: QMFB layer 5 marginal frequency profile for Nc = 64 P2 code. μs. The shape of the time-frequency characteristics is unique from those of the Frank, P1, and P2 codes. Figure L.11 shows the l = 5 layer indicating the bandwidth and code period. Here ∆f = 112.9 Hz and ∆t = 4.61 ms. A closer examination of the layer 5 frequency details reveal a diﬀerent distribution of the energy peaks within the bandwidth. The marginal frequency distribution for the P3 code is shown in Figure L.12. From Figure L.12 the four largest energy tiles (in order from largest to smallest) are 7, 9, 10, and 8. Again, this is distinct from the Frank, P1, and P2 codes and can be used to classify the detected P3 signal.

L.4

P4 Analysis

In this section, an Nc = 64 P4 code is examined with the QMFB. The P4 phase modulation for Nc = 64 is shown in Figure L.13. The QMFB for this P4 signal has L = 12 layers. The l = 2 layer (∆f = 1,166.67 Hz and ∆t = 571.99 μs) is shown in Figure L.14. The close-up view examines the time-varying frequency characteristics of the signal as it appears within two of the three filters. Figure L.15 shows the l = 5 layer (∆f = 112.9 Hz and ∆t = 4.61), demonstrating the P4 linear frequency modulation. The close-up view shows the major energy peaks about the carrier frequency (ninth filter). For the P4 code, the marginal frequency distribution shown in Figure L.16, reveals that the largest energy concentration is at the carrier frequency. the four largest energy tiles (in order from largest to smallest) are 9, 7, 10, and 8.

Appendix L: QMFB Results for P1, P2, P3, and P4

Figure L.9: P3 code phase values for Nc = 64.

789

790

Detecting and Classifying LPI Radar

Figure L.10: QMFB contour images for Nc = 64 P3 code with B = 1,000 Hz, T = 64 ms (signal only), showing (a) layer 2 output, and (b) close up of layer 2, showing detailed frequency changes due to phase codes.

Appendix L: QMFB Results for P1, P2, P3, and P4

791

Figure L.11: QMFB contour images for Nc = 64 P3 code with B = 1,000 Hz, T = 64 ms (signal only), showing (a) layer 5 output, and (b) close up of layer 5, showing resulting linear frequency modulation.

792

Detecting and Classifying LPI Radar

Figure L.12: QMFB layer 5 marginal frequency profile for Nc = 64 P3 code.

Figure L.13: P4 code phase values for Nc = 64.

Appendix L: QMFB Results for P1, P2, P3, and P4

793

Figure L.14: QMFB contour images for Nc = 64 P4 code with B = 1,000 Hz, T = 64 ms (signal only), showing (a) layer 2 output, and (b) close up of layer 2, showing detailed frequency changes due to phase codes.

794

Detecting and Classifying LPI Radar

Figure L.15: QMFB contour images for Nc = 64 P4 code with B = 1,000 Hz, T = 64 ms (signal only), showing (a) layer 5 output, and (b) close up of layer 5, showing resulting linear frequency modulation.

Appendix L: QMFB Results for P1, P2, P3, and P4

795

Figure L.16: QMFB layer 5 marginal frequency profile for Nc = 64 P4 code.

Appendix M

QMFB Results for T2, T3, and T4 Figure M.1(a) and Figure M.1(b) show the QMFB contour images for the polytime T2(2) code with B = 875 Hz and T = 16 ms, showing the layer 2 output. The code modulation period is indicated, and the number of code periods can also be identified. The close-up in Figure M.1(b) shows the unique time-frequency pattern due to the T2(2) phase modulation. Figure M.2(a) and Figure M.2(b) show the QMFB contour images for the polytime T2(2) code with B = 875 Hz and T = 16 ms, showing the layer 4 output. Note the bandwidth and code period can easily be indentified. In Figure M.3(a) and (b), the QMFB contour images for the polytime T3(2) code with B = 1,167 Hz, T = 16 ms (signal only) are shown. In Figure M.3(a) the layer 2 output is shown, and in Figure M.3(b) a close-up of layer 2 is used to indicate the frequency changes due to the phase codes. In Figure M.4, layer 4 is examined, and shows the bipolar frequency modulation characteristic of the T3(2) code. Also indicated are the bandwidth and code period. Layer 2 for the T4(2) code is shown in Figure M.5. All five code periods are shown, as well as the code period of 16 ms. Layer 4 is shown in Figure M.6. Interestingly enough, all of the polytime codes have a large frequency spike within each code period, due to the recycling of the phase modulation.

797

798

Detecting and Classifying LPI Radar

Figure M.1: QMFB contour images for polytime T2(2) code with B = 875 Hz, T = 16 ms (signal only), showing (a) layer 2 output, and (b) close-up of layer 2, showing detailed frequency changes due to phase codes.

Appendix M: QMFB Results for T2, T3, and T4

799

Figure M.2: QMFB contour images for polytime T2(2) code with B = 875 Hz, T = 16 ms (signal only), showing (a) layer 4 output, and (b) close-up of layer 4, showing resulting linear frequency modulation.

800

Detecting and Classifying LPI Radar

Figure M.3: QMFB contour images for polytime T3(2) code with B = 1,167 Hz, T = 16 ms (signal only), showing (a) layer 2 output, and (b) close-up of layer 2, showing detailed frequency changes due to phase codes.

Appendix M: QMFB Results for T2, T3, and T4

801

Figure M.4: QMFB contour images for polytime T3(2) code with B = 1,167 Hz, T = 16 ms (signal only), showing (a) layer 4 output, and (b) close-up of layer 4, showing resulting linear frequency modulation.

802

Detecting and Classifying LPI Radar

Figure M.5: QMFB contour images for polytime T4(2) code with B = 1,167 Hz, T = 16 ms (signal only), showing (a) layer 2 output, and (b) close-up of layer 2, showing detailed frequency changes due to phase codes.

Appendix M: QMFB Results for T2, T3, and T4

803

Figure M.6: QMFB contour images for polytime T4(2) code with B = 1,167 Hz, T = 16 ms (signal only), showing (a) layer 4 output, and (b) close-up of layer 4, showing resulting linear frequency modulation.

Appendix N

Cyclostationary Processing Results with FMCW ∆F = 500 Hz The extraction of the parameters from a wideband FMCW signal ∆F = 500 Hz using cyclostationary processing is not significantly diﬀerent, and is shown in Figure N.1. The modulation period for this example tm = 30 ms. Figure N.1(a) shows the modulation pattern with centroid at 2fc = 2 kHz. Note that the arrowhead pattern unique to the FMCW is still present, but has a bit more structure. With this resolution, ∆F can easily be measured; however, Rc cannot be measured. The closer examination shown in Figure N.1(b) reveals the unique modulation characteristic of the FMCW waveform. The value of Rc = 16.7 Hz is now easily identified giving a tm = 30 ms. The SNR = 0 dB case is shown in Figure N.2(a) and (b). Note that the cyclostationary results are fairly robust in significant amounts of noise.

805

806

Detecting and Classifying LPI Radar

Figure N.1: Frequency-smoothing SCD patterns for a ∆F = 500 Hz, tm = 30ms triangular FMCW signal with fc = 1 kHz, showing (a) complete FMCW modulation as one part of the bifrequency plane, and (b) closer examination showing Rc measurement.

Appendix N: Cyclostationary Results with FMCW ∆F = 500 Hz

807

Figure N.2: Frequency-smoothing SCD patterns for a ∆F = 500 Hz, tm = 30ms triangular FMCW signal with fc = 1 kHz, showing (a) the bifrequency plane with SNR = 0 dB, and (b) closer examination showing Rc measurement.

