High-order modulation for optical fiber transmission

Springer Series in

optical sciences founded by H.K.V. Lotsch Editor-in-Chief: W. T. Rhodes, Atlanta Editorial Board: A. Adibi, Atlanta T. Asakura, Sapporo T. W. H¨ansch, Garching T. Kamiya, Tokyo F. Krausz, Garching B. Monemar, Link¨oping H. Venghaus, Berlin H. Weber, Berlin H. Weinfurter, M¨unchen

143

Springer Series in

optical sciences The Springer Series in Optical Sciences, under the leadership of Editor-in-Chief William T. Rhodes, Georgia Institute of Technology, USA, provides an expanding selection of research monographs in all major areas of optics: lasers and quantum optics, ultrafast phenomena, optical spectroscopy techniques, optoelectronics, quantum information, information optics, applied laser technology, industrial applications, and other topics of contemporary interest. With this broad coverage of topics, the series is of use to all research scientists and engineers who need up-to-date reference books. The editors encourage prospective authors to correspond with them in advance of submitting a manuscript. Submission of manuscripts should be made to the Editor-in-Chief or one of the Editors. See also www.springer.com/series/624

Editor-in-Chief William T. Rhodes Georgia Institute of Technology School of Electrical and Computer Engineering Atlanta, GA 30332-0250, USA E-mail: [email protected]

Editorial Board Ali Adibi

Bo Monemar

Georgia Institute of Technology School of Electrical and Computer Engineering Atlanta, GA 30332-0250, USA E-mail: [email protected]

Department of Physics and Measurement Technology Materials Science Division Link¨oping University 58183 Link¨oping, Sweden E-mail: [email protected]

Toshimitsu Asakura Hokkai-Gakuen University Faculty of Engineering 1-1, Minami-26, Nishi 11, Chuo-ku Sapporo, Hokkaido 064-0926, Japan E-mail: [email protected]

Theodor W. H¨ansch Max-Planck-Institut f¨ur Quantenoptik Hans-Kopfermann-Straße 1 85748 Garching, Germany E-mail: [email protected]

Takeshi Kamiya Ministry of Education, Culture, Sports Science and Technology National Institution for Academic Degrees 3-29-1 Otsuka, Bunkyo-ku Tokyo 112-0012, Japan E-mail: [email protected]

Ferenc Krausz Ludwig-Maximilians-Universit¨at M¨unchen Lehrstuhl f¨ur Experimentelle Physik Am Coulombwall 1 85748 Garching, Germany and Max-Planck-Institut f¨ur Quantenoptik Hans-Kopfermann-Straße 1 85748 Garching, Germany E-mail: [email protected]

Herbert Venghaus Fraunhofer Institut f¨ur Nachrichtentechnik Heinrich-Hertz-Institut Einsteinufer 37 10587 Berlin, Germany E-mail: [email protected]

Horst Weber Technische Universit¨at Berlin Optisches Institut Straße des 17. Juni 135 10623 Berlin, Germany E-mail: [email protected]

Harald Weinfurter Ludwig-Maximilians-Universit¨at M Sektion Physik Schellingstraße 4/III 80799 M¨unchen, Germany E-mail: [email protected]

Matthias Seimetz

High-Order Modulation for Optical Fiber Transmission With 132 Figures

123

Dr. Matthias Seimetz Fraunhofer-Institut für Nachrichtentechnik Heinrich-Hertz-Institut Einsteinufer 37 10587 Berlin Germany [email protected]

ISSN 0342-4111 e-ISSN 1556-1534 ISBN 978-3-540-93770-8 e-ISBN 978-3-540-93771-5 DOI 10.1007/978-3-540-93771-5 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009926839 c Springer-Verlag Berlin Heidelberg 2009  This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: eStudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

To my parents

Preface

The deployment of high-order modulation formats in optical fiber transmission systems is presently seen as a promising way of increasing spectral efficiency and of making better use of the capacity of currently existing fiber infrastructure. Catering to this interest, this book presents possible ways of generating and detecting optical signals with high-order phase and quadrature amplitude modulation and characterizes their system and transmission properties. Several implementation options for high-order modulation optical transmitters are possible. Their optical and electrical parts are described and their individual signal properties are discussed. Receiver concepts with direct detection, homodyne differential detection and homodyne synchronous detection are illustrated—starting with optical frontends and ending with electrical data recovery. The description of transmitters and receivers provided in the first part of the book does not only help to demonstrate their functioning, but also allows their complexity and practicability to be estimated and compared. To advance understanding of the system and transmission behavior of high-order modulation formats for optical fiber transmission, various system parameters such as noise performances, optimal receiver filter bandwidths, required laser linewidths and the chromatic dispersion and self phase modulation tolerances of a wide range of modulation formats are highlighted in the second part of the book—considering different line codes and many transmitter and receiver configurations. Currently, the determination of attainable transmission distances for multi-span long-haul transmission using high-order modulation formats represents an exciting field of research. Recent results in this area are also covered by this book. This monograph is intended for researchers in the field of optical communications, as well as for system designers who would like to learn about the properties and complexity of optical systems employing high-order modulation. The author wishes to express his cordial thanks to his colleagues from the Fraunhofer Institute for Telecommunications, Heinrich-Hertz-Institut, and to Prof. Petermann for their technical assistance. Berlin, January 2009

Matthias Seimetz vii

Contents

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Part I Transmitters and Receivers 2

Transmitter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Transmitter Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 External Optical Modulators . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Pulse Carvers and Impulse Shapers . . . . . . . . . . . . . . . . . . . . . 2.2 Multi-Level Signaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 ASK Transmitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 DPSK Transmitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Serial DPSK Transmitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Parallel DPSK Transmitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Differential Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.4 Signal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Star QAM Transmitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Square QAM Transmitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Differential Quadrant Encoding . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Serial Square QAM Transmitter . . . . . . . . . . . . . . . . . . . . . . . . 2.6.3 Conventional IQ Transmitter . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.4 Enhanced IQ Transmitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.5 Tandem-QPSK Transmitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.6 Multi-Parallel MZM Transmitter . . . . . . . . . . . . . . . . . . . . . . . 2.6.7 Signal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

Receiver Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.1 Receiver Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.1.1 Optical and Electrical Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

15 15 15 18 21 23 23 25 26 27 28 32 34 37 37 38 42 47 51 52 54 56

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3.1.2 Delay Line Interferometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.1.3 2 × 4 90◦ Hybrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.1.4 3 × 3 Coupler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.2 Direct Detection Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.2.1 Direct Detection Receiver with DLIs . . . . . . . . . . . . . . . . . . . . 67 3.2.2 Direct Detection IQ Receiver with 2 × 4 90◦ Hybrid . . . . . . . 71 3.2.3 Data Recovery for Differential Detection . . . . . . . . . . . . . . . . 73 3.3 Fundamentals of Coherent Detection . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.3.1 Coherent Detection Principle . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.3.2 Coherent Detection with Amplifier Noise . . . . . . . . . . . . . . . . 82 3.3.3 Optical Quadrature Frontend . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.3.4 Polarization Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.4 Homodyne Receivers with Differential Detection . . . . . . . . . . . . . . . . 86 3.4.1 Phase Diversity Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.4.2 Digital Differential Demodulation . . . . . . . . . . . . . . . . . . . . . . 91 3.5 Homodyne Receivers with Synchronous Detection . . . . . . . . . . . . . . . 93 3.5.1 Carrier Synchronization Techniques . . . . . . . . . . . . . . . . . . . . 94 3.5.2 Optical Phase Locked Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.5.3 Digital Phase Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3.5.4 Data Recovery for Synchronous Detection . . . . . . . . . . . . . . . 111 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 4

Effort Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 4.1 Transmitter Complexity and Feasibility . . . . . . . . . . . . . . . . . . . . . . . . 119 4.2 Receiver Complexity and Feasibility . . . . . . . . . . . . . . . . . . . . . . . . . . 122

Part II System Performance 5

System Simulation Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.1 Data Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.2 Eye Opening Penalty for Multi-Level Eyes . . . . . . . . . . . . . . . . . . . . . 131 5.3 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 5.4 Semi-Analytical BER Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.4.1 DBPSK Direct Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.4.2 Extension to Higher-Order DPSK and Star QAM . . . . . . . . . 138 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

6

Fiber Propagation Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 6.1 Fiber Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 6.2 Chromatic Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 6.3 Kerr Nonlinearities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 6.4 Other Propagation Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 6.4.1 Nonlinear Scattering Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 6.4.2 Polarization Mode Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . 151 6.4.3 Nonlinear Phase Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

Contents

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7

Back-to-Back and Single-Span Transmission . . . . . . . . . . . . . . . . . . . . . . 155 7.1 Systems with Direct Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 7.1.1 OSNR Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 7.1.2 Optimal Receiver Filter Bandwidths . . . . . . . . . . . . . . . . . . . . 160 7.1.3 Laser Linewidth Requirements . . . . . . . . . . . . . . . . . . . . . . . . . 164 7.1.4 Chromatic Dispersion Tolerances . . . . . . . . . . . . . . . . . . . . . . . 166 7.1.5 Self Phase Modulation Tolerances . . . . . . . . . . . . . . . . . . . . . . 168 7.1.6 Nonlinear Phase Shift Compensation . . . . . . . . . . . . . . . . . . . . 171 7.1.7 Parameter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 7.2 Systems with Homodyne Differential Detection . . . . . . . . . . . . . . . . . 177 7.2.1 Noise Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 7.2.2 Laser Linewidth Requirements . . . . . . . . . . . . . . . . . . . . . . . . . 181 7.2.3 Transmission Parameter Tolerances . . . . . . . . . . . . . . . . . . . . . 182 7.2.4 Parameter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 7.3 Systems with Homodyne Synchronous Detection . . . . . . . . . . . . . . . . 185 7.3.1 Noise Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 7.3.2 Laser Linewidth Requirements . . . . . . . . . . . . . . . . . . . . . . . . . 188 7.3.3 Chromatic Dispersion Tolerances . . . . . . . . . . . . . . . . . . . . . . . 194 7.3.4 Self Phase Modulation Tolerances . . . . . . . . . . . . . . . . . . . . . . 198 7.3.5 Nonlinear Phase Shift Compensation . . . . . . . . . . . . . . . . . . . . 199 7.3.6 Parameter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

8

Multi-Span Long-Haul Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 8.1 8PSK Multi-Span Transmission Experiments . . . . . . . . . . . . . . . . . . . 208 8.1.1 Optical Inline CD Compensation . . . . . . . . . . . . . . . . . . . . . . . 208 8.1.2 Electrical CD Compensation at the Receiver . . . . . . . . . . . . . . 212 8.2 Star 16QAM Multi-Span Transmission Experiments . . . . . . . . . . . . . 213 8.2.1 Single-Channel Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 8.2.2 WDM Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 8.3 Comparison of Transmission Distances . . . . . . . . . . . . . . . . . . . . . . . . 219 8.4 Nonlinear Phase Shift Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . 221 8.4.1 Systems with Optical Inline CD Compensation . . . . . . . . . . . 221 8.4.2 Systems with Electrical CD Compensation . . . . . . . . . . . . . . . 224 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

9

Performance Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 9.1 Migration to Higher-Order Formats—Parameter Trends . . . . . . . . . . 227 9.2 Impact of the System Configuration and Pulse Shape . . . . . . . . . . . . . 230 9.3 Reduction of Attainable Transmission Distances . . . . . . . . . . . . . . . . . 232 9.4 Goals of Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236

A

Differential Encoders for 8DPSK / 16DPSK . . . . . . . . . . . . . . . . . . . . . . . 239

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Contents

B

Theoretical BER Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

Acronyms

Mathematical Symbols α αd B αN L β0 β1 β2 β3 χ1 χ3 δ1 δ2 1e 1f 1 f max 1λ 1n e f f (t) 1νe f f 1νlo 1νs 1ω 1ωest 1ωestmax δ P(t) 18i 1φk 1ϕ(t) 1ϕk 1ϕ I (t) 1ϕ M Z M (t)

Fiber attenuation Fiber attenuation in decibels Scaling factor for nonlinear phase noise compensation Propagation constant at ω = ωs Group delay per length unit at ω = ωs Chromatic dispersion at ω = ωs Dispersion slope at ω = ωs Linear susceptibility Third-order nonlinear susceptibility Spreading in the upper level of an eye diagram Spreading in the lower level of an eye diagram Eye spreading Reference noise bandwidth (frequency scale) Maximum resolvable frequency offset estimate Reference noise bandwidth (wavelength scale) Change of the effective refractive index Beat-linewidth after coherent detection Linewidth of the LO Linewidth of the signal laser Angular frequency offset after coherent detection Angular frequency offset estimate Maximum resolvable angular frequency offset estimate Laser intensity fluctuations due to intensity noise Phase error difference accumulating in D blocks Differential instantaneous phase samples Modulation phase difference of two consecutive symbols Modulation phase difference samples Relative phase shift of the MZM-branches in the I -arm Relative phase shift of the MZM-branches xiii

xiv

1ϕn (t) 1ϕn k 1ϕn s (t) 1ϕn k,d 1ϕ Q (t) 1t 1τ P M D ǫ0 ǫre f f ǫr η γ λ 3 λp λs ν  ω ω0 ωC W ωc ωlo ωs ωV C O ϕ(t) ϕ(t) ˙ 8(t) φ(t) ϕ(z, t) ϕ0 (t) ϕ1 (t) ϕ2 (t) ϕbk ϕ DL I ϕ DL I I ϕ DL I Q 8ek ϕ I Q M (t) ϕ I (t) 8i ϕk 8k φk ϕlo

Acronyms

Random phase change due to overall laser phase noise Overall laser phase noise samples Random phase change due to signal laser phase noise Random phase change due to phase noise after d symbols Relative phase shift of the MZM-branches in the Q-arm Rise time of the electrical driving signals Group delay difference of the PSP due to PMD Vacuum permittivity Effective relative permittivity Relative permittivity Quantum efficiency Nonlinear propagation coefficient Wavelength Diagonal matrix with eigenvalues of matrix A Eigenvalues of the matrix A Signal laser wavelength Filter order Normalized angular frequency ω − ωs Angular frequency Band-pass filter center frequency Angular frequency of a CW laser 3 dB bandwidth LO angular frequency Signal laser angular frequency Angular frequency of an electrical VCO Modulation phase Chirp of the optical information signal Phase error due to frequency offset and laser phase noise Instantaneous phase Time and location dependent modulation phase Initial phase offset after coherent detection Phase modulation in the upper MZM branch Phase modulation in the lower MZM branch Phase of a symbol before differential encoding Phase shift of a DLI Phase shift of the DLI in the I -branch Phase shift of the DLI in the Q-branch Residual phase error of the k-th symbol Phase modulation of an IQM Phase modulation in the I -arm (enhanced IQ TX) Corrected phase error estimate of the i-th block Phase of a symbol after differential encoding Phase error samples Instantaneous phase samples LO initial phase

Acronyms

ϕn (t) ϕn k ϕnlo (t) ϕn s (t) ϕN L ϕ P M (t) ϕ Q (t) ϕs 8 yk (s) ψ ψ˜ 9i σ2 σϕ2L σϕ2N L σϕ2N L ,Comp τd τgr τgr0 A An A A(t) a(t) a(z, t) abk Ae f f a I Q M (t) a I (t) Ak ak ak′ {an } a Q (t) b Bel bki bk, p bk bk Bn bn k Bopt q bk Bs

xv

Overall laser phase noise after coherent detection Overall laser phase noise samples LO phase noise Signal laser phase noise Nonlinear phase shift Phase modulation of a phase modulator Phase modulation in the Q-arm (enhanced IQ TX) Signal laser initial phase Moment generating function of y(tk ) Arbitrary phase shift Arbitrary phase shift at the hybrid input Phase error estimate of the i-th block Noise variance Phase error variance of the linear noise Nonlinear phase shift variance Nonlinear phase shift variance after compensation Loop delay time Group delay per length unit Group delay for ω = 0 Symbol alphabet Elements of alphabet A Receiver matrix Normalized complex modulation envelope Normalized modulation amplitude Time and location dependent modulation amplitude Amplitude of a symbol Effective core area Amplitude modulation of an IQM Amplitude modulation in the I -arm (enhanced IQ TX) Normalized complex modulation envelope samples Normalized modulation amplitude samples Modulation amplitude samples after phase estimation Data Sequence with elements an , n = (1..b) Amplitude modulation in the Q-arm (enhanced IQ TX) Length of a bit sequence Electrical receiver filter 3 dB bandwidth In-phase coordinate of a symbol Elements of vector bk Complex symbol in the k-th symbol interval Auxiliary vector equal to xk · U Optical noise bandwidth n-th bit of a symbol with m bits in the k-th symbol interval Optical receiver filter 3 dB bandwidth Quadrature coordinate of a symbol Signal bandwidth

xvi

BW D M c cn k d D D D(z, t) Dλ de Dmax dn k E e e Ecw (t) E I (t) elo Elo (t) ep E Q (t) es E s (t) E s (z, jω) E s (z, t) E˜ s (z, t) E s,avg ex ey ek/⊥ F F f Fd B F p, p fs G Gr h H H1 H2 He ( f ) Ho ( f ) H p, p I

Acronyms

Electrical bandwidth for WDM channel separation Speed of light n-th Square QAM coder output bit (k-th symbol interval) Delay in number of symbol durations Processing delay in number of blocks Electric flux density vector Time and location dependent electric flux density Dispersion parameter Height of an eye diagram Maximal accumulated chromatic dispersion n-th differentially encoded bit of a symbol with m bits Electrical field vector Electron charge Row vector used for Fourier transform Normalized electrical field of the signal laser Normalized electrical field in the I -branch LO polarization unit vector Normalized electrical field of the LO Elements of vector e Normalized electrical field in the Q-branch Signal laser polarization unit vector Normalized electrical signal field Fourier transform of E s (z, t) Time and location dependent electrical signal field p Electrical field normalized to Ae f f Average energy per symbol Polarization unit vector in x-direction Polarization unit vector in y-direction Polarization unit vectors of the noise Noise figure of an optical amplifier Diagonal matrix with Fourier frequency components Frequency Noise figure of an optical amplifier in decibels Diagonal elements of the matrix F Signal laser frequency Optical amplifier gain Resistor’s conductance Planck constant Diagonal transfer matrix of the optical receiver filter Receiver transfer matrix (upper DLI output) Receiver transfer matrix (lower DLI output) Transfer function of the electrical receiver filter Transfer function of the optical receiver filter Diagonal elements of the matrix H Identity matrix

Acronyms

I (t) I Ik I I D (t) I I (t) Ik ik I M (t) In I Qk I Q (t) i sh i sh I i sh Q i th kB L l le f f lel M m N n(t) n(ω, x) N0 n0 n2 n k/⊥ (t) nk/⊥ nB nc n ck n clad NClass I n cor e ne f f NF S NFW M nI n Ik ni nk N L O−AS E n L O−AS E (t) n p,k/⊥

xvii

Photocurrent in the I -branch after phase noise cancelation Received in-phase electrical signal samples Photocurrent in the intensity detection branch Photocurrent in the I -branch In-phase signal samples after phase estimation In-phase coordinate of a symbol, scaled to unity Corrective signal within an OPLL n-th order modified Bessel function of the first kind Received quadrature electrical signal samples Photocurrent in the Q-branch Shot-noise photocurrent Shot-noise photocurrent in the I -branch Shot-noise photocurrent in the Q-branch Thermal noise photocurrent Boltzmann constant Total number of samples considered for Fourier expansion Fiber length per span Effective length Interaction length Number of symbols Number of bits per symbol Phase estimation block length Optical amplifier noise Frequency and intensity dependent refractive index Amplifier noise two-sided PSD in one polarization Linear refractive index Nonlinear index coefficient Parallel / orthogonally polarized noise components Vector with the noise coefficients Binary data sequence order Complex noise Complex noise samples Refractive index of the fiber cladding Number of Class I symbols in a block of N symbols Refractive index of the fiber core Effective refractive index Number of fiber spans Number of mixing products generated by FWM In-phase component of complex noise In-phase noise samples Phase estimation segment counter Complex noise samples after raising to the M-th power Power spectral density of the LO-ASE noise LO-ASE noise Elements of vector nk/⊥

xviii

N ph nQ n Qk nS n sh k n sp NW D M P P(t) p(t) P(z, t) PL Plo PN L PN L (z, t) Pn PR X,avg PR X (t) Ps Ps,avg Psym PT X,avg PT X (t) p yk (y) Q Q(t) Qk qk Q p,q R r r1 r2 rB rS Sλ si,n sn sq,n si,n k sn k sq,n k S pS T t

Acronyms

Number of phase states Quadrature component of complex noise Quadrature noise samples Symbol sequence order Complex shot-noise samples Spontaneous emission parameter Number of WDM channels Electric polarization vector Instantaneous optical power Pulse shape of the electrical driving signals Time and location dependent optical power Linear electric polarization vector Power of the LO Nonlinear electric polarization vector Time and location dependent nonlinear polarization Noise power Average received optical power Received instantaneous optical power Power of the signal laser Average signal power Symbol error probability Average fiber input power Instantaneous fiber input power Probability density function of y(tk ) Transfer matrix of the electrical receiver filter Photocurrent in the Q-branch after phase noise cancelation Quadrature signal samples after phase estimation Quadrature coordinate of a symbol, scaled to unity Elements of the matrix Q Responsivity Core radius Amplitude of the inner circle of a Star QAM constellation Amplitude of the outer circle of a Star QAM constellation Bit rate Symbol rate Dispersion slope parameter Decision threshold in the in-phase branch Decision threshold for arg-decision Decision threshold in the quadrature branch Decision result at threshold si,n Decision result at threshold sn Decision result at threshold sq,n Number of samples per symbol Temperature Time

Acronyms

t′ T0 TB Tblock tc Te tk TS U u(t) u 1 (t) u 2 (t) u I (t) u I M Z M (t) u I P M (t) u I M (t) u P M (t) u Q (t) u Q M Z M (t) u Q P M (t) Vπ Vπ1 Vπ2 Wϕ˙ns W E cw (ω) X (t) x(t) x(z, t) x(z, ˜ t) x(z, jω) xk xk, p Xk X kClass I X k′ y(tk ) y˜ (tk ) zk/⊥ z p,k/⊥

xix

Retarded time scale t − τgr · z Time interval observed for semi-analytical BER estimation Duration of one bit Duration of one block for phase estimation Coherence time 1/e pulse duration of the electrical driving signals Sampling instants Duration of one symbol Unitary matrix with eigenvectors of matrix A Driving voltage Driving voltage for the upper MZM branch Driving voltage for the lower MZM branch Driving voltage of the MZM in the I -arm MZM driving voltage for the enhanced IQ TX (I -arm) PM driving voltage for the enhanced IQ TX (I -arm) Driving voltage for intensity modulation Driving voltage of a PM Driving voltage of the MZM in the Q-arm MZM driving voltage for the enhanced IQ TX (Q-arm) PM driving voltage for the enhanced IQ TX (Q-arm) Voltage for π phase shift (MZM power transfer function) Driving voltage for a phase shift of π, upper MZM branch Driving voltage for a phase shift of π, lower MZM branch Power spectral density of the signal laser frequency noise Power spectral density of the emitted CW light Received electrical signal phasor Complex signal envelope Time and location dependent complex p signal envelope Complex envelope normalized to Ae f f Fourier transform of x(z, t) Vector with Fourier coefficients of x(t) Elements of vector xk Received complex electrical signal samples Received Class I complex electrical signal samples Complex electrical signal samples after phase estimation Photocurrent at the decision gate at sampling instants tk Photocurrent after the BD at sampling instants tk Auxiliary vector equal to nk/⊥ · U Elements of vector zk/⊥

xx

Acronyms

Abbreviations A/D AFC ASE ASK AWGN BD BER BPSK BtB CD CL CMA CSRZ CW DB dB DBBS DBPSK DBSS DC DCF DD DFB DLI DMF DMT DPSK DQPSK DSF DSL DSP ECL EDE EDFA EO EOP FEC FF FFT FIR FSK FWM HHI

Analog to Digital Automatic Frequency Control Amplified Spontaneous Emission Amplitude Shift Keying Additive White Gaussian Noise Balanced Detector Bit Error Ratio Binary Phase Shift Keying Back-to-Back Chromatic Dispersion Closed Loop Constant Modulus Algorithm Carrier-Suppressed Return to Zero Continuous Wave Duobinary Decibel De Bruijn Bit Sequence Differential Binary Phase Shift Keying De Bruijn Symbol Sequence Direct Current Dispersion Compensating Fiber Direct Detection Distributed Feedback Delay Line Interferometer Dispersion Managed Fiber Discrete Multi-Tone Differential Phase Shift Keying Differential Quadrature Phase Shift Keying Dispersion Shifted Fiber Digital Subscriber Line Digital Signal Processor External Cavity Laser Electronic Distortion Equalization Erbium Doped Fiber Amplifier Eye Opening Eye Opening Penalty Forward Error Correction Feed Forward Fast Fourier Transform Finite Impulse Response Frequency Shift Keying Four Wave Mixing Heinrich-Hertz-Institut

Acronyms

I IF IM IP IQ IQM IS ISI LAN LED LMS LO LPF MC MGF MMA MMI MPOLSK MZM NRZ OOK OPLL OSNR OTDM PBC PBS PD PDF PDM PE PLL PM PMD PRBS PS PSD PSK PSP Q QAM QPSK RIN RR RX RZ

xxi

In-phase Intermediate Frequency Intensity Modulation Internet Protocol In-phase Quadrature In-phase Quadrature Modulator Impulse Shaper Inter-Symbol Interference Local Area Network Light Emitting Diode Least Mean Square Local Oscillator Low-pass Filter Monte Carlo Moment Generating Function Multiple Moduli Algorithm Multi-Mode Interference M-ary Polarization Shift Keying Mach-Zehnder Modulator Non-Return to Zero On-Off Keying Optical Phase Locked Loop Optical Signal to Noise Ratio Optical Time Division Multiplexing Polarization Beam Combiner Polarization Beam Splitter Photodiode Probability Density Function Polarization Division Multiplexing Phase Estimation Phase Locked Loop Phase Modulator Polarization Mode Dispersion Pseudo Random Binary Sequence Power Splitter Power Spectral Density Phase Shift Keying Principle States of Polarization Quadrature Quadrature Amplitude Modulation Quadrature Phase Shift Keying Relative Intensity Noise Ring Ratio Receiver Return to Zero

xxii

SBS SMF SNR SPM SRS SSMF TDC TX UMTS VCO WDM WLAN XPM

Acronyms

Stimulated Brillouin Scattering Single Mode Fiber Signal to Noise Ratio Self Phase Modulation Stimulated Raman Scattering Standard Single Mode Fiber Tunable Dispersion Compensation Transmitter Universal Mobile Telecommunications System Voltage Controlled Oscillator Wavelength Division Multiplexing Wireless Local Area Network Cross Phase Modulation

Chapter 1

Introduction

Abstract After a brief discussion of the evolution of optical networks in the last two decades, advanced modulation and coherent detection are pointed out as emerging key technologies for fulfilling the expected bandwidth demands of future optical fiber networks. Subsequently, an overview of current developments and today’s state of research in the fields of advanced modulation and coherent detection is given. Finally, the scope of this book is localized and the chapter’s contents are shortly outlined.

For millions of people around the world, surfing the Internet day to day to get information, check e-mails, dispatch shopping comfortably from their desk and download multimedia and data files has become a natural habit. However, for most of them, the sophisticated technology they are using to connect to the central office over a simple twisted copper pair with satisfactory transmission speed remains concealed. Originally laid to transmit voice signals up to 4 kHz bandwidth, twisted pairs could be utilized to transmit data signals up to 64 kbit/s with cable modems in the mid nineties. Today, digital subscriber line (DSL) technology has captured the market. Several hundred millions of subscribers worldwide have broadband access to the Internet via DSL, with transmission speeds of up to several Mbit/s in the local loop. These data rates can only be provided by using advanced transmission techniques like very high-order quadrature amplitude modulation (QAM) and discrete multi-tone (DMT), where the data band is divided into hundreds of separate channels, which are adaptively QAM modulated with the aid of intelligent bit loading algorithms [15]. In contrast to electrical systems, optical fiber communication systems are still very distant from a commercial practical implementation of high-order modulation formats. The difficult-to-handle optical phase and technological difficulties with cost-effectively manufacturing more complex high-speed electronic devices restrict the presently installed optical systems almost exclusively to a simple deployment of intensity modulation (IM) on the transmitter side and direct detection (DD) at the receiver end. For optical systems, all system concepts beyond IM-DD can still be

M. Seimetz, High-Order Modulation for Optical Fiber Transmission, Springer Series in Optical Sciences 143, DOI 10.1007/978-3-540-93771-5 1, c Springer-Verlag Berlin Heidelberg 2009

1

2

1 Introduction

qualified as advanced. However, favored by the very low fiber attenuation of about 0.2 dB/km across several THz of bandwidth, optical fiber communication is superior to other wireline or wireless communication technologies and can support very high capacities of several Tbit/s over many thousand kilometers, even when advanced modulation formats are not employed.

Reduction of Costs by Innovative Technologies

Fig. 1.1 Enhancement of capacit y · distance/cost through innovative technology in optical communication networks, based on [12]

Capacity ⋅ Distance / Cost

With the objective of reducing costs per information bit in optical communication networks, per fiber capacities and optical transparent transmission lengths have been stepped up by the introduction of new technology in recent years. A crucial innovation was the Erbium-doped fiber amplifier (EDFA) at the beginning of the nineties [30]. Using EDFAs, long distances can be bridged without electro–optical conversion. Furthermore, the wavelength division multiplex (WDM) technology which allows a lot of wavelength channels to be simultaneously transmitted over one fiber, has benefited from the high bandwidth of the EDFA, since several WDM channels can be amplified using only one EDFA. During the nineties, the capacity-distance product was further enhanced by employing other optical key technologies such as optical dispersion compensation, Raman amplification and advanced optical fibers, as well as through electronic means such as forward error correction (FEC) and the adaptive compensation of chromatic dispersion (CD) and polarization mode dispersion (PMD). Figure 1.1 illustrates the enhancement of capacit y · distance/cost through innovative technology.

Coherent Adaptive Detection CD & PMD Kerr Comp. Comp. Raman Advanced Amp. Modulation FEC

WDM CD Comp.

Present

EDFA

Time

In WDM systems, cost reduction is not only achieved by increasing the transparent transmission lengths and the transmitted per fiber capacities, but also by sharing optical components over many channels. An important performance measure is spectral efficiency, which is defined as the ratio of the data rate per channel to the WDM channel spacing. For higher spectral efficiency and a fixed per-channel

1 Introduction

3

data rate, more channels can be placed within the limited wavelength window of the shared components so that the transmitted data volume increases. One possible approach aimed to increase the capacity of ultra long-haul transoceanic submarine WDM transmission systems, is making the most of the available bandwidth of standard C-band optical amplifiers by increasing spectral efficiency. Two emerging optical key technologies which are seen as a possible further step towards even more cost effective optical networks, are advanced optical modulation and coherent detection. Through the adoption of high-order modulation formats, higher spectral efficiencies can be reached through the reduced symbol rate and the spectral narrowing therewith aligned. Furthermore, as was theoretically shown in [13], only coherent detection permits convergence to the ultimate limits of spectral efficiency. Several bit/s/Hz per polarization can be transmitted with unconstrained coherent detection, even considering the impact of fiber nonlinearity. On the other hand, when employing these new technologies, the complexity of the transmitters and receivers increases, so that cost reduction due to higher spectral efficiency has to be weighed up against higher hardware costs, as illustrated in Fig. 1.2. Continuing research and future investigations will help judge the economic potential of highorder modulation and coherent detection. Thereby, the transmission characteristics and the reachable transparent transmission lengths, which are largely unknown for high-order modulation formats, must be also considered.

Advanced Modulation Coherent Detection

More complex components

Higher spectral efficiency, sharing components

Reach? Higher costs

Cost reduction

Fig. 1.2 Economical issues for the introduction of advanced modulation and coherent detection

Advanced Optical Modulation The electrical field in single mode fibers (SMF) exhibits three physical parameters that can be used to carry information. Besides amplitude and phase, polarization can also be exploited for modulation. Plenty of different modulation formats based on the modulation of all the quadratures of the optical field were proposed in the early nineties, primarily in association with coherent detection. However, these investigations received relatively little attention because the necessary complex high-speed electronics were rarely available. Moreover, the emergence of the EDFA offered

4

1 Introduction

completely new perspectives for simple IM-DD systems so that there was enough potential to increase capacity even without high-order modulation. Thus, the investigation of high-order modulation formats remained mainly confined to the description of some transmitter and receiver structures and the calculation of theoretical bit error ratio (BER) noise performances. A summary of this early work can be found for instance in [2]. Having optimized optical systems with binary intensity modulation (also denoted as on–off keying, OOK) and direct detection over the years using the technologies described above, a new interest in alternative optical modulation formats emerged in the late nineties. At first, there was interest in obtaining higher robustness against fiber propagation effects and extending transmission reach, rather than the pursuit of higher spectral efficiencies. Differential binary phase shift keying (DBPSK, sometimes simply denoted as DPSK) was shown to feature higher robustness against nonlinear effects [31, 34]. The DBPSK format seemed to be attractive because direct detection can be further employed by placing a simple optical interferometer in front of the photodiode, so that the effort growth compared to systems with IM-DD is relatively small. Moreover, the influence of the optical pulse shape was examined, and return to zero (RZ) signals were shown to have different transmission properties than nonreturn to zero (NRZ) signals. Data modulation formats with auxiliary phase coding attracted attention in the optimization of the transmission behavior of binary intensity modulation. For instance, optical duobinary (DB) exhibits higher tolerance against chromatic dispersion. Modulation formats with auxiliary phase coding are not covered by this book. Further information can be obtained from [52]. In recent years, the investigation of optical high-order modulation formats has begun to play an important role in several research projects. By encoding m = log2 M data bits on M symbols, the symbol rate is reduced by m compared to the data rate, and higher spectral efficiencies can be obtained due to the spectral narrowing. On the one hand, high-order modulation allows upgrading to higher channel data rates by using existing lower-speed equipment, and thus exceeding the limits of present high-speed electronics and digital signal processing. On the other hand—when keeping the data rate constant—the transmission with lower symbol rates allows for smaller channel spacings and brings about a higher tolerance against transmission impairments such as chromatic dispersion and polarization mode dispersion. However, these benefits are accompanied by a reduced tolerance to noise and self phase modulation (SPM), and with a higher complexity of components. The most simple optical multi-level signaling scheme is M-ary amplitude shift keying (ASK), where information is encoded in several intensity levels. It was shown in [49] and [56], that M-ary ASK requires high optical signal to noise ratios (OSNR) for direct detection, especially in optically amplified links due to the intensity dependence of the signal-spontaneous beat noise. For instance, a 2.5 times higher dispersion tolerance compared to OOK can be achieved by 4ASK, but only among acceptance of a 5 dB power penalty due to noise. Thus, the use of M-ary ASK formats should mainly be considered for short reach applications. M-ary ASK formats are not further discussed in this book.

1 Introduction

5

As the logical next step after DBPSK, differential quadrature phase shift keying (DQPSK) was the first optical multi-level phase modulation format whose transmission characteristics were intensively examined, for instance in [32, 53]. Since it features good transmission performance and doubled spectral efficiency, DQPSK is presently seen as a promising candidate for future networks, in spite of the greater effort required for practical realization of the transponder hardware. Many of the recently proposed long-haul dense WDM transmission records are based on systems with RZ-DQPSK modulation. Encouraged by the current trends and today’s progress in high-speed electronics and digital signal processing technology, even higher-order modulation formats are being investigated in present research projects. With direct detection, 8-ary differential phase shift keying (8DPSK) has been theoretically examined by Ohm [28] and Yoon et al. [54], and experimentally demonstrated by Serbay et al. [42]. By using coherent detection, 8-ary PSK has been experimentally reported by Tsukamoto et al. [47], Seimetz et al. [39], Freund et al. [9], Zhou et al. [57] and Yu et al. [55]. The transmission performance of the 16PSK / 16DPSK formats is presented in detail within this book. By combining intensity and phase modulation, the number of phase states can be reduced for the same number of symbols, leading to larger Euclidean distances between the symbols. The symbols can be arranged in different circles (Star QAM) or can be positioned in a square (Square QAM). Star QAM experiments have been reported with four phase levels in [29] and [41, 43] for 2ASK-DQPSK and 4ASKDQPSK, respectively. The 2ASK-8DPSK format, which is denoted in the following as Star 16QAM, has been investigated by computer simulations in [35] and experimentally in [40], and is extensively discussed within this book, just as different Square QAM formats. Very recently, Square 16QAM has been experimentally demonstrated in [33, 51]. Even higher-order Square QAM experiments have been shown so far only for moderate symbol rates [25].

Coherent Detection In many wireline and wireless telecommunication systems, receivers are based on coherent detection because coherent receivers feature a high receiver sensitivity and can select a channel from a frequency comb by tuning the oscillator to the desired frequency, as it is known from radio. In optical fiber communication, coherent systems were an important topic of investigation in the late eighties and early nineties. With the emergence of the EDFA, the former advantage of a higher receiver sensitivity—compared to direct detection—disappeared. Comparable sensitivities could be achieved by direct detection receivers with optical preamplifiers [46]. Thus, as it had for the high-order modulation formats, research into this area ceased, the more so as the components were complex and costly. Nowadays however, coherent optical systems are reappearing as an area of interest [19]. The linewidth requirements have relaxed with increasing channel data rates, and sub-MHz linewidth lasers have recently been developed [6, 16].

6

1 Introduction

More recently, the high-speed digital signal processing available allows for the implementation of critical operations like phase locking, frequency synchronization and polarization control in the electronic domain through digital means. Former concepts for carrier synchronization with optical phase locked loops (OPLL) [1, 7, 14, 17, 18, 27] can be replaced by subcarrier OPLLs [4] or digital phase estimation [20–23, 26, 36, 37, 45, 48]. Thus, under the new circumstances, the chances of cost effectively manufacturing stable coherent receivers are increasing. In addition to the already mentioned potentials of spectral efficiency, coherent detection provides several advantages. Coherent detection is very beneficial within the design of optical high-order modulation systems because all the optical field parameters (amplitude, phase, frequency and polarization) are available in the electrical domain. Therefore the demodulation schemes are not limited to the detection of phase differences as for direct detection, but arbitrary modulation formats and modulation constellations can be received. Furthermore, the preservation of the temporal phase enables more effective methods for the adaptive electronic compensation of transmission impairments like chromatic dispersion and nonlinearities [11, 44]. When used in WDM systems, coherent receivers can offer tunability and enable very small channel spacings, since channel separation can be performed by high-selective electrical filtering. Two main challenges for the practical fabrication of coherent receivers are the implementation of carrier synchronization and the successful fabrication of key components like the optical hybrids [38]. Within this book, both coherent receivers and direct detection receivers are considered.

Exploding Data Traffic and Bandwidth Demands In today’s communication society, the need for optical data transmission capacity is exploding. The Internet is evolving into a multimedia broadband Internet with services like video on demand, video telephony, online gaming, remote working and interactive entertainment. The number of broadband subscribers is growing daily, and future network scenarios plan to provide broadband access with 100 Mbit/s to the home and several Gbit/s to the office via copper, wireless and all-optic solutions, as depicted in Fig. 1.3. From the year 2000 on, the global network traffic has been dominated by internet protocol (IP) data. Studies of traffic in 2005 indicated a global traffic growth of 115% per year. Assuming a traffic growth of just 50%, the currently installed Atlantic capacity will be saturated in only a few years. Even when acting on the rather conservative assumption of only 20% capacity growth, the estimated ultra long-haul capacity per fiber pair will be 50-100 Tbit/s in 2025 [8]. With the aid of recent technological advancements, optical fiber transmission capacities have steadily been increased and impressive records were achieved in research laboratories. The highest single wavelength channel data rate was obtained in the labs of the Heinrich-Hertz-Institut (HHI), where 2.56 Tbit/s could be transmitted over 160 km dispersion managed fiber (DMF) by combining the techniques of optical time division multiplexing (OTDM), polarization division multiplexing (PDM)

1 Introduction

7 50 Tbit/s long distance traffic

Core Network

WDM, IP 10 Gbit/s to the company

Metro Network WDM, IP

Access Network

Business Ring LAN

2.5 Gbit/s to the office

WLAN

100 Mbit/s to the home

UMTS

Fig. 1.3 Possible future network scenario (LAN: local area network, WLAN: wireless LAN, UMTS: universal mobile telecommunications system)

and DQPSK modulation [50]. In [10], the record per fiber capacity of 25.6 Tbit/s could be achieved by transmitting 160 wavelength channels with 160 Gbit/s perchannel data rate in the C-band and the L-band over 240 km, employing PDM, Raman amplification and RZ-DQPSK modulation. A record spectral efficiency of 4.2 bit/s/Hz was obtained in [57] by using a very narrow WDM channel grid of 25 GHz at a channel data rate of 114 Gbit/s. This was enabled by applying RZ-8PSK modulation and PDM. A transparent optical transmission distance of 18000 km was bridged by [24] in the laboratory with a capacity of 1.09 Tbit/s, and a distance of 13100 km by [3] with a capacity of 0.96 Tbit/s in a field trial. Moreover, a record capacity-distance product of 41.82 Pbit/s·km could be achieved in [5] by transmitting 164 PDM-QPSK channels with a channel data rate of 100 Gbit/s over a length of 2550 km, while using Raman amplification and coherent detection. The current records are summarized in Table 1.1. Table 1.1 Current fiber optic transmission records (records are printed in bold face) Cap. (Tbit/s)

Dist. (km)

Cap. · Dist. (Pbit/s · km)

Sp. Eff. (bit/s/Hz)

Number of channels

Ch. rate (Gbit/s)

Year

Ref.

2.56 25.6 0.91 1.09 0.96 16.4

160 240 640 18000 13100 2550

0.41 6.14 0.58 19.62 12.58 41.82

3.2 4.2 0.2 0.3 2.0

1 160 8 109 96 164

2560 160 114 10 10 100

2006 2008 2008 2003 2004 2008

[50] [10] [57] [24] [3] [5]

8

1 Introduction

Intention, Scope and Outline of the Book In spite of the brilliant experimental results and technological progress in optical networking in the last few years, the capacities reached so far will not suffice to handle projected future IP traffic. The introduction of optical high-order modulation formats and coherent detection could be the next important step towards higher network capacities and higher spectral efficiencies. However, today’s network operators have to handle the steadily growing volume of data traffic in an economic manner. They must be able to estimate whether these new technologies can be cost-efficiently integrated in existing optical networks and also in which network segments they can reasonably be deployed. Catering to the increasing interest in optical systems with high-order modulation and coherent detection, this book aims to give an insight into possible system configurations, their complexity and practical feasibility, their system and transmission properties, and an appropriate choice of parameters. It is intended for researchers in the field of optical communications, as well as for system designers who would like to learn about the setup and the properties of optical systems employing high-order modulation. It helps answering the following questions: What do the transmitters and receivers look like? In the first part, this book gives a detailed functional description of transmitter and receiver structures possible for the generation and detection of optical PSK / DPSK and QAM signals. The description of different transmitters in Chapter 2 provides all the information relevant to their functioning and includes optical and electrical transmitter parts. It contains detailed information such as the concrete assembly of the coders and levelgenerators. Moreover, the electrical field for the optical transmitter output signals is analytically derived and differences in signal characteristics are emphasized. Subsequently, Chapter 3 illustrates different receiver concepts which can be employed to detect optical high-order modulation signals—starting with optical frontends and ending with electrical data recovery. Receivers are detailed for three different detection schemes: direct detection, homodyne differential detection and homodyne synchronous detection. The latter scheme gains more and more interest since highspeed digital signal processing is newly available which enables carrier synchronization to be accomplished through digital means. Therefore, a special focus is brought to carrier recovery through digital phase estimation. How great is the additional effort required by a system upgrade? When upgrading a system to a more sophisticated modulation format, the additional effort required is determined significantly by the enhanced complexity of the transmitters and receivers. Based on the information provided in Chap. 2 and Chap. 3, the complexity of different transmitter and receiver configurations is compared and discussed in Chapter 4. How does the system react to transmission impairments? The second part of the book deals with the system and transmission characteristics of high-order modulation formats. When the interest in alternative modulation formats came up again

1 Introduction

9

a few years ago, the main intention of the research was to obtain a higher robustness against transmission impairments. The optimum modulation format should be resilient against amplified spontaneous emission (ASE) noise and laser phase noise, tolerant to CD and PMD, robust to fiber nonlinearities and inaccuracies in dispersion maps, and unsusceptible to narrow optical filtering, thereby enabling high spectral efficiency. However, in practice, every modulation format has its own strengths and weaknesses. After a discussion of system simulation aspects in Chapter 5 and the degradation effects of optical fiber transmission in Chapter 6, it is the aim of Chapter 7 to show the individual strengths and drawbacks of high-order optical modulation formats in relation to their particular transmission characteristics, namely noise performance, the optimal receiver filter bandwidths, the linewidth requirements and the CD and SPM tolerances. Phase modulation formats up to 16PSK / 16DPSK and different QAM formats (Star 16QAM, Square 16QAM and Square 64QAM) are characterized for various system configurations, considering nearly all transmitter and receiver schemes described in the first part of the book. Which transparent optical transmission lengths can be bridged? Chapter 7 is restricted to the back-to-back case and to single-span systems without amplifier noise on the link, whereas Chapter 8 discusses the performance and the distances attainable for optical systems with high-order modulation for multi-span long-haul transmission. The achievable transmission distances can not exactly be identified by an isolated examination of the behavior of a format with respect to particular transmission impairments, because degradation effects interact which each other during transmission. In fact, the performance of a modulation format can be only evaluated precisely for the specific system in which it is operated. Currently, the determination of attainable transmission distances for multi-span long-haul transmission using high-order modulation formats represents an exciting field of research. Some recent results of the research group of the author are presented in Chap. 8. Which spectral efficiencies and network capacities can be obtained? The application of high-order modulation formats promises an enhancement of spectral efficiency and therefore an extension of network capacities. The expected increase of spectral efficiency depends on the order of the modulation format and may be about the ratio of the data rate to the symbol rate in systems operated in the linear regime. However, the spectral efficiencies attainable in practice can only be determined through investigation of specific WDM systems, with particular attention to channel filtering, crosstalk, and inter-channel nonlinearities. These issues are subjects for future research and out of the scope of the current edition of this book which covers mainly single-channel transmission. Finally, Chapter 9 summarizes the major trends in system performance resulting from migration to higher-order modulation formats obtained in the second part of the book and points out goals of future research in this field.

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References 1. Barry, J.R., Kahn, J.M.: Carrier synchronization for homodyne and heterodyne detection of optical quadriphase-shift keying. IEEE Journal of Lightwave Technology 10(12), 1939–1951 (1992) 2. Betti, S., et al.: Coherent Optical Communication Systems. John Wiley & Sons (1995) 3. Cai, J.X., et al.: RZ-DPSK field trial over 13,100 km of installed non slope-matched submarine fibers. In: Proceedings of Optical Fiber Communication Conference (OFC), PDP34 (2004) 4. Camatel, S., et al.: 2-PSK homodyne receiver based on a decision driven architecture and a sub-carrier optical PLL. In: Proceedings of Optical Fiber Communication Conference (OFC), OTuI3 (2006) 5. Charlet, G., et al.: Transmission of 16.4Tbit/s capacity over 2550km using PDM QPSK modulation format and coherent receiver. In: Proceedings of Optical Fiber Communication Conference (OFC), PDP3 (2008) 6. Chen, X., et al.: Distributed feedback fiber laser with a novel structure. In: Proceedings of Optical Fiber Communication Conference (OFC), OME10 (2005) 7. Chiou, Y., Wang, L.: Effect of amplifier noise on laser linewidth requirements in long haul optical fiber communication systems with Costas PLL receivers. IEEE Journal of Lightwave Technology 14(10), 2126–2134 (1996) 8. Desurvire, E.: Optical communications in 2025. In: Proceedings of European Conference on Optical Communication (ECOC), Mo2.1.3 (2005) 9. Freund, R., et al.: 30 Gbit/s RZ-8-PSK transmission over 2800 km standard single mode fibre without inline dispersion compensation. In: Proceedings of Optical Fiber Communication Conference (OFC), OMI5 (2008) 10. Gnauck, A.H., et al.: 25.6-Tb/s WDM transmission of polarization-multiplexed RZ-DQPSK signals. IEEE Journal of Lightwave Technology 26(1), 79–84 (2008) 11. Hebebrand, C., et al.: Performance of electronic dispersion compensation for multi-level modulation formats using homodyne coherent detection. In: Proceedings of European Conference on Optical Communication (ECOC), We3.P.80 (2006) 12. Kahn, J.M., Ho, K.P.: Ultimate spectral efficiency limits in DWDM systems. In: Proceedings of OptoElectronics and Communications Conference. Yokohama, Japan (2002) 13. Kahn, J.M., Ho, K.P.: Spectral efficiency limits and modulation/detection techniques for DWDM systems. IEEE Journal of Selected Topics in Quantum Electronics 10(2), 259–272 (2004) 14. Kahn, J.M., et al.: Heterodyne detection of 310-Mb/s quadriphase-shift keying using fourthpower optical phase-locked loop. IEEE Photonics Technology Letters 4(12), 1397–1400 (1992) 15. Kaiser, G.: FTTX concepts and applications. John Wiley & Sons, Inc., Hoboken, New Jersey (2006) 16. Kasai, K., et al.: A13 C2 H2 frequency-stabilized, polarization-maintained erbium fibre ring laser with no frequency modulation. In: Proceedings of European Conference on Optical Communication (ECOC), Th1.3.5 (2004) 17. Kazovsky, L.G.: Decision-driven phase-locked loop for optical homodyne receivers: Performance analysis and laser linewidth requirements. IEEE Journal of Lightwave Technology LT-3(6), 1238–1247 (1985) 18. Kazovsky, L.G.: Balanced phase-locked loops for optical homodyne receivers: Performance analysis, design considerations, and laser linewidth requirements. IEEE Journal of Lightwave Technology LT-4(2), 182–195 (1986) 19. Kazovsky, L.G.: Homodyne phase-shift-keying systems: Past challenges and future opportunities. In: Proceedings of Optical Fiber Communication Conference (OFC), OTuL3 (2005) 20. Kikuchi, K.: Coherent detection of phase-shift keying signals using digital carrier-phase estimation. In: Proceedings of Optical Fiber Communication Conference (OFC), OTuI4 (2006) 21. Koc, U., et al.: Digital coherent quadrature phase-shift-keying (QPSK). In: Proceedings of Optical Fiber Communication Conference (OFC), OThI1 (2006)

References

11

22. Louchet, H., et al.: Improved DSP algorithms for coherent 16-QAM transmission. In: Proceedings of European Conference on Optical Communication (ECOC), Tu.1.E.6 (2008) 23. Ly-Gagnon, D.S., et al.: Unrepeated 210-km transmission with coherent detection and digital signal processing of 20-Gb/s QPSK signal. In: Proceedings of Optical Fiber Communication Conference (OFC), OTuL4 (2005) 24. Mollenhauer, L.F., et al.: Demonstration of 109×10G dense WDM over more than 18,000 km using novel, periodic-group-delay-complemented dispersion compensation and dispersionmanaged solitons. In: Proceedings of European Conference on Optical Communication (ECOC), Th4.3.4 (2003) 25. Nakazawa, M., et al.: Polarization-multiplexed 1 Gsymbol/s, 64 QAM (12 Gbit/s) coherent optical transmission over 150 km with an optical bandwidth of 2 GHz. In: Proceedings of Optical Fiber Communication Conference (OFC), PDP26 (2007) 26. Noe, R.: PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I&Q baseband processing. IEEE Photonics Technology Letters 17(4), 887–889 (2005) 27. Norimatsu, S., et al.: An 8 Gb/s QPSK optical homodyne detection experiment using externalcavity laser diodes. IEEE Photonics Technology Letters 4(7), 765–767 (1992) 28. Ohm, M.: Optical 8-DPSK and receiver with direct detection and multilevel electrical signals. IEEE/LEOS Workshop on Advanced Modulation Formats pp. 45–46 (2004) 29. Ohm, M., Speidel, J.: Receiver sensitivity, chromatic dispersion tolerance and optimal receiver bandwidths for 40 Gbit/s 8-level optical ASK-DQPSK and optical 8-DPSK. In: Proc. 6th Conference on Photonic Networks, pp. 211–217. Leipzig, Germany (2005) 30. Olsson, N.A.: Lightwave systems with optical amplifiers. IEEE Journal of Lightwave Technology 7(7), 1071–1082 (1989) 31. Rohde, M., et al.: Robustness of DPSK direct detection transmission format in standard fiber WDM systems. Electronics Letters 36, 1483–1484 (1999) 32. Rosenkranz, W.: Robust multi-level phase shift modulation in high-speed WDM transmission. Proceedings of the SPIE 5625, 241–252 (2005) 33. Sakamoto, T., et al.: 50-km SMF transmission of 50-Gb/s 16 QAM generated by quad-parallel MZM. In: Proceedings of European Conference on Optical Communication (ECOC), Tu.1.E.3 (2008) ¨ 34. Seimetz, M.: Untersuchung der Phasenmodulation als alternatives Ubertragungsverfahren f¨ur optische Netze in Wellenl¨angen-Multiplex-Technik (WDM-Netze). Diplomarbeit, Technische Fachhochschule Berlin (2000) 35. Seimetz, M.: Optical receiver for reception of M-ary star-shaped quadrature amplitude modulation with differentially encoded phases and its application. German patent, DE 10 2006 030 915.4 (2006) 36. Seimetz, M.: Performance of coherent optical Square-16-QAM-systems based on IQtransmitters and homodyne receivers with digital phase estimation. In: Proceedings of NFOEC, NWA4 (2006) 37. Seimetz, M.: Laser linewidth limitations for optical systems with high-order modulation employing feed forward digital carrier phase estimation. In: Proceedings of Optical Fiber Communication Conference (OFC), OTuM2 (2008) 38. Seimetz, M., Weinert, C.M.: Options, feasibility and availability of 2 × 4 90◦ -hybrids for coherent optical systems. IEEE Journal of Lightwave Technology 24(3), 1317–1322 (2006) 39. Seimetz, M., et al.: Coherent RZ-8PSK transmission at 30Gbit/s over 1200km employing homodyne detection with digital carrier phase estimation. In: Proceedings of European Conference on Optical Communication (ECOC), vol. 3, pp. 265–266 (2007) 40. Seimetz, M., et al.: Transmission reach attainable for single-polarization and PolMux coherent Star 16QAM systems in comparison to 8PSK and QPSK at 10Gbaud. In: Proceedings of Optical Fiber Communication Conference (OFC), OTuN2 (2009) 41. Sekine, K., et al.: Proposal and demonstration of 10-Gsymbol/sec 16-ary (40 Gbit/s) optical modulation / demodulation scheme. In: Proceedings of European Conference on Optical Communication (ECOC), We3.4.5 (2004) 42. Serbay, M., et al.: Experimental investigation of RZ-8DPSK at 3 × 10.7Gb/s. In: the 18th Annual Meeting of the IEEE Lasers & Electro-Optics Society, WE3. Sydney, Australia (2005)

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1 Introduction

43. Serbay, M., et al.: 42.8 Gbit/s, 4 bits per symbol 16-ary Inverse-RZ-QASK-DQPSK transmission experiment without Polmux. In: Proceedings of Optical Fiber Communication Conference (OFC), OThL2 (2007) 44. Spinnler, B., et al.: Chromatic dispersion tolerance of coherent optical communication systems with electrical equalization. In: Proceedings of Optical Fiber Communication Conference (OFC), OWB2 (2006) 45. Taylor, M.G.: Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments. IEEE Photonics Technology Letters 16(2), 674–676 (2004) 46. Tonguz, O.K., Wagner, R.E.: Equivalence between preamplified direct detection and heterodyne receivers. IEEE Photonics Technology Letters 3(9), 835–837 (1991) 47. Tsukamoto, S., et al.: Coherent demodulation of optical 8-phase shift-keying signals using homodyne detection and digital signal processing. In: Proceedings of Optical Fiber Communication Conference (OFC), OThR5 (2006) 48. Tsukamoto, S., et al.: Optical homodyne receiver comprising phase and polarization diversities with digital signal processing. In: Proceedings of European Conference on Optical Communication (ECOC), Mo4.2.1 (2006) 49. Walklin, S., Conradi, J.: Multilevel signaling for increasing the reach of 10Gb/s lightwave systems. IEEE Journal of Lightwave Technology 17(11), 2235–2248 (1999) 50. Weber, H.G., et al.: Single channel 1.28Tbit/s and 2.56Tbit/s DQPSK transmission. Electronics Letters 42(3) (2006) 51. Winzer, P., Gnauck, A.H.: 112-Gb/s polarization-multiplexed 16-QAM on a 25-GHz WDM grid. In: Proceedings of European Conference on Optical Communication (ECOC), Th.3.E.5 (2008) 52. Winzer, P.J., Essiambre, R.J.: Advanced optical modulation formats. Proceedings of the IEEE 94(5), 952–985 (2006) 53. Wree, C., et al.: Differential quadrature phase-shift keying for cost-effective doubling of the capacity in existing WDM systems. In: Proc. 4th Conference on Photonic Networks, pp. 161–168. Leipzig, Germany (2003) 54. Yoon, H., et al.: Performance comparison of optical 8-ary differential phase-shift keying systems with different electrical decision schemes. Optics Express 13(2), 371–376 (2005) 55. Yu, J., et al.: 17 Tb/s (161x114 Gb/s) PolMux-RZ-8PSK transmission over 662km of ultra-low loss fiber using C-band EDFA amplification and digital coherent detection. In: Proceedings of European Conference on Optical Communication (ECOC), Th.3.E.2 (2008) 56. Zhao, J., et al.: Analytical investigation of optimization, performance bound, and chromatic dispersion tolerance of 4-amplitude-shifted-keying format. In: Proceedings of Optical Fiber Communication Conference (OFC), JThB15 (2006) 57. Zhou, X., et al.: 8x114Gb/s, 25-GHz-spaced, PolMux-RZ-8PSK transmission over 640km of SSMF employing digital coherent detection and EDFA-only amplification. In: Proceedings of Optical Fiber Communication Conference (OFC), PDP1 (2008)

Chapter 2

Transmitter Design

Abstract This chapter gives a detailed overview of how optical high-order modulation signals are generated. It describes transmitters for the generation of optical ASK-signals, DPSK-signals and QAM-signals and considers star-shaped and square-shaped QAM constellations (Star QAM and Square QAM). Since all the transmitters are composed of fundamental key components (laser, modulators, pulse carver), the functionality of these components is discussed at the beginning of this chapter. The subsequent description of the different transmitters includes optical transmitter parts as well as electrical parts. It contains much detailed information such as the concrete assembly of the coders and level-generators. The quality of the transmitter output signals has a critical influence on the overall system performance. Therefore the electrical field for the optical output signals is analytically derived for all transmitters shown, and differences in signal characteristics, symbol transitions and chirp behavior are emphasized. This helps us understand the system behavior of the transmitters discussed later on in Chap. 7.

2.1 Transmitter Components The following subsections briefly describe some fundamental key components of optical transmitters for high-order modulation.

2.1.1 Lasers The ideal carrier for optical transmission is a lightwave with constant amplitude, frequency and phase. In practice, however, this perfect carrier can unfortunately not be generated. In the last decades, optical light sources have been increasingly improved. Light emitting diodes (LED) with very high spectral widths of several tens of nanometers and low output powers and multi-mode Fabry-Perot lasers with

M. Seimetz, High-Order Modulation for Optical Fiber Transmission, Springer Series in Optical Sciences 143, DOI 10.1007/978-3-540-93771-5 2, c Springer-Verlag Berlin Heidelberg 2009

15

16

2 Transmitter Design

some discrete spectral lines and a total spectral width of several nanometers can now be replaced with single-mode distributed feedback (DFB) lasers or external cavity lasers (ECL) with linewidths in the sub-MHz region. When performing direct modulation (which means that the data is modulated onto the laser drive current), the width of the emitted optical spectrum is determined by the incidental frequency modulation of the laser under amplitude modulation, often referred to as chirping of the laser, when the laser linewidth is small compared with the chirp-induced spectral broadening. To avoid this effect, external modulation can be employed. Then the laser acts as a continuous wave (CW) light source. Throughout this book, which deals with advanced modulation and detection schemes, only single-mode lasers and external modulation are considered. The normalized electrical field of an ideal optical carrier as emitted from a CW laser can be expressed in complex notation as p (2.1) Ecw (t) = Ps · e j (ωs t+ϕs ) · es √ In (2.1), Ps represents the field amplitude, ωs /(2π ) the frequency, ϕs the initial phase and es the polarization of the optical carrier. The character “s” indicates the signal laser. In practice, laser phase and amplitude noise, often called “intensity noise”, have to be taken into account. They have their origin in spontaneous emission photons which induce intensity fluctuations δ P(t) and phase fluctuations, which are represented by the signal laser phase noise ϕn s (t). p Ecw (t) = Ps + δ P(t) · e j (ωs t+ϕs +ϕns (t)) · es . (2.2)

The laser phase noise is caused by spontaneous emission photons, not generated in phase with the stimulated emission photons but with random phase [7]. In the time domain, the evolution of the actual phase can be understood as a random walk. Within a time interval τ , the phase exhibits a random phase change of 1ϕn s (t) = ϕn s (t) − ϕn s (t − τ ).

(2.3)

Since the phase changes 1ϕn s (t) are caused by a high number of independent noise events—more precisely the generation of spontaneous emission photons—they can be modeled as Gaussian distributed according to the Central Limit Theorem. Furthermore, when assuming a white power spectral density of frequency noise ϕ˙n s (t), which represents a realistic practical assumption [8, 13], the variance of the phase change 1ϕn s (t) can be expressed as h1ϕn2s (τ )i = Wϕ˙ns · |τ | =

2|τ | , tc

(2.4)

2.1 Lasers

17

where Wϕ˙ns is the constant power spectral density of the frequency noise and tc represents the coherence time which physically denotes the maximum delay difference up to which two components of the emitted optical field can stably interfere. When further neglecting intensity noise, the power spectral density of the optical field can be shown to exhibit the Lorentzian-shaped spectrum W E cw (ω) =

2tc Ps . 1 + [(ω − ωs )tc ]2

(2.5)

The laser linewidth of the signal laser is defined as the full-width half-maximum bandwidth of this power spectral density and is specified by 1νs =

Wϕ˙ns 1 = . 2π πtc

(2.6)

When the laser linewidth given by (2.6) is introduced into (2.4), the variance of the phase change 1ϕn s (t) can be calculated by h1ϕn2s (τ )i = 2π 1νs |τ |,

(2.7)

showing that the phase uncertainty increases with the laser linewidth and the observed time interval. A more detailed analysis of the mechanisms and statistics of phase and frequency noise can be found in [13]. As will become clear later on in this book, laser phase noise can have a limiting effect on system performance, especially for high-order modulation formats with many phase states and when employing coherent synchronous detection. Intensity noise can also lead to significant degradation in system performance, in particular for coherent detection with high local oscillator (LO) laser powers and when not implementing balanced detection [12, 18]. In the data sheets of laser diodes, the relative intensity noise (RIN) is usually specified. The RIN, integrated over a reference bandwidth 1 f , relates the variance of the intensity fluctuations to the squared mean power: Z

1f 0

RI N( f ) d f =

hδ P 2 (t)i . hP(t)i2

(2.8)

The mean optical power hP(t)i is equivalent to the signal laser output power Ps or the output power of the LO laser Plo , respectively, because hδ P(t)i = 0. In a simple approach, the intensity fluctuations can be modeled with Gaussian statistics and a white noise spectrum [2]. In reality, the RIN has more complex spectral characteristics, as can be observed for instance from [13, 20]. RIN values of laser diodes typically range from -160 dB/Hz to -130 dB/Hz.

18

2 Transmitter Design

2.1.2 External Optical Modulators The optical part of high-order modulation transmitters is composed of one or more fundamental external optical modulator structures, which are briefly described in this subsection: the phase modulator (PM), the Mach-Zehnder modulator (MZM) and the optical IQ modulator (IQM). The speed attainable as well as the characteristics of the transmitter output signals depends on the properties of the technology and materials used for the modulators. An optical phase modulator can be fabricated as an integrated optical device by embedding an optical waveguide in an electro-optical substrate, mostly Li N bO3 , see Fig. 2.1a. By utilizing the fact that the refractive index of a material, and thus the effective refractive index n e f f of the waveguide, can be changed by applying an external voltage via a coated electrode, the electrical field of the incoming optical carrier can be modulated in phase [20].

a

electro-optic substrate

u1 (t )

b

u(t ) Ein (t )

Eout (t )

waveguide

Ein (t )

Eout (t )

electrode

u2 (t )

Fig. 2.1 a Integrated optical phase modulator. b Integrated optical Mach-Zehnder modulator.

Phase modulation ϕ P M (t) is a function of the wavelength λ, the length of the electrode lel (interaction length) and the change of the effective refractive index 1n e f f (t). When solely considering the Pockels effect [20], the change of the refractive index can be assumed to be linear to the applied external voltage u(t). ϕ P M (t) =

2π · 1n e f f (t) · lel ∼ u(t) λ

(2.9)

In the specifications, the necessary driving voltage for achieving a phase shift of π, denoted as Vπ , is typically given. Thus, the relation of the incoming optical carrier E in (t) and the outgoing phase modulated optical field E out (t), when neglecting the constant optical phase shift of the modulator, can be expressed as u(t)

E out (t) = E in (t) · e jϕ P M (t) = E in (t) · e j Vπ π .

(2.10)

2.1 Modulators

19

By utilizing the principle of interference, the process of phase modulation can also be used to cause an intensity modulation of the optical lightwave, when the interferometric structure shown in Fig. 2.1b is employed. This represents a dual-drive Mach-Zehnder modulator. In the case of dual-drive MZMs, the phase modulators in both arms can be driven independently, in contrast to single-drive MZMs. The incoming light is split into two paths, both equipped with phase modulators. After acquiring some phase differences relative to each other, the two optical fields are recombined. The interference varies from constructive to destructive, depending on the relative phase shift. Without considering the insertion loss, the transfer function of a MZM is given by  1  E out (t) = · e jϕ1 (t) + e jϕ2 (t) . E in (t) 2

(2.11)

In (2.11), ϕ1 (t) and ϕ2 (t) represent phase shifts in the upper and lower arms of the MZM. For a specified driving voltage to obtain a phase shift of π in the upper and lower arms, Vπ1 and Vπ2 , respectively, and with the driving voltages u 1 (t) and u 2 (t) as defined in Fig. 2.1b, phase shifts are related to the driving signals with ϕ1 (t) =

u 1 (t) u 2 (t) π, ϕ2 (t) = π. Vπ1 Vπ2

(2.12)

When operating the MZM in the push-push mode, which means that an identical phase shift ϕ(t) = ϕ1 (t) = ϕ2 (t) is induced in both arms (for instance with u 1 (t) = u 2 (t) = u(t) and Vπ1 = Vπ2 = Vπ ), a pure phase modulation is achieved, so that the relation between the electrical input and output field is given by (2.10) as for the simple PM. On the other hand, when one arm gets the negative phase shift of the other arm (ϕ1 (t) = −ϕ2 (t), e.g. with u 1 (t) = −u 2 (t) = u(t)/2 and Vπ1 = Vπ2 = Vπ ), the MZM is operated in the push-pull mode and a chirp-free amplitude modulation is obtained. The input and output fields are then related with     u(t) 1ϕ M Z M (t) π , (2.13) = E in (t) · cos E out (t) = E in (t) · cos 2 2Vπ where 1ϕ M Z M (t) = ϕ1 (t) − ϕ2 (t) = 2ϕ1 (t) is the induced phase difference between the fields of the upper and lower arm. By squaring (2.13), the power transfer function of the MZM is obtained:   Pout (t) 1 1 1 1 u(t) = + · cos (1ϕ M Z M (t)) = + · cos π . (2.14) Pin (t) 2 2 2 2 Vπ It should be noted that u(t) was defined in a way that u(t) = Vπ induces a phase shift of π for the PM as well as a phase shift of π in the power transfer function of the MZM when it is operated in the push-pull mode. In Fig. 2.2, two different MZM operation principles are illustrated. For achieving modulation in intensity, the MZM can be operated at the quadrature point, with a DC bias of −Vπ /2 and a peak-to-peak modulation of Vπ (see Fig. 2.2a). When the

20

2 Transmitter Design

MZM is operated at the minimum transmission point (see Fig. 2.2b), with a DC bias of −Vπ and a peak-to-peak modulation of 2Vπ , a phase skip of π occurs when crossing the minimum transmission point. This becomes apparent from the field transfer function. This way, the MZM can be used for binary phase modulation and for modulation of the field amplitude in each branch of an optical IQ modulator. a

b

Operating the MZM at the quadrature point

Operating the MZM at the minimum transmission point

1

1

OP

0

0 Vπ

-1 -2Vπ

2V π

Field transfer function Power transfer function

-Vπ

OP

0 u(t)

Vπ

2Vπ

-1 -2Vπ

Field transfer function Power transfer function

-Vπ

0 u(t)

Vπ

2Vπ

Fig. 2.2 Operating the MZM in the quadrature point (a) and the minimum transmission point (b)

Mach-Zehnder modulators can be implemented in Lithium Niobate (Li N bO3 ), Gallium Arsenide (Ga As) and Indium Phosphide (I n P) [23]. Typical Vπ driving voltages range from approximately 3 V to about 6 V. A third fundamental modulator structure is the optical IQ modulator. It can be composed of a PM and two MZMs, and is commercially available in an integrated form [1]. As illustrated in Fig. 2.3a, the incoming light is equally split into two arms, the in-phase (I ) and the quadrature (Q) arm. In both paths, a field amplitude modulation is performed by operating the MZMs in the push-pull mode at the minimum transmission point. Moreover, a relative phase shift of π/2 is adjusted in one arm, for instance by an additional PM. This way, any constellation point can be reached in the complex IQ-plane after recombining the light of both branches (see Fig. 2.3b). Within the IQ modulator pictured in Fig. 2.3a, the induced phase differences of the MZMs in the upper and lower paths are 1ϕ I (t) =

u Q (t) u I (t) π, 1ϕ Q (t) = π. Vπ Vπ

(2.15)

When neglecting any insertion loss and setting the driving voltage of the PM to u P M = −Vπ /2, the field transfer function of the IQM can be expressed as     E out (t) 1ϕ I (t) 1ϕ Q (t) 1 1 = cos + j cos . (2.16) E in (t) 2 2 2 2

2.1 Pulse Carving

21

a Optical IQ modulator

b Principle of IQ modulation

uI (t )

Q

Amplitude Modulation in the Q-arm

Ein (t )

Q

(t) ⋅ e

jϕIQM (t)

Eout (t )

I Reachable Signal Space

uPM = −Vπ / 2

Amplitude Modulation in the I-arm

uQ (t )

Fig. 2.3 a Optical IQ modulator. b Principle of IQ modulation.

By using (2.15) and (2.16), the amplitude modulation a I Q M (t) and the phase modulation ϕ I Q M (t), performed by the IQM, can be calculated by s     E out (t) 1 u I (t) u Q (t) 2 2 cos a I Q M (t) = π + cos π , (2.17) = E in (t) 2 2Vπ 2Vπ      u Q (t) u I (t) π , cos π . ϕ I Q M (t) = arg cos 2Vπ 2Vπ

(2.18)

In (2.18), the arg [I, Q] operation denotes the calculation of the angle of a complex value from the real and imaginary parts in the range between −π and π .

2.1.3 Pulse Carvers and Impulse Shapers The shape of the transmitted optical pulses significantly affects the overall performance of optical fiber transmission systems. The pulse shape used in most commercial systems is NRZ, where a pulse filling the entire bit slot is transmitted for all symbols with non-zero power. The power does not always go to zero when passing from one symbol to another. In the case of RZ pulses, the optical power goes to zero within each symbol period. Therefore, power is smaller during the symbol transitions and the undesired frequency modulation (chirp) arising during the phase transitions can not take effect or is at least reduced, depending on the optical pulse width and the rise time of the electrical driving signals.

22

2 Transmitter Design

Optical signals with RZ pulse shape can be created either by electronically generating RZ waveforms or by carving RZ pulses in the optical domain, using an extra optical pulse carver. When employing the latter method, RZ pulses with a duty cycle of 50% can be generated with a MZM, which is operated at the quadrature point and driven with a sinusoidal electrical signal with a peak-to-peak amplitude of Vπ , a frequency corresponding to the symbol rate r S = 1/TS and a phase offset of −π/2. The electrical driving signal is given by u(t) = Vπ /2 · sin(2πt/TS − π/2) − Vπ /2, where TS denotes the duration of one symbol. The field transfer function of the optical RZ pulse carver for generating RZ pulses with a duty cycle of 50% is defined as     t π π π E out (t) = cos · sin 2π − − . (2.19) E in (t) 4 TS 2 4 Even when employing optical pulse carving, the final optical pulse form at the transmitter output depends also on the shape of the electrical driving signals. These can be formed by electrical impulse shapers (IS) before feeding into the modulator driving electrodes. In system simulations, electrical pulses without overshoots and with specified rise times can be generated by filtering a rectangular input time function with a non-causal linear time invariant filter with the Gaussian shaped impulse response h(t) = √

2 2 · e−(2t/Te ) . π Te

(2.20)

The resulting output pulse of the electrical impulse shaper is given by the convolution of the rectangular signal with the impulse response h(t) and is specified by      1 2t 2 (t − TS ) p(t) = · er f c − er f c . (2.21) 2 Te Te In (2.20) and (2.21), Te represents the filter time constant, which can be approximately related to the electrical rise time 1t as 1t ≈

3 Te , 4

(2.22)

as long it is assumed that the symbol time TS is much longer than the filter time constant Te [2]. Having now discussed some fundamental components used in the various transmitters for high-order modulation, some basics for multi-level signaling are briefly presented in Sect. 2.2. Afterwards, the transmitters for particular modulation formats are described in detail.

2.3 ASK Transmitters

23

2.2 Multi-Level Signaling In digital optical transmission with high-order modulation, m data bits, denoted here as b1k , b2k , .., bm k , are collected and mapped to a complex symbol bk chosen from an alphabet A of elements An (n = 1..M, M = 2m ). Each symbol bk can be interq preted as a complex phasor with the in-phase and quadrature coordinates bki and bk , respectively, q

bk = bki + jbk ,

(2.23)

and with amplitude and phase states given by q i h 2 q2 q abk = bki + bk , ϕbk = arg bki , bk .

(2.24)

One of the M = 2m symbols is assigned to each symbol interval (denoted by the integer k, which has a range of 1 to ∞) of length TS = m · TB , where r B = 1/TB is the data rate. The assignment of respective combinations of m bits to symbols with particular amplitude and phase states (bit mapping) is defined in a so called “constellation diagram”. For the best optical signal to noise ratio (OSNR) performance, bit mapping should be arranged so that only one bit per symbol differs from a neighboring symbol (Gray coding). The symbols are transmitted on the reduced symbol rate r S = 1/TS = r B /m. For the theoretical description of the electrical driving signals in Sect. 2.6, the in-phase and quadrature symbol coordinates are scaled to unity, limiting the maximum coordinates of the I-axis and Q-axis to one. These normalized in-phase and quadrature coordinates are denoted as i k and qk throughout this book. By scaling q the symbol coordinates bki and bk to unity, the normalized in-phase and quadrature coordinates i k and qk can be expressed as ik =

bki i bmax

q

, qk =

bk

q bmax

,

(2.25)

q

i where bmax and bmax are given by q

i bmax = max {|Re {An }|} , bmax = max {|I m {An }|} . n

n

(2.26)

The relation between i k and qk and the data bits is specified by the bit mapping used respectively and illustrated more precisely later on.

2.3 ASK Transmitters The most simple optical multi-level signaling scheme is the M-ary ASK, where information is encoded into several intensity levels. The binary ASK (2ASK), usually

24

2 Transmitter Design

denoted as OOK, is the standard modulation format in commercially deployed optical transmission systems. The 2ASK constellation diagram defines only two symbol points. Just one bit b1k is assigned to each symbol, as it is depicted in Fig. 2.4b. Figure 2.4a shows a 2ASK transmitter when performing external modulation.

a

CW

b Data

IS

MZM RZ

MZM

2ASK signal

q

{b1}

0

1

i

Pulse carving

Fig. 2.4 a 2ASK transmitter with external modulation. b 2ASK constellation diagram.

The optical part consists of a CW laser, an optional MZM for RZ pulse carving and a MZM for intensity modulation, which is operated at the quadrature point. A nice side effect of using a MZM for intensity modulation, is the nonlinear compression of the MZM transfer function at high and low transmission, which can suppress ripples on electrical driving signals. The electrical data signal can be formed by an impulse shaper as explained in Sect. 2.1.3. The optical transmitter output signal for RZ-ASK, when neglecting laser noises and polarization, can be described by       p π t π π u(t) π · cos sin 2π − − , (2.27) E s (t) = Ps · e j (ωs t+ϕs ) · cos 2Vπ 4 TS 2 4 whereas the second cosine-term disappears in the case of NRZ. The electrical driving signal for 2ASK is defined as X
u(t) = −Vπ + Vπ · b1k · p (t − kTS ) , b1k ∈ {0, 1} . (2.28) k

High-order ASK formats have been investigated in [21] and [24] where it was shown that they require high signal to noise ratios for direct detection, especially in optically amplified links due to the intensity dependence of the signal-ASE noise. In principle, they can be generated with the same optical transmitter. However, multilevel electrical signals would have to be produced by an adequate electrical driving circuit to drive the MZM. The generation of multi-level electrical driving signals is quite challenging for high data rates because the eye spreading increases when overlapping different binary electrical signals to create a multi-level signal, which leads to a degradation of the system performance. The eye-spreading can be defined as 1e = (δ1 + δ2 )/de ,

2.4 DPSK Transmitters

25

where δ1 and δ2 describe the ripples (or the spreadings) in the upper and lower levels and de is the height of the eye diagram, as shown in Fig. 2.5. For instance, if two binary signals are summed to a quaternary signal, the eye spreading is increased by a factor of three [6].