Appendix O

Cyclostationary Processing Results with Frank Signal, Nc = 16 For the signal examined, fc = 1 kHz, cpp = 1, fs = 7 kHz, and Nc = 16 phase subcodes. The frequency-smoothing SCD is generated using ∆k = 16 Hz with N = 1,024. One of the four modulation patterns generated in the SCD is shown in Figure O.1(a). As in previous examples, the pattern centroid is located at γ = 2fc . For the Frank code this is a bit more diﬃcult to identify, due to the diﬀerent slopes of phase shift within each single code period T . Generally, it lies in the center of the cross-hatch area inside the lesser SCD amplitude (faded) regions. That is, the cross-hatch region of interest is not symmetrical about the centroid. Location of the centroid can be used to determine the bandwidth on the cycle frequency axis, but there is a more straightforward method for determining the bandwidth in the bifrequency plane. To do this we first outline the cross-hatch region (larger amplitude SCD) with a parallelogram (shown by dashed lines). The top and bottom corners of the parallelogram are colocated at the same cycle frequency, and the left and right corners are colocated at the same frequency (f = 0). This information helps identify the parallelogram position, and the bandwidth B can be estimated more accurately. For the Frank code, the Rc measurement is related to the code period as Rc = 1/T = 1/Nc tb . In Figure O.1(b), a closer examination shows that the Rc measurement is straightforward, and for this signal Rc = 62.5 Hz. The number of subcodes within a code period is then Nc = B/Rc = 16. Figure O.2 shows the bifrequency analysis for the Frank code in the presence of noise. In Figure O.2(a), the Frank code modulation is 809

810

Detecting and Classifying LPI Radar

Figure O.1: Frequency-smoothing SCD patterns for the Frank code with Nc = 16, fc = 1 kHz, and cpp = 1, showing (a) one of four Frank code modulation patterns and measurement parallelogram, and (b) closer examination with Rc measurement.

Appendix O: Cyclostationary Results with Frank Signal, Nc = 16

811

Figure O.2: Frequency-smoothing SCD patterns for the Frank code with Nc = 16, fc = 1 kHz, cpp = 1, and SN R = 0 dB, showing (a) one of four Frank code modulation patterns on the bifrequency plane with the measurement parallelogram, and (b) closer examination illustrating the Rc measurement.

812

Detecting and Classifying LPI Radar

shown with an SN R = 0 dB. Note the position of the parallelogram to enclose the cross-hatch region. Also note the corner locations and the bandwidth measurement. Figure O.2(b) shows the Rc measurement. In summary, the unique pattern of the wideband Frank code lets us determine all of the signal parameters using the SCD bifrequency plane.

Appendix P

Cyclostationary Processing Results for P1, P2, P3, and P4 P.1

P1 Code Analysis

In this section we investigate the time-smoothing SCD for the P1 signal, and illustrate the corresponding extraction technique. The signal examined is a P1 phase-modulated signal with fc = 1 kHz, Nc = 64 subcodes, and cpp = 1 (wideband). Figure P.1(a) shows the complete bifrequency plane, and reveals that the P1 code also presents itself in an insect pattern. Compared to the Frank code signal, however, note that the insect is pointed to the left. This is expected, since the time-frequency slope as measured by the Wigner distribution and quadrature mirror filtering is opposite to that of the Frank code. As illustrated in Figure P.1(b), the bandwidth is measured on the cycle frequency axis in a similar fashion to the Frank code, except that the head is on the left. Correlation with the frequency axis measurement of B is also illustrated. Also indicated in Figure P.1(b) is a box that is examined in closer detail to illustrate the Rc measurement. Figure P.2(a) and (b) illustrate the measurement of Rc = 1/T . Figure P.2(b) indicates Rc = 15.5 Hz, giving a modulation period of 64 ms. Again, since the number of subcodes used by LPI radar are most often a power of 2 (e.g., 64 = 26 ), an accurate result can be obtained even from a bifrequency plane with small SNR. Here Nc = B/Rc = 64.

813

814

Detecting and Classifying LPI Radar

Figure P.1: Time-smoothing SCD insect patterns for the P1 code with Nc = 64, fc = 1 kHz, and cpp = 1, with (a) the complete bifrequency plane, and (b) closer examination of one of the four modulation patterns illustrating the bandwidth measurements.

Appendix P: Cyclostationary Results for P1, P2, P3, and P4

815

Figure P.2: Close examination of time-smoothing SCD for the P1 code with Nc = 64, fc = 1 kHz, and cpp = 1, with (a) modulation cycles, and (b) the measurement of Rc .

816

P.2

Detecting and Classifying LPI Radar

P2 Code Analysis

The time-smoothing SCD results for the P2 code are illustrated in Figure P.3(a). The P2 modulation has the expected insect shape, however, it is pointing to the right (similar to the Frank code). Note also the distinct nulls present in the bifrequency. The bandwidth is measured in a similar manner to the P1 and Frank code; however, the bifrequency nulls must be used as illustrated in Figure P.3(b). One advantage of using the bifrequency plane for measuring Rc for the subcode period tb and number of subcodes N is the nonspecific position in the bifrequency plane, where Rc can be measured. As shown in Figure P.4(a) and (b), any (γ, k) region can be used to estimate the value of Rc .

P.3

P3 Code Analysis

The time-smoothing SCD results for the P3 code are shown in Figure P.5. The signal has fc = 1 kHz, Nc = 64 (64 subcodes), and cpp = 1. The insect modulation pattern points to the right and the measurements of B and Rc , as well as N and cpp, are the same as the above cases.

P.4

P4 Code Analysis

The time-smoothing SCD results for the P4 code are shown in Figure P.6. The signal has fc = 1 kHz, Nc = 64, and cpp = 1. The insect modulation pattern points to the right and the measurements of B and Rc , as well as N and cpp, are the same as above.

Appendix P: Cyclostationary Results for P1, P2, P3, and P4

817

Figure P.3: Time-smoothing SCD insect patterns for the P2 code with Nc = 64, fc = 1 kHz, and cpp = 1, with (a) the complete bifrequency plane, and (b) closer examination of one of the four modulation patterns illustrating the bandwidth measurements.

818

Detecting and Classifying LPI Radar

Figure P.4: Close examination of time-smoothing SCD for the P2 code with Nc = 64, fc = 1 kHz, and cpp = 1, with (a) modulation cycles, and (b) the measurement of Rc .

Appendix P: Cyclostationary Results for P1, P2, P3, and P4

819

Figure P.5: Time-smoothing SCD insect patterns for the P3 code with Nc = 64, fc = 1 kHz, and cpp = 1 with (a) the complete bifrequency plane, and (b) closer examination of one of the four modulation patterns illustrating the bandwidth measurements.

820

Detecting and Classifying LPI Radar

Figure P.6: Time-smoothing SCD insect patterns for the P4 code with Nc = 64, fc = 1 kHz, and cpp = 1 with (a) the complete bifrequency plane, and (b) closer examination of one of the four modulation patterns illustrating the bandwidth measurements.

Appendix Q

Cyclostationary Processing Results for T2, T3, and T4 Polytime Codes Q.1

Polytime T2(2) Code Analysis

In this section, the frequency-smoothing SCD is used to examine the polytime T2(2) code. The T2(2) code also has an fc = 1 kHz, and has a time-modulated binary phase shift (of various widths). Figure Q.1(a) shows the bifrequency plane and the four modulation patterns. Figure Q.1(b) shows one of the four unique patterns, and illustrates how the bandwidth of the signal can be measured. Comparison with the T1(2) code shows that the bandwidth is exactly one-half as large as in the T1(2) code. For the T2(2) signal shown in Figure Q.1(b), B = 875 Hz. Figure Q.2 shows a closer examination of the bifrequency plane, and the measurement of Rc = 1/T = 62.5 Hz. This gives the estimate for the code period as T = 16 ms. Note also that an SCD spot does not exist at γ = 2fc , k = 0 and is an additional method to distinguish between the two bifrequency patterns.

Q.2

Polytime T3(2) Code Analysis

In this section, the frequency-smoothing SCD is used to examine the polytime T3(2) code. The T3(2) code also has an fc = 1 kHz, and has a time-modulated binary phase shift (of various widths) across a modulation bandwidth ∆F = 600 Hz. Figure Q.3(a) shows the bifrequency plane and the four modulation 821

822

Detecting and Classifying LPI Radar

Figure Q.1: Frequency-smoothing SCD patterns for the polytime T2(2) code with fc = 1 kHz, showing (a) the complete bifrequency plane, and (b) closer examination of one of the four modulation patterns illustrating the bandwidth measurement.