δ1 Eye spreading

de

Δ e = ( δ1 + δ 2 ) / d e

δ2

Fig. 2.5 Definition of eye spreading for a binary signal, based on [6]

2.4 DPSK Transmitters Figure 2.6 shows constellation diagrams of different DPSK formats. All the constellation points lie in one circle. Bit mapping can theoretically be chosen arbitrarily. Here it is arranged in Gray code, so that only one bit per symbol differs from a neighboring symbol, leading to the best noise performance. q

q

{b1}

1

0

{b1 , b2 }

11

10

01

i

i

00

DBPSK q

011

010

DQPSK q

{b1 , b2 , b3 }

0111

{b1 ,.., b4 }

0110

0010 0011

0101

001

0100

110

000

0001 0000

1100

i

i 1101

Fig. 2.6 DPSK constellation diagrams with Gray coded bit mappings

100

111 101

8DPSK

1000 1001

1111 1110

1010

1011

16DPSK

26

2 Transmitter Design

Basically, optical DPSK signals can be constituted by many different transmitter types. Optical complexity can be reduced through increased electrical complexity and vice versa. A single PM or MZM in the optical part would be sufficient to generate arbitrary DPSK signals. However, multi-level electrical driving signals are required for high-order DPSK formats in that case. Their generation increases the electrical effort and is problematic due to the eye spreading problem. Another option is to use an optical IQ modulator alone. In this situation, the necessary number of states of electrical driving signals corresponds to the number of projections of the symbols to the I-axis and the Q-axis. From a practical point of view, the IQ modulator is not the best choice for generating high-order DPSK signals because all constellation points lie in one circle, and the distances between the signal states of the in-phase and quadrature driving signals are short. The discussion of DPSK transmitters within this book is restricted to configurations which require solely binary electrical driving signals. In Sect. 2.4.1 and Sect. 2.4.2, respectively, two different configurations are presented which are denoted here as “serial DPSK transmitter” and “parallel DPSK transmitter”.

2.4.1 Serial DPSK Transmitter One way of generating optical DPSK signals with binary electrical driving signals is to use m consecutive PMs, where m is the number of bits per symbol. This transmitter is shown in Fig. 2.7, and is called serial transmitter throughout this book. After the first PM (phase shift π), a DBPSK signal is obtained. After the second PM (phase shift π/2) a DQPSK signal is obtained, and so on.

b1k CW

d mk Differential Encoder

Data

1:m DEMUX

bmk

IS IS

d1k MZM RZ

IS

IS

u PM1 (t )

u PM 2 (t )

u PM 3 (t )

u PM m (t )

PM

PM

PM

PM

π

π/2

π/4

π/2(m-1)

DBPSK

DQPSK

8DPSK

MDPSK

Fig. 2.7 DPSK transmitter with binary electrical driving signals, serial configuration

2.4 Parallel DPSK Transmitter

27

In the electrical part of the transmitter,the data signal is first parallelized with a 1:m demultiplexer. Parallelized data bits b1k , b2k , .., bm k are then fed into a differential DPSK encoder, whose complexity and configuration generally depends on the order of the DPSK modulation, the structure of the optical transmitter part, as well as the used bit mapping of the data to the constellation points. The differential encoding is performed to enable differential detection, or to resolve phase ambiguity arising from carrier synchronization at the receiver (as described in Sect. 3.5). When employing synchronous detection techniques without differential decoding, the differential encoder can be omitted and only PSK signals generated. The functionality of the differential encoders is discussed in more detail in Sect. 2.4.3.  At the differential encoder’s outputs, the encoded output data d1k , d2k , .., dm k is obtained and passed to electrical impulse shapers and subsequently to the optical modulators as illustrated in Fig. 2.7. The NRZ output signal of the serial DPSK transmitter for a DPSK format with m bits per symbol is given by E s (t) =

p

Ps · e j (ωs t+ϕs ) · e j

u P M (t) 1 π Vπ

· ej

u P M (t) 2 π Vπ

· ... · e j

u P Mm (t) π Vπ

,

(2.29)

with the binary electrical driving voltages u P Mn (t) =


Vπ X · dn k · p (t − kTS ) , 2n−1

(2.30)

k

where n = {1, 2, .., m}, and dn k ∈ {0, 1} represents the n-th differentially encoded bit of a symbol consisting of m bits in the k-th symbol interval.

2.4.2 Parallel DPSK Transmitter A second DPSK transmitter configuration, which also uses binary electrical driving signals, is composed of a combination of an optical IQ modulator and consecutive phase modulators, in the following called parallel transmitter and depicted in Fig. 2.8. The optical IQ modulator accomplishes a DQPSK modulation, and higherorder DPSK signals are generated by the consecutive PMs. The electrical transmitter part is identical to the one for the serial transmitter, with the exception of the internal setup of the differential encoder. To accomplish DQPSK modulation, the Mach-Zehnder modulators in the I-arm and the Q-arm of the IQM are operated at the minimum transmission point and driven by binary electrical driving signals X
u I (t) = −2Vπ + 2Vπ · d1k · p (t − kTS ) , (2.31) k

u Q (t) = −2Vπ + 2Vπ ·

X k


d2k · p (t − kTS ) .

(2.32)

28

2 Transmitter Design

b1k

d mk Differential Encoder

Data

1:m DEMUX

bmk

IS IS IS

d1k

IS

u I (t ) u PM 3 (t )

MZM CW

MZM RZ

3dB

3dB -90°

MZM

uQ (t )

DQPSK

u PM m (t )

PM

PM

π/4

π/2(m-1)

8DPSK

MDPSK

Fig. 2.8 Parallel DPSK transmitter with binary electrical driving signals

The driving signals of the consecutive phase modulators are defined by (2.30) for n = {3..m}. The optical output signal of the parallel DPSK transmitter for NRZ line coding is specified by E s (t) =

p

Ps · e j (ωs t+ϕs ) · a I Q M (t) · e jϕ I Q M (t) · e j

u P M (t) 3 π Vπ

· ... · e j

u P Mm (t) π Vπ

, (2.33)

where a I Q M (t) and ϕ I Q M (t) describe the amplitude and phase modulation of the IQM, given by (2.17) and (2.18), respectively, and the parameter Vπ is assumed to be the same for all the modulators used, for simplicity.

2.4.3 Differential Encoding  In the differential encoder, the data bits b1k , b2k , .., bm k , which are mapped to symbols as defined by the original bit mapping, for instance the Gray coded bit mapping in Fig. 2.6, are encoded in a way to represent phase differences. To achieve this, appropriate absolute phase states ϕk must be adjusted at the encoder output for given phase differences ϕbk and previously given absolute phase states ϕk−1 according to ϕk = ϕk−1 + ϕbk . The symbol assignment at the encoder output, which describes the mapping of the differentially encoded bits d1k , d2k , .., dm k into symbols with absolute phase states ϕk , must be defined according to a particular optical transmitter configuration in order to drive the optical modulators adequately to obtain the desired absolute phase states. Different symbol assignments are appropriate at the encoder output for the serial and the parallel DPSK transmitter, as shown in Fig. 2.9. Therefore different encoders are needed for each of the two configurations. For the serial transmitter, the symbol assignment must be arranged in chronologically increasing order, as illustrated in

2.4 Differential Encoding q

01

29 q

{d1 , d 2 }

010

011

q

{d1 , d 2 , d3 }

0100

0101 0110

001

{d1 ,.., d 4 }

0011 0010

0111 10

00

100

000

i

0001 0000

1000

i

i 1001

11

q 01

1011

110

q

{d1 , d 2 }

111 010

11

1111 1110

1010

111

101

1100

1101

q

{d1 , d 2 , d3 }

1111

1110

0100

110

{d1 ,.., d 4 }

1101 1100

0101 011

101

i

1011 1010

0110

i

i 0111

10

00

100

000 001

DQPSK

8DPSK

Serial transmitter

Parallel transmitter

1001 1000

0000 0001

0010

0011

16DPSK

Fig. 2.9 Symbol assignment to absolute phase states at the differential encoder output for the serial DPSK transmitter (top) and the parallel DPSK transmitter (bottom)

the upper part of Fig. 2.9 for DQPSK, 8DPSK and 16DPSK, respectively. As regards the parallel transmitter, the symbols must be assigned differently. For instance, when driving the MZM in the I-arm and the Q-arm of the IQM, each with a logical one, an optical phase of π/4 is obtained, in contrast to the serial configuration, where an optical phase of 3/2 · π results for driving both PMs with a logical one. The symbol assignment for the parallel transmitter used here is shown in the bottom part of Fig. 2.9 for DQPSK, 8DPSK and 16DPSK, respectively. Because the absolute phase is not relevant for differential detection, the symbol assignments can also be arbitrarily rotated for both transmitters.  In any differential encoder, the data bits of the current symbol b1k , b2k , .., bm k , representing the current phase difference, are combined with the previous encoder output bits d1k−1 , d2k−1 , .., dm k−1 , representing the absolute optical phase of the previous symbol, in a logical circuit, in order to specify the next encoder output bits  d1k , d2k , .., dm k which define the current optical phase. The general structure of a differential encoder is depicted in Fig. 2.10. The following paragraphs derive logical relations which characterize the logical circuit of the differential encoders for different DPSK transmitters. They are only valid for employing the Gray coded bit mapping to phase differences and the symbol assignment to absolute phases as defined in Fig. 2.6 and Fig. 2.9, respectively. Other mappings are possible, but would yield other relations.

30

2 Transmitter Design

Fig. 2.10 General structure of a differential encoder

TS TS TS

d mk Logical circuit

bmk b2k b1k

d 2k d1k

Differential Encoders for DBPSK and DQPSK In the case of DBPSK, differential encoding can be achieved easily. A logical one in the current data indicates a phase change of π . By combining the current data bit with the previous encoder output bit in a simple XOR gate, the next encoder output bit is obtained. The encoders required within DQPSK transmitters are yet more complex. They have to provide two output bits d1k and d2k , which depend on the input data bits b1k and b2k , as well as on the previous encoder output bits d1k−1 and d2k−1 . Within the serial transmitter, the encoder output signals are taken to drive the two PMs. The first PM changes the phase between 0 and π, and the second one changes the phase between 0 and π/2. In this way, the four absolute phase states 0, π/2, π, and 3/2 · π can be adjusted with a symbol assignment in chronologically increasing order. The truth table for the DQPSK encoder of the serial transmitter is given by Table 2.1. Table 2.1 Truth table for the differential encoder appropriate for the serial DQPSK transmitter d1k

d2k

ϕk

d1k−1 d2k−1 ϕk−1

b1k

b2k

ϕbk

0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

0 0 0 0 π/2 π/2 π/2 π/2 π π π π 3/2 · π 3/2 · π 3/2 · π 3/2 · π

0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0

1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1

0 3/2 · π π π/2 π/2 0 3/2 · π π π π/2 0 3/2 · π 3/2 · π π π/2 0

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

0 π/2 π 3/2 · π 0 π/2 π 3/2 · π 0 π/2 π 3/2 · π 0 π/2 π 3/2 · π

2.4 Differential Encoding

31

By using Karnaugh maps, for instance, the logical relations for the encoder output bits d1k and d2k can easily be derived from Table 2.1 for the serial transmitter: d1k = b2k d1k−1 d2k−1 + b1k d1k−1 d2k−1 + b1k d1k−1 d2k−1 + b2k d1k−1 d2k−1 , (2.34) d2k = b1k b2k d2k−1 + b1k b2k d2k−1 + b1k b2k d2k−1 + b1k b2k d2k−1 .

(2.35)

In (2.34) and (2.35), “+” denotes logical OR, the particular terms are associated by logical AND, and the “overlines” indicate logical negation. In practice, the encoder can be implemented using the adequate AND and OR gates. Due to the different symbol assignment at the encoder output, the differential encoder of the parallel transmitter differs from the one of the serial transmitter. Its truth table is shown in Table 2.2. The corresponding logical relations for the two encoder output bits d1k and d2k for the parallel DQPSK transmitter are d1k = b1k d1k−1 d2k−1 + b2k d1k−1 d2k−1 + b1k d1k−1 d2k−1 + b2k d1k−1 d2k−1 , (2.36) d2k = b2k d1k−1 d2k−1 + b1k d1k−1 d2k−1 + b2k d1k−1 d2k−1 + b1k d1k−1 d2k−1 . (2.37)

Table 2.2 Truth table for the differential encoder appropriate for the parallel DQPSK transmitter d1k

d2k

ϕk

d1k−1 d2k−1 ϕk−1

0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

5/4 · π 5/4 · π 5/4 · π 5/4 · π 3/4 · π 3/4 · π 3/4 · π 3/4 · π 7/4 · π 7/4 · π 7/4 · π 7/4 · π π/4 π/4 π/4 π/4

0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

5/4 · π 3/4 · π 7/4 · π π/4 5/4 · π 3/4 · π 7/4 · π π/4 5/4 · π 3/4 · π 7/4 · π π/4 5/4 · π 3/4 · π 7/4 · π π/4

b1k

b2k

ϕbk

0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0

1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1

0 π/2 3/2 · π π 3/2 · π 0 π π/2 π/2 π 0 3/2 · π π 3/2 · π π/2 0

32

2 Transmitter Design

Differential Encoders for Higher-Order DPSK Formats In the same manner, one can specify differential encoders for the higher-order DPSK transmitters. Starting from the constellation diagrams with bit mappings and symbol assignments defined in Fig. 2.6 and Fig. 2.9, respectively, truth tables can be established. Subsequently, the corresponding Karnaugh maps can be evaluated in order to determine the logical relations of the encoders. Since the equations resulting for 8DPSK and 16DPSK are quite bulky, they are given in Appendix A. It becomes apparent here that the complexity of the differential encoder grows significantly with the increasing order of the phase modulation. For 16DPSK, the differential encoder is very complex. For instance, the relation for the encoder output bit d1k has 30 OR combined terms, each consisting of 4-7 AND combined inputs. Now having provided all the relevant functional information about the setup of the serial and parallel DPSK transmitters, the following subsection discusses the properties of their output signals.

2.4.4 Signal Properties The structure of the transmitter affects the signal characteristics and the transmission properties of the generated optical DPSK signals, due to the fact that the symbol transitions (amplitude and phase transitions) of the transmitters are different, especially in the case of NRZ. An optical high-order modulation signal at the transmitter output can be generally described by p (2.38) E s (t) = Ps · e j (ωs t+ϕs ) · a(t) · e jϕ(t) ,

where A(t) = a(t) · e jϕ(t) represents the normalized complex modulation envelope of the optical signal with time dependent amplitude a(t) and phase ϕ(t). The squared amplitude a 2 (t) times the CW laser power Ps represents the instantaneous signal power (which is proportional to the signal intensity). Another important parameter, which has a significant influence on the transmission performance, is the derivative of the optical phase ϕ(t) ˙ = dϕ(t)/dt. It is a measure for the undesired frequency modulation occurring during the symbol transitions, usually denoted as chirp. The complex envelope of the DPSK transmitter output signals can be extracted from (2.29) and (2.33). The normalized intensity eyes, the IQ diagrams (I m {A(t)} versus Re {A(t)}, where a(t) is scaled here to unity for illustration purposes) and the chirp characteristics are plotted for both transmitter types discussed above and both pulse shapes for 8DPSK modulation in Fig. 2.11, assuming a data rate of 40 Gbit/s and an electrical rise time of 1/4 of the symbol duration.

2.4 DPSK Transmitters - Signal Properties Serial transmitter, NRZ

Serial transmitter, RZ

0.372

Time

0.2 0

1.122

0.372

0 -2.5

0.372

Time

2.5 0 -2.5

1.122

5

x 10

0 -2.5

0.372

Time

1.122

x 10

Intensity

1

-1

5

0

5

0.372

x 10

Time

1

2.5 0 -2.5

11

0 -2.5 0.372

Time

1.122

x 10

11

-5

1.122

2.5

-5

0

Re [A(t)]

11

-2.5 -5

1.122

2.5

-5

0

2.5

11

11

0.372 Time

5

1.122

0

Re [A(t)]

2.5

Time

-1 -1

11

-5

1.122

0.372

1

1

Chirp ⋅ Norm. Int. (1/s)

x 10

Time

0

Chirp (1/s)

Chirp (1/s) 0.372

Chirp ⋅ Norm. Int. (1/s)

Chirp (1/s)

0 -2.5

0.2 0

1.122

0

Re [A(t)] x 10

0.4

-1 -1

5

Time

0.6

1

1

11

-5

Chirp ⋅ Norm. Int. (1/s)

0.372

Chirp (1/s)

0

2.5

-5

0

1.122

0

Re [A(t)]

5

0.2

-1 -1

x 10

0.4

Im [A(t)]

0

-1

5

0.6

1

Im [A(t)]

Im [A(t)]

1

Time

Norm. Intensity

0.4

Chirp ⋅ Norm. Int. (1/s)

0

0.6

0.8

Im [A(t)]

0.2

Parallel transmitter, RZ 1

0.8

Intensity

0.4

Norm. Intensity

0.6

Parallel transmitter, NRZ 1

1 0.8

Intensity

Norm. Intensity

Intensity

Norm. Intensity

1 0.8

33

5

0.372 x 10

Time

1.122

Time

1.122

11

2.5 0 -2.5 -5

0.372

Fig. 2.11 Optical signal properties of different 8DPSK transmitters

When the serial transmitter and NRZ pulse shape are employed, symbol transitions are conducted on circles, and there is constant power during phase changes. Chirp appears during the symbol transitions, and its magnitude depends on the steepness of the phase jumps. An intuitive measure for the disturbing effect of the chirp during transmission is the product of the chirp and the intensity as is shown in the bottom eye diagrams of Fig. 2.11. It becomes apparent that the chirp has a strong effect for the serial transmitter and NRZ pulse shape, due to permanent full power. In the case of RZ, there is almost no optical power during phase changes, and only a very small residual impact of the chirp can be determined. For the parallel transmitter, the impact of the chirp is reduced even for the NRZ pulse shape. The symbol transitions are different due to the usage of an IQ modulator, and power is reduced for some transitions (intensity dips). The chirp shows high peaks when the point of origin is crossed in the IQ diagram (the phase jumps abruptly by ±π). However this is not problematic because no optical power exists at this moment. The product of the chirp and the intensity is clearly reduced compared with the serial NRZ transmitter, so a better transmission performance can be expected.

34

2 Transmitter Design

2.5 Star QAM Transmitters When compared with pure phase modulation, combined phase and amplitude modulation (quadrature amplitude modulation, QAM) exhibits a reduced number of phase states for the same number of symbols. The constellation points can be arranged in a square (Square QAM formats) or they can lie on multiple circles (Star QAM formats). The phases are arranged with equal spacing for Star QAM formats, as shown for Star 16QAM in Fig. 2.13, so the phase difference of any two symbols corresponds to a phase state defined in the constellation diagram and phase information can be differentially encoded as for DPSK formats. Thus, Star QAM signals with differentially encoded phases are suitable to be detected by receivers with differential detection. By contrast, Square QAM signals are conveniently detected by coherent synchronous receivers, but can also be detected by differential detection when phase pre-integration is employed at the transmitter [9]. To accomplish the generation of Star QAM signals with differentially encoded phases, the same equipment can be used as for DPSK transmitters just described. The DPSK transmitters—in serial or parallel configuration—only have to be extended by an additional MZM for intensity modulation, to be able to place symbols on different intensity rings. In principle, arbitrary Star QAM constellations are possible. The Star 8QAM format (2ASK-DQPSK) was investigated in [11]. A Star 8QAM transmitter can be composed of a DQPSK transmitter followed by an additional MZM and can use the same differential encoders as a DQPSK transmitter. The transmitter for Star 16QAM (2ASK-8DPSK) consists of an 8DPSK transmitter, extended by a MZM for intensity modulation, as shown in Fig. 2.12 for the serial configuration.

b1k CW

IS 8DPSK Differential Encoder

Data

1:4 DEMUX

b4k

d 3k d 2k d1k

MZM RZ

IS IS IS

u PM1 (t )

u PM 2 (t )

u PM 3 (t )

PM

PM

PM

π

π/2

π/4

u IM (t ) MZM

Star 16QAM

Fig. 2.12 Optical Star 16QAM transmitter with differential phase encoding, serial configuration

Figure 2.13 illustrates the Star 16QAM constellation diagrams with Gray coded bit mapping (Fig. 2.13a) and symbol assignments at the encoder output for the serial and parallel transmitters (Fig. 2.13b and Fig. 2.13c).

2.5 Star QAM Transmitters a

q 0111 0101 0100

1101 1100

1110

{b1 , b2 , b3 , b4 }

0110 0010

r1 r2

q

0110

0000 0001

1001 1000

i 1010 1001

1011

b 0111

0011

1000 1010

1111

35 0101

0100 0010

r1 r2

c

{d1 , d 2 , d3 , b4 }

0101

0011

0100 0111 0110

0000 0001

i

1110 1100

0000 1111

1011

q

1111

1101 1110 1100

r1 r2

1010 1011

i

1000 0010 1001

0001

1101

{d1 , d 2 , d 3 , b4 }

0011

Fig. 2.13 Star 16QAM Gray coded original bit mapping (a) and symbol assignments at the encoder output for the serial transmitter (b) as well as the parallel transmitter (c)

As for 16DPSK, four bits are mapped to one symbol. However, high spectral efficiency can be obtained here without using the very complex differential 16DPSK encoder. Instead, 8DPSK encoders can be employed. When compared with 8DPSK, the constellation diagram consists of a second circle with eight more symbols. The fourth bit b4k indicates if a symbol belongs to the inner or the outer circle and is used to drive the additional MZM. One degree of freedom which can optimize the OSNR performance for Star QAM formats with only two amplitude states, is the ring ratio R R = r2 /r1 , where r1 and r2 are the amplitudes of the inner and outer circle, respectively, as illustrated in Fig. 2.13. The influence of the ring ratio on the OSNR performance is discussed later on in the second part of this book. Another Star QAM constellation with 16 symbols, composed of four amplitude and four phase states (4ASK-DQPSK), has been investigated in [19]. The definition of only four phase states has the advantage that data recovery is easier to accomplish for differential detection. On the other hand, the use of more than two amplitude states leads to high OSNR requirements for intensity detection and therefore to a poor overall OSNR performance. Generally, when using the serial NRZ-Star QAM transmitter, an optical Star QAM signal with only two amplitude states can be mathematically described by   uPM (t) u P M (t) p m−1 π u I M (t) j Vπ1 π j j (ωs t+ϕs ) V π ·e · ... · e · cos π . (2.39) E s (t) = Ps · e 2Vπ In (2.39), the phase modulator driving signals u P M1 (t)...u P Mm−1 (t) are again defined by (2.30) with n = {1..(m − 1)}. The electrical driving signal for intensity modulation depends on the desired ring ratio, and is specified by     2 arccos R1R 2 arccos R1R X
· Vπ + · Vπ · bm k · p (t − kTS ) , (2.40) u I M (t) = − π π k

where bm k ∈ {0, 1} corresponds to the last data bit of a symbol with m bits in the k-th symbol interval.

36

2 Transmitter Design

Similarly, the last phase modulator of the parallel DPSK transmitter, whose output signal is given by (2.33), can be replaced with an intensity modulator to obtain the parallel Star QAM transmitter. Its output signal is then given by p E s (t) = Ps · e j (ωs t+ϕs ) · a I Q M (t) · e jϕ I Q M (t)   uPM (t) u P M (t) m−1 π u I M (t) j Vπ3 π j V π ·e · ... · e · cos π . (2.41) 2Vπ In Fig. 2.14, the eye diagrams of the normalized intensity, the IQ diagrams, and the chirp characteristics are depicted for the serial and the parallel Star 16QAM transmitter, considering NRZ and RZ pulse shapes and assuming a ring ratio of 1.8, a data rate of 40 Gbit/s and an electrical rise time of 1/4 of the symbol period.

Serial transmitter, NRZ

Serial transmitter, RZ

0.5

Time

0.2 0

1.5

0.5

-1

0

-1

0.5

Time

0 -2.5

1.5

5

Chirp (1/s)

-2.5

5

0.5

Time

0

0.5

Time

Intensity

1

-1

1.5

5

0 -2.5

5

0.5 x 10

Time

0

Time

1.5

x 10

1

11

0 -2.5 -5

1.5

-2.5 0.5

0

2.5

11

2.5

-5

1.5

Re [A(t)]

11

-5

1.5

-2.5 -5

0

2.5

11

2.5

x 10

Time

0

Re [A(t)]

0

x 10

0.5

-1 -1

11

-5

1.5

2.5

Time

0

1

2.5

11

0.5

0

Chirp ⋅ Norm. Int. (1/s)

Chirp (1/s)

-2.5

Chirp ⋅ Norm. Int. (1/s)

Chirp (1/s)

0

x 10

0.2 0

1.5

1

Re [A(t)] 5

Time

0.4

-1

1

11

-5

Chirp ⋅ Norm. Int. (1/s)

0.5

Chirp (1/s)

0

2.5

-5

0

1.5

0.6

1

Re [A(t)]

5

0.2

-1 -1

x 10

0.4

Im [A(t)]

0

x 10

0.6

1

Im [A(t)]

Im [A(t)]

1

Time

Norm. Intensity

0.4

Chirp ⋅ Norm. Int. (1/s)

0

0.6

0.8

Im [A(t)]

0.2

1

0.8

Intensity

0.4

0.8

Intensity

Norm. Intensity

Intensity

Norm. Intensity

0.6

Parallel transmitter, RZ

1

Norm. Intensity

1

1 0.8

5

Parallel transmitter, NRZ

5

0.5

x 10

Time

1.5

11

2.5 0 -2.5 -5

0.5

Time

1.5

Fig. 2.14 Optical signal properties of different Star 16QAM transmitters

The same conclusions can be drawn as for 8DPSK. The impact of the chirp, which appears at the phase transitions, is reduced when the parallel configuration is employed, and is almost eliminated when RZ pulses are transmitted. This becomes apparent from the product of the chirp and the intensity (bottom diagrams in Fig. 2.14), introduced as an intuitive performance measure in Sect. 2.4.4.

2.6 Differential Quadrant Encoding

37

2.6 Square QAM Transmitters In Star QAM constellations described in the last section, first suggested by Cahn in 1960 [3], the same number of symbols is placed on different concentric circles. Star QAM signals can easily be generated by enhancing a phase modulation transmitter for an additional intensity modulation and can be differentially detected. On the other hand, these constellations are not optimal as regards noise performance, because symbols on the inner ring are closer together than symbols on the outer ring. In order to improve noise performance, Hancock and Lucky suggested placing more symbols on the outer ring than on the inner ring [5], leading to constellations with more balanced Euclidean distances. But they came to the conclusion that such systems are more complicated to implement. In 1962, the Square QAM constellation, shown in Fig. 2.15 for Square 16QAM, was introduced for the first time by Campopiano and Glazer [4]. Indeed, Square QAM signals are conveniently detected by coherent synchronous receivers and offer only a small improvement in noise performance, but—thinking in terms of two quadrature carriers—relatively simple modulation and demodulation schemes are possible, due to the regular structure of the constellation projected on the in-phase and quadrature axis. Today, the Square QAM is widely used in electrical systems. In optical transmission systems, however, it is still very distant from a commercial practical implementation. The next sections illustrate different transmitter options for generating optical Square QAM signals, which are denoted here as “serial Square QAM transmitter”, “conventional IQ transmitter”, “enhanced IQ transmitter”, “Tandem-QPSK transmitter” and “multi-parallel MZM transmitter”. Each of these transmitters features different properties of its output signals and different complexities of its optical and electrical parts, which can be traded off. Detailed information about the electrical parts is provided, especially for two particular modulation formats: Square 16QAM, to which a special focus is brought in this book, and Square 64QAM, which is included here as a very ambitious format. Before going into the details of the transmitters, Sect. 2.6.1 outlines the differential quadrant encoding which must be employed for all transmitter configurations when the quadrant ambiguity arising at the carrier synchronization at the receiver shall be resolved through differential coding.

2.6.1 Differential Quadrant Encoding A n times π/2 (n = 0, 1, 2, 3) phase ambiguity (quadrant ambiguity) arises at the carrier synchronization for synchronous detection of Square QAM signals, which can be resolved by so-called differential quadrant encoding. This encoding scheme combines a DQPSK encoding with a specific bit mapping, and was proposed by Weber in [22]. Two of the m bits of a Square QAM symbol determine the quadrant and are differentially encoded using a DQPSK differential encoder. This way, these two bits can be unambiguously recovered even if the absolute position of the received

38

2 Transmitter Design

constellation diagram is ambiguous with n times π/2. The remaining (m − 2) bits can also be determined correctly for any n times π/2 rotation when the bit mapping is arranged as rotation symmetric with respect to these bits. As an undesired consequence, the bit mapping is then not further Gray coded, leading to an OSNR performance degradation compared with Gray coded bit mappings. Gray coded Square QAM signals can be received for instance when sending training sequences.

a

q

{b1 , b2 , b3 , b4 }

b

q

{d1 , d 2 , b3 , b4 }

1111

1110

0101

0111

0111

0110

1101

1111

1101

1100

0100

0110

0101

0100

1100

1110

1010

1000

0000

0001

0010

0000

1000

1001

1011

1001

0010

0011

0011

0001

1010

1011

i

i

Fig. 2.15 a Bit mapping used for Square 16QAM, appropriate for differential quadrant encoding. b Symbol assignment after the DQPSK differential encoder.

Figure 2.15a shows a non Gray coded Square 16QAM bit mapping which is appropriate for differential quadrant encoding. It can be observed that any rotation of n times π/2 (n = 0, 1, 2, 3) causes no difference to the last two bits b3k and b4k . The first two bits, b1k and b2k , determine the quadrant and are encoded with a DQPSK differential encoder. When using the differential encoder of the parallel DQPSK transmitter described in Sect. 2.4.3, the differentially encoded bits d1k and d2k at the encoder output are assigned to the quadrants as illustrated in Fig. 2.15b.

2.6.2 Serial Square QAM Transmitter In contrast to Star QAM constellations, the phases are arranged unequally spaced in Square QAM constellations, so that it is not possible to adjust all the phase states of the symbols by simply driving consecutive phase modulators with binary electrical driving signals. In [6], it was shown that any optical QAM signal can be generated by using a single dual-drive MZM (see Fig. 2.1b). In this case, however, the necessary number of states of electrical driving signals is quite high (e.g. 16-ary driving signals are needed for Square 16QAM), and a big electrical effort has to be engaged in to enable the simplicity of the optical part.

2.6 Serial Square QAM Transmitter

39

d1k d 2k

Level Generator

b1k b2k b3k bmk

DQPSK Differential Encoder

Data

1:m DEMUX

Another transmitter with a simple optical part capable of creating any QAM constellation is constituted by only two consecutive optical modulators: a MZM for adjustment of the amplitude state and a consecutive PM to set the phase. This transmitter is denoted as serial Square QAM transmitter throughout this book and is shown in Fig. 2.16. One more MZM can be employed for RZ pulse carving. The simplicity of the optical receiver part necessitates the use of a complex electrical level generator, since electrical driving signals with a high number of states must be generated (12-ary electrical driving signals are required for phase modulation in the case of Square 16QAM, for instance).

IS IS

uIM (t ) MZM RZ

CW

MZM

u PM (t ) PM

Square QAM

Fig. 2.16 Square QAM transmitter, serial configuration

The optical output signal of the serial Square QAM transmitter for NRZ pulse shape is given by   p u P M (t) u I M (t) j (ωs t+ϕs ) · cos (2.42) E s (t) = Ps · e π · e j Vπ π . 2Vπ In order to adjust the desired amplitude and phase levels, the multi-level electrical driving signals for the MZM and the PM must be chosen as  q   i k2 + qk2 X 2Vπ arcsin  √  · p (t − kTS ), (2.43) u I M (t) = −Vπ + · π 2 k

u P M (t) =

 
Vπ X · arg i k , qk · p (t − kTS ) . π

(2.44)

k

Equations (2.43) and (2.44) are generally applicable to any QAM constellation, and i k and qk represent the normalized symbol coordinates. For Square 16QAM, for instance, it holds i k ∈ {−1, −1/3, 1/3, 1} and qk ∈ {−1, −1/3, 1/3, 1}, and the nor-

40

2 Transmitter Design

 malized symbol coordinates i k and qk are related to the data bits d1k , d2k , b3k , b4k as defined by the bit mapping shown in Fig. 2.15b and as specified in Table 2.3.  Table 2.3 Relation between the data bits d1k , d2k , b3k , b4k , the normalized symbol coordinates i k and qk , the normalized symbol amplitudes and the symbol phases for Square 16QAM after differential quadrant encoding for the bit mapping defined in Fig. 2.15b d1k

d2k

b3k

b4k

ik

qk

Normalized amplitude

Phase (◦ )

0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

-1/3 -1/3 -1 -1 -1/3 -1 -1/3 -1 1/3 1 1/3 1 1/3 1/3 1 1

-1/3 -1 -1/3 -1 1/3 1/3 1 1 -1/3 -1/3 -1 -1 1/3 1 1/3 1

1/3 0.74 0.74 1 1/3 0.74 0.74 1 1/3 0.74 0.74 1 1/3 0.74 0.74 1

225 251.57 198.43 225 135 161.57 108.43 135 315 341.57 288.43 315 45 71.57 18.43 45

The arcsin-function in (2.43) makes sure to approach the appropriate intensity levels while taking the cosine field transfer function of the MZM into account. In [16], the electrical driving signals were classified as ideal and non-ideal. The so-called “ideal” driving signals, which are not very practical to generate, can be regarded as a theoretical approach to completely compensate for the MZM characteristic, so that the electrical pulse shape is directly transposed to the optical field amplitude. The “non-ideal” driving signals presented here yield correct intensity and phase states, but lead to small differences during the symbol transitions because they do not fully compensate for the cosine MZM characteristic. When observing (2.43), for instance, the corresponding “ideal” driving signal would be obtained by applying the arcsin-function to the whole sum. More details about this classification of the driving signals can be found in [16]. One of the main challenges for the practical implementation of the serial Square QAM transmitter is the generation of the multi-level electrical driving signals with an electrical level generator. The level-generator is located behind the differential encoder, as depicted in Fig. 2.16, and acts as a digital-to-analog converter. Figure 2.17 shows a possible setup of the level-generator for Square 16QAM, composed of AND-, NOR-, XOR- and XNOR-gates, an inverter, and attenuators. It illustrates the complexity of the electrical part in the serial Square QAM transmitter.

2.6 Serial Square QAM Transmitter

41

Level generator Inverter

d1k d 2k

-1

+ PS

XOR

α 12-ary signal to PM

0.5 XNOR

+

α

IS

u PM (t )

0.25 XOR

b3k

AND

PS

α 0.1

XOR AND

α 0.4

b4k

PS AND

NOR

3-ary signal to MZM α

+

IS

uIM (t )

0.22 XOR

α 0.53

Attenuators

Fig. 2.17 Electrical level generator for the serial Square 16QAM transmitter, PS: power splitter

An optical Square 16QAM signal has 3 amplitude levels and 12 different phase q √   2 2 states. The normalized amplitudes (given by i k + qk / 2) and phases (arg i k , qk , in degrees) assigned to particular symbols after the differential encoder are listed in Table 2.3. When considering the generation of the 3-ary electrical driving signal for the MZM, the normalized amplitude is “1” if b3k and b4k are both logical one (application of an AND-gate), “1/3” if b3k and b4k are both logical zero (NOR-gate), and “0.74” if b3k and b4k are different (XOR-gate), respectively (see Table 2.3). This yields the configuration of the lower part of the level generator depicted in Fig. 2.17. The amplitude states of the MZM driving signal have to be further adjusted to compensate for the nonlinear MZM characteristic, resulting in the attenuation values shown in Fig. 2.17. For the generation of the 12-ary driving signal for the phase modulator, it can be observed from Table 2.3 that the phase is equal to 18.43◦ plus n times 90◦ if b3k is logical one and b4k is logical zero (realization by an XOR-gate and an AND-gate), equal to 45◦ plus n times 90◦ if b3k and b4k are both logical zero or both logical one (XNOR), equal to 71.57◦ plus n times 90◦ if b3k is logical zero and b4k is logical one (XOR, AND), and that d1k and d2k determine the quadrant,

42

2 Transmitter Design

and thus the value of n (n = 0, 1, 2, 3). To obtain a PM driving signal normalized to one, the appropriate values of the attenuators are also given in Fig. 2.17. With the level generator described, the driving signals for the MZM and the PM are generated with the adequate relative values. It should be noted that the given attenuation values are only valid if the logical gates are operated with DC coupling at the outputs to obtain unipolar digital output signals. In practice, both signals must be amplified by modulator drivers to obtain the appropriate driving voltages for the modulators.

2.6.3 Conventional IQ Transmitter

cmk

Level Gen.

c1k

Level Gen.

d1k d 2k

Square QAM Coder

b1k b2k b3k bmk

DQPSK Differential Encoder

Data

1:m DEMUX

It can be concluded from Sect. 2.6.2 that the serial Square QAM transmitter features a simple optical part, but requires a complex electrical level-generator which can not easily be implemented for high data rates. Due to the beneficial projection of the constellation points on the in-phase and quadrature axis, it is an advantage to generate square shaped constellations with IQ transmitters. This way, the number of states of the driving signals and thus the electrical complexity can effectively be reduced in comparison with the serial Square QAM transmitter. In Fig. 2.18, the setup of the conventional IQ transmitter for Square QAM is illustrated.

IS IS

u I (t ) MZM

CW

MZM RZ

3dB

3dB -90°

MZM

Square QAM Signal

uQ (t )

Fig. 2.18 Conventional IQ transmitter for Square QAM

The optical IQ modulator is also used within the parallel DPSK and Star QAM transmitter (see Sect. 2.4.2 and Sect. 2.5) to perform a DQPSK modulation. Whereas the in-phase and quadrature driving signals are binary for DQPSK, multi-level electrical driving signals are required to generate higher-order optical Square QAM constellations. The number of levels of the electrical driving signals is equal to the number of projections of the symbol points to the I-axis and the Q-axis (e.g. quaternary driving signals are required for Square 16QAM).

2.6 Conventional IQ Transmitter

43

The optical output signal of the conventional IQ transmitter for Square QAM for NRZ pulse shape can be simply described by p E s (t) = Ps · e j (ωs t+ϕs ) · a I Q M (t) · e jϕ I Q M (t) . (2.45) In (2.45), a I Q M (t) and ϕ I Q M (t) are the amplitude and phase modulation of the IQM, which are defined in (2.17) and (2.18), respectively. The in-phase and quadrature driving signals are now multi-level and specified as u I (t) = −Vπ +

 2Vπ X  · arcsin (i k ) · p (t − kTS ) , π

u Q (t) = −Vπ +

 2Vπ X  · arcsin (qk ) · p (t − kTS ) . π

(2.46)

k

(2.47)

k

For the ideal driving case, the arcsin-function would have to be applied to the whole sum in both equations [16]. In order to generate the appropriate driving signals with simple level generators, the symbol assignment after the differential DQPSK encoder (see differential quadrant encoding, Sect. 2.6.1) must be rearranged by another coder, which is denoted as Square QAM coder in the following. In practice, it is possible to implement this coder together with the DQPSK differential encoder as one single component, possibly through the use of digital signal processing.

q

{d1 , d 2 , b3 , b4 }

q

{c1 , c2 , c3 , c4 }

0111

0110

1101

1111

0101

0111

1101

1111

0101

0100

1100

1110

0100

0110

1100

1110

0010

0000

1000

1001

0001

0011

1001

1011

0011

0001

1010

1011

0000

0010

1000

1010

i

i

Fig. 2.19 Rearranging of the symbols by the Square 16QAM coder within the conventional IQ transmitter

Figure 2.19 illustrates how the bits have to be rearranged for Square 16QAM. By rotating the symbols in the n-th quadrant by n times π/2, the differentially encoded first bit d1k and the third bit b3k as well as the differentially encoded second bit d2k and the fourth bit b4k are arranged in chronologically increasing order with increasing signal levels in the in-phase and quadrature arms, respectively. Table 2.4 shows the truth table for the rearrangement of the symbols. It also illustrates the

44

2 Transmitter Design

relation between the normalized symbol coordinates i k and qk , used in (2.46) and (2.47), the data bits d , d , b , b and the output bits of the Square 16QAM 3 4 1 2 k k k k  coder, denoted as c1k , c2k , c3k , c4k , for the conventional IQ transmitter. Table 2.4 Truth table of the Square QAM coder and relation of the data bits and the normalized symbol coordinates i k and qk when using the conventional IQ transmitter for Square 16QAM d1k

d2k

b3k

b4k

c1k

c2k

c3k

c4k

ik

qk

0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1

1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1

-1/3 -1/3 -1 -1 -1/3 -1 -1/3 -1 1/3 1 1/3 1 1/3 1/3 1 1

-1/3 -1 -1/3 -1 1/3 1/3 1 1 -1/3 -1/3 -1 -1 1/3 1 1/3 1

Because the symbol rearrangement is confined to the particular quadrants, the first two bits are not changed by the Square QAM coder, so that c1k = d1k and c2k = d2k . By analyzing the truth table given in Table 2.4, the following logical relations can easily be derived for the third and the fourth output bit of the Square 16QAM coder: c3k = d1k d2k b3k + d1k d2k b4k + d2k b3k b4k + d1k d2k b4k + d1k b3k b4k , (2.48) c4k = d1k b3k b4k + d1k d2k b3k + d1k d2k b4k + d1k d2k b3k + d2k b3k b4k . (2.49) The new symbol assignment allows for the use of a simple level generator to generate the quaternary electrical driving signals in the in-phase and quadrature arms. This level generator is shown in Fig. 2.20, and is far less complex than for the serial Square 16QAM transmitter. The bits c1k and c3k are used as inputs for the levelgenerator in the in-phase arm, and the bits c2k and c4k are used as inputs for the one in the quadrature arm. As can be seen from (2.46) and (2.47), the driving amplitude has to take the value −Vπ if both input bits are logical zero, − arcsin (1/3) · 2Vπ /π if the first input bit is logical zero and the second logical one, arcsin (1/3) · 2Vπ /π if the first input bit is logical one and the second logical zero, and Vπ if both input bits are logical one. The DC coupled unipolar input signals simply have to be added with the appropriate weights, and the resulting signal must be passed via a DC blocker

2.6 Conventional IQ Transmitter

45

to the consecutive impulse shaper, and then to a modulator driver to provide for the required MZM driving voltages.