Appendix Q: Cyclostationary Results for T2, T3, and T4 Codes

823

Figure Q.2: Close examination of the frequency-smoothing SCD pattern for the polytime T2(2) code, illustrating the Rc measurement. patterns. Figure Q.3(b) shows one of the four unique patterns. The distance from the centroid to the corner of the dot pattern on the k = 0 axis is 2∆F . For the T3(2) signal shown in Figure Q.3(b), ∆F = 600 Hz. Figure Q.4 shows a closer examination of the bifrequency plane, and the measurement of Rc = 1/T = 62.5 Hz. This also correctly gives the estimate for the code period as T = 16 ms. Note also that an SCD spot does exist at (γ = 2fc , k = 0).

Q.3

Polytime T4(2) Code Analysis

In this section the frequency-smoothing SCD is used to examine the polytime T4(2) code. The T4(2) code also has an fc = 1 kHz, and has a time-modulated binary phase shift (of various widths) across a modulation bandwidth ∆F = 600 Hz. Figure Q.5(a) shows the bifrequency plane and the four modulation patterns. Figure Q.5(b) shows one of the four unique patterns. The distance from the centroid to the corner of the dot pattern on the k = 0 axis is also 2∆F . For the T4(2) signal shown in Figure Q.5(b), ∆F = 600 Hz. Figure Q.6 shows a closer examination of the bifrequency plane, and the measurement of Rc = 1/T = 62.5 Hz. This also correctly gives the estimate for the code period as T = 16 ms. Note also that an SCD spot does exist at (γ = 2fc , k = 0).

824

Detecting and Classifying LPI Radar

Figure Q.3: Frequency-smoothing SCD patterns for the polytime T3(2) code with fc = 1 kHz showing (a) the complete bifrequency plane, and (b) closer examination of one of the four modulation patterns illustrating the bandwidth measurement.

Appendix Q: Cyclostationary Results for T2, T3, and T4 Codes

825

Figure Q.4: Close examination of the frequency-smoothing SCD pattern for the polytime T3(2) code, illustrating the Rc measurement.

826

Detecting and Classifying LPI Radar

Figure Q.5: Frequency-smoothing SCD patterns for the polytime T4(2) code with fc = 1 kHz, showing (a) the complete bifrequency plane, and (b) closer examination of one of the four modulation patterns illustrating the bandwidth measurement.

Appendix Q: Cyclostationary Results for T2, T3, and T4 Codes

827

Figure Q.6: Close examination of the frequency-smoothing SCD pattern for the polytime T4(2) code, illustrating the Rc measurement.

List of Symbols There are not enough symbols in the English and Greek alphabets to allow the use of each letter or symbol once. Consequently, some symbols may be used to denote more than one variable, but their use should be clear from the context.

Symbols a A A A A A A ˜ avg A An A2 An Ae b b b(n) bsc B B B B B

multiplying coeﬃcients for envelope approximation detector complex leakage signal signal amplitude Albersheim SNR coeﬃcient coeﬃcients for seastate model continuous aperiodic autocorrelation function feature vector from time-frequency image moving average filter output normalized, filtered marginal frequency distribution power reflection coeﬃcient of target excitation coeﬃcients eﬀective area of the radar receive antenna spiral rate constant multiplying coeﬃcient for envelope approximation detector Wiener filter output number of samples per subcode Albersheim SNR coeﬃcient coeﬃcients for seastate model feedthrough signal under vector modulator control positive real parameter for Taylor array absolute signal bandwidth

829

830

Detecting and Classifying LPI Radar B Ba BIR BIV BI BRi c c cdf cn cpp C C C Cf (t, ω, φ) C(td , α; Tr , αr ) C(x) Ci CD (τ ) CDA (τ ) CI (τ ) Cl CM R CM Cu CWDx ( , ω) d d dγ da de da dc D Df e(t) ec (t) eR (t)

conical spiral base diameter bandwidth after demodulation intercept receiver front-end RF bandwidth intercept receiver video bandwidth intercept receiver bandwidth radar receiver input bandwidth speed of light window function selection variable cumulative distribution function radial basis function centers cycles of the carrier frequency per subcode Hamming window coeﬃcient channel capacity coeﬃcients for seastate model Cohen’s general class of time frequency distributions cross-correlation cosine Fresnel integral weighting factor output of digital correlation receiver output of digital-analog correlation receiver output of ideal analog correlation receiver spiral circumference outer diameter connectivity measure reference connectivity measure spiral circumference in feed region Choi-Williams distribution antenna element spacing conical spiral apex diameter length of route γ aperture dimension in azimuth aperture dimension in elevation diameter of circular antenna duty cycle delay angular frequency per volt of FMCW transmitted noise plus FMCW signal noise FMCW plus sine transmitted signal noise plus FMCW echo of moving target

List of Symbols E E ER ERPR ERPJ ERPC f1b f2b fb fc fl fu fu fclk f (t) fd max fbmax fHL fl (n),flI (n) fm fj fs (y) fcr fs fc1 fc2 f (k1 , k2 ) fI f0 F (u, v) Fi F˙ F˙ I FI FR F (u) Fγμ,ν F1 , F2

amplitude of noise plus FMCW signal energy amplitude of noise plus FMCW echo eﬀective radiated power of radar eﬀective radiated power of jammer eﬀective radiated power of data communication node upslope beat frequency downslope beat frequency beat frequency carrier frequency lower frequency limit of spiral antenna upper frequency limit of spiral antenna unambiguous Doppler frequency clock frequency continuous signal random binary phase modulation Doppler tolerance maximum beat frequency hard-limiting nonlinearity kernel function for Wigner-Ville distribution video modulation signal FSK transmitted frequency sigmoid nonlinearity function critical frequency sampling frequency first frequency of a two-tone signal second frequency of a two-tone signal time-frequency image single sawtooth FMCW signal frequency constant frequency rectangle flux power incident on a target chirp rate angular frequency increment per sample intercept receiver noise factor radar receiver noise factor array pattern time dependent flow coeﬃcient spiral antenna feed points

831

832

Detecting and Classifying LPI Radar g g G G G G(x) Gr Gt GIt GI gn (τ ) h ha,b (t) h h h(k1 , k2 ) h(n) (q) hlk hF 2layer ht H H H(u, v) Hd (u, v) H(ω) H0 (z) H1 (z) i I I I(t, ω) Ib I(j) Ic IBar IR

response of the receiver Tikhonov’s regularization parameter antenna gain filter transfer function Gabor time-frequency distribution antenna taper function antenna receive gain along boresight antenna transmit gain along boresight antenna transmit gain in side lobe intercept receiver antenna gain modulation function height single prototype wavelet correlation integral impulse response filter mask histogram received signal from scatterer q transmitter l, rcvr k F2-layer height from Earth’s surface dipole height above ground number of hidden layers in multilayer perceptron entropy 2D filter transfer function ideal lowpass filter transfer function antialiasing filter transfer function highpass filter lowpass filter number of the sample in a given frequency inphase term neural network input nodes intensity image transmission loss measure of information in jth message circulator isolation Barrick’s transmission loss network reach

List of Symbols j k k kres K Kμ (t) Kmax KνJ l L L L L L(n) Lc LIR LP 2 LRR LRT Lx Lμ,ν γ L1 L2 M M M M M M MSE MSW n n n n n n n(t) nr

833

frequency index Boltzmann’s constant discrete frequency index frequency resolution normalizing constant capability value of node μ maximum number of targets simultaneously identified jammer capability value quadrature mirror filter layer index total length of spiral antenna system losses total number of wavelet layers overlap sliding factor between each short time FFT sum of the square of the coeﬃcients circulator loss losses between intercept receiver antenna to receiver two way transmission path loss through ionosphere losses between the antenna and receiver losses between the transmitter and the antenna transmission line loss information flow parameter one-way atmospheric transmission factor two-way atmospheric transmission factor number of pulse compressors (random binary phase modulation) square root of number of subcodes for Frank, P1, P2 number of LPI transmitters in MIMO configuration sampled data length number of channel pair regions on the bifrequency plane Grenander’s uncertainty condition mean sum of squares of network errors mean sum of squares of network weights and biases cyclostationary order time index number of reference cells in CFAR width of data path in the accumulator discrete index of Doppler frequency number of continuous antenna beams in elevation stack receiver thermal noise number of resolution elements in scan volume

834

Detecting and Classifying LPI Radar N N N N N N NI Nc Nc Nd Ne Nm Np Nr NI NB NF NF NI NRB NT NT NT NP NX NY NF NI NF Nμ Nμ,ν p(t) p(τ ) pj pr pt pdf

number of code periods used in correlation receiver number of arms interleaved within spiral antenna number of statistically independent noise samples FFT size number of receivers in MIMO configuration total number of discrete samples of time discrete short time FFT size number of subcodes, processing gain feature vector dimension number of sections in subdivided scan volume electron density maximum electron density total number of quadrature mirror samples feature vector dimension integration intervals number of Barker phase codes number of transmitted continuous frequencies number of tiles displayed in frequency number of noncoherent integration intervals number of range bins containing clutter number of tiles displayed in time total number of phase slots in the FSK/PSK waveform number of nodes connected in the network nepers beginning target state in Markov chain ending target state in Markov chain coherent processing interval FFT record length record length total number of nodes connected to node μ total number of routes between node μ and ν aperiodic rectangular window function autocorrelation of the transmitted waveform probability of transmitting jth message surface wave received power from target surface wave radiated power in presence of ground probability density function

List of Symbols P Prad Pin P DD P GR Pavg Pd Pf a Prerad Pt Ptot PN (Z) PCW PRC PRT PT R P GI Q Q(λμ ) r r rb re rk rl r1 R R R Rc Rc Rd Rfootprint RI RImax Rk Rmax Rcancel,dB Ru

number of polyphase code periods transmitted radiated power from the antenna total input power to the antenna power density at a range R processing gain adaptive average transmitted power probability of detection probability of false alarm surface wave power reradiated by target peak power of pulsed emitter total power at receiver using circulator square law detector output with no target present average power of CW transmitter clutter power within a range bin received signal power of the radar from the target signal power to the intercept receiver intercept receiver processing gain quadrature term knowledge function discrete time index radial distance radial distance to layer’s base Earth’s radius (6,3781.1 km) aperiodic autocorrelation coeﬃcients received signal at antenna l spiral antenna generating function range neural network regularization maximum spiral radius code rate continuous cross-correlation function range error due to Doppler shift OTHR range along Earth’s surface range between LPI radar and intercept receiver maximum intercept range for intercept receiver target range or path length in kilometers maximum detection range of the LPI radar reflected power cancelation depth unambiguous range

835

836

Detecting and Classifying LPI Radar Rx (τ ) Rxα (τ ) R(rtb ) R(ρ, θ) RC RJ RQ RT s(f ) s(f ˙ ) s(t) sl (n) s1 (t) s2 (t) S S(t) S(x) I (n, k) SXN Sx (f ) Si,j Sv (f ) Sx (f ) Sxα (f ) α SX TW γ SX NI Sd S1,2 SNRIo SNRIi SNRnet SNRRi SNRRo SNR1 t tb td tm tI tp

time average autocorrelation function cyclic autocorrelation of a complex time series x(t) periodic autocorrelation function Radon transform range of communication node range of jammer network richness target range single sweep FMCW spectrum roll-oﬀ rate single sweep FMCW spectrum complex signal orthogonal polyphase complex signal transmitted signal upslope transmitted signal downslope slope of polyphase modulation in time-frequency plots complex stationary process sine Fresnel integral estimated timed smoothed periodogram power spectral density target scattering coeﬃcient with i, j = V or H noise plus FMCW correlation output spectrum power spectral density spectral correlation density continuous time-smoothed cyclic periodogram discrete time-smoothed cyclic periodogram output of up converter MXR1 in noise radar number neurons in first, second hidden layers in MLP intercept receiver output SNR from signal processor intercept receiver input SNR to signal processor SNR for netted radar minimum SNR required at the radar input output, Albersheim SNR SNR for single monostatic radar time subcode period or duration round trip propagation time delay modulation period smallest radar coherent integration time transmitted frequency duration

List of Symbols t0 t0 T T Tf Th Thλ Tint Tp TA TB TN TN TR T0 TW u(t) v, V ∨i Vt Vt w(t) wST (f ) wCT (t) wl (t) We (f ) Wn Wx (t, ω), WX (ω, t) W (ν) WN , WM x0 X Xn Xq XT XW F (ω, τ ) Xr (f ) XTW (t, f )

837

coherent processing interval signal time of arrival code period threshold multiplier frame time noise radar threshold eigenvalue threshold measurement time in noise receiver time for target to pass through range cell lower limit angle threshold upper limit angle threshold short time FFT window pulse repetition interval delay of RF delay line standard temperature in Kelvin short-time FFT window length periodic complex envelope target velocity eigenvector selection threshold voltage maximum closing velocity of the target weighting function frequency domain taper function time domain cosine-Tukey amplitude taper function additive symmetric zero mean Gaussian noise power spectrum of transmitted noise plus FMCW signal perceptron weighting vector Wigner-Ville distribution Fourier transform of window window functions for Choi-Williams cyclic frequency constant training matrix for principal components analysis n-dimensional perceptron input vector position of scatterer Fourier transform of x(t) windowed Fourier transform of x(t) Fourier transform of the cyclic autocorrelation function continuous short time Fourier transform

838

Detecting and Classifying LPI Radar XN I (n, k) XW (a, b) y1 , y2 ym ypn z(t) Z Z0 α αk |χ(τ, ν)| |χN T (τ, ν)| |χT (τ, ν)| δ δ δ δ(k) δF δφ δI δR ∆i,j ∆α ∆ν ∆f ∆t ∆tmin ∆k ∆F ∆F I ∆R ∆RI ∆v ∆w ∆Θ ∆ω η r

γ

discrete Fourier transform wavelet transform CFAR noise power levels layer semithickness output of radial basis function delay product waveform of x(t) square law detector response free space impedance (377 Ω) cycle frequency (continuous time) linear transform of continuous time signal ambiguity function magnitude ambiguity function for N reference correlators single period ambiguity function sensitivity ratio spiral antenna rotation angle range diﬀerence between direct and multipath echoes Kroeneker’s delta function bandwidth increment phase error from perfect quadrature intercept receiver sensitivity radar receiver sensitivity cell value in the diﬀerence triangle cycle frequency resolution change in Doppler oﬀset frequency resolution time resolution minimum time delay that can be detected points spacing in frequency FMCW modulation bandwidth eﬀective modulation bandwidth range resolution eﬀective range resolution first blind speed coherent processing interval target extent in azimuth spectral width of the beat frequency aperture eﬃciency relative error discrete time cycle frequency

List of Symbols γ γ γ γres γ(t) Γ

λ λ λC2 λd λf λmin λT ΛOODA μ μ μ ν ν ω ωr ωIF ωLO Ω Ωa Ωe Ωs φ(ξ, τ ) φc φi φi φi,j φk φl φr φ1

route index noncoherent integration eﬃciency FMCW flyback factor cycle frequency resolution target reflectivity profile voltage reflection coeﬃcient discrete time index QMFB layer number wavelength information rate of source decision tempo deployment tempo fighting tempo minimum information rate characteristic tempo maximum operational tempo node index local mean refractive index of ionosphere Doppler frequency oﬀset node index radian frequency scan rate intermediate radian frequency local oscillator angular frequency frequency boundary scan coverage in azimuth scan coverage in elevation scan volume kernel function for time-frequency distribution phase modulation P3, P4 phase sequence incidence angle Frank, P1, P2 polyphase sequence general phase modulation function orthogonal polyphase sequence phase shift FMCW phase

839

840

Detecting and Classifying LPI Radar φT 1 φT 2 φT 3 φT 4 φ0 Φ(t) φ(p) ψ |ψ(τ, ν)| Ψb ρ ρλ ρejφ ρ(t) ρV σ σ1 σ2 σ2 σ0 σ0i σnj σmin σs σs σsr σF S σT τ τd τR τtk , τrl θa θe θn θs θstart θstop θ0 ξ(p, q) ξi