Level generator

c1k / c2k

+ c3k / c4k

α

IS

u I (t ) / uQ (t )

DC blocker

0.64

Fig. 2.20 Level generator for the conventional Square 16QAM IQ transmitter

The Square 64QAM constellation is composed of 64 symbols in a square array. In Fig. 2.21, a Square 64QAM constellation diagram with rotation symmetric symbol assignments after differential quadrant encoding is shown.

01

q

270°

{b3 , b4 , b5 , b6 } {d1 , d 2 }

1111

1110

1011

1010

0101

0111

1101

1111

1101

1100

1001

1000

0100

0110

1100

1110

0111

0110

0011

0010

0001

0011

1001

1011

0101

0100

0001

0000

0000

0010

1000

1010

180°

00

11

i

90°

1010

1000

0010

0000

0000

0001

0100

0101

1011

1001

0011

0001

0010

0011

0110

0111

1110

1100

0110

0100

1000

1001

1100

1101

1111

1101

0111

0101

1010

1011

1110

1111

10

Fig. 2.21 Rotation symmetric Square 64QAM constellation diagram after differential quadrant encoding; the bits in the corners are the first two bits of a symbol, being differentially encoded; the arrows indicate the rearrangement of the symbols by the Square 64QAM coder.

46

2 Transmitter Design

One symbol carries the information of six bits. The first two bits d1k and d2k , which are differentially encoded by a DQPSK differential encoder to enable resolving the quadrant ambiguity of the carrier synchronization at the receiver, are equal within each quadrant and depicted in the corners of the constellation diagram. The last four bits b3k ...b6k are arranged as rotation symmetric, so a quadrant ambiguity at the receiver has also no impact on the information recovery of these data bits. The symbols have 10 different amplitudes and 52 different phases. Due to the high number of different phase states, only an IQ transmitter seems to be feasible for signal generation. For the conventional IQ transmitter, the in-phase and quadrature driving signals have eight levels each. Like for Square 16QAM, the symbols should be rearranged by a Square QAM coder for Square 64QAM to produce a symbol assignment that allows for the usage of simple level generators to generate the 8-ary electrical in-phase and quadrature electrical driving signals. When rearranging the bits as indicated by the arrows in Fig. 2.21, the first, third and fifth bits are sorted in chronologically increasing order with increasing signal levels in the in-phase arm, and in the same way the second, fourth and sixth bits with increasing signal levels in the quadrature arm. The resulting constellation diagram with re-assigned symbols behind the Square 64QAM coder is shown in Fig. 2.22.

q

01

{c3 , c4 , c5 , c6 } {c1 , c2 }

0101

0111

1101

1111

0101

0111

1101

1111

0100

0110

1100

1110

0100

0110

1100

1110

0001

0011

1001

1011

0001

0011

1001

1011

0000

0010

1000

1010

0000

0010

1000

1010

11

i

00

0101

0111

1101

1111

0101

0111

1101

1111

0100

0110

1100

1110

0100

0110

1100

1110

0001

0011

1001

1011

0001

0011

1001

1011

0000

0010

1000

1010

0000

0010

1000

1010

10

Fig. 2.22 Symbol assignment after the Square 64QAM coder, optimized for the Square 64QAM level generator

2.6 Enhanced IQ Transmitter

47

 When denoting the input bits as d1k , d2k , b3k , b4k , b5k , b6k , and the output bits as c1k , c2k , c3k , c4k , c5k , c6k , the logical circuit of the Square 64QAM coder can be described as follows: c3k = d1k b3k b4k + d2k b3k b4k + d2k b3k b4k + d1k d2k b4k + d1k d2k b3k , (2.50) c4k = d1k d2k b4k + d1k d2k b3k + d1k d2k b3k + d1k b3k b4k + d2k b3k b4k , (2.51) c5k = d1k d2k b5k + d1k d2k b6k + d2k b5k b6k + d1k d2k b6k + d1k b5k b6k , (2.52) c6k = d1k b5k b6k + d1k d2k b5k + d1k d2k b6k + d1k d2k b5k + d2k b5k b6k . (2.53) The first two bits do not change, so it holds true that c1k = d1k and c2k = d2k . The output bits c1k , c3k and c5k serve as inputs for the Square 64QAM level generator in the in-phase arm, and the remaining three bits as inputs for the level generator in the quadrature arm. The Square 64QAM level generators must generate 8-ary electrical driving signals with the appropriate amplitude levels, which can be deducted from (2.46) and (2.47). The normalized symbol coordinates in (2.46) and (2.47) are given as i k ∈ {−1, −5/7, −3/7, −1/7, 1/7, 3/7, 5/7, 1} and qk ∈ {−1, −5/7, −3/7, −1/7, 1/7, 3/7, 5/7, 1} and can be related to the data bits using the bit mappings illustrated in Fig. 2.21 and Fig. 2.22.

2.6.4 Enhanced IQ Transmitter When the conventional IQ transmitter is used, the number of levels of the electrical driving signals required for a particular modulation format is equal to the number of states of i k and qk , respectively. With the aim of further reducing the number of states of the electrical driving signals, a modified IQ transmitter configuration can be employed, which is denoted here as enhanced IQ transmitter [17]. By replacing the amplitude modulation in each arm with separate intensity and phase modulations, the necessary number of levels of the driving signals can be reduced to half in comparison with the conventional IQ configuration. To accomplish intensity modulation, a MZM can be used in each arm which is operated at the quadrature point. The negative values on the I-axis and the Q-axis are reached by varying the phase between 0 and π, using phase modulators or MZMs operated at the minimum transmission point. Because the phase has to be varied only between 0 and π , binary signals are sufficient for phase modulation for any modulation format. This way, the eye spreading problem, arising with the generation of multi-level electrical driving signals, can be mitigated in practice.

48

2 Transmitter Design

CW

MZM RZ

d1k d 2k

c1k Square 16QAM Coder

b1k b2k b3k b4k

DQPSK Differential Encoder

Data

1:4 DEMUX

The application of the enhanced IQ transmitter is of special interest for Square 16QAM. Only binary driving signals are required here for all the modulators. This results in a simpler electrical transmitter part without level generators, composed of just a 1 : 4 demultiplexer, the coders and the modulator drivers. In Fig. 2.23, the enhanced IQ transmitter is illustrated for Square 16QAM, composed of MZMs for intensity modulation and PMs for phase modulation here.

c2 k c3k c4 k

IS IS IS IS

u I PM (t ) uQPM (t ) u I MZM (t ) uQMZM (t )

MZM

PM

MZM

PM

3dB

3dB -90°

Square 16QAM

Fig. 2.23 Enhanced IQ transmitter for Square 16QAM

When defining the electrical driving signals of the Mach-Zehnder modulators for the non-ideal driving case in the in-phase and quadrature branches as u I M Z M (t) = −Vπ +

 2Vπ X  · arcsin (|i k |) · p (t − kTS ) , π

u Q M Z M (t) = −Vπ +

 2Vπ X  · arcsin (|qk |) · p (t − kTS ) , π

(2.54)

k

(2.55)

k

and with the driving signals of the phase modulators in both arms given by u I P M (t) =

 Vπ X  · (−sign (i k ) + 1) · p (t − kTS ) , 2

u Q P M (t) =

 Vπ X  · (−sign (qk ) + 1) · p (t − kTS ) , 2

(2.56)

k

k

the field transfer function of the enhanced IQ transmitter can be expressed as

(2.57)

2.6 Enhanced IQ Transmitter

49





uI (t) PM E out (t) u I M Z M (t) 1 = cos π e j Vπ π E in (t) 2 2Vπ   u Q (t) PM u Q M Z M (t) 1 π e j Vπ π + j cos 2 2Vπ 1 1 = · a I (t) · e jϕ I (t) + j · a Q (t) · e jϕ Q (t) . 2 2

(2.58)

The optical Square QAM output signal of the enhanced IQ transmitter for NRZ pulse shape is p E s (t) = Ps · e j (ωs t+ϕs ) · a(t) · e jϕ(t) , (2.59)

where the amplitude and phase of the normalized complex envelope follow from (2.58) by applying complex arithmetic and are given by a(t) =


1q 2 a I (t) + a 2Q (t) + 2a I (t)a Q (t) sin ϕ I (t) − ϕ Q (t) , 2 ϕ(t) = arg {a I (t) cos ϕ I (t) − a Q (t) sin ϕ Q (t), a I (t) sin ϕ I (t) + a Q (t) cos ϕ Q (t)}.

(2.60)

(2.61)

The rearrangement of the bits must be accomplished in a different way than for the conventional IQ transmitter. Figure 2.24 illustrates how the symbols after the differential encoder must be rearranged for Square 16QAM within the enhanced IQ transmitter using a Square QAM coder.

q

{d1 , d 2 , b3 , b4 }

q

{c1 , c2 , c3 , c4 }

0111

0110

1101

1111

0111

0101

1101

1111

0101

0100

1100

1110

0110

0100

1100

1110

0010

0000

1000

1001

0010

0000

1000

1010

0011

0001

1010

1011

0011

0001

1001

1011

i

i

Fig. 2.24 Symbol reassignment within the Square 16QAM enhanced IQ transmitter

Only four symbols in the second and the fourth quadrant have to change their positions to generate a symbol assignment where the first bit d1k = c1k and the second bit d2k = c2k (both inverted) define if a phase shift of π is performed by the phase modulators in the in-phase and the quadrature arms, respectively. The

50

2 Transmitter Design

inverters can be saved, because the resulting rotation of π does not matter at the receiver when differentially quadrant encoding is employed. By the third bit c3k and the fourth bit c4k the intensity levels in the in-phase and quadrature arms are specified as low or high, respectively. Table 2.5 shows the truth table for symbol rearrangement. It also illustrates the relation between the normalized symbol coordinates i k and qk , used in  (2.54)–(2.57), and the data bits d , d , b , b as well as the four output bits 1 2 3 4 k k k k  c1k , c2k , c3k , c4k of the Square 16QAM coder for the enhanced IQ transmitter. Table 2.5 Truth table of the Square QAM coder and relation of the data bits and the normalized symbol coordinates i k and qk when using the enhanced IQ transmitter for Square 16QAM d1k

d2k

b3k

b4k

c1k

c2k

c3k

c4k

ik

qk

0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

0 0 1 1 0 1 0 1 0 1 0 1 0 0 1 1

0 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1

-1/3 -1/3 -1 -1 -1/3 -1 -1/3 -1 1/3 1 1/3 1 1/3 1/3 1 1

-1/3 -1 -1/3 -1 1/3 1/3 1 1 -1/3 -1/3 -1 -1 1/3 1 1/3 1

The logical circuit of the Square QAM coder for the enhanced Square 16QAM transmitter is defined by (2.62) and (2.63). These relations can be easily derived from the truth table given by Table 2.5. Both first bits do not change (so it holds true that c1k = d1k and c2k = d2k ), and the third and fourth output bits are related to the input bits as c3k = d1k d2k b3k + d1k d2k b3k + d1k d2k b4k + d1k d2k b4k ,

(2.62)

c4k = d1k d2k b3k + d1k d2k b3k + d1k d2k b4k + d1k d2k b4k .

(2.63)

The optical part of the enhanced IQ transmitter can be simplified by performing the separate intensity and phase modulations in each arm with only one component. For this purpose, a dual-drive MZM can be used, driven simultaneously in the pushpull mode for intensity modulation and in the push-push mode for phase modulation. However, the driving signals for intensity and phase modulation must be electrically combined in that case before being injected into the MZM inputs [16].

2.6 Tandem-QPSK Transmitter

51

2.6.5 Tandem-QPSK Transmitter

b1k b2k b3k b4k

DQPSK Differential Encoder

Data

1:4 DEMUX

Another transmitter also requiring only binary electrical driving signals for Square 16QAM is denoted as Tandem-QPSK transmitter throughout this book and can be composed of an optical IQ modulator followed by a DQPSK modulator. The latter can be implemented either with one more IQ modulator, or with two consecutive phase modulators, as depicted in Fig. 2.25.

d1k d 2k

IS IS IS IS

u PM1 (t ) u PM 2 (t ) u I (t ) uQ (t )

MZM CW

MZM RZ

3dB

3dB -90°

MZM

PM

PM

π

π/2 Square 16QAM

Fig. 2.25 Optical Tandem-QPSK transmitter for Square 16QAM

Like for the enhanced IQ transmitter, the MZMs within the IQ modulator achieve modulation in intensity. This way, only positive values on the in-phase and quadrature axis are addressed. As regards Square 16QAM, the MZMs are driven by binary electrical signals, and a constellation composed of four symbols in the first quadrant is created. In a similar way to the enhanced IQ transmitter, the electrical driving signals of the MZMs are defined here as u I (t) = −Vπ +

i   2Vπ X h · arcsin i k1 · p (t − kTS ) , π

u Q (t) = −Vπ +

i   2Vπ X h · arcsin qk1 · p (t − kTS ) , π

(2.64)

k

(2.65)

k

where i k1 and qk1 represent the normalized symbol coordinates in the first quadrant of the constellation diagram and are directly related to the data bits b3k and b4k , respectively. For the bit mapping depicted in Fig. 2.15a, i k1 = 1(1/3) for b3k = 1(0) and qk1 = 1(1/3) for b4k = 1(0). Operating the IQ modulator in this way has the same effect as interfering a DQPSK signal with a CW wave, as proposed in [10]. With two consecutive phase modulators which perform phase shifts of π and π/2, respectively, the three other quadrants can be approached, thus creating a

52

2 Transmitter Design

complete Square QAM constellation. It is a beneficial side-effect of this transmitter type that—initiated through signal generation—the resulting constellation is inherently symmetric in rotation as regards the data bits b3k and b4k , so that no additional Square QAM coder for symbol rearrangement is needed to constitute a rotation symmetric symbol assignment which is required to handle the quadrant ambiguity at the receiver. It should be noted that the differential encoder for the serial DQPSK transmitter must be employed when performing the quadrant shift with two consecutive phase modulators as shown in Fig. 2.25. With the amplitude and phase modulation of the IQ modulator, a I Q M (t) and ϕ I Q M (t), defined by (2.17) and (2.18), respectively, and with the phase modulator driving signals u P M1 (t) and u P M2 (t) given by (2.30) as for the serial DPSK transmitter (n = 1, 2), the optical output signal of the Tandem-QPSK transmitter for NRZ pulse shape can be described by E s (t) =

p

Ps · e j (ωs t+ϕs ) · a I Q M (t) · e jϕ I Q M (t) · e j

u P M (t) 1 π Vπ

· ej

u P M (t) 2 π Vπ

. (2.66)

The Tandem-QPSK transmitter is a promising option for practically implementing Square 16QAM systems, since the driving signals are binary and the signal generation is well suited for creating rotation symmetric constellations.

2.6.6 Multi-Parallel MZM Transmitter Another option for generating Square QAM signals, which has been recently proposed in [14, 15], is to use a multi-parallel MZM transmitter. Its setup for Square 16QAM is illustrated in Fig. 2.26. By arranging two IQ modulators in parallel, a Square 16QAM signal can be synthesized from two QPSK signals. The so-called “large-amplitude QPSK” is created by the upper IQM and determines the quadrant to which the symbol is mapped. The “small-amplitude QPSK” is obtained after the attenuator in the lower branch (attenuation 6 dB) and fixes the position of a symbol within the quadrant. The Square 16QAM constellation is finally assembled by the combination of both QPSK signals. All MZMs are operated at the minimum transmission point. The Square 16QAM signal is generated by driving them only with binary electrical signals, so that the transmitter is free from handling multi-level electrical driving signals—just like the enhanced IQ transmitter and the Tandem-QPSK transmitter. The Square 16QAM transmitter shown in Fig. 2.26 is denoted as quad-parallel MZM transmitter because four MZMs are used in parallel. Generally, a M-ary Square QAM signal can be created by a multi-parallel MZM transmitter being composed of m/2 optical IQMs and accordingly m MZMs. The power attenuation in the n-th IQM branch must then be chosen as (n − 1) · 6 dB. To generate the modulator driving signals, the same coders as those appropriate for the conventional IQ transmitter can be employed in the electrical part of the multi-parallel MZM transmitter. In Fig. 2.19, it is shown how the bit mapping

d1k d 2k

53 c1k Square 16QAM Coder

b1k b2k b3k b4k

DQPSK Differential Encoder

Data

1:4 DEMUX

2.6 Multi-Parallel Transmitter

c2 k c3k c4 k

IS IS IS IS

u I L (t ) IQ-Modulator 1 MZM 3dB

3dB MZM

-90°

CW

MZM RZ

uQL (t )

3dB

3dB

u I S (t ) IQ-Modulator 2

Square 16QAM

MZM 3dB

3dB MZM

-90°

α 6dB

uQS (t )

Fig. 2.26 Quad-parallel MZM transmitter for generation of Square 16QAM signals

after differential encoding must be rearranged by a Square QAM coder for Square 16QAM to create a symbol assignment suitable for driving the four MZMs of the quad-parallel MZM transmitter. To create the large-amplitude QPSK, the MZMs in the in-phase and quadrature branches in the upper IQM branch are driven by X
u I /Q L (t) = −2Vπ + 2Vπ · c1/2k · p (t − kTS ) , (2.67) k

where c1k = d1k and c2k = d2k represent the first and second output bit of the Square 16QAM coder, respectively. The driving signals for the generation of the small-amplitude QPSK depend on the third and fourth Square 16QAM coder output bits and are specified by X
u I /Q S (t) = −2Vπ + 2Vπ · c3/4k · p (t − kTS ) . (2.68) k

After combining the QPSK signals of both branches in a 3 dB coupler at the output of the quad-parallel MZM transmitter, the optical Square 16QAM output signal at the lower output port of the 3 dB coupler—when neglecting constant phase shifts and assuming NRZ line coding—is given by E s (t) =

h 1p Ps · e j (ωs t+ϕs ) · a I Q M L (t) · e jϕ I Q M L (t) 2  1 jϕ I Q M S (t) + a I Q M S (t) · e . 2

(2.69)

54

2 Transmitter Design

In (2.69), a I Q M L/S (t) and ϕ I Q M L/S (t) describe the amplitude and phase modulation of the IQM in the upper / lower branch. These can be calculated with (2.17) and (2.18) when applying the electrical driving signals defined by (2.67) and (2.68).

2.6.7 Signal Properties In the following paragraphs, the signal properties at the transmitter outputs are discussed for selected Square QAM transmitters. The amplitude and phase characteristics of the optical transmitter output signals for NRZ pulse shape are defined for the serial Square QAM transmitter by (2.42), for the conventional IQ transmitter by (2.45)–(2.47) using (2.17) and (2.18), for the enhanced IQ transmitter by (2.60) and (2.61), and for the Tandem-QPSK transmitter by (2.66). To obtain the optical output signals for RZ pulse shape, the transfer function of the pulse carver given by (2.19) must additionally be considered. In Fig. 2.27, the intensity eye diagrams, the IQ diagrams (with a(t) scaled to unity) and the chirp characteristics are depicted for NRZ pulse shape, assuming a data rate of 40 Gbit/s and an electrical rise time of 1/4 of the symbol duration. a

b

Serial TX

Conventional IQ TX

c

Enhanced IQ TX

d

Tandem QPSK TX

2

0.2

Time

0.2 0

1.5

0.5

0

Re [A(t)]

-5

0.5

5

0

0.5

Time

Time

0 -2.5

0.5

1.5

Time

5

x 10

0 -2.5 -5

Intensity

5

0

0.5

1.5

Time

x 10

0.5

0 -2.5 -5

1.5

0.5

5

11

x 10

2.5 0 -2.5 -5

1.5

Time

11

2.5

1

2.5

Time

Chirp ⋅ Norm. Int. (1/s)

Chirp ⋅ Norm. Int. (1/s)

x 10

x 10

-5

1.5

0

Re [A(t)] 11

-2.5

11

2.5

-1

Re [A(t)]

-2.5

11

1

2.5

-5

1.5

0

11

Chirp (1/s)

0

0

-1 -1

x 10

1.5

1

1

2.5

-2.5

0.5

Time

Chirp (1/s)

5

0.2 0

1.5

0

Re [A(t)]

Chirp (1/s)

Chirp (1/s)

0

11

x 10

0.4

-1 -1

1

2.5

0.6

1

Im [A(t)]

Im [A(t)]

Im [A(t)] 0

11

Chirp ⋅ Norm. Int. (1/s)

0.5

0.8

Time

-1 -1

-5

0

1.5

1

0

-1

5

0.5

Time

1

5

1

Im [A(t)]

0.5

0.4

1.5

Chirp ⋅ Norm. Int. (1/s)

0

0.6

Norm. Intensity

0.4

0.8

Intensity

0.6

Norm. Intensity

0.8

1

Intensity

Norm. Intensity

1

Intensity

Norm. Intensity

1

0.5

1.5

5

x 10

2.5 0 -2.5 -5

0.5

Time

Fig. 2.27 Optical signal properties of different Square 16QAM transmitters (NRZ)

1.5

Time

2.6 Square QAM Signal Properties

55

From the intensity eye diagrams in Fig. 2.27, it can be observed that there are undershoots for the optical IQ transmitters (the intensity goes to zero). When the enhanced IQ structure is employed, where the amplitude modulation is replaced with separate intensity and phase modulations, additional overshoots arise at the symbol transitions. As a result of the separate phase modulation, the optical power can be temporarily higher than it is for the constellation points with the highest power level. This becomes equally apparent in the corresponding constellation diagram, where phasors with an amplitude greater than one are possible during the symbol transitions. A comparison of the constellation diagrams shows that there are symbol transitions through zero for the IQ transmitters but not for the serial transmitter and the Tandem-QPSK transmitter, where optical power is always greater than zero. When considering chirp, the best transmission performance can be expected from the conventional IQ transmitter, since the product of chirp and normalized intensity is comparatively small. The chirp characteristic of the other transmitters is more disadvantageous because chirp appears simultaneously with high power levels. Figure 2.28 illustrates the signal characteristics for some further selected cases (“ideal” driving, shorter electrical rise time, RZ pulse shape). a

Conventional IQ TX, ideal driving, NRZ

b

Enhanced IQ TX, reduced rise time, NRZ

c

Tandem QPSK TX, RZ

2 1

0.6 0.4 0.2 0

0.5

Time

Norm. Intensity

Norm. Intensity

1.5 1 0.5 0

1.5

0.5

0

-1 0

0

-1

Re [A(t)]

x 10

5

x 10

5

0.5

Time

-2.5 -5

1.5

11

Chirp ⋅ Norm. Int. (1/s)

2.5 0 -2.5

0.5

Time

1.5

5

0.5

Time

0

-5

1.5

0.5

Time

1.5

11

x 10

2.5 0 -2.5 -5

x 10

-2.5

11

x 10

1

2.5

0

Chirp ⋅ Norm. Int. (1/s)

-5

0

Re [A(t)]

Chirp (1/s)

-2.5

1.5

11

2.5

0

Time

0

1

11

Chirp (1/s)

Chirp (1/s)

0.5

-1 -1

2.5

Chirp ⋅ Norm. Int. (1/s)

0

0

Re [A(t)]

-5

0.2

1.5

1

1

11

5

0.4

-1 -1

5

0.6

1

Im [A(t)]

Im [A(t)]

1

Time

0.8

Im [A(t)]

Norm. Intensity

1 0.8

0.5

Time

1.5

5

x 10

2.5 0 -2.5 -5

0.5

Time

1.5

Fig. 2.28 Optical signal properties of Square 16QAM transmitters for “ideal” driving (a), shorter rise time (b) and RZ pulse shape (c), selected cases

56

2 Transmitter Design

The use of the “ideal” driving signals (which were discussed in Sect. 2.6.2 and can be regarded as a theoretical approach to compensate for the cosine characteristic of the MZM) leads to only small differences, as is exemplarily shown for the conventional IQ transmitter in Fig. 2.28a. A comparison with Fig. 2.27b shows that the eyes are not as steep as with the “non-ideal” driving case, and that the symbol transitions are only slightly different (when the conventional IQ transmitter is used, symbol transitions take the shortest way between the constellation points for “ideal” driving). To cope with the overshoots of the enhanced IQ transmitter for NRZ, either steeper driving signals for phase modulation must be applied (resulting in shorter overshoots, but higher chirp, as depicted in Fig. 2.28b for a rise time of 1/16 of the symbol duration), or RZ pulse shape must be used. RZ pulse carving leads to similar eyes and constellation diagrams in any configuration, and eliminates unwanted intensity ripples at symbol transitions for the enhanced IQ transmitter. Moreover, the influence of chirp is reduced when using RZ, as exemplarily shown for the TandemQPSK transmitter in Fig. 2.28c.

References 1. Covega corporation, http://www.covega.com 2. VPIsystems, Photonic Modules Reference Manual, 2005 3. Cahn, C.R.: Combined digital phase and amplitude modulation communication system. IRE Transactions on Communications CS-8, 150–155 (1960) 4. Campopiano, C.N., Glazer, B.G.: A coherent digital amplitude and phase modulation system. IRE Transactions on Communications CS-10, 90–95 (1962) 5. Hancock, J.C., Lucky, R.W.: Performance of combined amplitude and phase modulated communication system. IRE Transactions on Communications CS-8, 232–237 (1960) 6. Ho, K.P., Cuei, H.W.: Generation of arbitrary quadrature signals using one dual-drive modulator. IEEE Journal of Lightwave Technology 23(2), 764–770 (2005) 7. Hooijmans, P.W.: Coherent Optical System Design. John Wiley & Sons (1994) 8. Kazovsky, L.G.: Optical Fiber Communication Systems. Artech House (1996) 9. Kikuchi, N., Sasaki, S.: Optical dispersion-compensation free incoherent multilevel signal transmission over single-mode fiber with digital pre-distortion and phase pre-integration techniques. In: Proceedings of European Conference on Optical Communication (ECOC), Tu.1.E.2 (2008) 10. Kikuchi, N., et al.: Proposal of inter-symbol interference (ISI) supression technique for optical multilevel signal generation. In: Proceedings of European Conference on Optical Communication (ECOC), Tu4.2.1 (2006) 11. Ohm, M., Speidel, J.: Receiver sensitivity, chromatic dispersion tolerance and optimal receiver bandwidths for 40 Gbit/s 8-level optical ASK-DQPSK and optical 8-DPSK. In: Proc. 6th Conference on Photonic Networks, pp. 211–217. Leipzig, Germany (2005) 12. Patzak, E., Langenhorst, R.: Sensitivity degradation of conventional and balanced 3 × 3 port phase diversity receivers due to thermal and local oscillator intensity noise. Electronics Letters 25(8), 545–547 (1989) 13. Petermann, K.: Laser diode modulation and noise. Kluwer Academic, Dordrecht / Boston / London (1988) 14. Sakamoto, T., et al.: 50-Gb/s 16 QAM by a quad-parallel Mach-Zehnder modulator. In: Proceedings of European Conference on Optical Communication (ECOC), PDP2.8 (2007)

References

57

15. Sakamoto, T., et al.: 50-km SMF transmission of 50-Gb/s 16 QAM generated by quad-parallel MZM. In: Proceedings of European Conference on Optical Communication (ECOC), Tu.1.E.3 (2008) 16. Seimetz, M.: Multi-format transmitters for coherent optical M-PSK and M-QAM transmission. In: Proceedings of ICTON, Th.B1.5. Barcelona (2005) 17. Seimetz, M.: Optical IQ-transmitter with a serial IQ-modulator. German utility patent, DE 20 2006 000 197.2 (2006) 18. Seimetz, M.: Phase diversity receivers for homodyne detection of optical DQPSK signals. IEEE Journal of Lightwave Technology 24(9), 3384–3391 (2006) 19. Sekine, K., et al.: Proposal and demonstration of 10-Gsymbol/sec 16-ary (40 Gbit/s) optical modulation / demodulation scheme. In: Proceedings of European Conference on Optical Communication (ECOC), We3.4.5 (2004) 20. Voges, E., Petermann, K.: Optische Kommunikationstechnik. Springer Verlag, Berlin / Heidelberg (2002) 21. Walklin, S., Conradi, J.: Multilevel signaling for increasing the reach of 10Gb/s lightwave systems. IEEE Journal of Lightwave Technology 17(11), 2235–2248 (1999) 22. Weber, W.J.: Differential encoding for multiple amplitude and phase shift keying systems. IEEE Transactions on Communications COM-26(3), 385–391 (1978) 23. Winzer, P.J., Essiambre, R.J.: Advanced optical modulation formats. Proceedings of the IEEE 94(5), 952–985 (2006) 24. Zhao, J., et al.: Analytical investigation of optimization, performance bound, and chromatic dispersion tolerance of 4-amplitude-shifted-keying format. In: Proceedings of Optical Fiber Communication Conference (OFC), JThB15 (2006)

Chapter 3

Receiver Configurations

Abstract This chapter describes receiver configurations for the detection of optical signals with high-order modulation. At the beginning of the chapter, receiver key components (filters, delay line interferometer, optical hybrids) are discussed. Afterwards, receivers are detailed for three different detection schemes: direct detection, homodyne differential detection and homodyne synchronous detection. A complete analytical description of the optical and electrical receiver parts is thereby provided, starting with optical frontends and ending with electrical data recovery. Direct detection receivers are shown to be capable of detecting arbitrary modulation formats with differentially encoded phases such as DPSK and Star QAM formats. Subsequently, homodyne receivers with differential detection are presented and shown to be suitable for detecting the same signals as is possible with direct detection. Finally, homodyne synchronous detection which is appropriate for arbitrary highorder modulation formats is highlighted. A particular stress is laid on carrier synchronization, which was traditionally performed using an optical phase locked loop. Its current state is briefly reviewed. Digital phase estimation schemes are discussed in more detail, because digital coherent receivers gain more and more interest due to high-speed digital signal processing newly available.

3.1 Receiver Components The following subsections describe some key components used within optical receivers for high-order modulation.

3.1.1 Optical and Electrical Filters Filters act as crucial and multi-purpose components in optical receivers. In direct detection receivers with optical pre-amplification, an optical band-pass filter should

M. Seimetz, High-Order Modulation for Optical Fiber Transmission, Springer Series in Optical Sciences 143, DOI 10.1007/978-3-540-93771-5 3, c Springer-Verlag Berlin Heidelberg 2009

59

60

3 Receiver Configurations

be located behind the pre-amplifier to limit the noise bandwidth and thus reduce noise components falling and beating into the detection bandwidth, resulting in a higher receiver sensitivity. Furthermore, optical band-pass filters are used for WDM channel separation. In the electrical domain, low-pass filters are employed to further reduce amplifier noise, as well as the receiver’s shot-noise and thermal noise. In Signal and System theory, mostly ideal filters are observed—like the ideal low-pass filter, which transmits all frequencies inside the pass-band without any distortion and completely rejects frequencies inside the stop-band [16]; or the matched filter, whose impulse response matches the received signal and which maximizes the output signal to noise ratio [54]. In system simulations, optical band-pass filters are often modeled as non-causal Gaussian filters with Gaussian amplitude and real-valued transfer function, providing a first-step approximation of a real filter. The transfer function of a Gaussian optical band-pass filter is given by [2] Ho (ω) = e

− 0.5·ln (2)·2 2ν ωc

2ν

·(ω−ω0 )2ν

.

(3.1)

In (3.1), ω0 represents the center frequency, ωc is the 3 dB bandwidth, and ν is the filter order. Electrical filters are often modeled as Bessel filters. They can be physically implemented and exhibit a linear phase response and an excellent step response with minimal overshoot and ringing [2]. The normalized transfer function of an electrical Bessel low-pass filter can be described as He (S) =

Bν (S = 0) , S = jωτgr0 , Bν (S)

(3.2)

where ν again denotes the filter order, and τgr0 the group delay for ω = 0. The polynomials Bν (S) for ν = 1 and ν = 2 are specified by B1 (S) = 1 + S and B2 (S) = 3 + 3S + S 2 , respectively. The polynomials for higher orders can be calculated recursively by the relation [68] Bν (S) = (2ν − 1) · Bν−1 (S) + S 2 · Bν−2 (S).

(3.3)

The 3 dB bandwidth of the electrical Bessel low-pass filter can be related to the group delay τgr0 by ωc = 1.3616/τgr0 for ν = 2, and can be approximately calculated for higher filter orders with √ (2ν − 1) · ln 2 , ν ≥ 3. (3.4) ωc ≈ τgr0 More detailed information about Bessel filters and other practical filter realizations can be found in [68].

3.1 Delay Line Interferometer

61

3.1.2 Delay Line Interferometer In order to evaluate the phase information of an optical signal without using coherent detection techniques, phase information must be converted to intensity information before the detection process, since intensity alone can be detected by a photodiode. The optical component, which is commonly used for this purpose, is a delay line interferometer (DLI). As illustrated in Fig. 3.1, the received light is split by a 3 dB coupler into two branches. In one branch, the optical signal is delayed by one symbol duration TS . Additionally, an arbitrary phase shift ϕ DL I can be accomplished in one of the branches before the light of both branches is recombined in a second 3 dB coupler.

E# o u t1

Fig. 3.1 Structure of a delay line interferometer (DLI)

Ein1

TS

Eout1

Ein2

ϕDLI

Eout2

E# o u t 2

With the nomenclature used in Fig. 3.1 for the 3 dB coupler at the DLI input, the input and output relationship of a single lossless 3 dB coupler can be expressed in matrix notation as       1 E˜ out1 1 j E in 1 =√ · . (3.5) · j 1 E in 2 E˜ out2 2 One property of the 3 dB coupler is that the relative phase shift experienced by both added input fields is 90◦ at the upper and -90◦ at the lower coupler output. Thus, the difference of these relative phase shifts is 180◦ . For this reason, the 3 dB coupler is often denoted as 180◦ hybrid. When feeding a signal E in 1 into the upper port of the input coupler of the DLI, and when neglecting the common phase shift within the interferometer length, the two fields obtained at the DLI output ports are E out1 (t) =

1 1 E in 1 (t − TS ) − E in 1 (t)e jϕ DL I , 2 2

1 1 E out2 (t) = j E in 1 (t − TS ) + j E in 1 (t)e jϕ DL I . 2 2

(3.6)

(3.7)

For a DLI input signal with time dependent modulation amplitude a(t) and modulation phase ϕ(t), which is corrupted by laser phase noise ϕn s (t),

62

3 Receiver Configurations

E in 1 (t) =

p

Ps · e j (ωs t+ϕs ) · a(t) · e jϕ(t) · e jϕns (t) ,

(3.8)

the optical power at the DLI outputs—when further neglecting frequency drift effects (so that ωs remains constant)—can be specified by 1 1 Ps · a 2 (t) + Ps · a 2 (t − TS ) 4 4   1 − Ps · a(t)a(t − TS ) cos 1ϕ(t) + 1ϕn s (t) + ϕ DL I , 2

∗ Pout1 (t) = E out1 (t) · E out (t) = 1

(3.9)

1 1 Ps · a 2 (t) + Ps · a 2 (t − TS ) 4 4   1 + Ps · a(t)a(t − TS ) cos 1ϕ(t) + 1ϕn s (t) + ϕ DL I , (3.10) 2

∗ Pout2 (t) = E out2 (t) · E out (t) = 2

where the modulation phase difference between two consecutive symbols, 1ϕ(t), and the phase change due to laser phase noise at the DLI outputs, 1ϕn s (t), are defined as 1ϕ(t) = ϕ(t) − ϕ(t − TS ), 1ϕn s (t) = ϕn s (t) − ϕn s (t − TS ).

(3.11)

For the derivation of (3.9) and (3.10), it is further assumed that an integer number of wavelengths fits into the symbol time (ωs · TS = 2mπ, m ∈ N0 ) because an extra relative phase shift would otherwise occur. It can be concluded from (3.9) and (3.10) that the optical power at the DLI outputs depends on the current modulation amplitude a(t), the modulation amplitude delayed by one symbol duration a(t − TS ), the modulation phase difference 1ϕ(t), the laser phase noise 1ϕn s (t) with a variance of h1ϕn2s i = 2π 1νs TS and the DLI phase shift ϕ DL I . For an ideal DPSK with constant a(t) = a(t − TS ) and for negligible laser phase noise, the DLI output signals can be used for evaluation of 1ϕ(t) when an appropriate DLI phase shift ϕ DL I is adjusted. In principle, one of the DLI output ports is sufficient for signal detection (single-ended detection). To eliminate the first two terms in (3.9) and (3.10) and not waste half the power, however, a balanced detector should be employed. In practice, the symbol delay TS is implemented by using different path lengths within the DLI. Its accuracy is not critical in terms of hitting the symbol time, but rather in terms of fine-tuning the length difference with sub-wavelength accuracy to control the interference conditions.

3.1.3 2 × 4 90◦ Hybrid The 2 × 4 90◦ hybrid is a key component in optical receivers for high-order modulation because it enables the detection of the in-phase and quadrature components of an optical signal. It can be used within coherent receivers to superposition the signal light and the LO light, as well as for conversion of the phase difference information

3.1 2 × 4 90◦ Hybrid

63

into intensity information in direct detection receivers, provided that an optical delay of one symbol time is foreseen at one of the hybrid inputs. When generally defining the two input signals of the 2 × 4 90◦ hybrid as (3.12) E in 1 (t) = E in 1 (t) · e jφ1 (t) , E in 2 (t) = E in 2 (t) · e jφ2 (t) , the following output powers are desired at the four hybrid outputs (n = 0, 1, 2, 3) to enable the detection of the in-phase and quadrature components

2 1 2 1 E in 1 (t) + E in 2 (t) 4 4   1 + E in 1 (t) E in 2 (t) · cos φ1 (t) − φ2 (t) − n · 90◦ + ψ ,(3.13) 2

∗ Poutn (t) = E outn (t) · E out (t) = n

where the phase shift ψ is allowed to be arbitrary, since the initial phases of the input signals are arbitrary as well. It can be observed that the beating terms of two adjacent output signals are in quadrature, respectively, and the remaining output signals can be used to employ balanced detection. The quadrature property can be exploited to detect the in-phase and quadrature components of high-order modulation signals, as well as for the implementation of special coherent receivers such as the phase diversity receiver [30], the image-rejection receiver [23] and receivers with optical phase locked loops [12, 27]. To provide the desired powers specified by (3.13) at the four outputs, the 2 × 4 90◦ hybrid (when assuming a lossless device with ideal uniformity) must exhibit the field transfer function  jψ    e 11 e jψ12 E out1 (t)    E out (t) 1 e jψ21 j · e jψ22  E in (t) 1 2 ·  = · (3.14)  E out3 (t) 2 e jψ31 −e jψ32  E in 2 (t) , E out4 (t) e jψ41 − j · e jψ42 where the phase coefficients ψ11 ..ψ42 must satisfy the phase condition ψ11 − ψ12 = ψ21 − ψ22 = ψ31 − ψ32 = ψ41 − ψ42 = ψ.

(3.15)

Since the difference of the relative phase shifts of the added input fields at the four outputs is n times 90◦ , this component is denoted as a 90◦ hybrid. Different implementation options for the 2 × 4 90◦ hybrid and their practical feasibility are discussed in detail in [61]. Figure 3.2 illustrates three different options for implementation of the hybrid. One possibility, shown in Fig. 3.2a, is to construct the hybrid with four 3 dB couplers and an additional phase shifter in one branch. When setting the phase shift in the lower branch to 90◦ and using the inputs and outputs as defined in Fig. 3.2a, the transfer function of the whole component is equal to (3.14) with ψ = 0 [61]. The configuration should be implemented in an integrated form to achieve sufficient IQ balance. A version fabricated on Li N bO3 is analyzed and discussed in [19]. The device is commercially available [1] and can be adjusted with six different electrodes.

64

3 Receiver Configurations

a

3dB couplers + phase shifter

Ein1

Ein2

b Ein1 Ein2

3dB 3dB

c

4x4 MMI coupler

4x4 MMI

90°

Eout1 Eout4 Eout2 Eout3

Ein1 Ein2

3dB

Eout3 Eout1

3dB

Eout4 Eout2

3dB coupler + PBS PBS

Eout1 Eout2

PBS

Eout3 Eout4

3dB

Fig. 3.2 Options for implementation of the 2 × 4 90◦ hybrid

Four electrodes control the uniformity of the 3 dB couplers (which is a measure of the differences in the output port powers). With the remaining two electrodes, the phase shifts in the upper and the lower branches can be set [26]. This allows the adjustment of phase shifts of ψ 6= 0, which can be a beneficial feature for rotating received constellation diagrams into the appropriate position. To ensure orthogonality, the relative phase shift between two branches has to be tuned to 90◦ . Imprecise relative phase shifts lead to a degradation of the IQ balance, whereas the asymmetries of the 3 dB couplers affect the power symmetry of the hybrid output signals and thus the symmetry of the subsequent balanced detection processes. For commercial application, even for the integrated implementation of this component on Li N bO3 , it is necessary to establish an active control loop to stabilize the 90◦ phase relation. Even though the hybrid on Li N bO3 is commercially available, the active control loop is not, and would have to be implemented with ones own resources. A possible design for the active control loop was proposed in [61]. The most promising option for obtaining a stable commercial 2 × 4 90◦ hybrid component without the need of an additional active control, involves exploiting the properties of a 4 × 4 multi-mode interference (MMI) coupler. Using the appropriate inputs, as shown in Fig. 3.2b for instance, and for accurate waveguide dimensioning, this component inherently exhibits the desired phase relations [50, 61]. Unfortunately, 4 × 4 MMI couplers are commercially not available at present. However, they are a very interesting alternative because they promise stable phase relations. Furthermore, MMI couplers are broadband. This makes them suitable for multiband WDM applications. In addition, the balanced detectors of the receiver can be integrated on the chip, so that the whole optical receiver frontend can be integrated, possibly with polarization diversity. The device has to be carefully designed in order

3.1 3 × 3 Coupler

65

to achieve equal splitting ratios together with the appropriate phase relations, as it was shown using simulations in [61]. A third option of the 2 × 4 90◦ hybrid which has been realized with discrete components [36], as well as in an integrated form [35], is a configuration with a 3 dB coupler in combination with two polarization beam splitters (PBS), as depicted in Fig. 3.2c. This arrangement, however, requires specific polarization states from the signals feeding into the hybrid inputs. One input signal must be linearly polarized at 45◦ with respect to the PBS reference directions, and the other one must be circularly polarized:
1 Ein 1 (t) = √ · ex + e y · E in 1 (t) · e jφ1 (t) , 2  1  ◦ Ein 2 (t) = √ · ex + e y e j90 · E in 2 (t) · e jφ2 (t) . 2

(3.16)

(3.17)

When using these input polarizations, the outputs fields of the two polarization beam splitters are obtained as jφ (t)
  1 1   + E in 2 (t) · e jφ2 (t)
2 ex · E in 1 (t) · e Eout1 jφ1 (t) + E in (t) · e jφ2 (t) · e j90◦  1 2 Eout   2 e y · E in 1 (t) · e 
 , (3.18) 2    Eout3  =  21 ex · E in 1 (t) · e jφ1 (t) − E in 2 (t) · e jφ2 (t)  jφ (t) jφ (t) j90◦
 1 Eout4 e · E (t) · e 1 − E (t) · e 2 · e 2 y

in 1

in 2

and result again in the optical powers given by (3.13) with ψ = 0. So far, solutions were implemented using free space optics [38]. A fiber-based approach could be even more difficult to implement. For lab experiments, it is advantageous that this setup can be configured with discrete components.

3.1.4 3 × 3 Coupler One way to avoid the deployment of a 2 × 4 90◦ hybrid and to be able to detect in-phase and quadrature components anyway, is to use a 3 × 3 fiber coupler. An ideal lossless 3 × 3 coupler with perfect uniformity provides the functionality of a 120◦ hybrid with an input and output relationship [53]       1 1 1 E in 1 E out1 1 ◦ ◦  E out2  = √ · 1 e j120 e− j120  ·  E in 2 . (3.19) ◦ ◦ 3 E in 3 E out3 1 e− j120 e j120

In practice, non-ideal uniformity and lossy couplers result in deviations from the ideal phase relations [52, 53]. When feeding the two signals defined by (3.12) into

66

3 Receiver Configurations

the first and second input of the 3 × 3 coupler, the optical power at the output n (n = 1, 2, 3) is given by 2 1 2 1 E in 1 (t) + E in 2 (t) 3 3   2 + E in 1 (t) E in 2 (t) cos φ1 (t) − φ2 (t)+(n − 1) 120◦ . (3.20) 3

∗ Poutn (t) = E outn (t) · E out (t) = n

It becomes apparent that the cosine terms of the three output powers are 120◦ out of phase with each other. From these signals, two signals 90◦ out of phase and with the same amplitude can be easily constructed by performing the following operations [35, 43, 53]: PI (t) = Pout1 (t) − Pout2 (t)
2 = √ E in 1 (t) E in 2 (t) · sin φ1 (t) − φ2 (t) + 60◦ , 3

(3.21)

 1  PQ (t) = √ · Pout1 (t) + Pout2 (t) − 2Pout3 (t) 3
2 = √ E in 1 (t) E in 2 (t) · cos φ1 (t) − φ2 (t) + 60◦ . 3

(3.22)

In practice, these operations can be performed electronically or by digital means after photo-detection.

3.2 Direct Detection Receivers Receiver schemes for the detection of optical high-order modulation signals can be roughly divided into two basic groups: Direct detection and coherent detection. Direct detection receivers, whose functionality is shown in this section, are convincingly simple. No phase, frequency or polarization control is necessary. Although only the intensity of the optical field can be detected by a simple photodiode, the information encoded in the optical phase can also be obtained when employing additional optics. By using an optical interferometer, the phase difference information of two consecutive symbols can be converted into intensity information, which then can be detected by a photodiode. This allows for the detection of arbitrary DPSK signals. With a separate intensity detection branch, arbitrary Star QAM signals with differentially encoded phases can also be received when appropriate data recovery methods are employed. In Sect. 3.2.1 and Sect. 3.2.2, different receiver configurations with direct detection are described. One option is to use DLIs for phase detection, another option to employ a 2 × 4 90◦ hybrid combined with a delay of one symbol duration in front

3.2 Direct Detection Receiver with Delay Line Interferometers

67

of one of the hybrid inputs. Subsequently, Sect. 3.2.3 illustrates for a wide range of modulation formats how data recovery can be accomplished in receivers with differential detection.

3.2.1 Direct Detection Receiver with DLIs The usual way for constructing direct detection receivers is employing DLIs to convert differential phase modulation into intensity modulation before photodiode square-law detection.

Multiple DLI Receiver One receiver option—whose optical part is shown in Fig. 3.3—is to use N ph /2 DLIs with appropriate phase shifts, where N ph represents the number of phase states (N ph = M for MDPSK signals). For the detection of DPSK signals, only the branch with the DLIs (phase detection branch) is needed. Another branch (intensity detection branch) must be provided for a separate evaluation of the intensity when detecting Star QAM signals. Phase information can be demodulated by performing binary decisions on the resulting N ph /2 electrical photocurrents. Intensity detection branch

Intensity

Phase detection branch

DLI 1

DLI 2 3dB

To data recovery

1:Nph /2

DLI Nph /2-1

DLI Nph /2 BD

Fig. 3.3 Direct detection receiver composed of N ph /2 DLIs; for the detection of DPSK signals the phase detection branch is sufficient. A separate intensity detection branch must be provided in the case of the detection of Star QAM signals. BD: balanced detector

68

3 Receiver Configurations

The receiver concept with multiple DLIs was investigated for 8DPSK in [71]. Unfortunately, the optical effort becomes quite high for modulation formats with a high number of phase states. Four DLIs are needed for 8DPSK, and as many as eight DLIs for 16DPSK. For this reason, the following description of direct detection receivers composed of DLIs is restricted to a configuration with only two DLIs.

IQ Receiver with DLIs Generally, two DLIs are sufficient to obtain the phase difference information of arbitrary DPSK and Star QAM signals by detecting their in-phase and quadrature components (IQ receiver). However, decisions on multi-level electrical signals with multiple thresholds become necessary for modulation formats with N ph > 4 in that case. The setup of the optical receiver part for Star QAM is shown in Fig. 3.4. Intensity

Intensity detection branch

I ID (t ) Phase detection branch

EI ,1 (t ) In-phase

TS

EI (t )

E s (t )

ϕ DLI

I

EI ,2 (t )

I I (t )

3dB 3dB

EQ ,1 (t )

EQ (t )

Quadrature

TS

ϕ DLI

Q

DLI

IQ (t )

EQ ,2 (t ) BD

Fig. 3.4 Direct detection IQ receiver composed of two DLIs; in the case of the detection of DPSK signals, the phase detection branch is sufficient. A separate intensity detection branch must be provided for the detection of Star QAM signals.

The received signal E s (t), which is specified by (3.8) when neglecting all transmission impairments, is split by a coupler into the intensity detection branch and the phase detection branch. Here, the coupler is assumed to be a 3 dB coupler. The output current of the photodiode in the intensity detection branch is R E s (t) E s∗ (t) + i sh + i th = · a 2 (t) · Ps + i sh + i th . (3.23) I I D (t) = R · √ · √ 2 2 2 This photocurrent is proportional to the CW power Ps and the square of the modulation amplitude a 2 (t). Thus, the power of a symbol is detected in the intensity detection branch. In (3.23), R represents the responsivity of the photodiode, which is equal to R=η

2π e , hωs

(3.24)

3.2 Direct Detection Receiver with Delay Line Interferometers

69

where e = 1.6 · 10−19 C is the charge per electron, hωs /2π is the energy per photon with h = 6.63 · 10−34 J s being the Planck constant, and η is the quantum efficiency of the photodiode that corresponds to the average number of electrons generated per photon. The two variables i sh and i th in (3.23) describe the photocurrent shotnoise

2 and  the thermal noise of the

2 receiver, respectively. Their variances are given by i sh = 2 · e · hI I D i · Bel and i th = 4 · k B · T · G r · Bel , where Bel represents the electrical receiver bandwidth, k B is the Boltzmann constant, T is the temperature, and G r is the resistor’s conductance of the electrical circuit [66]. To enhance the sensitivity, an optical pre-amplifier, commonly followed by an optical filter, is typically placed in front of the DD receiver (not shown in Fig. 3.4). The complex noise of the optical amplifier, whose baseband representation is defined here as n(t) = n k (t)ek + n ⊥ (t)e⊥ , can be partitioned into noise components polarized in parallel and orthogonally with respect to the signal, denoted as n k (t) and n ⊥ (t), and can be assumed to be additive white Gaussian noise (AWGN) with a two-sided power spectral density (PSD) per polarization of N0 = n sp (G − 1) h · f s ,

(3.25)

where n sp represents the spontaneous emission parameter and G is the amplifier gain [51, 66]. The variance of the in-phase and quadrature components of n k (t) and n ⊥ (t) is given by σ 2 = σ I2 = σ Q2 = (N0 /2)· Bn , where Bn is the optical noise bandwidth. When taking the amplifier noise into account but neglecting optical filtering, the photocurrent in the intensity detection branch becomes R 2 R = 2 R = 2

I I D (t) =

i∗ ih h Es (t) + n(t)e jωs t Es (t) + n(t)e jωs t + i sh + i th h i |Es (t)|2 + Es (t)n∗ (t)e− jωs t + E∗s (t)n(t)e jωs t + |n(t)|2 + i sh + i th i Rh |E s (t)|2 + E s (t)n ∗k (t)e− jωs t + E s∗ (t)n k (t)e jωs t | {z } 2 | {z } Signal power

R + 2

Signal-ASE noise

i h n k (t) 2 + |n ⊥ (t)|2 +i sh + i th , | {z }

(3.26)

ASE-ASE noise

In comparison with (3.23), two new noise components arise which are the signalASE noise and the ASE-ASE noise. For the detection of symbols with sufficiently high signal power and for small optical noise bandwidth, the signal-ASE noise becomes dominant compared with the ASE-ASE noise. The shot-noise and the thermal noise can be usually neglected in systems with optical amplification. The following description intends to demonstrate the general functionality of the direct detection receiver for high-order modulation, so all the noise sources mentioned are not further regarded. A more detailed discussion of the impact of amplifier noise on the receiver performance, where optical and electrical filtering and the whole receiver structure are considered, is carried out in Sect. 5.4.

70

3 Receiver Configurations

As illustrated in Fig. 3.4, the second output of the coupler at the receiver input meets the phase detection branch. In the phase detection branch, the signal is split by another coupler for detection of the in-phase and quadrature components. When assuming 3 dB couplers and taking the phase shifts of the couplers into account, two fields with a phase difference of 90◦ are obtained at the upper and the lower output of the second coupler E I (t) =

p 1 ◦ · a(t) · Ps · e j(ωs t+ϕs ) · e jϕ(t) · e jϕns (t) · e j90 , 2

E Q (t) =

p 1 ◦ · a(t) · Ps · e j(ωs t+ϕs ) · e jϕ(t) · e jϕns (t) · e j180 . 2

(3.27)

(3.28)

When looking at the in-phase branch and considering the transfer characteristic of the DLI defined by (3.6) and (3.7), the electrical fields obtained at the two DLI outputs are E I,1 (t) =

E I,2 (t) =

p 1 ◦ · a(t − TS ) · Ps · e j(ωs t+ϕs ) · e jϕ(t−TS ) · e jϕns (t−TS ) · e j90 4 p 1 ◦ + a(t) Ps · e j(ωs t+ϕs ) · e jϕ(t) · e jϕns (t) · e− j90 · e jϕ DL I I , (3.29) 4 p 1 ◦ · a(t − TS ) · Ps · e j(ωs t+ϕs ) · e jϕ(t−TS ) · e jϕns (t−TS ) · e j180 4 p 1 ◦ + a(t) Ps · e j(ωs t+ϕs ) · e jϕ(t) · e jϕns (t) · e j180 · e jϕ DL I I , (3.30) 4

with ϕ DL I I representing the phase shift of the DLI in the in-phase branch. When detecting the fields given by (3.29) and (3.30), the two photocurrents within the balanced detectors (BD) are given by R R Ps · a 2 (t) + Ps · a 2 (t − TS ) 16 16   R − · Ps · a(t)a(t − TS ) · cos 1ϕ(t) + 1ϕn s (t) + ϕ DL I I , (3.31) 8

I I,1 (t) = R · E I,1 (t) · E ∗I,1 (t) =

R R Ps · a 2 (t) + Ps · a 2 (t − TS ) 16 16   R + · Ps · a(t)a(t − TS ) · cos 1ϕ(t) + 1ϕn s (t) + ϕ DL I I , (3.32) 8

I I,2 (t) = R · E I,2 (t) · E ∗I,2 (t) =

where the difference of the modulation phase of two consecutive symbols, 1ϕ(t), and the phase error due to laser phase noise, 1ϕn s (t), were defined in (3.11). The variance of the phase error is given by h1ϕn2s i = 2π 1νs TS .

3.2 Direct Detection IQ Receiver with 2 × 4 90◦ Hybrid

71

Within the balanced detector, both photocurrents are subtracted. The first two terms are the same in (3.31) and (3.32), and disappear after balanced detection. The photocurrent after balanced detection becomes I I (t) = I I,2 (t) − I I,1 (t)   R = · Ps · a(t)a(t − TS ) · cos 1ϕ(t) + 1ϕn s (t) + ϕ DL I I . (3.33) 4

In the same manner, when performing the same calculations for the quadrature branch, the quadrature photocurrent is obtained as I Q (t) = I Q,2 (t) − I Q,1 (t)   R · Ps · a(t)a(t − TS ) · cos 1ϕ(t) + 1ϕn s (t) + ϕ DL I Q . (3.34) = 4

In (3.34), ϕ DL I Q denotes the phase shift of the DLI in the quadrature branch. When detecting DQPSK signals, for instance, ϕ DL I I should be set to −45◦ and ϕ DL I Q to −135◦ to enable that decisions on binary electrical signals in the in-phase and quadrature arms can be performed. Generally, by choosing the phase shifts of the DLI as ϕ DL I I = 0◦ and ϕ DL I Q = −90◦ , the in-phase and quadrature components of arbitrary DPSK constellations can be obtained. When further neglecting the laser phase noise, the in-phase and quadrature photocurrents are I I (t) =

R · Ps · a(t)a(t − TS ) · cos [1ϕ(t)] , 4

(3.35)

I Q (t) =

R · Ps · a(t)a(t − TS ) · sin [1ϕ(t)] . 4

(3.36)

For DPSK formats, a(t) and a(t −TS ) are not modulated, so that phase difference information 1ϕ(t) can easily be recovered from the photocurrents given by (3.35) and (3.36). By contrast, the dependence of (3.35) and (3.36) on the non-delayed and delayed modulation amplitudes can complicate the recovery of phase difference information for Star QAM. Nevertheless, data recovery can be accomplished for arbitrary Star QAM modulation formats with differentially encoded phases, as will be shown in Sect. 3.2.3.

3.2.2 Direct Detection IQ Receiver with 2 × 4 90◦ Hybrid Another IQ receiver with direct detection can be composed of a 2 × 4 90◦ hybrid with an additional delay of one symbol duration in front of one of the hybrid inputs. This alternative receiver configuration is functionally equivalent to the direct detection receiver with two DLIs and is illustrated in Fig. 3.5.

72

3 Receiver Configurations Intensity

Intensity detection branch

I ID (t ) Phase detection branch In-phase

Ein 1 (t )

Es (t ) 3dB 3dB

ψ# TS

I I (t ) 2x4 90° Hybrid

Quadrature

IQ (t )

Ein 2 (t ) BD

Fig. 3.5 Direct detection IQ receiver whose setup is based on a 2 × 4 90◦ hybrid; for the detection of DPSK signals the phase detection branch is sufficient. A separate intensity detection branch must be provided for the detection of Star QAM signals.

A part of the receiver, which consists of the intensity detection branch and two couplers, is identical to the DLI configuration. When observing the phase detection branch and assuming the use of 3 dB couplers, the input fields of the 2×4 90◦ hybrid are given by E in 1 (t) = E in 2 (t) =

p 1 ◦ ˜ · a(t) · Ps · e j(ωs t+ϕs ) · e jϕ(t) · e jϕns (t) · e j90 · e j ψ , 2

p 1 ◦ · a(t − TS ) · Ps · e j(ωs t+ϕs ) · e jϕ(t−TS ) · e jϕns (t−TS ) · e j180 , 2

(3.37)

(3.38)

where the angle ψ˜ corresponds to an arbitrary phase shift in front of the upper hybrid input. The fields described by (3.37) and (3.38) combine in the optical 2 × 4 90◦ hybrid, whose field transfer function is defined in (3.14) and (3.15). The phase shift ψ introduced there is set to zero for all following calculations. Altering the arbitrary phase shift ψ˜ in front of the hybrid input has the same effect on the hybrid output signals as altering the phase shift ψ within the hybrid would have. The four optical signals at the hybrid outputs are detected by two balanced detectors. When connecting the appropriate hybrid outputs to the proper balanced detector inputs and neglecting amplifier noise, shot-noise, thermal noise and laser phase noise, the following photocurrents can easily be derived after the balanced detectors I I (t) = Iout4 (t) − Iout2 (t) =

h i R · Ps · a(t)a(t − TS ) · cos 1ϕ(t) + ψ˜ , 4

(3.39)

I Q (t) = Iout1 (t) − Iout3 (t) =

h i R · Ps · a(t)a(t − TS ) · sin 1ϕ(t) + ψ˜ . 4

(3.40)

It becomes apparent that the equations (3.39) and (3.40) are identical to (3.35) and ˜ which can also be interpreted as a relative phase shift (3.36) if the phase shift ψ,

3.2 Data Recovery for Differential Detection

73

between the upper and the lower input of the hybrid, is equal to zero. An advantage of the hybrid configuration, compared with the configuration with two DLIs, is that the 2 × 4 90◦ hybrid inherently features the orthogonal relation between the in˜ the whole received conphase and quadrature axes. By adjusting the phase shift ψ, stellation diagram can be rotated (the same effect can be achieved by setting the phase shift ψ when simultaneously adjusting the phase shifts in the upper and lower branches of the hybrid composed of 3 dB couplers and phase shifters, as described in Sect. 3.1.3). In the DLI configuration, however, the phase shifts in both DLIs have to be adjusted correctly to ensure appropriate orthogonality as well as the correct absolute phase. Finally, choosing a configuration will depend on practical implementation considerations.

3.2.3 Data Recovery for Differential Detection This section describes the data recovery for modulation formats with differentially encoded phases whose differential phase information is determined by IQ receivers with differential detection. Differential detection can be accomplished in the optical domain as shown for direct detection receivers in Sect. 3.2.1 and Sect. 3.2.2, or in the electrical domain after coherent detection as described in Sect. 3.4. Because phase differences are identified, no differential decoder is needed at the receiver when the phase was differentially encoded at the transmitter. The datarecovery circuits derived in this section are appropriate for recovering the data bits b1k , b2k , .., bm k of systems employing the bit mappings defined in Chap. 2. Figure 3.6 illustrates two different data recovery techniques which can be employed in optical IQ receivers with differential detection.

LPF Quadrature LPF

s q , nk

Data Recovery Logic

In-phase

….

b IQ-DECISION si , nk

….

bmk

b1k

Multiplexer

….

s Nphk

b1k Data Recovery Logic

LPF

….

Quadrature

s1k

ARG Operation

LPF

….

In-phase

Multiplexer

a ARG-DECISION Data

Data

bmk

Fig. 3.6 Data recovery techniques applicable within the phase detection branch of DPSK receivers. a Arg-decision. b IQ-decision. LPF: low-pass filter

74

3 Receiver Configurations

Usually, the electrical in-phase and quadrature photocurrents in the phase detection branch are low-pass filtered beforehand to achieve a better BER performance. Then they can be processed by the techniques shown in Fig. 3.6 to recover the data bits corresponding to the phase information. These techniques differ in the positioning of the thresholds, their practical implementation and their performance. For maximum distances between symbols and thresholds and for optimal noise performance, the thresholds should be positioned radially between the phase states as shown for 8DPSK and 16DPSK in Fig. 3.7c and Fig. 3.7d, respectively. This decision scheme is denoted here as “arg-decision”. The electrical receiver configuration for arg-decision is illustrated in Fig. 3.6a. By performing an arg-operation (calculation of the angle of a complex value) on the electrical in-phase and quadrature signals, a multi-level electrical signal whose states represent the received phase differences arises. A decision is performed on these multi-level signals, by applying the radially positioned thresholds. The outcome of the decision is processed by appropriate data recovery logic to obtain the data bits, which, in the end, can be multiplexed to obtain the original data stream. In practice, the arg-operation could be implemented by digital means. The performance then depends on the resolution of the analog-to-digital (A/D) converter used. Another option is performing the decisions directly on the in-phase and quadrature photocurrents as depicted in Fig. 3.6b. This technique is denoted here with “IQ-decision”. For DBPSK and DQPSK, decisions are performed on binary signals with an optimal threshold at zero. For higher-order DPSK formats, the in-phase and quadrature signals are multi-level and the decision circuits have multiple thresholds, as shown for 8DPSK in Fig. 3.7b and discussed in [49]. The thresholds must be adjusted according to the signal power received. The binary data at the output of the decision modules must be processed by appropriate data recovery logic which is different from the one for arg-decision. For IQ-decision, the thresholds are not optimally placed between the symbols, so a worse noise performance can be expected than for ideal arg-decision. To better understand the reconstruction of the information, the data recovery process is illustrated in greater detail in the following paragraphs. In the decision circuits, incoming signals are sampled once per symbol at sample times tk . In the case of IQ-decision, this provides the electrical in-phase and quadrature signal samples I Ik and I Q k . The decision results si,n k and sq,n k (logical one or zero) for IQ-decision in the k-th symbol interval at the outputs of the decision circuit in the in-phase and quadrature arms are specified by   1 I Q k > sq,n 1 I Ik > si,n , (3.41) , sq,n k = si,n k = 0 I Q k < sq,n 0 I Ik < si,n where si,n and sq,n represent the thresholds in the in-phase and quadrature branches, respectively.

3.2 Data Recovery for Differential Detection

75

a DQPSK, IQ-DECISION

b 8DPSK, IQ-DECISION

{b1 , b2 } 10

{b1 , b2 , b3 }

011 010

11

001 Sq,1

Sq,1

000

110

Sq,2 00

100

111

01

101

Si,1

c

Si,2

d

8DPSK, ARG-DECISION

16DPSK, ARG-DECISION S5

S3

S2

S7

010

001

S4

S1 S8

110

S4

S6

{b1 , b2 , b3 }

011

Si,1

S3 0111 0110 0010

0101

0011 S2

0100

0001

1100

000

S8 100

111 101 S6

S1

0000 S16

S9 S5

{b1 , b2 , b3 , b4 }

1000

1101 S10

1001 S15

1111 S11

1110 1010 1011

S7

S12

S14

S13

Fig. 3.7 Positioning of the thresholds for DPSK data recovery in the case of IQ-decision (a,b) and arg-decision (c,d)

When looking specifically at the data recovery for DQPSK and using the bit mapping shown in Fig. 3.7a, the first bit b1k is obtained from the decision result sq,1k at threshold sq,1 (decision circuit in the Q-branch) and the second bit b2k is equal to the decision result si,1k at threshold si,1 (decision circuit in the I-branch), placing both thresholds optimally at zero. IQ-decision for 8DPSK can be accomplished by placing two thresholds in the in-phase and the quadrature arms respectively. The positioning of these thresholds is illustrated in Fig. 3.7b. The data in the k-th symbol interval can be obtained from a data recovery logic defined by b1k = sq,2k + si,2k sq,1k ,

(3.42)

b2k = si,2k + si,1k sq,1k ,

(3.43)

b3k = si,1k sq,2k + si,2k sq,1k .

(3.44)

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3 Receiver Configurations

In the case of arg-decision, the phase difference information is determined using the electrical in-phase and quadrature signal samples by calculating  1ϕk = arg I Ik , I Q k . (3.45)

The signal samples after the arg-operation can be evaluated by a decision module with N ph thresholds, where N ph denotes the number of phase states. The thresholds sn should be optimally placed at sn = (2n − 1)π/N ph for n = (1, .., N ph /2) and sn = (2n − 1)π/N ph − 2π for n = (N ph /2 + 1, .., N ph ). The decision results sn k for arg-decision at the N ph outputs of the decision circuit in the symbol interval k are  1 1ϕk > sn . (3.46) sn k = 0 1ϕk < sn  The data recovery logic required to obtain the data bits b1k , b2k , .., bm k is different from the one required for IQ-decision. For 8DPSK and the bit mapping shown in Fig. 3.7c, the data recovery circuit is specified by b1k = s4k + s8k ,

(3.47)

b2k = s2k + s6k ,

(3.48)

b3k = s1k s3k + s5k s7k .

(3.49)

When looking at 16DPSK, IQ-decision can be expected to exhibit very poor performance due to small distances between the signal levels and the thresholds in the in-phase and quadrature arms. Therefore, only arg-decision is considered here. With the thresholds and bit mappings illustrated in Fig. 3.7d, the four information bits b1k , b2k , b3k and b4k can be recovered with the data recovery logic b1k = s8k + s16k ,

(3.50)

b2k = s4k + s12k ,

(3.51)

b3k = s2k s6k + s10k s14k ,

(3.52)

b4k = s1k s3k + s5k s7k + s9k s11k + s13k s15k .

(3.53)

The remainder of this section deals with the data recovery for Star QAM formats [58]. As can be observed from the equations (3.35) and (3.36) or (3.39) and (3.40) respectively, the in-phase and quadrature photocurrents are not only dependent on the phase difference between consecutive symbols but also on the non-delayed and

3.2 Data Recovery for Differential Detection

77

delayed modulation amplitudes a(t) and a(t − TS ). These amplitudes are ideally equal for DPSK formats and then do not affect the evaluation of the in-phase and quadrature signals for designation of the phase difference information. However, for Star QAM formats, the product a(t) · a(t − TS ) can take different values which depend on the amplitudes of two consecutive symbols. To illustrate this, the constellation diagrams received in the phase detection branch, constructed from the in-phase and quadrature photocurrents after differential detection, are shown in Fig. 3.8 for Star 8QAM (ASK-DQPSK) and Star 16QAM (ASK-8DPSK). It can be observed that what were originally two amplitude states have changed to three possible amplitude states as a result of the differential detection process.

IQ

IQ

II Fig. 3.8 Star QAM constellation diagrams received in the phase detection branch after differential detection

Star 8QAM (ASK-DQPSK)

II Star 16QAM (ASK-8DPSK)

With the arg-decision scheme it is still possible to determine the phase difference information by performing an arg-operation as described in (3.45). To recover the bits encoded in the phase differences, the same data recovery logic can be used as for the DPSK format with the same number of phase states. 8DPSK data recovery is appropriate for Star 16QAM, for instance. The bit encoded in the amplitude can simply be recovered by a binary decision in the intensity detection branch. Data recovery using IQ-decision, where the signals in the in-phase and quadrature branches are evaluated separately, is only easy to accomplish for Star QAM formats with a maximum of four phase states. When the phases are positioned at π/4 + n · π/2 (n = 0, 1, 2, 3), phase difference information can be obtained by performing binary decisions at zero on the signals in the in-phase and quadrature branches. But this works only if the thresholds can be set to zero and just one phase information bit must be recovered in each branch. Thus, this method is limited to Star QAM formats with only four phase states. It was used for ASK-DQPSK in [49] and for 16APSK (4ASK-DQPSK) in [62]. Additional effort must be undertaken to be able to perform IQ-decision for Star QAM signals with more than four phase states. In that case, the information from the intensity detection branch can be used to normalize the constellation and get rid of the unwanted amplitude information within the in-phase and quadrature photocurrents [58]. This process is denoted as “normalization” throughout this book and is illustrated in Fig. 3.9 for two different implementation options.

78

3 Receiver Configurations a

b

Normalization to original QAM constellation In-phase

x

Normalization to one DPSK circle In-phase

x

y Intensity

x x/y

x/y

x/y

y

y

Intensity TS

TS y

Quadrature

x x/y

y Quadrature

x

y x

x/y

x/y

Fig. 3.9 ”Normalization”, necessary when performing IQ-decision for Star QAM formats with more than four phase states

For the implementation option depicted in Fig. 3.9a, the received constellation is normalized to the original QAM constellation by dividing the in-phase and quadrature photocurrents given by (3.35) and (3.36) by the square root of the signal from the intensity branch defined by (3.23), which is delayed by one symbol duration. After this process, the in-phase and quadrature photocurrents are given by r r R · Ps R · Ps · a(t) · cos [1ϕ(t)] , I Q (t) = · a(t) · sin [1ϕ(t)] . (3.54) I I (t) = 8 8 These signals represent the original Star QAM constellation and can be evaluated using any conventionally employed decision scheme for Star QAM formats. Another option is normalizing the received constellation to one circle by dividing the in-phase and quadrature signals by the square root of the non-delayed and the delayed signal from the intensity branch, as illustrated in Fig. 3.9b. This way, the signals after normalization become independent of the modulation amplitudes. I I (t) =

1 1 · cos [1ϕ(t)], I Q (t) = · sin [1ϕ(t)]. 2 2

(3.55)

Using the in-phase and quadrature signals given by (3.55), the data bits corresponding to the phase information can be determined in the same way as for DPSK formats with the same number of phase states. Arbitrary DPSK and Star QAM formats with differentially encoded phases can be demodulated by applying the methods described in this section. The practical implementation of critical operations such as normalization and arg-calculation is a challenge for high data rates and can prospectively be performed by using highspeed digital signal processing technology.

3.3 Coherent Detection Principle

79

3.3 Fundamentals of Coherent Detection When employing coherent detection, all the information of the optical signal wave (amplitude, frequency, phase and polarization) is transferred to the electrical domain. In the case of the detection of optical signals with high-order modulation, this has the advantage that demodulation can be performed completely electrically, and optical complexity—in terms of interferometric optical demodulation structures for the conversion of phase to intensity modulation—can be reduced. Moreover, coherent receivers exhibit enhanced possibilities for electronic compensation of transmission impairments and can be used as flexible tunable WDM receivers with highly selective channel separation. On the other hand, coherent detection does not only provide for the availability of the desired field parameters in the electrical domain but also necessitates a controlled state of the remaining field parameters in order to be able to evaluate the information in demand.

3.3.1 Coherent Detection Principle To better understand the principles of coherent detection and see how the field parameters of the optical information signal are made available in the electrical domain, let us first observe the simple structure shown in Fig. 3.10. I I ,1 (t )

EI,1 (t)

Es (t)

3dB

Elo (t) Fig. 3.10 Principle of coherent detection

I I (t )

EI,2 (t) LO

BD

I I ,2 (t )

It becomes apparent that the optical information signal is interfered with the light of a LO laser before photo-detection, e.g. in a 3 dB coupler. With the normalized electrical field of the received optical information signal defined like before as p (3.56) Es (t) = Ps · e j (ωs t+ϕs ) · a(t) · e jϕ(t) · e jϕns (t) · es ,

and the CW light of the LO given by p Elo (t) = Plo · e j (ωlo t+ϕlo ) · e jϕnlo (t) · elo ,

(3.57)

where Ps and Plo represent the CW powers, ωs and ωlo are the angular frequencies, ϕs and ϕlo are the initial phases, ϕn s (t) and ϕnlo (t) represent the laser phase noise, and es and elo are the polarization unit vectors of the signal and the LO light, the resulting photocurrents within the balanced detector are

80

3 Receiver Configurations

I I,1 (t) =

I I,2 (t) =

1 1 1 R · (Es + jElo ) · (Es + jElo )∗ + i sh 1 = R Ps · a 2 (t) + R Plo + i sh 1 2 p 2 2 (3.58) +R Ps Plo · a(t) · es elo · sin [1ωt + ϕn (t) + ϕ0 + ϕ(t)], 1 1 1 R · ( jEs + Elo ) · ( jEs + Elo )∗ + i sh 2 = R Ps · a 2 (t) + R Plo + i sh 2 2 p 2 2 (3.59) −R Ps Plo · a(t) · es elo · sin [1ωt + ϕn (t) + ϕ0 + ϕ(t)],

where i sh 1 and i sh 2 represent the shot-noise photocurrents of the two photodiodes, and the angular frequency offset 1ω, the overall laser phase noise ϕn (t) and the initial phase offset ϕ0 are defined as 1ω = ωs − ωlo , ϕn (t) = ϕn s (t) − ϕnlo (t), ϕ0 = ϕs − ϕlo .

(3.60)

The variance of the random phase change due to the overall laser phase noise within a time interval τ , 1ϕn (t) = ϕn (t) − ϕn (t − τ ), can be calculated by h1ϕn2 (τ )i = 2π 1νe f f |τ |,

(3.61)

where 1νe f f is the beat-linewidth and given by the sum of the linewidth of the signal laser, 1νs , and the linewidth of the LO, 1νlo , [17] 1νe f f = 1νs + 1νlo .

(3.62)

The first and second terms are equal in (3.58) and (3.59) and represent the directly detected signal power and LO power, respectively. They are not interesting for evaluating signal information because it is usually true that Ps << Plo . During the balanced detection process (assuming an ideal symmetric balanced detection) they disappear anyway and only the beating term which contains all the field parameters of the superimposed optical fields remains I I (t) = I I,1 (t) − I I,2 (t) p = 2R Ps Plo · a(t) · es elo · sin [1ωt + ϕn (t) + ϕ0 + ϕ(t)] + i sh .(3.63)

In (3.63), i sh = i sh 1 − i sh 2 is the overall photocurrent after balanced

2  shot-noise 2 i + hi 2 i when assuming uncordetection, whose variance is given by i sh = hi sh sh 2 1 related noise events of the two photodiodes. Two fundamental coherent detection principles can be distinguished: homodyne and heterodyne detection. In the case of homodyne detection, the carrier frequencies of the signal laser and the LO laser aspire to be identical and the optical spectrum is directly converted to the electrical baseband. One of the main challenges for homodyne receivers, especially for homodyne synchronous (non-differential) detection, is the implementation of the carrier synchronization which synchronizes the carrier frequencies and phases of the signal laser and the LO.