T1(n) polytime sequence T2(n) polytime sequence T3(n) polytime sequence T4(n) polytime sequence initial angle of spiral antenna basis set Euler function of positive p grazing angle ambiguity function of mismatched receiver solid angle within the half-power beam contour spiral antenna generating function spiral antenna generating function in wavelengths complex correlation coeﬃcient periodic rectangular window voltage standing wave ratio spread of radial basis function total received power in noise radar total power in delayed replica in noise radar white Gaussian noise power incremental backscattering coeﬃcient of the sea mean sea backscatter coeﬃcient for seastate i elements of radial basis function covariance matrix minimum detectable radar cross section transmitted noise signal power Shearman’s definition of backscattering cross-section power in the noise radar received signal free-space backscattering cross-section target radar cross section oﬀset time delay dwell time pulse width propagation time delay 3 dB beamwidth in azimuth 3 dB beamwidth in elevation target azimuth angle Radon projection angle for maximum intensity beginning of target’s position in azimuth end of target’s position in azimuth angle of main lobe peak multichannel time-frequency LPI detector target reflectivity

Glossary AARGM ACF ADC AEA ALCM AMRFC AO AOA AOA AREPS ARES ARM ARMIGER ARSR ASCM ATR AWACS AZ B-F BMEWS BPF BPSK C2 CARA CCD CFAR CMRA COSPAR CSIST

Advanced antiradiation guided missile Autocorrelation function Analog-to-digital converter Airborne electronic attack Air launched cruise missile Advanced multifunction RF concept Acousto-optic Analysis of alternatives Angle of arrival Advanced Refractive Eﬀects Prediction System Aﬀordable reactive strike missile Antiradiation missile Antiradiation missile with intelligent guidance and extended range Air route surveillance system Antiship capable missile Automatic target recognition Airborne warning and control system Azimuth Bifrequency Ballistic missile early warning system Bandpass filter Binary phase shift keying Command and control Combined Altitude Radar Altimeter Charge coupled device Constant false alarm rate Cruise Missile Radar Altimeter Committee of Space Research Chung-Shan Institute of Science and Technology

841

842

Detecting and Classifying LPI Radar CW CWD DAC DARPA DC DDS DFT DFSM DIP DLVA DoD DRFM DSP EA EL ELINT EP ERP ES EW EWO FAM FET FFT FH FIR FLAPS FLIR FMCW FOT FOV FSK GAO GCS GDA GOCFAR GPS GUI

Continuous waveform Choi-Williams distribution Digital-to-analog converter Defense Advanced Research Projects Agency Direct current Direct digital synthesizer Discrete Fourier transform Direct frequency-smoothing method Digital information pheromones Detector logarithmic video amplifiers Department of Defense Digital radio frequency memory Digital signal processing Electronic attack Elevation Electronic intelligence Electronic protection Eﬀective radiated power Electronic support Electronic warfare Electronic warfare oﬃcer FFT accumulation method Field eﬀect transistor Fast Fourier transform Frequency hopping Finite impulse response Flat parabolic surface Forward looking infrared Frequency modulation CW Optimum working frequency Field of view Frequency shift keying General accounting oﬃce Ground control station Great deluge algorithm Greatest-of constant false alarm rate Global positioning system Graphical user interface

Glossary HARD HARM HCI HDAM HEMT HTS HTS HPM IADS ICAP IF IFF IG IIR IMU INS IR IRI IRST ISAR ISL JCC JORN JSR JSTARS LAMPS LAN LANTIRN LCM LNA LO LPF LPI LPID LPIT LPRF LUT MALD MALI MATLAB MF

843

Helicopter and Aircraft/Radar Detection High-speed antiradiation missile Human computer interface HARM destruction of enemy air defense attack module High electron mobility transistor High temperature superconductor HARM targeting system High power microwave Integrated air defense system Increased capability Intermediate frequency Identification friend or foe Ionosphere index Imaging infrared Inertial measurement unit Inertial navigation system Infrared International Reference Ionosphere Infrared search and track Inverse synthetic aperture radar Integrated side lobe level JORN coordination center Jindalee over-the-horizon network Jam-to-signal ratio Joint Surveillance and Target Attack Radar System Light Airborne Multipurpose System Local area network Low-Altitude Navigation and Targeting Infrared for Night Least common multiple Low noise amplifier Local oscillator Lowpass filter Low probability of intercept Low probability of identification Low probability of intercept toolbox Low pulse repetition frequency Lookup table Miniature Air Launched Decoy Miniature Air Launched Interceptor Matrix Laboratory Matched filter

844

Detecting and Classifying LPI Radar MFAB MIMO MIP MLP MMIC MMW MRSR MTD MTI MUF NATO NCW OLPI OODA OTH OTHR PACF PAF PAGE PALS PANDORA PCA PDW PG PGM PLL PPI PRF PRI PSD PSK PSL PWVD QMF QMFB RAAF RAM RBF RBPC RCS RF

Marginal frequency adaptive binarization Multiple input multiple output Millions of instructions per second Multilayer perceptron Monolithic microwave integrated circuit Millimeter wave Multirole Survivable Radar Moving target Doppler Moving target indication Maximum usable frequency North Atlantic Treaty Organization Network centric warfare Omnidirectional LPI radar Observation-orientation-decision-action Over-the-horizon Over the horizon radar Periodic autocorrelation function Periodic ambiguity function Portable air-defense guard equipment Precision Approach and Landing System Parallel array for numerous diﬀerent operational research activities Principal components analysis Pulse descriptor word Passive guidance Precision guided munitions Phase-locked loop Planned position indicator Pulse repetition frequency Pulse repetition interval Power spectral density Phase shift keying Peak side lobe level Pseudo Wigner-Ville distribution Quadrature mirror filter Quadrature mirror filter bank Royal Australian air force Rolling airframe missile Radial basis function Random binary phase code Radar cross section Radio frequency

Glossary RISP RNR RNFR RNFSR RPC RF RPM RPV RX RTIC RTOC RWR SAM SAR SATCOM SAW SCD SCR SEAD SEI SFDR SIGINT SJR SLR SNR SSBM SSN STAP STC STFT SVD TALS TCR TEL T-F TJS TOA TR UAV UCARS

Relative to isotropic antenna at same position Random noise radar Random noise plus FMCW radar Random noise FMCW plus sine radar Reflected power canceler Radio frequency Revolutions per minute Remotely piloted vehicles Receiver Real time into the cockpit Real time out of the cockpit Radar warning receiver Surface-to-air missile Synthetic aperture radar Satellite communication Surface acoustic wave Spectral correlation density Signal-to-clutter ratio Suppression of enemy air defense Specific emitter identification Spurious free dynamic range Signals intelligence Signal-to-jam ratio Side lobe ratio Signal-to-noise ratio Single-sideband modulator Sun spot number Space time adaptive processing Sensitivity time control Short-time Fourier transform Singular value decomposition Tactical Automatic Landing System Target-to-clutter ratio Transporter erector launcher Time-frequency Tactical Jamming System Time of arrival Transmit and receive Unmanned aerial vehicle UAV Common Automatic Recovery System

845

846

Detecting and Classifying LPI Radar UHF U.K. URSI U.S. USAF UT UTC UWB VCO VHF VLSI VSTOL WGN WRF WT WVD WWII XNOR XOR

Ultra high frequency United Kingdom Union of Radio Science International United States United States Air Force Universal time Coordinated universal time Ultra wideband Voltage controlled oscillator Very high frequency Very large scale integrated circuits Vertical stationary take-oﬀ and landing White Gaussian noise Waveform repetition frequency Wavelet transform Wigner-Ville distribution World War II Exclusive not OR Exclusive OR

About the Author Phillip E. Pace is a professor in the department of electrical and computer engineering at the Naval Postgraduate School (NPS). He received B.S. and M.S. degrees from Ohio University in 1983 and 1986, respectively, and a Ph.D. from the University of Cincinnati in 1990 — all in electrical and computer engineering. Prior to joining NPS, he spent 2 years at General Dynamics Corporation, Air Defense Systems Division, as a design specialist in the Radar Systems Research Engineering Department. Before that, he was a member of the technical staﬀ at Hughes Aircraft Company, Radar Systems Group, for 5 years. He was selected for the Outstanding Research Achievement Award in 1994, 1995, and 1998 for his work at NPS in electronic warfare, and received the 1995 Association of Old Crows (AOC) Academic Training Award. Dr. Pace directs the NPS Center for Joint Services Electronic Warfare, has been the chairman of the Navy’s Threat Missile Simulator Validation Working Group since October 1998, and was a participant on the Navy’s NULKA Blue Ribbon Panel in January 1999. He is the author of the textbook Advanced Techniques for Digital Receivers (Artech House, 2000), and has been a principal investigator on numerous research projects in the areas of receiver design, signal processing, electronic warfare, and weapon systems analysis. Dr. Pace invented the concept of symmetrical number systems, has five patents, over thirty journal publications and is a senior member of the IEEE.