3.3 Coherent Detection Principle

81

In the case of heterodyne detection, the frequencies of the signal laser and the LO are chosen to be different, so that the field information of the optical signal wave is transferred to an electrical carrier at an intermediate frequency (IF) which corresponds to the frequency difference of the signal laser and the LO (1ω). The IF must be at least as high as the baseband bandwidth of the information signal. On the one hand, heterodyne detection permits simple demodulation schemes and enables carrier synchronization with an electrical phase locked loop. On the other, the occupied electrical bandwidth for heterodyne detection is more than twice as high as for homodyne detection, and image-rejection techniques are required to allow for acceptable spectral efficiencies for WDM. Therefore, when considering spectral efficiency and the practical feasibility at high data rates, homodyne receivers are superior to their heterodyne counterparts and seem to be a better choice for future optical networks. For this reason, coherent receiver configurations described in this book are restricted to homodyne detection. Actual research about heterodyne detection of optical signals with high-order modulation can be found in [20, 41, 42], where very high-order Square QAM transmission has been experimentally demonstrated at moderate symbol rates. From (3.63) it can be observed that for evaluation of the signal information in demand (for phase and quadrature amplitude modulation: the modulation phase ϕ(t) and / or the normalized modulation amplitude a(t)) all the remaining parameters must be controlled to take defined states. In homodyne receivers, the frequencies of the signal laser and the LO aspire to be equal, whereas a stable IF at 1ω = ωs − ωlo is desired in heterodyne receivers. An uncompensated difference of the initial phases ϕ0 causes a fixed phase offset. The overall phase noise ϕn (t) leads to a random walk of the phase which corresponds to a permanent rotation of the received constellation diagram in arbitrary directions for quadrature detection of high-order modulation signals. Furthermore, the polarizations of the signal laser and the LO have to be aligned properly to obtain a maximal photocurrent. The availability of polarization information provides an auxiliary degree of freedom for optical transmission systems. Pure polarization modulation schemes such as M-ary polarization shift keying (MPOLSK), where information is encoded into different states of polarization [4], and combined QAM and polarization modulation (M-4Q-QAM), where all the four quadratures of the optical field are exploited [9], can be realized. A more simple way of making use of polarization is given by polarization division multiplexing (PDM). Here, the spectral efficiency of any modulation format can be approximately doubled. The derivation of the photocurrent given by (3.63) ignores the influence of the thermal noise of the receiver. For sufficiently high LO powers, the thermal noise can be neglected [13] and the shot-noise becomes the dominant noise source (shot-noise limited detection). The determination of the shot-noise limited receiver performance is the traditional way of characterizing coherent receivers. However, optical transmission systems with coherent detection and optical amplifiers on the link or in front of the receiver are no longer shot-noise limited but limited by the amplifier noise (amplifier noise limited detection). The influence of amplifier noise on the coherent detection process is briefly examined in Sect. 3.3.2.

82

3 Receiver Configurations

3.3.2 Coherent Detection with Amplifier Noise When the noise of an optical amplifier, whose low-pass representation was defined in Sect. 3.2.1 as n(t) = n k (t)ek + n ⊥ (t)e⊥ , is incorporated into the coherent detection process, the electrical field at the upper input of the balanced detector of the receiver shown in Fig. 3.10 is given by i 1 h E I,1 (t) = √ · Es (t) + n(t)e jωs t + jElo (t) , 2

(3.64)

where Es (t) and Elo (t) were defined by (3.56) and (3.57), respectively. The resulting photocurrent at the upper photodiode within the balanced detector—when the same polarizations of the received signal and the LO laser (es = elo ) are assumed, for simplicity—is specified by I I,1 (t) = R · E I,1 (t) · E∗I,1 (t) + i sh 1 i Rh ∗ |Es (t)|2 + |Elo (t)|2 − jEs (t)Elo = (t) + jE∗s (t)Elo (t) 2 i Rh Es (t)n∗ (t)e− jωs t + E∗s (t)n(t)e jωs t + |n(t)|2 + 2 i Rh ∗ + jElo (t)n∗ (t)e− jωs t − jElo (t)n(t)e jωs t + i sh 1 2  R R R ∗ |E s (t)|2 + |Elo (t)|2 + − j E s (t)Elo (t) + j E s∗ (t)Elo (t) = 2 | {z } 2 | {z } 2 | {z } Signal power

LO power

Signal-LO beating

i R Rh + E s (t)n ∗k (t)e− jωs t + E s∗ (t)n k (t)e jωs t + 2 | {z } 2 Signal-ASE noise

i h n k (t) 2 + |n ⊥ (t)|2 {z } | ASE-ASE noise

i Rh ∗ + j Elo (t)n ∗k (t)e− jωs t − j Elo (t)n k (t)e jωs t +i sh 1 . 2 | {z }

(3.65)

LO-ASE noise

The first three terms (signal and LO power, signal-LO beating) describe the photocurrent without amplifier noise given by (3.58). The signal-ASE noise and the ASE-ASE noise are known from the direct detection receiver discussed in Sect. 3.2.1. In coherent receivers, the additional LO-ASE noise is usually dominant compared with all the other noise components [11, 17]. In the same manner, the photocurrent of the lower photodiode within the balanced detector I I,2 (t) can be derived. The electrical field at the lower input of the balanced detector is i 1 h (3.66) E I,2 (t) = √ · jEs (t) + jn(t)e jωs t + Elo (t) , 2

3.3 Coherent Detection with Amplifier Noise

83

and the photocurrent of the lower photodiode within the balanced detector can be described by I I,2 (t) = R · E I,2 (t) · E∗I,2 (t) + i sh 2  R R R ∗ j E s (t)Elo (t) − j E s∗ (t)Elo (t) = |E s (t)|2 + |Elo (t)|2 + 2 2 2 i R h i Rh n k (t) 2 + |n ⊥ (t)|2 + E s (t)n ∗k (t)e− jωs t + E s∗ (t)n k (t)e jωs t + 2 2 i Rh ∗ + (3.67) − j Elo (t)n ∗k (t)e− jωs t + j Elo (t)n k (t)e jωs t + i sh 2 . 2

When neglecting all noise components except for the LO-ASE noise and assuming full correlation of the noise events of both branches, the photocurrent after balanced detection is given by I I (t) = I I,1 (t) − I I,2 (t)   ∗ = R − j E s (t)Elo (t) + j E s∗ (t)Elo (t) i h ∗ +R j Elo (t)n ∗k (t)e− jωs t − j Elo (t)n k (t)e jωs t p = 2R Ps Plo · a(t) · sin [1ωt + ϕn (t) + ϕ0 + ϕ(t)] | {z } Signal-LO beating

o ∗ + 2R · Re − j Elo (t)n k (t)e jωs t . {z } | n

(3.68)

LO-ASE noise

The signal and LO powers have disappeared after balanced detection. The signal information is contained in the signal-LO beating term which is the same as derived before in (3.63). The LO-ASE noise can be written as o n ∗ n L O−AS E (t) = 2R · Re − j Elo (t)n k (t)e jωs t n    
o ∗ = 2R · Re − j Elo (t)e jωs t · Re n k (t) + j I m n k (t) p
 = 2R Plo · Re n k (t) · sin 1ωt − ϕnlo (t) − ϕlo p 
+2R Plo · I m n k (t) · cos 1ωt − ϕnlo (t) − ϕlo . (3.69)

  The variances of Re n k (t) and I m n k (t) are given by σ I2 = σ Q2 = (N0 /2) · Bn . When neglecting the phase noise of the LO laser ϕnlo (t), the LO-ASE noise can be interpreted as Gaussian noise with a power spectral density of N L O−AS E = 2R 2 Plo N0 .

(3.70)

Compared with direct detection, where the power of the signal-ASE noise depends on the power of the detected symbols, the noise is symbol-power independent for coherent detection limited by LO-ASE noise.

84

3 Receiver Configurations

3.3.3 Optical Quadrature Frontend To be able to detect the in-phase and quadrature components of high-order optical modulation signals, an optical quadrature frontend must be employed, where the signal and LO light are superposed in a 2 × 4 90◦ hybrid whose output signals are detected by two balanced detectors. The setup of the optical quadrature frontend is shown in Fig. 3.11.

Eout1 (t )

In-phase

I I (t )

Es (t) Elo (t) Fig. 3.11 Optical quadrature frontend for coherent detection of the in-phase and quadrature components of high-order modulation signals

2x4 90° Hybrid

Eout3 (t ) Eout2 (t ) Quadrature

IQ (t ) Eout4 (t )

BD

The field transfer function of the hybrid is defined by (3.14) and (3.15). When setting the phase shift ψ to zero and neglecting phase shifts commonly experienced by both input fields, the hybrid output fields (without amplifier noise) are     Es (t) + Elo (t) Eout1 (t) Eout (t) 1 Es (t) + jElo (t) 2     (3.71) Eout3 (t) = 2 ·  Es (t) − Elo (t) . Es (t) − jElo (t) Eout4 (t) After detecting the output fields Eout1 (t) and Eout3 (t) with the upper and Eout2 (t) and Eout4 (t) with the lower balanced detector, the in-phase and quadrature photocurrents are obtained as I I (t) = R · Eout1 (t) · E∗out1 (t) − R · Eout3 (t) · E∗out3 (t) p = R Ps Plo a(t) es elo cos [1ωt + ϕn (t) + ϕ0 + ϕ(t)] + i sh I , (3.72) I Q (t) = R · Eout2 (t) · E∗out2 (t) − R · Eout4 (t) · E∗out4 (t) p = R Ps Plo a(t) es elo sin [1ωt + ϕn (t) + ϕ0 + ϕ(t)] + i sh Q , (3.73)

where i sh I and i sh Q are the overall shot-noise photocurrents in the in-phase and quadrature arms, respectively.

3.3 Polarization Diversity

85

3.3.4 Polarization Diversity As can be observed from (3.63) and (3.72)–(3.73), the photocurrents depend on the polarization of the signal and LO light. Parallel polarizations are necessary to obtain a maximal photocurrent. For slow polarization variations, adjusting the polarization manually in lab experiments suffices. For commercial application, polarization diversity which increases the effort should be implemented. Polarization diversity can be implemented by using two polarization beam splitters and doubling the optical frontend as shown in Fig. 3.12 for the quadrature receiver. The optical information signal is allowed to exhibit an arbitrary polarization state and is split proportionately to the power corresponding to the PBS reference directions. The LO must be polarized at 45◦ with respect to the PBS reference directions for even LO power splitting. Signal light then interferes with the LO light in both quadrature optical frontends with defined parallel polarization. The illustration chosen here has to be understood schematically. In practice, both separated polarization components of the information signal at the PBS outputs exhibit the same linear polarization state, and it suffices when the LO light—whose polarization must then be aligned to the polarization of the signal at the two PBS outputs—is equally split with a 3 dB coupler.

Es (t) PBS

I I (t )

Optical Quadrature Frontend Combination Network

Elo (t) PBS

Optical Quadrature Frontend

I Q (t )

Fig. 3.12 Configuration of a polarization diversity receiver; PBS: polarization beam splitter

After photo-detection, the photocurrents are combined electrically. If the signal’s polarization components have a relative phase delay, then the photocurrents of both frontends exhibit this delay as well. This must be considered during the combination. Several combination schemes are discussed in [17]. Simply adding the in-phase signals of both frontends, as well as the quadrature signals, leads to a penalty compared with ideal polarization control, even if phase matching is ensured. Currently, digital coherent receivers for detection of high-order modulation signals with polarization division multiplexing are extensively investigated [57, 72]. These receivers use the same optical frontend as illustrated in Fig. 3.12 for polarization diversity. In the electrical domain, the four photocurrents at the outputs of the two optical quadrature frontends are analog-to-digital converted. Afterwards, polarization de-multiplexing and compensation of degradation effects is accomplished by adaptive digital equalization. More details can be found in Sect. 3.5.3.

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3 Receiver Configurations

3.4 Homodyne Receivers with Differential Detection In contrast to direct detection receivers, homodyne receivers with differential detection accomplish the differential demodulation in the electrical domain after homodyne detection. Homodyne differential detection can be performed either by analog means (“phase diversity receivers”) as illustrated in Sect. 3.4.1, or by digital differential demodulation as described in Sect. 3.4.2. In the description of homodyne receivers with differential detection presented in these sections, the shot-noise and the amplifier noise are neglected and the in-phase and quadrature photocurrents at the outputs of the optical quadrature frontend are assumed to be p (3.74) I I (t) = R Ps Plo · a(t) · cos [1ωt + ϕn (t) + ϕ0 + ϕ(t)], p I Q (t) = R Ps Plo · a(t) · sin [1ωt + ϕn (t) + ϕ0 + ϕ(t)].

(3.75)

Starting from these photocurrents, it is shown in the next two sections how amplitude information a(t) and phase difference information 1ϕ(t) = ϕ(t) − ϕ(t − TS ) can be recovered for ASK, DPSK and Star QAM formats by means of homodyne differential detection.

3.4.1 Phase Diversity Receivers In the late eighties, optical homodyne receivers using a multi-branch structure and appropriate analog electrical processing were extensively investigated for the binary modulation formats 2ASK, binary frequency shift keying (2FSK), and DBPSK, for instance in [10, 29, 30]. These receivers are traditionally called “phase diversity receivers”, although the term “phase diversity” is not necessarily confined to homodyne differential detection and can also be used more generally for all receivers employing multiple branches with different relative phase relations. After homodyne detection with the optical quadrature frontend, the squared amplitude information of optical ASK and QAM signals can be obtained by squaring and adding the in-phase and quadrature signals given by (3.74) and (3.75) as shown in Fig. 3.13a. I (t) = I I2 (t) + I Q2 (t) = R 2 Ps Plo a 2 (t)

(3.76)

It can be observed that all the phase information, including the phase noise, is effectively disposed because (3.76) is not dependent on ϕn (t), ϕ(t) and ϕ0 . Moreover, arbitrary frequency offsets 1ω are allowed in principle, and no automatic frequency control is needed for the ASK phase diversity receiver. In practice, the electrical receiver bandwidth limits the tolerable frequency offset.

3.4 Phase Diversity Receivers a

87

2-branch ASK phase diversity receiver

I I (t ) 2x4 90° Hybrid

IQ (t )

( )2 I (t )

+ ( )2

LO BD

b

3-branch ASK phase diversity receiver

( )2 3x3 Coupler

( )2

+

I (t )

( )2

LO DC blocker

Fig. 3.13 Homodyne phase diversity receivers for ASK employing a two-branch structure (a) and a three-branch structure (b)

Phase diversity receivers can also be based on a three-branch structure using a 3 × 3 coupler as depicted in Fig. 3.13b, where a 3-branch ASK phase diversity receiver is shown without balanced detection so that additional DC blocks are necessary to cancel the DC current emerging from the directly detected LO light. As illustrated in Sect. 3.1.4, the signals after the 3 × 3 coupler in the three branches are 120◦ out of phase with each other. The cancelation of phase information for the three-branch structure becomes apparent from the simple trigonometric relation     3 cos2 [φ] + cos2 φ + 120◦ + cos2 φ + 240◦ = . 2

(3.77)

Thus, after squaring and adding the signals of the three branches, the resulting photocurrent is no longer dependent on phase information. The amplitude is not the only signal parameter that can be evaluated with phase diversity receivers. Phase modulated signals with differentially encoded phases can be demodulated just as well. When a DBPSK signal is detected by an optical quadrature frontend, phase difference information can be obtained by implementing the electronic demodulation network shown in Fig. 3.14. Starting from the in-phase and quadrature photocurrents given by (3.74) and (3.75), the signal after the electronic network can be calculated as

88

3 Receiver Configurations Q

I I (t )

× TS

2x4 90° Hybrid

I (t ) +

IQ (t )

I

TS

× LO BD

DBPSK

Fig. 3.14 Homodyne phase diversity receiver for DBPSK composed of a quadrature optical frontend and an electronic demodulation network

I (t) = I I (t) · I I (t − TS ) + I Q (t) · I Q (t − TS )

= R 2 Ps Plo a(t)a(t − TS ) · cos [1ωt + ϕn (t) + ϕ0 + ϕ(t)] · cos [1ω · (t − TS ) + ϕn (t − TS ) + ϕ0 + ϕ(t − TS )] +R 2 Ps Plo a(t)a(t − TS ) · sin [1ωt + ϕn (t) + ϕ0 + ϕ(t)] · sin [1ω · (t − TS ) + ϕn (t − TS ) + ϕ0 + ϕ(t − TS )].

(3.78)

Defining once again the difference of the modulation phase of two consecutive symbols as 1ϕ(t) = ϕ(t) − ϕ(t − TS ), and the phase change due to laser phase noise within the symbol duration as 1ϕn (t) = ϕn (t)−ϕn (t − TS ), (3.78) can be simplified to the following equation by applying simple trigonometric calculations: I (t) = R 2 Ps Plo a(t)a(t − TS ) · cos [1ϕ(t) + 1ϕn (t) + 1ωTS ].

(3.79)

In the case of an idealized DBPSK, where 1ϕ(t) takes the values 0 and π and where it holds true that a(t) = a(t − TS ) = 1, and when neglecting the phase noise and the frequency offset whose influence is discussed later on, a bipolar binary photocurrent results and the data can be obtained by binary decisions at zero. The phase diversity concept can be extended to arbitrary DPSK formats and Star QAM modulation with differentially encoded phases. In [40], phase diversity is investigated for higher-order DPSK formats for optical systems with coherence multiplexing. Recently, a phase diversity receiver for DQPSK was analyzed in [59]. Whereas the electronic network shown in Fig. 3.14 yields the in-phase component of arbitrary DPSK signals given by (3.79), the quadrature component can be obtained by multiplying the in-phase and quadrature photocurrents with the delayed photocurrents crossover and then subtracting the results Q(t) = I Q (t) · I I (t − TS ) − I I (t) · I Q (t − TS )

= R 2 Ps Plo a(t)a(t − TS ) · sin [1ωt + ϕn (t) + ϕ0 + ϕ(t)] · cos [1ω · (t − TS ) + ϕn (t − TS ) + ϕ0 + ϕ(t − TS )] −R 2 Ps Plo a(t)a(t − TS ) · cos [1ωt + ϕn (t) + ϕ0 + ϕ(t)] · sin [1ω · (t − TS ) + ϕn (t − TS ) + ϕ0 + ϕ(t − TS )]. (3.80)

3.4 Phase Diversity Receivers

89

By applying trigonometric calculations, (3.80) can easily be simplified and the quadrature photocurrent becomes Q(t) = R 2 Ps Plo a(t)a(t − TS ) · sin [1ϕ(t) + 1ϕn (t) + 1ωTS ].

(3.81)

The resulting configuration of a phase diversity receiver which is qualified to detect the in-phase and quadrature components of arbitrary DPSK signals is shown in Fig. 3.15. The part of the receiver for detecting the in-phase component I (t) is equal to the phase diversity receiver for DBPSK depicted in Fig. 3.14.

× TS

I (t )

I I (t )

×

+

TS

2x4 90° Hybrid

IQ (t )

TS

×

-

-

Q(t )

LO BD

TS

×

Fig. 3.15 Homodyne phase diversity receiver for detection of the in-phase and quadrature components of arbitrary DPSK signals

It should be noted that the phase noise is not completely canceled for the DPSK phase diversity receiver (in contrast to the ASK phase diversity receiver). The demodulation is based on differential phase detection and phase noise becomes critical if the phase change between two consecutive symbols takes considerable values. Phase noise requirements are slightly more stringent than for direct detection, but they are in a similar range (see Sect. 7.2.2). Moreover, frequency offsets are a critical task for phase detection in phase diversity receivers. Fixed frequency offsets lead to corresponding fixed phase rotations of 1ω TS and frequency offset drifts lead to slow varying rotations of the constellation diagram. Thus, automatic frequency control (AFC, see Sect. 3.5.2) must be implemented in practice which is not as critical as an optical phase locked loop because the frequency offset drift δ1ω/δt is relatively slow. The differentially encoded phase information contained in 1ϕ(t) in (3.79) and (3.81) can be evaluated by the DPSK data recovery methods described in Sect. 3.2.3, in the same way as for the direct detection receivers. By performing a separate detection of intensity information, the DPSK phase diversity receiver concept can be extended to detect Star QAM signals with differ-

90

3 Receiver Configurations

entially encoded phases. The designation of intensity information can be based on coherent detection, for instance by applying the ASK phase diversity concept as depicted in Fig. 3.16.

Electronic Network ASK Phase Diversity

I I (t ) 2x4 90° Hybrid

Intensity

In-phase

IQ (t )

Electronic Network DPSK Phase Diversity

LO

Quadrature

BD

Fig. 3.16 Homodyne phase diversity receiver for detection of Star QAM signals with differentially encoded phases, intensity detection based on ASK phase diversity

Alternatively, intensity information can be determined by direct detection—by employing an additional intensity detection branch as for the Star QAM direct detection receiver. This receiver concept is shown in Fig. 3.17 and has the drawback that the typical benefits of homodyne detection (the possibility of selecting WDM channels by just tuning the LO and the enhanced possibilities for electronic mitigation of transmission impairments) can not be exploited for the intensity detection branch. Furthermore, an optical amplifier must be used in the intensity detection branch to obtain a similar sensitivity to the phase detection branch. Intensity detection branch Intensity

Phase detection branch

I I (t ) In-phase 3dB

2x4 90° Hybrid

IQ (t )

Electronic Network DPSK Phase Diversity

Quadrature

LO BD

Fig. 3.17 Homodyne phase diversity receiver for detection of Star QAM signals with differentially encoded phases, intensity detection based on direct detection

Data recovery for the Star QAM phase diversity receivers can be accomplished with the same methods as used for the direct detection receivers. These methods are described in Sect. 3.2.3. The data bits encoded in the amplitude can be directly obtained from the intensity signals. The phase difference information contained in

3.4 Digital Differential Demodulation

91

the in-phase and quadrature signals after the electronic network can either be evaluated by arg-decision or IQ-decision. In the latter case, a normalization (see Fig. 3.9) becomes necessary for detection of Star QAM signals with more than four phase states because the signals after the electronic network, defined by (3.79) and (3.81), are dependent on the current amplitude a(t) and the amplitude a(t − TS ) delayed by one symbol duration. When being compared with direct detection receivers which enable detection of the same modulation formats, homodyne receivers with differential detection offer enhanced possibilities for electronic distortion equalization (EDE) and allow the selection of WDM channels with high selectivity using a tunable LO. On the other hand, direct detection receivers do not require any frequency synchronization and polarization control. In [59], the potential of the phase diversity receiver for electronic distortion equalization and its suitability for WDM is highlighted. In phase diversity receivers for WDM, no optical filter is needed to detect the desired wavelength channel. In fact, unwanted interference terms (direct detection interference, channel cross-channel interference) are eliminated by balanced detection. Finally, the desired channel can be separated from other channels using an electrical lowpass filter which must be placed directly behind the optical quadrature frontend (in front of the electronic network). This enables highly selective channel separation and spectrally efficient WDM transmission. Moreover, in [59] the impact of particular receiver impairments such as RIN, phase noise, frequency offset, receiver asymmetries (e.g. gain and delay imbalance) and WDM channel crosstalk on a phase diversity receiver for DQPSK are analyzed. In principle, the electrical part of the phase diversity receivers discussed in this section can also be implemented by digital means. However, when digital signal processing is employed, the receiver illustrated in Sect. 3.4.2 is a simpler implementation option.

3.4.2 Digital Differential Demodulation An alternative receiver concept for homodyne differential detection becomes feasible with recently available high-speed digital signal processing technology and is shown in Fig. 3.18. The in-phase and quadrature signals at the outputs of the optical quadrature frontend, defined by (3.74) and (3.75), are sampled by an A/D-converter, for instance once per symbol. This provides the in-phase sample I Ik and the quadrature sample I Q k at the k-th symbol interval p   (3.82) I Ik = R Ps Plo · ak · cos 1ωtk + ϕn k + ϕ0 + ϕk , p   I Q k = R Ps Plo · ak · sin 1ωtk + ϕn k + ϕ0 + ϕk ,

(3.83)

92

3 Receiver Configurations

A/D 2x4 90° Hybrid

I Ik

I Qk

IQ (t )

EDE

I I (t )

A/D

ARG-Operation ARG-Operation

Digital differential demodulation

φk TS

Δφk

-

φk −1

LO BD

Fig. 3.18 Homodyne receiver with digital differential demodulation

where ak , ϕk and ϕn k represent the samples of the modulation amplitude, the modulation phase and the overall laser phase noise respectively. Optionally, electronic distortion equalization can be applied first. By performing an arg-operation on the in-phase and quadrature samples, the instantaneous phase of the current symbol can then be calculated as  φk = arg I Ik , I Q k = 1ωtk + ϕn k + ϕ0 + ϕk . (3.84)

By subtracting the phase sample delayed by one symbol time φk−1 from the current phase sample φk , the current phase difference 1φk can be determined as 1φk = φk − φk−1 = 1ϕk + 1ϕn k + 1ωTS ,

(3.85)

with the samples of the modulation phase difference and phase change due to laser phase noise being defined as 1ϕk = ϕk −ϕk−1 and 1ϕn k = ϕn k −ϕn k−1 , respectively. In practice, these steps necessitate only a table-lookup for phase determination and a subtraction operation for phase differentiation. Since differential demodulation is employed, the absolute phase is not important and laser phase noise becomes not critical until the phase noise induced phase change takes considerable values within the symbol duration TS . In [32], a homodyne receiver with digital differential demodulation is investigated for DQPSK modulation. Additionally to the impact of phase noise, the influence of frequency offset is studied in this publication through simulations and experiments. The algorithm for the digital frequency offset estimation employed in [32] is easy to implement and capable of dealing with large frequency offsets (0.94 GHz at 10 Gbaud) without any significant penalty. Of course, Star QAM signals with differentially encoded phases can be demodulated using the homodyne receiver with digital differential demodulation just as well. The amplitude information can be obtained from the in-phase and quadrature samples by simply calculating ak2 = I I2k + I Q2 k .

(3.86)

Finally, data recovery can be accomplished by employing the arg-decision scheme described in Sect. 3.2.3.

3.5 Homodyne Receivers with Synchronous Detection

93

3.5 Homodyne Receivers with Synchronous Detection In homodyne receivers with differential detection, the phase information of the optical information signal is determined by differential phase detection. As a result, the LO phase does not have to be synchronized with the carrier phase of the signal (asynchronous detection). By contrast, the absolute phases of the information signal are designated with homodyne synchronous detection after mixing the signal with the LO reference carrier. This way, higher receiver sensitivities can be obtained than for differential detection, where the delayed modulation signal—which is also noisy—acts as a reference signal during differential demodulation. Moreover, synchronous detection has the advantage that arbitrary modulation formats can be conveniently received because demodulation is not based on the determination of phase differences but on absolute phases. On the other hand, a carrier synchronization becomes necessary—a challenging task for practical implementation. However, its chances for a successful commercial implementation are growing because laser linewidth and frequency offset requirements become more relaxed with increasing data rates. Furthermore, recent progress in high-speed digital signal processing technology permits the application of digital carrier synchronization techniques to optical receivers. Before going into the details of carrier synchronization, let us first have a look at its need for homodyne synchronous detection. The in-phase and quadrature photocurrents emerging at the outputs of the optical quadrature frontend for coherent detection are specified by p (3.87) I I (t) = R Ps Plo · a(t) · cos [1ωt + ϕn (t) + ϕ0 + ϕ(t)] + n I , p I Q (t) = R Ps Plo · a(t) · sin [1ωt + ϕn (t) + ϕ0 + ϕ(t)] + n Q ,

(3.88)

where 1ω represents the frequency offset, ϕn (t) is the overall laser phase noise and ϕ0 is the initial phase offset which are all defined in (3.60). The parameters n I and n Q correspond to additive noise in the in-phase and quadrature branches respectively. In the case of shot-noise limited detection, n I and n Q can be substituted by the shot-noise photocurrents in the in-phase and quadrature branches, i sh I and i sh Q , respectively (see Sect. 3.3.1 and Sect. 3.3.3). In systems with optical amplifiers limited by the LO-ASE noise, n I and n Q can be interpreted as the LO-ASE noise n L O−AS E I (t) and n L O−AS E Q (t) in the in-phase and quadrature branches, respectively. The LO-ASE noise is discussed in Sect. 3.3.2. The goal is to recover the modulation information contained in a(t) and ϕ(t). The complex phasor which describes the received amplitude and phase in the IQ-plane is given by p (3.89) X (t) = I I (t) + j I Q (t) = R Ps Plo · A(t) · e j8(t) + n c , where A(t) represents the normalized complex envelope containing the modulation information, 8(t) is the phase error due to the frequency offset, the laser phase noise

94

3 Receiver Configurations

and the initial phase offset, and n c is the complex shot-noise / amplifier noise. These parameters are defined by A(t) = a(t) · e jϕ(t) , 8(t) = 1ωt + ϕn (t) + ϕ0 , n c = n I + jn Q .

(3.90)

As can be observed from the received in-phase and quadrature signals given by (3.87) and (3.88) or from the complex phasor defined in (3.89), the recovery of information can fail due to the shot-noise / amplifier noise, as well as for an uncompensated phase error which causes an arbitrary rotation of the constellation diagram. For cancelation of the phase error, carrier synchronization which compensates for laser phase noise, frequency offset and initial phase offset is needed.

3.5.1 Carrier Synchronization Techniques The aim of carrier synchronization is to estimate the phase error 8(t) from the received signal and then to rotate the constellation diagram to the appropriate position by correcting the received phase with the determined phase error. The individual phase error contributors (the laser phase noise and the frequency offset) can be treated separately or using a joint frequency and phase estimation technique. Frequency and phase recovery techniques can be classified into three main categories: data aided, decision directed and non data aided. When trying to extract the phase error from the received signal, this is impaired by the complex noise n c , which also contributes to the received phase, as well as by data modulation. The latter impairment can be disposed by employing data aided carrier recovery. Here, a part of the data sequence is known. This is usually achieved by applying burst-mode transmission and sending a preamble with a known pattern at the beginning of each burst. If the data sequence is not known a priori, decision directed or non data aided carrier recovery techniques must be employed. For decision directed carrier synchronization, the data is assumed to be estimated properly by the data recovery and substitutes the true data. A similar performance as for data aided carrier recovery can be reached at the steady state for a high signal to noise ratio and thus few decision errors. As a third option, non data aided techniques neither make use of the knowledge of the current data values nor their estimates—the received information signal alone is used to determine the phase error. Carrier recovery techniques can be further classified according to the receiver configuration used. In closed loop receiver concepts, a corrective signal proportional to the phase error is generated and fed back to synchronize the phases of the signal and the LO. This way, the constellation diagram can be held locked in a fixed position by permanently compensating for newly appearing phase offsets. In contrast, feedback of a control signal is not required in an open loop concept, which is denoted as feed forward (FF) carrier recovery. Here, desired parameters are directly extracted from the received signal and a correction is performed afterwards.

3.5 Optical Phase Locked Loop

95

Homodyne optical receivers with an optical phase locked loop (OPLL, closed loop scheme) were extensively studied at the end of the eighties and at the beginning of the nineties [3, 8, 25, 27, 28, 47]. This work is briefly reviewed in Sect. 3.5.2. The OPLL is suitable for high-speed analog implementation. Recently, high-speed digital signal processing technology has emerged and there has been renewed interest in coherent detection. In “digital coherent receivers”, as they have often been referred to recently, digital equalization is performed very efficiently by digital means, and carrier recovery is accomplished using digital phase estimation. The problems associated with the OPLL—its stringent laser linewidth requirements and difficult practical implementation—can be avoided. In the current edition, this book does not cover equalization in detail, but digital phase estimation is precisely described for some selected schemes in Sect. 3.5.3. Phase estimation schemes based on feed forward and closed loop concepts and various modulation formats such as PSK, Star QAM and Square QAM are thereby considered.

3.5.2 Optical Phase Locked Loop Homodyne receivers with optical phase locked loop have been investigated in different variants, particularly for binary phase shift keying (BPSK) and quadrature phase shift keying systems.

Optical Phase Locked Loops for BPSK To understand the principles of the OPLL, one simple implementation option which is denoted as Costas loop is depicted in Fig. 3.19.

I I (t )

to decision

LPF

BPSK signal 2x4 90° Hybrid

× IQ (t ) LPF

LO BD Loop Filter

Fig. 3.19 Optical Costas loop receiver for BPSK

I M (t )

96

3 Receiver Configurations

In combination with the electrical multiplier behind, the optical quadrature frontend acts as a phase detector which generates a corrective signal proportional to the phase error. Assuming (3.87) and (3.88) and neglecting the complex noise n c , the corrective signal behind the multiplier can be derived as I M (t) = I I (t) · I Q (t) =

1 2 R Ps Plo · a 2 (t) · sin [28(t) + 2ϕ(t)], 2

(3.91)

with the phase error 8(t) as defined in (3.90). For BPSK modulation, it is ideally true that a 2 (t) = 1 and ϕ(t) = n · 180◦ (n ∈ {0, 1}), so that the modulation is eliminated and I M (t) ∼ sin [28(t)]. For small phase errors, I M (t) is approximately linearly dependent on the phase error, so that I M (t) ∼ 28(t). The corrective signal is filtered by a loop filter which regulates the bandwidth of the OPLL and has to be dimensioned properly to obtain stable operation of the loop. The filtered corrective signal is fed into a tunable LO which adjusts the frequency of the LO lightwave subject to the phase error. The optical Costas loop discussed above is based on a non data aided carrier recovery scheme and is analyzed in [8, 12, 18, 67] with respect to laser linewidth requirements and optimal splitting ratio, the latter of which defines the fraction of power provided in the in-phase and quadrature arms. An alternative OPLL structure for BPSK is described in [28] and denoted as “balanced OPLL”. This OPLL features a simple configuration, functioning with a 180◦ hybrid instead of a 90◦ hybrid. However, a residual carrier must be provided by the transmitted signal (which can be achieved using an incomplete phase modulation and phase shifts of less than 180◦ ), and the modulation impact is not completely canceled, which leads to a performance degradation due to data to phase-lock crosstalk [28]. The data to phase-lock crosstalk can be considerably reduced by applying a decision directed configuration [24, 63], where the decision circuit’s output signal is subtracted from the phase error signal before it is fed into the loop filter. A third OPLL structure for BPSK, based on a decision directed carrier recovery scheme, is analyzed in [27] and denoted there as “decision driven OPLL”. The linewidth requirements here are more relaxed than for the balanced OPLL. As for the improved balanced OPLL, decision results are used to eliminate the modulation information. However, the deployment of a 90◦ hybrid is as necessary as for the optical Costas loop.

Optical Phase Locked Loops for QPSK Optical phase locked loops were also shown for QPSK, for instance in [3, 46, 47]. To illustrate the increasing complexity of the phase detector for higher-order modulation formats, the decision directed OPLL structure investigated in [46] is shown in Fig. 3.20. The principle operation of the loop can be understood by looking at the output signals of the three electrical multipliers. When not taking the decisions into account, it is true for the output signal of the first multiplier that I1 (t) ∼ sin [28(t) + 2ϕ(t)]. The signal after the second multiplier can be calculated as I2 (t) ∼ cos [28(t) + 2ϕ(t)]. Thus, a corrective signal I M (t) ∼ sin [48(t) + 4ϕ(t)]

3.5 Optical Phase Locked Loop

97 I I (t )

QPSK signal

Data I

LPF 2x4 90° Hybrid

× IQ (t )

Data Q

LPF LO BD

-

+ ×

Loop Filter

I M (t )

I 2 (t )

×

I1 (t )

Fig. 3.20 Decision directed OPLL for QPSK modulation, investigated in [46]

results after the third multiplier. In the case of QPSK, it can be ideally assumed ϕ(t) = 45◦ + n · 90◦ (n ∈ {0, 1, 2, 3}), so I M (t) becomes independent of the transmitted data stream. Because a corrective signal proportional to the four-fold phase error is generated, a quadrant ambiguity results, which can be solved by differentially encoding the transmitted data and employing differential decoding at the receiver. The decision directed OPLL for QPSK was experimentally demonstrated in [47] at a data rate of 8 Gbit/s. Instead of the multipliers, digital XOR gates were employed. The beat-linewidth of the external cavity lasers used in the experiment was 60 kHz. But even a phase noise this small resulted in an error floor caused by a loop propagation delay of 12 ns. It is shown in [46] that the loop delay of an OPLL becomes non-negligible if the loop delay time τd is greater than the bit duration 1/r B and that this loop delay becomes the dominant restriction for the linewidth requirements at high data rates. The required beat linewidths to keep the receiver sensitivity penalty below 1 dB at BER=10−10 are derived for the decision directed OPLL in [46] and are summarized for BPSK and QPSK in Table 3.1. Table 3.1 Required beat linewidths for a receiver sensitivity penalty of 1 dB at BER=10−10 for homodyne receivers with decision driven OPLL, for zero loop delay time τd and under consideration of τd , derived in [46] BPSK 1ν [H z] (τd ≫ 1/r B ) 1ν [H z] (τd = 0)

QPSK

2.04 · 10−3 /τ 5.99 · 10−4

d

· rB

2.86 · 10−4 /τd 9.56 · 10−5 · r B

For a data rate of r B = 40 Gbit/s, for instance, the required beat linewidths are 24 MHz and 3.86 MHz for BPSK and QPSK, respectively, when the loop delay can be neglected. However, when the loop delay is 12 ns as in the experiment performed

98

3 Receiver Configurations

in [47], the beat linewidth requirements change to 170 kHz and 24 kHz for BPSK and QPSK, respectively. This is beyond the specifications of laser diodes currently available for commercial applications. Even when neglecting the delay of the components, a cable length of about 2.4 m alone corresponds to a delay of 12 ns. Thus, very compact, preferably integrated structures have to be aspired to. Until now, homodyne detection experiments with OPLL were not reported for modulation formats beyond QPSK, although phase locked loop (PLL) schemes for higher-order PSK and QAM formats are known from electrical systems—for instance the decision directed carrier recovery with selective gated PLL for Square 16QAM described in [21, 69, 70]. In principle, these phase locked loop schemes could be adapted to optical receivers. However, the laser linewidth requirements become even more stringent for higher-order modulation formats, so that the implementation of OPLL receivers for these formats only seems to be realistic when loop delay is kept very small.

Subcarrier Based Optical Phase Locked Loop Another challenge for an OPLL is the practical implementation of the optical voltage-controlled oscillator (VCO). The optical counterpart to an electrical VCO is a tunable local laser. However, the requirements for fast frequency tuning make this component a complex and expensive optical device. Recently, a new solution for the implementation of the optical VCO was proposed in [6, 7], where the tunable LO is replaced by a simple continuous wave laser whose light is intensity modulated externally (for instance using a MZM) by the output signal of an electrical VCO as shown in Fig. 3.21.

Elo (t )

MZM

Fig. 3.21 Optical VCO composed of a CW laser, an intensity modulator and an electrical VCO, alternative solution to a tunable LO, proposed in [6]

Electrical VCO

Loop Filter

I M (t )

CW Optical VCO

The spectrum of the signal arising at the optical VCO output contains two main subcarriers at the frequencies (ωC W ± ωV C O ) /2π , where ωC W and ωV C O are the angular frequencies of the CW laser and the electrical VCO, respectively. The selection of one of the subcarriers provides an optical carrier, which can be fine-tuned with the speed and stability of the electrical VCO.

3.5 Digital Phase Estimation

99

Automatic Frequency Control In the homodyne receivers with differential detection discussed in Sect. 3.4, phase differences are detected, so no optical phase locked loop must be employed. Nevertheless, frequency offsets 1ω which cause phase offsets of 1ωTS , as well as frequency offset drifts δ1ω/δt must be compensated for. This can be accomplished with an automatic frequency control (AFC) loop. Frequency offsets can be detected by a delay line frequency discriminator which has been employed in [45] and is shown in Fig. 3.22.

I I (t )

Fig. 3.22 Delay line frequency discriminator for generation of the corrective signal within an automatic frequency control loop, see [45]

×

τ IQ (t )

- - Q(t )

I M (t ) Integrator

τ ×

The setup of the delay line frequency discriminator is similar to the quadrature part of the electronic network of the phase diversity receiver for DPSK formats shown in Fig. 3.15. The signal arising at the integrator input is Q(t) ∼ sin [1ωτ + ϕn (t) − ϕn (t − τ ) + 1ϕ(t)],

(3.92)

where τ in this case represents the delay of the electrical delay lines. Because the frequency drift is slow compared with the phase noise and the modulation, and when furthermore the expectation values of the phase noise and the modulation are assumed to be zero, a corrective signal I M (t) proportional to the integral of sin (1ωτ ) results after the integrator which represents a phase error signal and can be taken to drive the optical voltage controlled oscillator.

3.5.3 Digital Phase Estimation Homodyne optical receivers based on OPLLs suffer from implementation difficulties and stringent laser linewidth requirements, especially when migration to higherorder optical modulation formats is desired. Fortunately, recent advances in highspeed digital signal processing technology open the door to handle carrier synchronization in homodyne optical receivers with digital techniques. With high-speed digital signal processors (DSPs)—which can be successfully applied to optical transmission systems—tasks like electronic pre-distortion can be performed on the transmitter side. At the receiver end, coherent detection mechanisms in particular benefit from digital technology. In digital coherent receivers,

100

3 Receiver Configurations

transmission impairments like chromatic dispersion and nonlinearities can be digitally compensated for with electronic distortion equalization, and digital carrier synchronization allows for a free running LO which does not have to be phase locked by an OPLL. Figure 3.23 shows the basic setup of a digital coherent receiver with homodyne synchronous detection when polarization diversity and polarization division de-multiplexing are not employed.

IQ (t )

LO

LPF

A/D

A/D

I Ik

I Qk

Phase Estimation

2x4 90° Hybrid

LPF

Adaptive EDE

I I (t )

Timing Recovery

Digital signal processing

Ik to data recovery

Qk

BD

Fig. 3.23 Digital coherent receiver with homodyne synchronous detection employing adaptive electronic distortion equalization (EDE) and digital phase estimation; single-polarization scheme without polarization diversity and polarization de-multiplexing

After being low-pass filtered, the in-phase and quadrature signals I I (t) and I Q (t) are sampled by A/D-converters. The first functional block in the digital signal processing part is often a non-adaptive time or frequency domain equalizer (not shown in Fig. 3.23) which compensates for the main part of chromatic dispersion having accumulated along the fiber link [33, 56]. Afterwards, a timing recovery is accomplished in order to synchronize the sample rate with the signal‘s symbol rate. Widely used algorithms are the Gardner [14] and the square timing recovery [48] here. Timing recovery is typically followed by a time domain equalizer, which is usually implemented as a FIR filter whose coefficients are adapted using the constant modulus algorithm (CMA) or the decision-directed least mean square (LMS) algorithm. In order to ensure a proper operation of the equalizers, a sample rate of at least twice the symbol rate is mostly chosen (fractionally spaced equalizer). For digital phase estimation—the functional block behind the adaptive EDE—just one sample per symbol is required which must be properly selected for the case that more than one sample per symbol is utilized for equalization. Digital coherent receivers are often used for detection of signals with polarization division multiplexing [57, 72]. A digital coherent receiver with polarization de-multiplexing is shown in Fig. 3.24. It uses the same optical frontend as described in Sect. 3.3.4 for polarization diversity. In the electrical domain, the four photocurrents at the outputs of the balanced detectors are analog-to-digital converted and then further processed by the digital signal processing. Compensation for degradation effects as well as polarization de-multiplexing are accomplished by the adaptive digital equalization. The time domain equalizer is often implemented as a FIR butterfly equalizer here [56, 57]. Phase estimation can be performed by treating both polarizations independently or by using a joint-polarization approach [34].

3.5 Digital Phase Estimation

101 Digital signal processing

X Ik 2x4 90° Hybrid

A/D

A/D

Elo (t) PBS

Adaptive EDE

PBS

Timing Recovery

Es (t)

2x4 90° Hybrid

A/D

LO

Digital Phase Estimation

A/D

X Qk

YI k

YQk

BD

Fig. 3.24 Digital coherent receiver with homodyne synchronous detection employing adaptive electronic distortion equalization (EDE), digital phase estimation and polarization de-multiplexing

The following paragraphs skip timing recovery and equalization, but in detail describe carrier synchronization by digital phase estimation for the single-polarization receiver depicted in Fig. 3.23. When the in-phase and quadrature signals I I (t) and I Q (t) are sampled by A/Dconverters once per symbol at sampling instants tk (in the middle of the symbols, assuming an ideal clock recovery), the sampled signals I Ik and I Q k —when neglecting the electrical filtering—are defined by (3.82) and (3.83). The complex phasor obtained after sampling is then given by p (3.93) X k = I Ik + j I Q k = R Ps Plo · Ak · e j8k + n ck ,

where the samples of the normalized complex envelope Ak , the phase error 8k , and the complex noise n ck are defined as Ak = ak · e jϕk , 8k = 1ωtk + ϕn k + ϕ0 , n ck = n Ik + jn Q k .

(3.94)

In principle, the algorithms for phase estimation can be based on data aided, decision directed or non data aided techniques, as well as on feed forward or closed loop concepts. The phase estimation algorithms applied so far to optical receivers are mainly based on the non-data aided feed forward M-th power scheme which allows for abandoning the provision of pilot sequences and the feedback of decision results [15, 31, 38, 39, 44, 60, 64, 65]. In the next paragraph, the so-called “feed forward M-th power block scheme”, similar to the one investigated for QPSK in [15, 39], is described for MPSK, Star QAM and Square QAM formats. It is a candidate for commercial employment in the near future due to its relatively simple implementation.

102

3 Receiver Configurations

Feed Forward M-th Power Block Scheme When the phase error of an individual symbol is calculated, a fraction of this phase error is caused by phase drifting effects, but the remainder results from the shotnoise / amplifier noise. To be able to get an accurate estimate of the phase error 8k , it has to be isolated from the phase error caused by the shot-noise / amplifier noise. This can be attained by performing an averaging over a block of N symbols. In a M-th power phase estimation scheme with symbol-to-symbol correction, a phase error estimate is calculated individually for every symbol while averaging over a block of N symbols. This corresponds to a sliding window technique. A different approach, which can be denoted as “M-th power block scheme”, is to calculate a common phase error estimate for all N symbols within a block. On the one hand, the accuracy of the carrier phase estimation is reduced when applying this technique (the phases of each symbol within a block are corrected with the same phase error estimate). On the other hand, the M-th power block scheme leads to a reduced implementation complexity. A block diagram of the feed forward M-th power block scheme for MPSK is illustrated in Fig. 3.25. i-th block of N symbols

i-th corrected block of N symbols

X k = I I k + jI Qk

X k ' = I k + jQk

1:N DEMUX ...

X 1+ ( i −1) N X 2+ (i −1) N

1:N MUX

e

()

M

()

M

()

...

...

X '1+ ( i −1) N X '2 + ( i −1) N

X N + (i −1) N

-jΦ i

e

-jΦ i

...

X 'N + ( i −1) N

e

-jΦ i

M

∑ Ψi-1

1 M ⋅ arg (

)

Ψi

Φi = Ψi + ni ⋅ 2π/M ni

Ψi SEGMENT CHANGE DETECTOR Ψi - Ψi-1 < -π/M Ψi - Ψi-1 > π/M

ni = ni −1 + 1 ni = ni −1 − 1

else ni = ni −1

Fig. 3.25 Feed forward M-th power block scheme with field averaging for digital carrier phase estimation on differentially encoded MPSK signals

3.5 Digital Phase Estimation

103

The incoming in-phase and quadrature samples are first combined into complex samples X k = I Ik + j I Q k . The stream of complex samples is then parallelized by a 1 : N demultiplexer, where N denotes the number of samples per block (which corresponds to the number of symbols per  block, because the sampling rate is equal to the symbol rate). Thus, the samples X 1+(i−1)N , X 2+(i−1)N , ..., X N +(i−1)N are available in parallel in the i-th block. Parallelization is very useful with regard to practical implementation because the clock speeds of currently available DSPs are limited to about 1GHz, so that it is necessary to process samples in parallel to handling higher symbol rates. In the architecture shown in Fig. 3.25, the clock rate is reduced by a factor of N with respect to the symbol rate. An even higher degree of parallelization is possible when the incoming sample stream is demultiplexed into multiple blocks of N samples as done in [15, 39]. After demultiplexing, the N complex samples of the i-th block are raised to the M-th power to eliminate the phase modulation M  p X kM = R Ps Plo · Ak · e j8k + n ck p = (R Ps Plo ) M · akM · e j Mϕk · e j M8k + n k p = (R Ps Plo ) M · akM · e j M8k + n k ,

(3.95)

where n k contains the shot-noise / amplifier noise n ck raised to the M-th power and the multiple mixing terms of the shot-noise / amplifier noise and the signal, and with k = p + (i − 1)N , p ∈ {1, 2, ..., N }, in the i-th block. The phase modulation is canceled because it holds e j Mϕk = 1 for MPSK signals, whose modulation angles are given by ϕk = n · 2π/M with n ∈ {0, 1..., M − 1}. As mentioned above, averaging reduces the influence of the shot-noise / amplifier noise on the determination of the phase error estimate. In [64, 65], it is shown that the optimal phase estimate is attained by applying a Wiener filter. Another option— leading to a lower phase noise tolerance, but featuring more simple practical implementation—is to use a rectangular filter which calculates the arithmetic mean of the input samples while summing the input samples with equal weights. One approach with rectangular filtering, whichnis denoted here as field averaging, is to sum o 4 4 , ..., X 4N +(i−1)N as , X 2+(i−1)N the N parallel available raised samples X 1+(i−1)N shown in Fig. 3.25. The angle of the resulting phasor divided by M then yields an estimate 9i for the average phase error of the i-th block   N X 1  · arg  XM (3.96) 9i = p+(i−1)N . M p=1

On the one hand, averaging lowers the influence of the shot-noise / amplifier noise on the phase error estimate. On the other, an inherent error is introduced since an average phase error estimate is calculated, commonly used for the phase correction of all symbols in the block. An optimal block length N can be found as a trade-off between the shot-noise / amplifier noise and the phase noise effects.

104

3 Receiver Configurations

Since the angle values calculated by the arg-operation are limited to the interval ]−π, π], the phase error estimates 9i take values between −π/M and π/M and a M-fold phase ambiguity of n ·2π/M, n ∈ {0, 1, ..., M − 1}, is induced. This problem can be overcome by periodically sending synchronization sequences, or better still by the use of differential encoding. More precisely, DPSK signals are generated at the transmitter side, so that the absolute position of the constellation diagram at the receiver side is allowed to be ambiguous with n · 2π/M. It should be noted that a synchronous detection is performed nevertheless, because the demodulation is not based on determination of the phase differences of two consecutive symbols but on the designation of absolute signal phases relative to the LO reference carrier. The differential decoding is performed here on the logical plane by using a differential decoder after phase estimation and data recovery, as described in Sect. 3.5.4. Therefore, an improved OSNR performance can be expected in comparison with differential detection, although the performance limit of coherent synchronous detection can not be completely achieved due to error propagation effects during the differential decoding [5]. To indicate that synchronous detection is performed with digital phase estimation receivers, the phase modulation formats detected by homodyne synchronous receivers will be just denoted here as MPSK, even though MDPSK signals are sent by the transmitter. Although the use of differential coding can solve the problem of permanent false rotations of n · 2π/M with constant n, symbol errors arise if the phase ambiguity error of two consecutive blocks is different (change of n). This occurs if the random walk of the phase noise is passing one of the boundaries between two segments at n ·2π/M. In this case, the phase error estimate performs phase jumps (“cycle slips”) and does not follow the trajectory of the physical phase [39, 44]. The phase jumps must be corrected by performing a phase unwrapping and can be detected by a socalled “segment change detector” which is also shown in Fig. 3.25. A variable n i , representing the actual segment, is updated in each block, depending on whether a segment change has occurred or not. For positive phase jumps which can be detected by 9i − 9i−1 > π/M, the segment number n i is decremented by one, for negative phase jumps (9i − 9i−1 < −π/M), n i is incremented by one, and n i is left equal if no segment change has appeared. After that, the phase error estimate 9i in the i-th block is corrected by 8i = 9i + n i ·

2π , M

(3.97)

where 8i represents the corrected phase error estimate of the i-th block which is taken to correct the phase of the received symbols by calculating  p  X k′ = R Ps Plo · Ak · e j8k + n ck · e− j8i p (3.98) = R Ps Plo · Ak · e j (8k −8i ) + n ck · e− j8i ,

again with k = p + (i − 1)N , p ∈ {1, 2, ..., N }, in the i-th block. In (3.98), the quantity 8ek = 8k − 8i describes the residual phase error of the k-th symbol.

3.5 Digital Phase Estimation

105

In the scheme described here, the phase correction for segment changes defined by (3.97) is applied to all symbols of the block. In principle, it is sufficient to correct only the last symbol of each block as done in [15, 39]. In this case, however, correction has to be performed at the logical level during differential decoding, whereas the phase estimation and the differential decoding can be completely decoupled for the scheme presented here. As a result of phase noise, symbol errors can occur because phase errors 8k can not be distinguished from phase errors of 8k + n · 2π/M, n ∈ {0, 1, ..., M − 1} due to the M-fold phase ambiguity. This happens in spite of differential encoding and the appropriate detection of segment changes. The phase error estimate 8i becomes imprecise  and symbol errors can arise if the phase error walk exceeds a phase interval of −π/M, π/M within the block duration Tblock = N · TS . The deployment of field averaging defined by (3.96) yields phase error estimate inaccuracies when the summed phasors are not of the same length √ (R Ps Plo ) M · akM . Thus, field averaging might not be appropriate for phase estimation of highly distorted MPSK signals and can not be used for QAM formats without further modification. Field averaging can be improved and made usable for carrier phase estimation of Star QAM signals by normalizing the phasors to an amplitude of one before being summed. This scheme is denoted as normalized field averaging throughout this book. After normalizing the phasors of the raised complex fields, the average phase error estimate 9i is again obtained by calculating the angle of the resulting sum phasor divided by M   N X XM 1 p+(i−1)N . · arg  (3.99) 9i = M M p=1 X p+(i−1)N

In the case of Star QAM, the number of symbols M in (3.99) must be replaced with the number of phase states N ph .

In contrast to MPSK and Star QAM where the modulation phases are equally spaced and the modulation can be eliminated by raising the received complex signal samples to the N ph -th power, the phase states are not arranged equidistantly for Square QAM formats. However, the M-th power block scheme can still be applied when the constellation points are partitioned into two groups. This is illustrated for Square 16QAM in Fig. 3.26a and for Square 64QAM in Fig. 3.26b, the latter showing only one quadrant. The Class I symbols (solid points in Fig. 3.26) all exhibit modulation angles of π/4 + n · π/2, n ∈ {0, 1, 2, 3}, so that modulation information can be eliminated in the same way as for QPSK by raising to the fourth power when selecting only these symbols for determination of the phase error estimate. The selection of the Class I and Class II symbols can be accomplished by performing amplitude decisions on the received signal samples.

106

3 Receiver Configurations a

Square 16QAM

b Square 64QAM (one quadrant)

q

q

i

i Class I symbols

Class II symbols

Fig. 3.26 Class partitioning for Square 16QAM (a) and Square 64QAM (b)

In the case of Square 16QAM, the symbols on the inner and outer circle belong to Class I and the symbols on the middle circle to Class II (open points in Fig. 3.26). A symbol X k can be identified as a Class I symbol X kClass I when the decision s1k + s2k yields a logical one. The decision results s1k and s2k are specified by  1 |X k | > sn sn k = , n = (1, 2), (3.100) 0 |X k | < sn where s1 and s2 denote the thresholds in-between the inner and middle circle and the middle and outer circle, respectively, shown as dashed lines in Fig. 3.26a. On average, only half of the symbols are Class I symbols for Square 16QAM, so larger block lengths N are necessary to ensure that a sufficient number of Class I symbols is available in each block for appropriate averaging. The ratio of Class I and Class II symbols is even smaller for Square 64QAM, as shown in Fig. 3.26b. A quarter of the constellation points exhibit modulation angles of π/4 + n · π/2, but only three points in each quadrant can effectively be selected by amplitude decisions. Because the constellation points on the third circle are close to the thresholds, phase estimation probably yields better results when only the symbols on the inner and outer circle are selected for the calculation of the phase error estimate. The selection of just an eighth of the total number of constellation points leads to high necessary block lengths as illustrated later on in Sect. 7.3.2. The phase estimation procedure for Square QAM formats is summarized in Fig. 3.27. After demultiplexing the complex signal samples into blocks of N symbols, the class partitioning just described is performed. NClass I symbols of the N symbols of a block belong to Class I and are used to determine the phase error estimate 8i which is used to correct the phase of all the symbols in the block.

3.5 Digital Phase Estimation

107

i-th block of N symbols

i-th corrected block of N symbols

X k = I I k + jI Qk

X k ' = I k + jQk

1:N DEMUX

X 1+ ( i −1) N X 2+ (i −1) N

1:N MUX

...

X '1+ ( i −1) N X '2 + ( i −1) N

X N + (i −1) N

e

-jΦ i

e

-jΦ i

...

...

X 'N + ( i −1) N

e

-jΦ i

CLASS PARTITIONING Select the Class I points ..........

X kClassI

..........

CALCULATE PHASE ERROR ESTIMATE

Φi

as for QPSK (M = 4)

Fig. 3.27 Phase estimation procedure for Square QAM formats

The phase error estimate for Square QAM formats can be obtained in the same way as for QPSK by applying the feed forward M-th power block scheme, for instance. When symbols of the inner and the outer circle with different amplitudes are selected by the class partitioning, normalized field averaging must be employed. With M = 4, replacing N with NClass I and averaging only over the Class I symbols X kClass I , (3.99) changes to   NX 4 Class I X 1 kClass I . 9i = · arg  (3.101) 4 4 X k=1 kClass I The corrected phase error estimate 8i can then be calculated after segment change detection by (3.97).

Closed Loop M-th Power Block Scheme Alternatively, digital phase estimation can be based on closed loop concepts with feedback of a control signal. When the feed forward M-th power block scheme is employed, a phase error estimate is calculated for each block from a received constellation diagram with an arbitrary phase offset corresponding to the current phase error. In contrast, the position of the constellation diagram is permanently tracked when the closed loop M-th power block scheme is applied.

108

3 Receiver Configurations i-th block of N symbols

i-th corrected block of N symbols

X k = I I k + jI Qk

X k ' = I k + jQk

1:N DEMUX ...

X 1+ ( i −1) N X 2+ (i −1) N

1:N MUX

X N + (i −1) N

X '1+ ( i −1) N X '2 + ( i −1) N

...

X 'N + ( i −1) N

Φi-D e

-jΦ i-D

()

e

M

arg( )

-jΦ i-D

()

M

arg( )

-jΦ i-D

...

e

...

()

...

arg( )

e

-j∆Φi

e

-j∆Φi

...

e

-j∆Φi

M

∑ M ⋅N ∆Φi Φi-D

+ Φi

Fig. 3.28 Closed loop M-th power block scheme with argument averaging for digital carrier phase estimation of differentially encoded MPSK signals

The block diagram of the closed loop M-th power block scheme for MPSK is depicted in Fig. 3.28. Before calculating a new phase error estimate, the received signal samples are rotated by −8i−D which represents the negative of the phase error accumulated in the past. Afterwards, the symbols are in the appropriate position with the exception of the phase error difference 18i accumulated in the last D blocks. To minimize 18i and for relaxed linewidth requirements, the accumulated phase error 8i−1 of the last block should ideally be available for rotation of the current block (D = 1). However, this is not attainable in practice when the processing delay for the calculation of 8i is greater than one block length. For this reason, only the accumulated phase error 8i−D is available in the current block, with a processing delay of D block lengths. The processing delay, which has a comparable effect to the loop delay in OPLLs, leads to more stringent laser linewidth requirements for the closed loop than for the feed forward M-th power block scheme, which can be implemented without the need for using distant past results. For this reason, the closed loop scheme is only of practical interest in systems where laser phase noise is not a critical parameter.

3.5 Digital Phase Estimation

109

For determination of the phase error difference 18i , the same mechanisms can be adopted as for the feed forward M-th power block scheme. After rotating the signal samples by 8i−D and raising the rotated samples to the M-th power, field averaging or normalized field averaging can be employed. With field averaging, the current phase error difference is obtained analogous to (3.96) as   N  M X 1 18i = (3.102) X p+(i−1)N · e− j8i−D . · arg  M p=1

Another option for averaging, denoted here as argument averaging and illustrated in Fig. 3.28, is to calculate the arguments of the raised complex fields first, and then to average the arguments to obtain an estimate of the current phase error difference which is given by 18i =

 N M  X 1 . arg X p+(i−1)N · e− j8i−D · NM

(3.103)

p=1

Argument averaging is applicable to the closed loop concept where the constellation diagram is held constantly in a fixed position and the raised samples are centered around an average phase of near zero due to the permanent phase tracking. However, it can not be applied to the feed forward scheme where the samples are centered around an arbitrary phase. To give an example, average phase errors of zero and average phase errors of π/4 would both yield phase error estimates of zero for QPSK, because the arguments are calculated modulo 2π with values in the interval ]−π, π]. Since argument averaging is independent of phasor amplitudes, it is applicable to Star QAM and Square QAM formats. In the case of Square QAM, class partitioning must be performed before raising to the fourth power. Finally, the accumulated phase error of the current block, obtained after a processing delay of D block lengths, can be calculated by 8i = 8i−D + 18i ,

(3.104)

and the phase of all the symbols in the block is corrected by −8i . This has the same effect as correcting the symbols by −18i after rotation with 8i−D as illustrated in Fig. 3.28. After the correction, the corrected samples are obtained as p (3.105) X k′ = R Ps Plo · Ak · e j (8k −8i ) + n ck · e− j8i ,

with k = p + (i − 1)N , p ∈ {1, 2, ..., N }, in the i-th block and a residual phase error of 8ek = 8k − 8i .

The last paragraphs described two digital phase estimation schemes which feature a relatively simple implementation. Phase estimation can be improved by using more sophisticated techniques. For instance, block-by-block phase correction can be replaced with symbol-to-symbol phase correction. Averaging can be optimized by

110

3 Receiver Configurations

employing hyperbolic or Wiener filtering. Non data aided carrier recovery schemes can be replaced with decision directed techniques [22]. Moreover, enhanced phase estimation algorithms for Square QAM allow to incorporate all constellation points into the calculation of the phase error estimate [37, 55]. In the next paragraph, it is shown how a separate frequency offset estimation can be accomplished.

Digital Frequency Offset Estimation Generally, the phase error estimate 8i provides an estimate of the phase error 8k which contains the phase error due to the frequency offset 1ω, the initial phase offset ϕ0 and the phase noise ϕn k , as can be observed from (3.94). Because the walk of the phase must remain within a certain interval −π/M, π/M within the block length Tblock to avoid symbol errors, the frequency offset should be estimated separately before phase estimation, since permanent constant phase offsets of 1ω · Tblock are induced within each block duration. For instance, at a symbol rate of r S = 10 Gbaud and a block length of N = 8, a frequency offset of 1ω = 2π · 100 MHz shifts the phase by 1ω · Tblock = 2π · 100 MHz · 8 · 100 ps= 0.5 rad. This would significantly restrain the phase noise tolerance for QPSK, and lets the phase estimation fail for modulation formats with even more phase levels. One algorithm possible for frequency offset estimation is the phase differential algorithm. As for the M-th power phase estimation, the received samples are raised to the M-th power to eliminate phase modulation
p (3.106) X kM = (R Ps Plo ) M · akM · e j M 1ωtk +ϕ0 +ϕnk + n k .

Next, the current raised sample is multiplied by the complex conjugate of the raised M ), and when nesample delayed by d symbols. In the case of MPSK (akM = ak−d glecting the noise n k , for simplicity, one obtains X kM

·

M ∗ X k−d

= =

p

2M

(R Ps Plo ) · ak2M p (R Ps Plo )2M · ak2M

·e

h  i j M 1ω(tk −tk−d )+ ϕn k −ϕn k−d

· ejM

1ω·τ +1ϕn k




,

(3.107)

where τ = tk − tk−d = d · TS denotes the duration of d symbols, 1ω · τ is the phase offset accumulating during d symbols due to the frequency offset and 1ϕn k = ϕn k − ϕn k−d represents the phase noise induced random phase change within the time interval τ which can be assumed to be Gaussian distributed as illustrated in Sect. 2.1.1. Similarly to the isolation of the phase error induced by laser phase noise from the phase error induced by shot-noise / amplifier noise during digital phase estimation, the frequency offset can be isolated from the phase noise by averaging over a longer observation interval with N −d single estimates. This yields the frequency offset estimate   N X 1 ∗ M . (3.108) · arg  X kM · X k−d 1ωest = Mτ k=1+d

3.5 Data Recovery for Synchronous Detection

111

Since the angle values of the arg-operation are limited to the interval ]−π, π], the maximum resolvable frequency offset is given by 1 f max =

1ωestmax 1 1 rS = · (±π) = ± =± . 2π 2π Mτ 2Mτ 2Md

(3.109)

The frequency offset tolerance is reduced with increasing M and increasing d. On the other hand, the frequency estimation accuracy improves with increasing d, so there is a trade-off between estimation range and estimation accuracy [55].

3.5.4 Data Recovery for Synchronous Detection

TS

1k −1

d#mk d#

mk −1

b1k ….

….

TS

d#1k d#

bmk

Multiplexer

sM k

Data Recovery Logic

Qk

s1k ….

from carrier recovery

ARG Operation

Ik

Differential Decoder

After carrier synchronization, the constellation diagrams are appropriately aligned and data can be recovered. The position of the constellation diagram is still ambiguous due to the phase ambiguity of the carrier recovery. The phase ambiguity is 2π/M for MPSK formats, 2π/N ph for Star QAM formats and π/2 for Square QAM. However, this phase ambiguity induces no difficulties when data is differentially decoded after the data recovery. The recovery of information can be based on arg-decision or IQ-decision (see Sect. 3.2.3). Data recovery for synchronous detection of PSK signals with argdecision is illustrated in the block diagram in Fig. 3.29.

Data

Fig. 3.29 Data recovery for synchronous detection of arbitrary PSK signals using arg-decision

After performing the arg-operation and decision as described by (3.46), a data recovery logic assigns symbols with respective bits {d˜1k , d˜2k , .., d˜m k } to the absolute phase states. In principle, this symbol assignment to absolute phases can be chosen arbitrarily. To reverse the differential encoding of the transmitter and to resolve the phase ambiguity, a differential decoder is used after the data recovery logic which evaluates the differences of the absolute phases on a logical level. In the differential decoder for any PSK format, the bits of the current output symbol of the data recovery logic, denoted here as {d˜1k , d˜2k , .., d˜m k }, are combined with the previous output bits of the data recovery logic, defined by {d˜1k−1 , d˜2k−1 , .., d˜m k−1 }, to specify the current decoded symbol representing the original data bits {b1k , b2k , .., bm k }. The symbol assignment to phase differences at the output of the decoder is forced by the original bit mapping defined at the transmitter side.

112

3 Receiver Configurations

Since the symbol assignment to absolute phases can be chosen arbitrarily, the data recovery circuits for the differential detection of DPSK signals, which are described in Sect. 3.2.3, can be re-used for the synchronous detection of PSK signals. The decoder must then provide for the appropriate final conversion of the symbol mapping to absolute phase states defined by {d˜1k , d˜2k , .., d˜m k } to the original data information {b1k , b2k , .., bm k } representing the phase differences. When the same data recovery logic is used as for differential detection, the mappings of the input and output constellations of the differential decoder are identical. In the case of QPSK (m = 2), the truth table is then given by Table 3.2 and the following logical relations can easily be derived for the differential decoder b1k = d˜1k d˜2k d˜1k−1 + d˜1k d˜2k d˜2k−1 + d˜1k d˜2k d˜1k−1 + d˜1k d˜2k d˜2k−1 ,

(3.110)

b2k = d˜1k d˜1k−1 d˜2k−1 + d˜2k d˜1k−1 d˜2k−1 + d˜1k d˜1k−1 d˜2k−1 + d˜2k d˜1k−1 d˜2k−1 . (3.111)

Table 3.2 Truth table of the differential decoder for QPSK when using the data recovery logic described in Sect. 3.2.3 for the recovery of the data defined by the Gray coded bit mapping depicted in Fig. 2.6 (special case of equal input and output mappings) d˜1k

d˜2k

ϕk

d˜1k−1 d˜2k−1 ϕk−1

0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

3/2 · π 3/2 · π 3/2 · π 3/2 · π 0 0 0 0 π π π π π/2 π/2 π/2 π/2

0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

3/2 · π 0 π π/2 3/2 · π 0 π π/2 3/2 · π 0 π π/2 3/2 · π 0 π π/2

b1k

b2k

ϕbk

0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0

1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1

0 3/2 · π π/2 π π/2 0 π 3/2 · π 3/2 · π π 0 π/2 π π/2 3/2 · π 0

Alternatively to re-using the data recovery circuit employed for differential detection, it can be advantageous to design another data recovery logic which allows for the re-use of the differential encoder as a differential decoder. As can be observed from the comparison of (3.110)–(3.111) with the logical relations for the differential encoders given by (2.34)–(2.35) and (2.36)–(2.37), the QPSK decoder described above is not identical with both DQPSK encoders. However, it can be shown that the differential encoder for the parallel transmitter can be also used as a differential

3.5 Data Recovery for Synchronous Detection

113

decoder when the data recovery is based on the symbol assignment of the constellation diagram shown in Fig. 2.9, bottom left. The data recovery logic must then be defined as d˜1k = si,1k and d˜2k = sq,1k , in contrast to Sect. 3.2.3. In this special case, the DQPSK encoder and the QPSK decoder feature the same configuration. In the same manner, the logical circuits of the differential decoders for higherorder PSK formats can be derived. Knowing the symbol assignment to absolute phase states determined by the data recovery logic, and considering the original mapping of the data bits to symbols, the truth tables can be established for the particular decoders and the logical relations can easily be obtained by evaluating these truth tables. When looking at the data recovery for Star QAM formats, the bits containing the phase information can be obtained by arg-decision in the same way as for the PSK formats. In the case of Star 16QAM, the bit b4k —which encodes the amplitude information—can be recovered by performing a single decision on the magnitude q

of the detected QAM symbol which is given by ak′ = Ik2 + Q 2k . The ideal position of the threshold depends on the ring ratio adjusted at the transmitter. When the Star QAM signals have more than two amplitude levels, several decisions on a multi-level signal become necessary in order to obtain the different data bits which contain the amplitude information.

…. M −1) k

Qk

….

sq ,1k s( q ,

M −1) k

Data Recovery Logic

s( i ,

from carrier recovery

TS

TS

1k −1

d#2k d#

2k −1

b1k b2k

b3k ….

Ik

d#1k d#

bmk

Fig. 3.30 Data recovery for synchronous detection of Square QAM signals

Multiplexer

si ,1k

QPSK Differential Decoder

In the case of Square QAM, the position of the constellation diagram after carrier recovery is ambiguous with n times π/2 (n = 0, 1, 2, 3). This is denoted as quadrant ambiguity. For this reason, a differential quadrant encoding of two of the m bits of a symbol, b1k and b2k , is performed at the transmitter, as illustrated in Sect. 2.6.1, and must be reversed at the receiver by a QPSK differential decoder. The differential decoder is placed behind the data recovery logic and finally recovers the data bits b1k and b2k from the differentially encoded quadrant bits d˜1k and d˜2k and the delayed bits d˜1k−1 and d˜2k−1 , as shown in Fig. 3.30.

Data

114

3 Receiver Configurations

The remaining m − 2 data bits b3k , .., bm k are arranged so as to be symmetric in rotation, so that the quadrant ambiguity does not have any influence on them. No differential decoding is necessary to recover these bits. In Fig. 3.31, the constellation diagram of Square 16QAM is shown with the symbol assignment defined in Sect. 2.6, also illustrating the placement of the thresholds.

{d# , d# }

{b3 , b4 } 01

1

2

11 11

10

01

11

01

00

00

10

Sq,1

Sq,2 10

Fig. 3.31 Symbol assignment and placement of the thresholds for Square 16QAM data recovery

00

00

01 Sq,3

11 00

01 Si,3

10 Si,2

Si,1

11 10

The bits on the corners determine the quadrant and are easily obtained from a data recovery logic defined by d˜1k = si,2k and d˜2k = sq,2k , where the decision results of the decision circuits in the in-phase and quadrature branches are specified by   1 Q k > sq,n 1 Ik > si,n , (3.112) , sq,n k = si,n k = 0 Q k < sq,n 0 Ik < si,n

√ with n = (1, .., M −1) and si,n and sq,n representing the thresholds in the in-phase and quadrature branches, respectively. The data bits b1k and b2k are then obtained at the two outputs of the QPSK differential decoder. The remaining two data bits b3k and b4k can be recovered by a data recovery logic specified by b3k = si,1k sq,2k + si,2k sq,1k + si,3k sq,2k + si,2k sq,3k ,

(3.113)

b4k = si,2k sq,1k + si,3k sq,2k + si,2k sq,3k + si,1k sq,2k .

(3.114)

The constellation diagram of Square 64QAM together with the thresholds is depicted in Fig. 3.32—assuming the symbol assignment defined in Sect. 2.6. The two bits which define the quadrant are obtained in the same way as for Square 16QAM. After performing decisions at the thresholds si,4 and sq,4 , the differentially encoded bits d˜1k and d˜2k are decoded by a QPSK differential decoder. This yields the data bits b1k and b2k . By the way, the differential decoder has an identical configuration for all Square QAM formats.

3.5 Data Recovery for Synchronous Detection

115

{b3 , b4 , b5 , b6 } {d# , d# } 1

01

2

11 1111

1110

1011

1010

0101

0111

1101

1111

1101

1100

1001

1000

0100

0110

1100

1110

0111

0110

0011

0010

0001

0011

1001

1011

Sq,2

0101

0100

0001

0000

0000

0010

1000

1010

Sq,3

Sq,1

Sq,4 1010

1000

0010

0000

0000

0001

0100

0101

1011

1001

0011

0001

0010

0011

0110

0111

Sq,5

Sq,6

00

1110

1100

0110

0100

1000

1001

1100

1101

1111

1101

0111

0101

1010

1011

1110

1111

Si,7

Si,6

Si,5

Si,4

Si,3

Si,2

Si,1

Sq,7

10

Fig. 3.32 Symbol assignment and thresholds for Square 64QAM data recovery

The remaining four bits b3k , .., b6k are again arranged as rotation symmetric as it is depicted in Fig. 3.32. The logical circuit for the data recovery of these bits is defined by b3k = si,2k sq,4k + si,4k sq,2k + si,6k sq,4k + si,2k sq,6k ,

(3.115)

b4k = si,4k sq,2k + si,6k sq,4k + si,4k sq,6k + si,2k sq,4k ,

(3.116)

b5k = si,1k sq,4k + si,2k si,3k sq,4k + si,4k sq,1k + si,4k sq,2k sq,3k +si,7k sq,4k + si,5k si,6k sq,4k + si,4k sq,7k + si,4k sq,5k sq,6k ,

(3.117)

b6k = si,4k sq,1k + si,4k sq,2k sq,3k + si,7k sq,4k + si,5k si,6k sq,4k +si,4k sq,7k + si,4k sq,5k sq,6k + si,1k sq,4k + si,2k si,3k sq,4k . (3.118)

116

3 Receiver Configurations

References 1. CeLight, http://www.celight.com 2. VPIsystems, Photonic Modules Reference Manual, 2005 3. Barry, J.R., Kahn, J.M.: Carrier synchronization for homodyne and heterodyne detection of optical quadriphase-shift keying. IEEE Journal of Lightwave Technology 10(12), 1939–1951 (1992) 4. Benedetto, S., Poggiolini, P.: Theory of polarization shift keying modulation. IEEE Transactions on Communications 40(4), 708–721 (1992) 5. Cai, Y., Pilipetskii, A.N.: Comparison of two carrier phase estimation schemes in optical coherent detection systems. In: Proceedings of Optical Fiber Communication Conference (OFC), OMP5 (2007) 6. Camatel, S., et al.: Optical phase-locked loop for coherent detection optical receiver. Electronics Letters 40(6), 384–385 (2004) 7. Camatel, S., et al.: 2-PSK homodyne receiver based on a decision driven architecture and a sub-carrier optical PLL. In: Proceedings of Optical Fiber Communication Conference (OFC), OTuI3 (2006) 8. Chiou, Y., Wang, L.: Effect of amplifier noise on laser linewidth requirements in long haul optical fiber communication systems with Costas PLL receivers. IEEE Journal of Lightwave Technology 14(10), 2126–2134 (1996) 9. Cusani, R., et al.: An efficient multilevel coherent optical system: M-4Q-QAM. IEEE Journal of Lightwave Technology 10(6), 777–786 (1992) 10. Davis, A.W., et al.: Phase diversity techniques for coherent optical receivers. IEEE Journal of Lightwave Technology LT-5(4), 561–572 (1987) 11. Desurvire, E.: Erbium-Doped Fiber Amplifiers. John Wiley & Sons, Inc. (1994) 12. Djordjevic, I.B., et al.: Performance optimization and exact laser linewidth requirements evaluation for optical PSK homodyne communication systems with Costas loop or DDL. Journal of Optical Communications 20(5), 178–182 (1999) ¨ ¨ 13. Franz, J.: Optische Ubertragungssysteme mit Uberlagerungsempfang. Springer Verlag, Berlin/Heidelberg (1988) 14. Gardner, F.M.: A BPSK/QPSK timing-error detector for sampled receivers. IEEE Transactions on Communications COM-34(5), 423–429 (1986) 15. Goldfarb, G., Li, G.: BER estimation of QPSK homodyne detection with carrier phase estimation using digital signal processing. Optics Express 14(18), 8043–8053 (2006) 16. Haykin, S.: Communication Systems. John Wiley & Sons, Inc. (1994) 17. Ho, K.P.: Phase-Modulated Optical Communication Systems. Springer (2005) 18. Hodgkinson, T.G.: Costas loop analysis for coherent optical receivers. Electronics Letters 22(7), 394–396 (1986) 19. Hoffmann, D., et al.: Integrated optics eight-port 90◦ -hybrid on Li N bO3 . IEEE Journal of Lightwave Technology 7(5), 794–798 (1989) 20. Hongou, J., et al.: 1 Gsymbol/s, 64 QAM coherent optical transmission over 150 km with a spectral efficiency of 3 bit/s/Hz. In: Proceedings of Optical Fiber Communication Conference (OFC), OMP3 (2007) 21. Horikawa, I., et al.: Design and performance of a 200Mbit/s 16QAM digital radio system. IEEE Transactions on Communications COM-27(12), 1953–1958 (1979) 22. Ip, E., Kahn, J.M.: Feedforward carrier recovery for coherent optical communications. IEEE Journal of Lightwave Technology 25(9), 2675–2692 (2007) 23. Jorgensen, B.F., et al.: Analysis of amplifier noise in coherent optical communication systems with optical image rejection receivers. IEEE Journal of Lightwave Technology 10(5), 660–671 (1992) 24. Kahn, J.M.: BPSK homodyne detection experiment using balanced optical phase-locked loop with quantized feedback. IEEE Photonics Technology Letters 2(11), 840–843 (1990) 25. Kahn, J.M., et al.: Heterodyne detection of 310-Mb/s quadriphase-shift keying using fourthpower optical phase-locked loop. IEEE Photonics Technology Letters 4(12), 1397–1400 (1992)