847

Index A

Swiss Air Guard, 607 twinkle transmission, 607 warning radar and decoy, 608—609 Antiradiation missile (ARM), 4, AARGM, 569—571, 592—593 Alamo, 578—579 Alarm, 564, 597—599 antenna design, 559—566 ARES, 593 ARMIGER, 600 Corvus, 554 dual-mode, 567, 569 FT-2000, 604—606 HARM, 591—592 Harpy, 601—602 Kegler, 585—586 Kelt, 580—581 Kh-27, 585 Kickback, 587 Kilter, 584—585 Kingfish, 581—582 Kitchen, 579—580, Krypton, 565—566, 587—589 Kyle, 582—584 LPI processing, 572—576 Martel, 596—597 millimeter, 569—570 performance metrics, 577 Rolling airframe missile, 594—595 seeker, 566—571, 605 Shrike, 555, 589—590 Sidearm, 593—594 signal processing, 571—572 Standard, 591 STAR-1, 603—604

Abdullah, 553 Activation function, 630 AD1990 altimeter, 45 Adaptive binarization 637—639 Agility, 325—326 Alarm ARM, 564 Altimeter, 41—45 AD1990, 45 AHV-2100, 45 CARA, 42 CMRA, 43 GRA-2000, 44 HG-9550, 43 PA-5429, 44 Ambiguity function, 68 Amplitude weighting, 77 AMRFC, 13 Amplifier predetection, 28 postdetection, 28 AN/APG-77, 56—57 AN/APS-147, 56 AN/APQ-181, 56-57 Analog processor, 20 Analog to digtal converter, 20 Anti-ARM, 606—612 AN/TLQ-32 ARM-D decoy, 611 Cosmic Shield, 607 flaps decoy, 608—609 Gazetchik, 610—611 VHF/UHF, 607 Patriot, 607 position flexibility, 606 Swedish GLV200, 607

849

850

Detecting and Classifying LPI Radar

summary (Russian), 578 targets, 557 Tien Chien IIA, 598—599 Antiship missile RBS-15, 58—60 seeker technology, 301—305 Antenna, 5 aperture distribution, 7 bandwidth, 6 beamwidth (half-power), 5 dimension, 6 eﬀective area, 25 eﬃciency, 5 gain, 5 isotropic, 24 isolation (using circulator), 96—97 isolation (using RPC), 97—99 main lobe, 5 nonscanning, 12 pattern, 5—10 pencil beam, 6, 12 phased array, 6—7 radiation intensity, 8 scan pattern, 10—13 side lobe, 5—10 side lobe ratio, 5 simultaneous transmit, 13 spiral design, 559—566 stacked beam, 12 taper functions, 9 Atmospheric absorption, 17 transmission, 25 Autocorrelation function, 22 Autonomous classification authority, 621—622 feature extraction, 634—639 multilayer perceptron, 624, 629— 632 radial basis function, 624, 632— 633 results with MLP, 638—645, 667— 674 results with RBF, 642, 646—648, 674—681 time-frequency, 620—621

training, 631 Sheridan levels, 622-623 Autonommous parameter extraction Wigner-Ville with Radon, 688— 696 AHV-2100 altimeter, 45

B Back lobe, 5 Bandwidth fractional, 210 instantaneous fractional, 211 intercept receiver, 28—29 modulation (FMCW), 19—20 phase code, 127 radar, 26 Barker phase codes binary, 128—133 polyphase, 133—139 Basis functions, 468 Beamforming digital, 14 Beamwidth, 6 Beat frequency, 18, 103—104 bifrequency, 513,523—524, 699 Blind speed, 102 for OTHR, 264 Boltzmann’s constant, 26 Bottleneck, 333, 341

C Capability value, 326—327 jammer, 338 CARA altimeter, 42 CHAIN HOME, 553 Channel capacity, 334 unifying principal in EW, 334335 Chinese OTH-B, 272—276 Chinese remainder theorem, 267—269 Choi-Williams dist. BPSK analysis, 449, 452—454 classification, 634—637 comparison to WVD, 446 Costas analysis, 458, 461—462

Index demodulation, 400 FMCW analysis, 449—451 hybrid analysis, 458, 463 polyphase analysis, 455—457 polytime analysis, 455, 458—460 Classification, see Autonomous classification CMRA altimeter, 43 Coherent integration, 12 Combat losses, 557 Communications, 13 Compass Call, 556 Complete residue, 716—717 Compound Barker code, 128—129 Compression ratio, 127 Conical scan, 13 Connectivity measure extended, 333 generalized, 326—328 reference, 328—329 Continuous waveform, 16 Correlation processor, 21—24 coherence, 22 for noise, 238—243 Fourier transform,21 Corvus ARM, 554—555 Cosmic Shield, 607 Costas codes, 191—195 Critical frequency, 257 Cyclostationary processing BPSK analysis, 528—531, 532—534 Costas analysis, 540, 544 cycle frequency, 514 cycle frequency resolution, 519 cyclic autocorrelation, 514—515 cyclic spectral analysis, 515 demodulation, 400 direct frequency smoothing, 522—525 FFT accumulation method, 520—522 FMCW analysis, 531, 535—537, 805—807 FMCW parameter extraction, 699—704 Frank analysis, 809—812 Grenander’s uncertainty, 519

851 noise analysis, 543, 545—546 time-domain implementation, 516 polyphase analysis, 535, 537, 539—541, 809—820 polytime analysis, 540, 542—543, 821—827 spectral correlation density, 515—520

D Database, 638—640 Database extended, 660—666 Decision speed, 324 Decoy, 558—559 Demodulation, 400 Detection, homodyne, 18—20 maximum range, 26 range, 24—26 Detector envelope approximation, 84 linear 29 square-law, 28—29, 395 Diﬀerence triangle, 191—195 Digital RF memory, 396 Digital-to-analog converter, 92—93 Direct digital synthesizer, 20, generating linear FM using, 91—94, RPC using, 98—99 Direct RF sampling, 398—400 Distruction, 558 Doppler, clutter spectrum, 259—261 matrix correlation, 23 side lobe reduction, 23, 75—78, 110—113 zero, 22 Down conversion, 397—398 Duty cycle, 14—15 Dwell time, 11—13

E Eagle, 48—49 Eﬀective radiated power, 18

852

Detecting and Classifying LPI Radar

Electronic attack FMCW, 115 unifying principal, 334—335 joint airborne, 556 on information grid, 337—338 on netted radar, 352—360 Electronic protection, unifying principal, 334—335 Electronic warfare, 13 receivers, 387—388 Electronic warfare oﬃcer, 556 ELINT, 37 Emitter clustering, 687—688 Entropy, 333—336 Espenschied, Lloyd, 41 Extinction coeﬃcient, 25

range resolution, 189—191 orthogonal codes, 370—375 FSK — see Frequency hopping FSK/PSK — see Hybrid techniques

F

Hamming window, 77, 447 Hann window, 77 Harr fiter, 472—473 HARD, 48—49 HG-9550 altimeter, 43 Homodyne detection, 18 Human computer interface, 621—623 Hybird techniques, 195—198 target matched, 199—204

Fan beam, 6 Field of view, 10 resolution elements, 10 FM interrupted CW (OTHR), 282—287 FMCW radar advantages of, 81—82 block diagram, 18—20 modulation period, 102—104 out-of-band emission, 270—271 range-Doppler cross coupling, 102 received signal, 100—101 waveform design, 86—89, 91—94 waveform nonlinearities, 105—106 waveform spectrum, 89—91 Fourier transform, 7, 18 FFT accumulation method, 520522 FMCW range profile, 84 LPI detection, 576 Frame time, 11—13 Frank code example for PAF 71—75 peak side lobe, 75 polyphase, 139, 143—148 Frequency hopping advantages, 187—189 transmitted signal, 189

G Generalization, 630 Gibb’s phenomena, 474 Global information grid, 320 GOCFAR, 84—85, 104 GRA-2000 altimeter, 44 Grating lobes, 14 Growler EA-18G, 556

H

I Information rate, 334 Integration, 18—20 coherent, 28 LPI detection, 574—576 netted radar, 348—349 noncoherent eﬃciency, 29 noncoherent, 19, 20 postdetection, 85—86 Intercept receiver, 4 challenges, 400—402 maximum range, 28 Interrupted CW, 16 Ionospheric eﬀects (HF), 253—261

J Jam-to-signal ratio communication node, 337—338

Index radar node, 352—353 Jamming, 556, 621 JY-17a, 53—55

K Kh-31 ARM seeker, 565—566 Klipper (bandwidth), 28 Knowledge function, 335-336

L Landing systems, 45—47 PALS, 46 TALS, 46 UCARS, 46 LANTIRN, 58 Lethality, 326 Look-through, 388—389 Low noise amplifier, 84 Low probability of detection, 3 definition, 4 Low probability of intercept radar, antenna characteristics, 5—14 definition, 3, 31 deramping detection of, 576 discriminator, 573—574 multichannel detection, 574—576 netted, 342 origin of, 29 transmitter characteristics, 14—18 requirement, 4 sensitivity definition, 30—31 summary of characteristics, 18 Lowpass filtering, 648—651 Lookup table, 92 LPI toolbox (LPIT), 709—711 LPIsimNet, information network, 338—345 radar network, 353—360 tutorial, 721—739

853

M Main lobe, 5 MALD, 558—559 MALI, 59 Maneuverabilty,, 323—324 Markov chain, 85 Marginal frequency, 634—638, 651—656 Matched filter 22 Maximum usable frequency, 257 MIMO, 349—352 Missile systems, 58—62 MMIC, 116 Modified feature extraction, 648—660 Modified sinc filter, 473—474 Modulation, 16 bandwidth (FMCW), 20 period (FMCW), 20, 102—104 triangular,, 86—91 LPI, 36—37 Moving target indication, 107—108 MRSR, 55 Multifunction aperture, 13 Multilayer perceptron, 629—632 generalization, 630

N Narayanan noise radar, 215—219 PAF, PACF, 219—222 Netted LPI radar, 342-345 advantages, 346—347 LIPsimNet analysis, 353—360 MIMO, 349—352 orthogonal codes, 362—372 signal-to-noise ratio, 348—349 signal model, 349—352 use of noise in, 374, 376—377 Network centric warfare block diagram, 321 definition, 320 entropy, 333-336 global information grid, 320 information rate, 334 jam-to-signal ratio, 337—338 LPIsimNet, 338—345 metrics 326—337

854

Detecting and Classifying LPI Radar

network reach, 329—331 network richness, 333-336 receivers, 389—391 requirements, 322 sensor grid, 321 shooter grid, 322 Network reach, 329—331, 336 Network richness, 333-336 Noise radar correlation receivers, 238—243 MALI, 59 millimeter wave, 238 Narayanan design, 215—222 netted radar, 374, 376—377 principles, 212—215 random noise FMCW plus sine, 227, 229—234 random noise plus FMCW, 222—227 ultrawideband, 210—212

O OLPI, 13, 179—182 OODA, 324—325, 326 Operational tempo, 324 maximum, 336—337 Origin of LPI, 29 Orthogonal waveforms, 358, 361—362 frequency hopping, 370—375 MIMO, 350—352 OTHR, 377—378 polyphase codes, 362—370 OTHR systems Doppler spectrum, 259—261 ionosphere, 253—261 netted configurations, 377—378 sky wave, 252—280 sky wave waveforms, 265—271 surface wave, 276, 281—294 surface wave waveforms, 282—288 OTHR waveforms, 249—251

P P1 code, 148—151 P2 code, 152—155

P3 code, 152, 156—157 P4 code, 157, 160—162 PA-5429 altimeter, 44 PAGE, 51—52 PALS landing system, 46 PANDORA, 113—114 Patriot, 607 Peak power, 14 Perceptron single, 625—628 Perfect codes, 128 PACF, 69, 74—75 Periodic ambiguity, 67—78 definition, 69 generating results, 713—714 periodicity, 70 Periodic autocorrelation, 67—78 definition, 68—69 Pencil beam, 6 Phased array, 6—7, 12 Phase code, 21 advantages, 125—126 binary, 128—133 period, 127 rate, 127 range resolution, 127 transmitted signal, 126—127 Pilot radar, 31—36 technical characteristics, 33 sensitivity, 34 Platform centric, 319—320 Pointer, 50—51 Polarization, 6 Polyphase codes, 134—162 Barker, 134—142 Frank, 139, 143—148 orthogonal, 362—372 P1, 148—151 P2, 152—155 P3, 152, 156—157 P4, 157, 160—162 Polytime codes, 163—178 T1(n), 163—165 T2(n), 165, 168—171 T3(n), 169, 172—174 T4(n), 169, 175—178 Position flexibility, 606

Index Power attenuation coeﬃcient, 25 average, 15 density, 24—25 peak, 15 received, 25 Power management, 16—18 in seeker, 17 using constant SNR, 310—312 Prime number, 715 Primitive roots, 717—719 Principal components analysis, 648, 656—660 Probability of detection, 19 Probability of false alarm, 19 Processing gain, 19 FMCW, 20 intercept receiver, 28—29 phase code, 20 random binary phase modulation, 211 PSK — see polyphase code Pulse compression, 15—16, 18—24 Pulse descriptor words, 396 Pulsed radar, 14

Q Quadrature mirror filtering BPSK analysis, 489—494, 773—776 complex input example, 482—487 Costas analysis, 499, 502—503 demodulation, 400 FMCW analysis, 487—489, 771— 772 Frank analysis, 777—780 Harr filter, 472—473 hybrid analysis, 499, 504—505 noise analysis, 499, 506—508 polyphase analysis, 494—498, 777— 780, 781—795 polytime analysis, 495, 499—501, 797—803 polyphase parameter extraction, 695—699 short-time Fourier transform, 469 tree structure, 476—482

855 two channel analysis, 474—476 wavelet decomposition, 468 wavelet filters, 472—474 wavelet transform, 469—471 Quiet radar, 30 Quiet naval radar CRM-100, 53

R Radar pulsed conventional, 14, 35, 42 warning receiver, 37 Radar cross section free space backscattering, 291 low values, 306—307 microwave 290 Shearman’s definition, 291 Radial basis function, 624, 632—633 Euclidean norm, 632 Gaussian basis, 633 Radon transform, 689—692 Random binary phase, 234—237 PAF, PACF, 236—237 Random noise plus FMCW, 222—227 PAF, PACF, 225—228 Random noise FMCW plus sine, 227, 229—234 PAF, PACF, 230—234 Range detection, 24—26 interception, 27—29 maximum detection, 26, 30, 32 maximum interception, 27—28, 30 resolution, 102 RBS-15, 58—60 Receiver (intercept) challenges with, 400—402 sensitivity, 27—28 Receiver (radar) bandwidth, 26 comparison, 392—396 correlation, 23, 238—243 matched, 22, 108—110 mismatched, 24, 75—78, 110—113 noise factor, 26 sensitivity, 25—26

856

Detecting and Classifying LPI Radar

Reduced residue, 716—717 Reflected power canceler, 83 Reference signal, 21—24 Regularization, 630—631 Tikhonov’s parameter, 631 Resolution cycle frequency, 519 FMCW range, 102 sky wave OTHR, 264 phase code range, 127 velocity, 102

S Samples per subcode, 73 Scan pattern, 11-13 confusion, 13 raster scan, 11 Sea clutter, 308—310 Sea state, 308 Search mode processing FMCW, 101—105 Seekers airborne, 58—61 torpedo, 61—62 Sensitivity comparison, 29 intercept receiver, 27—28 Pilot’s, 35 radar, 25—26 receiver comparison, 395—396 Sensor grid, 321 Sheridan levels, 622—623 Short-time Fourier transform, 469 in cyclic spectrum estimation, 518—519 Side lobes, 5—10 ACF, PACF, PAF, 70—71 definitions of peak, 70—71 OTHR 265—266 Side lobe ratio, 5 Taylor, 9—10 Sigmoid, 625—626, 630 Signal-to-noise ratio, Albersheim relation, 19 input required (radar), 26 for netted radar, 348—349

output (radar), 26 Pilot’s required, 35 processing gain, 19 time-bandwidth, related to 19 Sinc filter, 473—474 Single sideband modulator, 92—94 Situational awareness, 323 Sky wave OTHR, 249—251 critical frequency, 257 detection range, 271—276 distance coverage 259 footprint, 274—276 Doppler clutter, 259—261 ionosphere eﬀects, 253—259 JORN, 261—263 LPI considerations, 265—271 maximum usable frequency, 257 waveform repetition frequency, 266—269 SMART-L, 11 Spearfish, 61 Spiral antenna, 559—566 Archimedean, 563—564 equiangular, 560—562 logarithmic, 559 conical, 559—560 conical equiangular, 564—565 STC, 82 Subcode, 20 number of, 20 period, 20—22 Superconductor, 118—119 Suppression beginnings, 553 definitions, 552—553 Eagle example, 331-333 enemy integrated air defense, 551—553 look-through, 388—389 Surface wave OTHR, 249—251, 276, 278, 281 detection range, 288—294 LPI considerations, 282—288 SWR 503, 281—283 Surveillance systems airborne 56—58 ground based, 48—55

Index Swarm, 391—392 Swedish GLV200, 607 Swiss Air Guard, 607

857

V Variant, 52—53 Vietnam, 555—556

T W TALS landing system, 46 Taper, 7—9, 12 Tapped delay line, 22—24 Target-to-clutter ratio, 312—315 Taylor distribution, 8—10, 12 Temperature, 26 Time-bandwidth, FMCW, 19 Time-frequency processing Choi-Williams distribution, 445—463 Gabor distribution, 574—576 quadrature mirror filtering, 467—509 Wigner-Ville distribution, 405—442 Time-on-target, 11—13 Time smoothing, 520—522 Track mode processing FMCW, 104—105 Training, 631 Transmission line, 95—96 Transmit, multiple simultaneous, 13 peak power, 14 power management, 16 Transmitter continuous waveform, 15 solid state, 15 Twinkle transmission, 607

U UCARS landing system, 46 Ultra-low (side lobes), 8 Uniform window, 77 Unmanned aerial vehicle, 391—392, 595—596

Wavelet filters, 472—474 Wavelet transform, 469—471 Weighting Hamming window, 77, 104 Hann window, 77 Welsh construction (Costas), 193—195 Wiener filter, 692— Wigner-Ville dist. (WVD), 405—442 BPSK analysis, 421—426 comparing polyphase results, 431—433 complex input example, 411—414 continuous 1-D, 406 discrete WVD, 407 demodulation, 400 FMCW analysis, 419—421, 741—743 Frank analysis, 745—747 FSK, FSK/PSK results, 438—441 kernel generation, 408 operator (ELINT), 442 polyphase analysis, 426—428, 745—747, 749—758 polyphase parameter extraction, 688—695 polytime analysis, 429—437, 759—769 pseudo WVD, 407 real input example, 409—411 two-tone input example, 414—418 Wild Weasel, 555, 573, 597

Y YGBSM, 551

Recent Titles in the Artech House Radar Series David K. Barton, Series Editor Adaptive Antennas and Phased Arrays for Radar and Communications, Alan J. Fenn Advanced Techniques for Digital Receivers, Phillip E. Pace Advances in Direction-of-Arrival Estimation, Sathish Chandran, editor Airborne Pulsed Doppler Radar, Second Edition, Guy V. Morris and Linda Harkness, editors Bayesian Multiple Target Tracking, Lawrence D. Stone, Carl A. Barlow, and Thomas L. Corwin Beyond the Kalman Filter: Particle Filters for Tracking Applications, Branko Ristic, Sanjeev Arulampalam, and Neil Gordon Computer Simulation of Aerial Target Radar Scattering, Recognition, Detection, and Tracking, Yakov D. Shirman, editor Design and Analysis of Modern Tracking Systems, Samuel Blackman and Robert Popoli Detecting and Classifying Low Probability of Intercept Radar, Second Edition, Phillip E. Pace Digital Techniques for Wideband Receivers, Second Edition, James Tsui Electronic Intelligence: The Analysis of Radar Signals, Second Edition, Richard G. Wiley Electronic Warfare in the Information Age, D. Curtis Schleher ELINT: The Interception and Analysis of Radar Signals, Richard G. Wiley EW 101: A First Course in Electronic Warfare, David Adamy EW 102: A Second Course in Electronic Warfare, David L. Adamy

EW 103: Tactical Battlefield Communications Electronic Warfare, David Adamy Fourier Transforms in Radar and Signal Processing, David Brandwood Fundamentals of Electronic Warfare, Sergei A. Vakin, Lev N. Shustov, and Robert H. Dunwell Fundamentals of Short-Range FM Radar, Igor V. Komarov and Sergey M. Smolskiy Handbook of Computer Simulation in Radio Engineering, Communications, and Radar, Sergey A. Leonov and Alexander I. Leonov High-Resolution Radar, Second Edition, Donald R. Wehner Introduction to Electronic Defense Systems, Second Edition, Filippo Neri Introduction to Electronic Warfare, D. Curtis Schleher Introduction to Electronic Warfare Modeling and Simulation, David L. Adamy Introduction to RF Equipment and System Design, Pekka Eskelinen Microwave Radar: Imaging and Advanced Concepts, Roger J. Sullivan Millimeter-Wave Radar Targets and Clutter, Gennadiy P. Kulemin Modern Radar Systems, Second Edition, Hamish Meikle Modern Radar System Analysis, David K. Barton Modern Radar System Analysis Software and User's Manual, Version 3.0, David K. Barton Multitarget-Multisensor Tracking: Applications and Advances Volume III, Yaakov Bar-Shalom and William Dale Blair, editors Principles of High-Resolution Radar, August W. Rihaczek Principles of Radar and Sonar Signal Processing, François Le Chevalier Radar Cross Section, Second Edition, Eugene F. Knott et al. Radar Evaluation Handbook, David K. Barton et al.

Radar Meteorology, Henri Sauvageot Radar Reflectivity of Land and Sea, Third Edition, Maurice W. Long Radar Resolution and Complex-Image Analysis, August W. Rihaczek and Stephen J. Hershkowitz Radar Signal Processing and Adaptive Systems, Ramon Nitzberg Radar System Analysis, Design, and Simulation, Eyung W. Kang Radar System Analysis and Modeling, David K. Barton Radar System Performance Modeling, Second Edition, G. Richard Curry Radar Technology Encyclopedia, David K. Barton and Sergey A. Leonov, editors Range-Doppler Radar Imaging and Motion Compensation, Jae Sok Son et al. Signal Detection and Estimation, Second Edition, Mourad Barkat Space-Time Adaptive Processing for Radar, J. R. Guerci Theory and Practice of Radar Target Identification, August W. Rihaczek and Stephen J. Hershkowitz Time-Frequency Transforms for Radar Imaging and Signal Analysis, Victor C. Chen and Hao Ling For further information on these and other Artech House titles, including previously considered out-of-print books now available through our In-Print-Forever® (IPF®) program, contact: Artech House

Artech House

685 Canton Street

46 Gillingham Street

Norwood, MA 02062

London SW1V 1AH UK

Phone: 781-769-9750

Phone: +44 (0)20 7596-8750

Fax: 781-769-6334

Fax: +44 (0)20 7630-0166

e-mail: [email protected]

e-mail: [email protected]

Find us on the World Wide Web at: www.artechhouse.com