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26. Kaplan, A., Achiam, K.: Li N bO3 integrated optical QPSK modulator and coherent receiver. In: Proceedings of ECIO, WeA3.2, pp. 79–82 (2003) 27. Kazovsky, L.G.: Decision-driven phase-locked loop for optical homodyne receivers: Performance analysis and laser linewidth requirements. IEEE Journal of Lightwave Technology LT-3(6), 1238–1247 (1985) 28. Kazovsky, L.G.: Balanced phase-locked loops for optical homodyne receivers: Performance analysis, design considerations, and laser linewidth requirements. IEEE Journal of Lightwave Technology LT-4(2), 182–195 (1986) 29. Kazovsky, L.G.: Phase- and polarization-diversity coherent optical techniques. IEEE Journal of Lightwave Technology 7(2), 279–292 (1989) 30. Kazovsky, L.G., et al.: Wide-linewidth phase diversity homodyne receivers. IEEE Journal of Lightwave Technology 6(10), 1527–1536 (1988) 31. Kazovsky, L.G., et al.: Homodyne phase-shift-keying systems: Past challenges and future opportunities. IEEE Journal of Lightwave Technology 24(12), 4876–4884 (2006) 32. Koc, U., et al.: Digital coherent quadrature phase-shift-keying (QPSK). In: Proceedings of Optical Fiber Communication Conference (OFC), OThI1 (2006) 33. Kuschnerov, M., et al.: Joint equalization and timing recovery for coherent fiber optic receivers. In: Proceedings of European Conference on Optical Communication (ECOC), Mo.3.D.3 (2008) 34. Kuschnerov, M., et al.: Joint-polarization carrier phase estimation for XPM-limited coherent polarization-multiplexed QPSK transmission with OOK-neighbors. In: Proceedings of European Conference on Optical Communication (ECOC), Mo.4.D.2 (2008) 35. Langenhorst, R.: Optische Koppelelemente f¨ur den koh¨arent optischen Mehrtorempf¨anger. Ph.D. thesis, Technische Universit¨at Berlin (1992) 36. Leeb, W.R.: Optical 90◦ hybrid for Costas-type receivers. Electronics Letters 26, 1431–1432 (1990) 37. Louchet, H., et al.: Improved DSP algorithms for coherent 16-QAM transmission. In: Proceedings of European Conference on Optical Communication (ECOC), Tu.1.E.6 (2008) 38. Ly-Gagnon, D.S., et al.: Unrepeated 210-km transmission with coherent detection and digital signal processing of 20-Gb/s QPSK signal. In: Proceedings of Optical Fiber Communication Conference (OFC), OTuL4 (2005) 39. Ly-Gagnon, D.S., et al.: Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation. IEEE Journal of Lightwave Technology 24(1), 12–21 (2006) 40. Meijerink, A., et al.: Balanced optical phase diversity receivers for coherence multiplexing. IEEE Journal of Lightwave Technology 22(11), 2393–2408 (2004) 41. Nakazawa, M., et al.: 20 Msymbol/s, 128 QAM coherent optical transmission over 500 km using heterodyne detection with frequency-stabilized laser. In: Proceedings of European Conference on Optical Communication (ECOC), Mo4.2.2 (2006) 42. Nakazawa, M., et al.: Polarization-multiplexed 1 Gsymbol/s, 64 QAM (12 Gbit/s) coherent optical transmission over 150 km with an optical bandwidth of 2 GHz. In: Proceedings of Optical Fiber Communication Conference (OFC), PDP26 (2007) 43. Nicholson, G., Stephens, T.D.: Performance analysis of coherent optical phase-diversity receivers with DPSK modulation. IEEE Journal of Lightwave Technology 7(2), 393–399 (1989) 44. Noe, R.: PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I&Q baseband processing. IEEE Photonics Technology Letters 17(4), 887–889 (2005) 45. Noe, R., et al.: New FSK phase-diversity receiver in a 150 Mbit/s coherent optical transmission system. Electronics Letters 24(9), 567–568 (1988) 46. Norimatsu, S., Iwashita, K.: Linewidth requirements for optical synchronous detection systemes with nonnegligible loop delay time. IEEE Journal of Lightwave Technology 10(3), 341–349 (1992) 47. Norimatsu, S., et al.: An 8 Gb/s QPSK optical homodyne detection experiment using externalcavity laser diodes. IEEE Photonics Technology Letters 4(7), 765–767 (1992) 48. Oerder, M., Meyr, H.: Digital filter and square timing recovery. IEEE Transactions on Communications 36(5), 605–612 (1988)

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49. Ohm, M., Speidel, J.: Receiver sensitivity, chromatic dispersion tolerance and optimal receiver bandwidths for 40 Gbit/s 8-level optical ASK-DQPSK and optical 8-DPSK. In: Proc. 6th Conference on Photonic Networks, pp. 211–217. Leipzig, Germany (2005) 50. Paiam, M.R., MacDonald, R.I.: Design of phased-array wavelength division multiplexers using multimode interference couplers. Applied Optics 36(21), 5097–5108 (1997) 51. Petermann, K.: Einf¨uhrung in die optische Nachrichtentechnik. Vorlesungsskript, Technische Universit¨at Berlin (2003) 52. Pietzsch, J.: Scattering matrix analysis of 3 × 3 fiber couplers. IEEE Journal of Lightwave Technology 7(2), 303–307 (1989) 53. Priest, R.G.: Analyis of fiber interferometer utilizing 3 × 3 fiber coupler. IEEE Journal of Quantum Electronics QE-18(10), 1601–1603 (1982) 54. Proakis, J.G.: Digital Communications. McGraw-Hill (2001) 55. Rice, F.: Bounds and algorithms for carrier frequency and phase estimation. Ph.D. thesis, University of South Australia (2002) 56. Savory, S.J.: Compensation of fibre impairments in digital coherent systems. In: Proceedings of European Conference on Optical Communication (ECOC), Mo.3.D.1 (2008) 57. Savory, S.J., et al.: Transmission of 42.8Gbit/s polarization multiplexed NRZ-QPSK over 6400km of standard fiber with no optical dispersion compensation. In: Proceedings of Optical Fiber Communication Conference (OFC), OTuA1 (2007) 58. Seimetz, M.: Optical receiver for reception of M-ary star-shaped quadrature amplitude modulation with differentially encoded phases and its application. German patent, DE 10 2006 030 915.4 (2006) 59. Seimetz, M.: Phase diversity receivers for homodyne detection of optical DQPSK signals. IEEE Journal of Lightwave Technology 24(9), 3384–3391 (2006) 60. Seimetz, M.: Laser linewidth limitations for optical systems with high-order modulation employing feed forward digital carrier phase estimation. In: Proceedings of Optical Fiber Communication Conference (OFC), OTuM2 (2008) 61. Seimetz, M., Weinert, C.M.: Options, feasibility and availability of 2 × 4 90◦ -hybrids for coherent optical systems. IEEE Journal of Lightwave Technology 24(3), 1317–1322 (2006) 62. Sekine, K., et al.: Proposal and demonstration of 10-Gsymbol/sec 16-ary (40 Gbit/s) optical modulation / demodulation scheme. In: Proceedings of European Conference on Optical Communication (ECOC), We3.4.5 (2004) 63. Sun, L., Ye, P.: Optical homodyne receiver based on an improved balance phase-locked loop with the data-to-phaselock crosstalk suppression. IEEE Photonics Technology Letters 2(9), 678–680 (1990) 64. Taylor, M.G.: Accurate digital phase estimation process for coherent detection using a parallel digital processor. In: Proceedings of European Conference on Optical Communication (ECOC), Tu4.2.6 (2005) 65. Taylor, M.G.: Coherent detection for optical communications using digital signal processing. In: Proceedings of Optical Fiber Communication Conference (OFC), OMP1 (2007) 66. Voges, E., Petermann, K.: Optische Kommunikationstechnik. Springer Verlag, Berlin / Heidelberg (2002) 67. Wang, Y., Leeb, W.R.: Sensitivity analysis and performance optimization of an optical Costas phase-locked loop. Journal of Optical Communications 8(1), 29–31 (1987) 68. von Wangenheim, L.: Aktive Filter in RC- und SC-Technik. H¨uthig Buch Verlag Heidelberg (1991) 69. Webb, W., Hanzo, L.: Modern Quadrature Amplitude Modulation. IEEE Press and Pentech Press (1994) 70. Xiong, F.: Digital Modulation Techniques. Artech House, Inc. (2000) 71. Yoon, H., et al.: Performance comparison of optical 8-ary differential phase-shift keying systems with different electrical decision schemes. Optics Express 13(2), 371–376 (2005) 72. Zhou, X., et al.: 8x114Gb/s, 25-GHz-spaced, PolMux-RZ-8PSK transmission over 640km of SSMF employing digital coherent detection and EDFA-only amplification. In: Proceedings of Optical Fiber Communication Conference (OFC), PDP1 (2008)

Chapter 4

Effort Comparison

Abstract When a system is upgraded to a more sophisticated modulation format, the additional effort required is determined, in large part, by the enhanced complexity of the transmitters and receivers. In this chapter, the complexity of different transmitter and receiver configurations is briefly discussed and compared.

It was illustrated at the beginning of this book that the deployment of high-order modulation formats and coherent detection is presently seen as a promising way of increasing the spectral efficiency of optical fiber transmission and of better exploiting the capacity of the currently installed fiber infrastructure. Some questions were posed in the introduction which system designers would like to have answered in order to rank the potential of this new technology. Two of these are: What do the transmitters and receivers look like? How great is the additional effort required by a system upgrade? The last two chapters have provided a lot of material which assists in answering these questions and have described the composition of many optical transmitters and receivers. Based on the information given in these chapters, an explicit discussion and comparison of the complexity of different transmitter and receiver configurations takes place in the following two sections.

4.1 Transmitter Complexity and Feasibility The suitability and feasibility of a particular transmitter concept depends on the modulation format it is applied to. For circular constellations, transmitter configurations with a single modulator or several consecutive modulators are favorable, whereas IQ-structure based transmitters are more beneficial for generating squareshaped constellations. Generally, the migration to higher-order formats brings about an increase in transmitter complexity. The upgrade can be performed by adding optical modulators and accordingly creating more elaborate optical modulator structures or by

M. Seimetz, High-Order Modulation for Optical Fiber Transmission, Springer Series in Optical Sciences 143, DOI 10.1007/978-3-540-93771-5 4, c Springer-Verlag Berlin Heidelberg 2009

119

120

4 Effort Comparison

providing more complex electrical level generators for the generation of multi-level electrical driving signals. As illustrated in Fig. 4.1, the overall complexity of the transmitters can be traded-off between the optical and electrical parts. Since eye spreading complicates the generation of high-quality multi-level electrical driving signals for high data rates through analog means, transmitters with binary electrical driving signals may be preferred.

Optical complexity

Electrical complexity

Fig. 4.1 Transmitter complexity: trade-off between the optical and electrical parts

Generation of multi-level driving signals

Trade-Off

More complex optical modulator structures

The description of DPSK and Star QAM transmitters in Sect. 2.4 and Sect. 2.5 focusses on configurations which require only binary electrical driving signals. Table 4.1 compares the complexity of these transmitters for various modulation formats. 2ASK acts as reference (“0”), and all the other formats are characterized with one or more “+” to evaluate their particular complexity. Table 4.1 Comparison of the complexity of DPSK and Star QAM transmitters with binary electrical driving signals for various modulation formats. Se.: Serial, Pa.: Parallel Mod. Format

Tx Type

PM/MZM/IQM Opt. Complexity Encoder Type

El. Complexity

2ASK

-

0/1/0

0

-

0

DBPSK

-

1/0/0

0

DBPSK

+

DQPSK

Se. Pa.

2/0/0 0/0/1

+ ++

DQPSK (Se.) DQPSK (Pa.)

++ ++

8DPSK

Se. Pa.

3/0/0 1/0/1

++ +++

8DPSK (Se.) 8DPSK (Pa.)

+++ +++

16DPSK

Se. Pa.

4/0/0 2/0/1

+++ ++++

16DPSK (Se.) 16DPSK (Pa.)

+++++ +++++

Star 16QAM

Se. Pa.

3/1/0 1/1/1

+++ ++++

8DPSK (Se.) 8DPSK (Pa.)

+++ +++

The complexity of the electrical part of the transmitters depends mainly on the complexity of the differential encoder. This complexity increases disproportionately to the number of differentially encoded phase states, so that the differential encoder becomes very complex for high-order DPSK formats such as 16DPSK. When comparing the optical part of the transmitters, the effort required in creating an IQ modulator within the parallel transmitter is higher than for the creation of a pure serial

4.1 Transmitter Complexity and Feasibility

121

configuration consisting of consecutive phase modulators. Furthermore, the optical effort required increases with the order of the modulation format and the corresponding increasing number of modulators. The number of necessary modulators given in Table 4.1 does not include the MZM used for RZ pulse carving. In principle, the high complexity of the optical transmitter part for higher-order DPSK and Star QAM formats can be reduced by using a single conventional IQ modulator, but this necessitates a further increase in electrical complexity because multi-level electrical driving signals must be generated. Moreover, it should be noted that the in-phase and quadrature driving signals for circular constellations with many phase states have very small distances between signal levels, which is detrimental for system implementation. As regards transmitters for Square QAM, five different transmitter structures are described in Sect. 2.6. The complexity of these transmitters for Square 16QAM is compared in Table 4.2. Table 4.2 Comparison of the complexity of different transmitters for Square 16QAM Transmitter

PM/MZM/IQM Opt. Compl. Enc. Type QAM Cod./Lev. Gen. El. Compl.

Serial QAM Convent. IQ Enhanced IQ Tandem-QPSK Quad-pa. MZM

1/1/0 0/0/1 2/0/1 2/0/1 0/0/2

+ ++ +++ ++++ +++++

DQPSK DQPSK DQPSK DQPSK DQPSK

No / Yes (+) Yes / Yes Yes / No No / No Yes / No

+++++ ++++ +++ ++ +++

The serial Square QAM transmitter features a simple optical part, but the electrical level generator must generate electrical driving signals with a high number of levels and is very complex. To generate square-shaped constellations, the conventional IQ transmitter is a good choice, featuring beneficial chirp characteristics and a moderate optical complexity, but still requiring multi-level electrical driving signals. However, a restriction to binary driving signals—and thus a decrease of electrical complexity—is possible even for Square QAM. The enhanced IQ transmitter, the Tandem-QPSK transmitter and the quad-parallel MZM transmitter require only binary driving signals for Square 16QAM (an electrical level generator is not needed) and are therefore three promising options for implementation of a practical system—in spite of their more complex optical parts. In any Square QAM transmitter and for any Square QAM order, the same differential encoder—a DQPSK encoder with relatively moderate complexity—is appropriate when the quadrant ambiguity arising at the carrier synchronization in the receiver shall be resolved by differential decoding. However, a further coder (denoted within this book as Square QAM coder) must then be provided in the conventional IQ transmitter, the enhanced IQ transmitter and the quad-parallel MZM transmitter to create a bit mapping which is symmetric in rotation.

122

4 Effort Comparison

The spectral efficiency of any modulation format can be doubled using polarization division multiplexing. In this case, the transmitter complexity is approximately double for any configuration. The respective transmitters can be rated on the basis of the effort spent in developing their optical and electrical transmitter parts, but also by considering the influence of individual signal properties such as intensity shape, symbol transitions and chirp characteristic on the overall system performance. This issue, among many others, is discussed in the second part of this book.

4.2 Receiver Complexity and Feasibility Various receiver configurations can be used to detect optical high-order modulation signals. These can be based on direct detection or coherent detection, as shown in Chap. 3. The receiver scheme suitable for a particular system must be chosen according to the modulation format received, as well as through consideration of the given system specifications (e.g. sensitivity, laser linewidth) and desired accessory functionalities, such as electronic equalization. Furthermore, the complexity and feasibility of the receivers represents an important criterion for a decision. Direct detection receivers are suitable for detecting DPSK and Star QAM signals. Their optical frontend can be constructed by delay line interferometers or a 2 × 4 90◦ hybrid. Table 4.3 summarizes the complexity of the optical and electrical parts of two different direct detection receivers described in Sect. 3.2.1: the multiple DLI receiver and the IQ receiver composed of DLIs.

Table 4.3 Complexity comparison of direct detection receivers (multiple DLI receiver and direct detection IQ receiver) for various modulation formats; BD: balanced detector, PD: photodiode Mod. Format

RX Type

DLI and BD

Opt. Complexity

El. Complexity

2ASK

-

-

0

0

DBPSK

-

1

+

0

DQPSK

Mult. DLI IQ

2 2

++ ++

+ +

8DPSK

Mult. DLI IQ

4 2

+++ ++

++ +++

16DPSK

Mult. DLI IQ

8 2

+++++ ++

+++ ++++

Star 16QAM

Mult. DLI IQ

4 (+1 PD) 2 (+1 PD)

++++ +++

+++ ++++

4.2 Receiver Complexity and Feasibility

123

Similarly to the transmitters, the complexity of the electrical receiver parts can, in principle, be reduced through the introduction of more complex optical structures, for instance a higher amount of delay line interferometers for direct detection. The multiple DLI receiver exhibits a high optical complexity for high-order formats, but electrical decisions can be performed very easily with fixed thresholds at zero. When an IQ receiver is employed and the number of delay line interferometers is reduced to two for any modulation format, decisions on multi-level electrical signals with multiple thresholds become necessary for modulation formats with more than two bits per symbol. Alternatively, the two DLIs can be replaced by a 2 × 4 90◦ hybrid (see Sect. 3.2.2). This IQ receiver then exhibits a similar optical complexity and the same electrical complexity as the direct detection IQ receiver with DLIs. The optical part of the IQ receivers is identical for all high-order phase modulation formats. As regards Star QAM, the additional intensity detection branch slightly increases the complexity in comparison to DPSK receivers. The complexity of the electrical part of the receivers is determined primarily by the number of decision circuits necessary and the complexity of the data recovery logic, and thus increases with the modulation format order. Table 4.4 compares the complexity of receivers adopting different detection schemes, including the direct detection IQ receiver, the homodyne receiver with differential detection and the digital coherent receiver with homodyne synchronous detection for single-polarization and polarization division multiplexing. Table 4.4 Complexity comparison of different detection schemes: direct detection, homodyne differential detection and digital homodyne synchronous detection for single-polarization and polarization division multiplexing (PDM) Receiver Scheme

90◦ Hy./BD

Opt. Compl.

Pol.-/Fre.-/Ph.-Syn. Decoder

El. Compl.

Direct Det. IQ Hom. Diff. Det. Hom. Syn. Det. Hom. Syn. PDM

1/2 1/2 1/2 2/4

0 + + ++

No / No / No Yes / Yes / No Yes / Yes / Yes No / Yes / Yes

0 + ++ ++++

No No Yes Yes

The optical frontend of homodyne receivers for high-order modulation is usually composed of a 2 × 4 90◦ hybrid followed by two balanced detectors. Although the complexity of the optical frontend of the direct detection IQ receiver and the homodyne receivers is similar (the optical complexity is rated here slightly higher for the homodyne receivers due to the LO required additionally), the direct detection IQ receiver is simpler, since a carrier synchronization is not needed. When performing homodyne differential detection, differential demodulation must be implemented in the electrical domain. Thereby, the laser phase noise is not such a critical task, but frequency synchronization and polarization alignment of the signal and the LO wave must be ensured. In the case of homodyne synchronous detection, the carrier phase synchronization becomes a practical challenge, especially for highorder modulation formats. Fortunately, high-speed digital signal processing offers

124

4 Effort Comparison

new alternatives for the implementation of carrier synchronization. Receivers with homodyne synchronous detection in particular are reliant on digital technology to replace the analog optical phase locked loop with digital phase estimation. When comparing direct detection receivers and homodyne receivers, it should be borne in mind that, in homodyne receivers, the polarization of the signal and LO waves must be aligned by a polarization control or better the optical quadrature frontend should be doubled to implement polarization diversity. In the latter case, it is a nice side-effect that signals with polarization division multiplexing can be received without further modifications of the optical frontend. This, however, necessitates a significantly more complex electrical receiver part. The data recovery logic of direct detection IQ receivers is similar to that of homodyne receivers. Multi-level in-phase and quadrature photocurrents arise for higherorder formats, and the effort required for electrical data recovery increases according to the order of the modulation format. When the phase ambiguity of the carrier synchronization is resolved by differential coding, a differential decoder must be placed behind the carrier recovery in homodyne synchronous receivers. As for carrier synchronization, digital signal processing can greatly facilitate data recovery for direct detection and coherent detection and will play an important role in future receiver realizations. Despite their higher complexity, coherent receivers offer their own benefits such as the high receiver sensitivity (even under abdication of optical pre-amplification), an enhanced potential for the electronic mitigation of transmission impairments, a possible application as tunable WDM receivers, as well as suitability for detection of arbitrary modulation formats with homodyne synchronous detection. When looking ahead, it is a future challenge for practical system implementation to develop integrated novel optical modulator structures and high-speed digital-toanalog converters for the generation of high-quality multi-level electrical driving signals on the transmitter side. At the receiver end, practical solutions which integrate the whole optical frontend (the 2 × 4 90◦ hybrid together with the balanced detectors) in a single chip are being developed. Moreover, further technological progress and improved algorithms in the field of digital signal processing are indispensable for the future commercial implementation of optical transmitters and receivers for high-order modulation formats. The first part of this book illustrated the generation and detection of optical highorder modulation signals and provided a detailed insight into the setup, complexity and properties of various transmitter and receiver configurations. The second part of the book now to come deals with the system and transmission characteristics of optical high-order modulation signals and discusses the influence of many transmitter and receiver configurations described in the first part of the book on system performance. This allows the different transmitters and receivers to be rated, not only on the basis of their complexity and practical feasibility as performed in this chapter, but also by considering aspects of their system performance.

Chapter 5

System Simulation Aspects

Abstract Computer simulations offer a cost-effective way of estimating the physical properties and the performance of communication systems before practical system implementation. In this chapter, some aspects relevant for the simulation of optical fiber transmission systems with high-order modulation are briefly discussed. The discussion covers data sequences and performance measures commonly used for system characterization. Moreover, a detailed illustration of semi-analytical BER estimation provides a deeper insight into the noise characteristics within direct detection receivers.

5.1 Data Sequences An appropriate choice of data sequences is of crucial importance for reliable results in system simulations and experiments, especially when investigating high-order modulation formats. In the simulation of optical transmission systems, pseudo random binary sequences (PRBS) are widely used for representation of the data. In this section, three pseudo random binary sequences and the proper choice of data sequences according to the system memory length are discussed.

Maximum Length Sequences By using a linear feedback shift register with n B binary storage elements and feedbacks at the appropriate locations, a so-called maximum length sequence with a period of 2n B − 1 which contains all possible n B -bit patterns except for the one with n B zeros can be produced. Each pattern appears only once within each period. Several options exist for generating maximum length sequences for given n B [6]. It can be observed from the polynomials listed in [6] where the feedbacks have to be placed. Initially, the shift register is loaded with an initial value, often denoted as

M. Seimetz, High-Order Modulation for Optical Fiber Transmission, Springer Series in Optical Sciences 143, DOI 10.1007/978-3-540-93771-5 5, c Springer-Verlag Berlin Heidelberg 2009

127

128

5 System Simulation Aspects

seed, which can be any number between 1 and 2n B − 1. A change of seed causes a shift of the periodic sequence.

De Bruijn Bit Sequences In order to be able to simulate the effects of inter-symbol interference (ISI) in a system with binary modulation and a memory length of n B bits correctly, one has to ensure that all possible n B -bit patterns are incorporated in the used bit sequence. When enhancing a maximum length sequence by adding a zero digit to the run with n B − 1 zeros, a pseudo random binary sequence results which contains all n B -bit patterns. Such a sequence is called “de Bruijn bit sequence”. In a de Bruijn bit sequence, the ones and zeros occur each with a probability of 1/2.

De Bruijn Symbol Sequences For modulation formats with more than one bit per symbol, the requirement of containing all n B -bit patterns changes to the requirement of containing all n S -symbol patterns, where n S must be chosen according to the memory length of the system in symbols. A de Bruijn symbol sequence with b = m·M n S bits contains all n S -symbol patterns of M symbols, each consisting of m bits. When looking at Star 16QAM, for instance, the de Bruijn symbol sequence has 163 = 4096 symbols when considering all 3-symbol patterns. Four bits are assigned to each symbol, so that the resulting binary data sequence has a length of b = 4096 · 4 = 16384 bits. For higher memory lengths and high-order modulation formats, de Bruijn symbol sequences become quite long and can exceed the limits of simulative feasibility. When using shorter sequences, ISI-induced signal distortions are not further accounted for ideally. Like de Bruijn bit sequences, de Bruijn symbol sequences can be generated by using linear feedback shift registers. Instead of the modulo-2 arithmetic, arithmetic in Galois fields must then be used [6].

Choice of Data Sequences According to the System Memory Length The required data sequence length is determined by the number of symbols which can interact in the investigated system due to ISI. Inter-symbol interference is caused by optical and electrical filtering, as well as by linear and nonlinear fiber degradation effects. For a nonlinear dispersive channel, all the ISI caused by dispersion and intrachannel Kerr nonlinearities can be captured by considering the number of symbols in a time interval τ corresponding to the relative time shift experienced by two spectral components separated by the width of the signal spectrum Bs [16]. Thus, the approximate required order of the data sequence n S can be estimated by nS c ≥ τ = Dmax 2 Bs + 1. rS fs

(5.1)

5.1 Data Sequences

129

5

1E-2

a

b

4

De Bruijn bit 2

3 2

DQPSK NRZ 8DPSK RZ

De Bruijn bit 2

1E-4 1 0 2

12

1E-3 BER

Eye Opening Penalty [dB]

When considering only CD and observing a simple fiber link without CD compensation, Dmax simply represents the maximum dispersion which has accumulated on the link. For instance, a maximum accumulated dispersion of Dmax = 320 ps/nm corresponds to a length of 20 km for a single mode fiber with a dispersion coefficient of Dλ = 16 ps/(nm·km). With f s = 193.1 THz, r B = 40 Gbit/s and r S = r B /m = Bs , the de Bruijn symbol sequence order must be chosen as n S ≥ (6, 3, 2, 2, 2) for m = (1, 2, 3, 4, 6) which leads to relaxed requirements on the data sequence length of b = M n S · m = (26 , 43 · 2, 82 · 3, 162 · 4, 642 · 6). In practical systems with chromatic dispersion, intra-channel Kerr nonlinearities and CD compensation, Dmax stands for the maximum magnitude reached by the accumulated dispersion at locations in the dispersion map where the signal power is sufficiently large to generate nonlinear effects. When looking at a fiber link of length l = 80 km with
100% CD post-compensation, for instance, the effective length le f f = 1 − e−α·l /α, corresponding to the length beyond which the additionally accumulating nonlinear phase shift becomes negligible [1], is about 21km for an attenuation of αdb = 0.2 dB/km. In that case, Dmax ≈ 320 ps/nm can also be assumed when implying that the dispersion beyond the effective length can be ideally compensated for. To better illustrate the influence of the data sequence type and length on system characterization, some examples are given in the following paragraphs. Figure 5.1a shows the dependence of the eye opening penalty (EOP, defined in Sect. 5.2) on different de Bruijn bit and de Bruijn symbol sequences for linear fiber transmission, an accumulated dispersion of 320 ps/nm and a data rate of 40 Gbit/s for some selected modulation formats and direct detection. Inter-symbol interference induced by optical and electrical receiver filters with 3 dB bandwidths of Bopt = 2.5 · r S and Bel = 0.75 · r S is also included.

14

De Bruijn bit 216

Star 16QAM RZ Square 64QAM NRZ

4 6 8 10 12 14 16 18 20 Length of data sequence log2 b

1E-5 -37

-36 -35 -34 -33 Received Power [dBm]

-32

Fig. 5.1 a EOP dependence on the data sequence length b for 320 ps/nm accumulated dispersion at 40 Gbits/s for different modulation formats; Solid lines: de Bruijn bit sequences of length b = 2n B ; Symbols: de Bruijn symbol sequences with a period of b = m · M n S bits. b BER vs. received power for different de Bruijn bit sequences and back-to-back MC simulations for Square 64QAM.

A de Bruijn bit sequence with the same data sequence length b as the corresponding de Bruijn symbol sequence, for instance b = 212 = 4 · 163 , does not contain all

130

5 System Simulation Aspects

symbol patterns of the de Bruijn symbol sequence. However, as becomes apparent from Fig. 5.1a, the choice of a 212 de Bruijn bit sequence is sufficiently accurate for the modulation formats with m = (2, 3, 4) and the single-span system scenario with Dmax = 320 ps/nm observed here. When using de Bruijn symbol sequences, the order should be at least n S = 5 for m = 2 (211 = 2 · 45 ), n S = 4 for m = 3 (211 < 3 · 84 ), and n S = 3 for m = 4 (214 = 4 · 163 ). Whereas a simulation of deterministic distortions with data sequences not containing all the ISI-relevant symbol transitions can only lead to an underestimation of the EOP, the bit error ratio (BER) can be overestimated by the use of too short de Bruijn bit sequences with too many poorly performing symbol patterns when simulating noise. This becomes apparent from Fig. 5.1b which shows the backto-back BER performance for NRZ-Square 64QAM for different de Bruijn bit sequence lengths, obtained by Monte Carlo (MC) simulations (see Sect. 5.3). The 212 de Bruijn bit sequence overestimates the BER because too many bad symbol patterns are contained. A 216 de Bruijn bit sequence leads to more accurate results. An even better choice would be a 643 de Bruijn symbol sequence. However, this yields a data sequence length of b = 643 · 6 = 1572864 which can hardly be simulated with currently available memory sizes. Figure 5.2 illustrates the back-to-back performance of 16DPSK determined by MC simulations (a) and semi-analytical BER estimation (b) described in Sect. 5.4, again for 3 dB receiver filter bandwidths of Bopt = 2.5 · r S and Bel = 0.75 · r S and a data rate of 40 Gbit/s. For MC simulations, the use of 212 de Bruijn bit sequences and adequate de Bruijn symbol sequences leads to very similar results. The variations here are rather caused by MC estimate inaccuracies than by the particular choice of the data sequences. When lower BER values in the range of 10−9 are determined with semi-analytical BER estimation, de Bruijn symbol sequences with appropriate average distributions of the symbol patterns should be used. An OSNR difference of 1 dB can be observed in Fig. 5.2b between the back-to-back performances for NRZ, caused by a different consideration of the ISI induced by the receiver filters.

1E-2

1E-3

a

b

16DPSK NRZ

16DPSK NRZ De Bruijn 3 symbol 16

16DPSK RZ

BER

BER

1E-3

De Bruijn 3 symbol 16

1E-5

16DPSK RZ

1E-7

De Bruijn 3 symbol 16 + 12 de Bruijn bit 2

1E-4 De Bruijn symbol 163

1E-5 18

20

1E-9 De Bruijn bit 212

22 24 OSNR [dB]

26

De Bruijn bit 212

28

1E-11 22

24

26

28 30 32 OSNR [dB]

34

36

Fig. 5.2 16DPSK back-to-back performance determined by MC simulations (a) and semianalytical BER estimation (b) for 40 Gbit/s when using 212 de Bruijn bit sequences and 163 de Bruijn symbol sequences for NRZ (solid lines) and RZ (dashed lines)

5.2 Eye Opening Penalty

131

When looking at multi-span long-haul transmission, the data sequence length requirements can hardly be fulfilled when high magnitudes of accumulated chromatic dispersion lead to inter-symbol interference across many symbols. This is particularly problematic for systems without optical in-line CD compensation.

5.2 Eye Opening Penalty for Multi-Level Eyes A signal passing through a transmission system is degraded by stochastic and deterministic degradation effects. An easy way to characterize the quality of digital signals degraded by deterministic distortions is the determination of the eye opening penalty (EOP). When sampling a binary signal once per bit period at a specified sample time, the eye opening is defined as the difference of the minimum value of the “one” state and the maximum value of the “zero” state. The eye opening penalty for binary signals is defined as the ratio of the eye opening of the non-distorted reference eye, E Or e f , and the eye opening of the distorted eye, E O, and usually given in decibels E O P = 10 lg

E Or e f [d B]. EO

(5.2)

For high-order modulation, the electrical signals have multiple states and data recovery is accomplished by performing several decisions at different thresholds. In this case, the ratio of the eye openings of the reference eye to the distorted eye is calculated for all the eye openings of the multi-level eye relevant for decision. The maximum value defines the eye opening penalty of the multi-level eye   E On,r e f [d B], (5.3) E O P = max 10 lg n E On where n corresponds here to the number of eye openings relevant for decision. For arg-decision, the EOP can be calculated from the multi-level eyes arising after the arg-calculation, whereas the EOP must be identified individually for the signals in the in-phase and quadrature branches for IQ-decision. In the latter case, the larger value finally determines the overall system performance. Figure 5.3 schematically shows how the reference eye (left) and the distorted eye (right) are received in the in-phase and quadrature branches for 8PSK. When employing IQ-decision, only the two inner eye openings are relevant for the decision process (as observable from Fig. 3.7b) and the EOP of the multi-level signal in each branch can be calculated using (5.3) with n = {1, 2}.

132

5 System Simulation Aspects Reference eye

EO1,ref EO2,ref

Distorted eye

EO1 EO2

Fig. 5.3 Determination of the EOP for multi-level eyes; The reference eye and the distorted eye (how they are received in the in-phase and quadrature branch) and the relevant eye openings are schematically shown here for 8PSK and IQ-decision.

5.3 Monte Carlo Simulations The most significant criterion for performance characterization in digital transmission systems is the BER, which is simply defined as the ratio between the bits received with errors and the number of bits that have been transmitted. An intuitive approach to the simulative determination of the BER is sending a preferably long input bit sequence through the investigated system and then simply counting the bit errors of the output bit sequence and relating them to the total number of transmitted bits. This method is denoted as Monte Carlo (MC) simulation. An advantage of the MC method is its general applicability to the simulation of arbitrary systems and the ability to consider all deterministic and stochastic degradation effects. On the other hand, the accuracy of the calculated BER estimate strongly depends on the total number of simulated bits b. A fairly large number of bits must be simulated in order to obtain accurate estimates. As a rule of thumb, the simulation of b = 10/BER bits is required for a confidence interval of 95% with an uncertainty factor of two on the error rate scale, corresponding to a few tenths of a dB on the OSNR scale [6]. Thus, the determination of BER values lower than 10−6 necessitates the consideration of more than ten million bits and turns out to be too complex even for the strength of modern computers. √ With increasing b, the confidence interval narrows relatively slowly with 1/ b, so a trade-off must be found between computational effort and statistical accuracy. Because the computing time increases disproportionally with increasing b (the computational effort for the fast fourier transform scales with b · lg b), simulations should be split into multiple runs. A reduced number of bits is then simulated in each run, whereat the random number seeds of the noise generators must be readapted in each run for an appropriate simulation of noise.

5.4 Semi-Analytical BER Estimation for DBPSK Direct Detection

133

5.4 Semi-Analytical BER Estimation A method which allows for the determination of low BER values without very long run-times is the semi-analytical BER estimation. “Semi-analytical” means that parts of this method are based on analytical derivations but other parts on numerical calculations. With knowledge of the exact statistics of the photocurrents appearing at the decision gates it becomes possible to estimate the BER by integration over the probability density function (PDF), without needing to simulate a very large number of bits as necessary in MC simulations. Unfortunately, in many cases the determination of the exact PDF turns out to be difficult. As a first approach, the photocurrent statistics are often approximated by a Gaussian PDF. However, it has been shown that this yields inaccurate results for pre-amplified direct detection systems limited by signal-ASE noise, especially for the detection of DPSK signals [5, 11]. Several closely related methods used to exactly evaluate the bit error probability of optically pre-amplified direct detection systems have been proposed. They are mainly directed towards OOK, for instance in [4, 7, 8, 11]. By incorporating the altered receiver structure with delay line interferometers and balanced detection into the analysis, the semi-analytical BER estimation is extended to binary and highorder DPSK formats in [3, 5, 9, 14], as well as to Star 16QAM and different receiver configurations in [9].

5.4.1 DBPSK Direct Detection Next, the fundamental theory of semi-analytical BER estimation is illustrated on the basis of the DBPSK direct detection receiver. The system model of the receiver is shown in Fig. 5.4.

Ho ( f )

x (t )

x(t ) + n(t )

y# (t )

TS

BPF

ϕDLI

DLI

He ( f ) LPF

y (t k )

BD

Fig. 5.4 System model used for semi-analytical BER estimation for DBPSK direct detection

If it is assumed that only signal fractions within a time interval (tk − T0 , tk ) are relevant for the decision of each symbol at the sampling instants tk , the complex √ envelope x(t) = Ps · a(t) · e jϕ(t) of the electrical field at the receiver input p E s (t) = Ps · a(t) · e jϕ(t) · e j(ωs t+ϕs ) = x(t) · e j(ωs t+ϕs ) (5.4)

134

5 System Simulation Aspects

can be interpreted as periodic with T0 at each sampling instant tk , and can be expanded in a Fourier series x(t) ≃

L X

p=1

xk, p · e j2π( p−L/2)(t−tk )/T0 = xk · e T ∗ ,

(5.5)

with the fourier coefficients defined as xk, p =

  L 1X qT0 − j2qπ( p−L/2)/L x tk − T0 + e , L L

(5.6)

q=1

which are represented by a vector with L rows xk . The elements of the row vector e in (5.5) are given by ep = e

(t−tk ) − j 2π( p−L/2) T 0

,

(5.7)

where “T ” and “*” denote transposition and complex conjugation, respectively. The total number of samples considered for the Fourier expansion is given by L = S pS T0r S , with S pS denoting the number of samples per symbol. The duration T0 chosen should be large enough to take all the relevant inter-symbol interference caused by filtering into account. As for the signal, the noise n(t) = n k (t)ek + n ⊥ (t)e⊥ emerging at the optical pre-amplifier can also be expanded into a fourier series (the expansion of a centered stochastic process into uncorrelated random variables is known as Karhunen-Lo`eve expansion in the literature). This way, the noise components, polarized in parallel and orthogonally with respect to the signal, and denoted here as n k (t) and n ⊥ (t), respectively, can be expressed as n k/⊥ (t) ≃

L X

p=1

n p,k/⊥ · e j2π( p−L/2)(t−tk )/T0 = nk/⊥ · e T ∗ ,

(5.8)

with the fourier coefficients n p,k/⊥ =

  L qT0 − j2qπ( p−L/2)/L 1X n k/⊥ tk − T0 + e . L L

(5.9)

q=1

As will become clear later, the method described here for semi-analytical BER estimation implies a restriction to stationary Gaussian noise with zero mean in front of the optical receiver filter. This is valid, for instance, in single-span systems without noise on the transmission link where the overall noise in front of the optical filter input is solely confined to the ASE-noise of the optical pre-amplifier and can be assumed to be additive white Gaussian noise (AWGN) with a two-sided power spectral density (PSD) per polarization given by (3.25). The variance of the in-phase and quadrature components of each of the elements of nk/⊥ is given as σ p2 = σ 2 = (N0 /2) · Bn = (N0 /2) · L/T0 · 1/L = N0 /(2T0 ).

5.4 Semi-Analytical BER Estimation for DBPSK Direct Detection

135

Usually, noise performance of optical receivers is characterized with the OSNR in decibels, which is defined here by the ratio of the average signal power Ps,avg and the noise power in both polarizations within the reference bandwidth 1 f   Ps,avg O S N Rd B = 10 lg . (5.10) 2 · N0 · 1 f

 In this context, the average signal power is given as Ps,avg = |x(t)|2 , and 1 f = 1λ · f s2 /c, where c is the speed of light. Normally, the reference bandwidth 1λ is set to 0.1nm, and the OSNR is specified in front of the optical receiver filter. After having described the signal and noise in front of the optical receiver filter, the exact PDF can be derived at the decision gate. The optical filter can be described with a diagonal matrix H, whose elements result from the low-pass equivalent transfer function Ho ( f )   p − L/2 . (5.11) H p, p = Ho T0 The transfer characteristic of the DLI with respect to the upper output is incorporated in the analysis by defining the diagonal matrix   1 · H · F − I · e jϕ DL I , 2

(5.12)

  1 · H · jF + jI · e jϕ DL I . 2

(5.13)

H1 =

where F is a diagonal matrix with diagonal elements F p, p = e j2π( p−L/2)·TS /T0 and I represents a identity matrix with the same size as F. The matrix H1 accounts for the overall transfer characteristic of the receiver up to the upper DLI output. Analogously, the overall transfer function with respect to the lower DLI output can be described by the diagonal matrix H2 =

Because the spontaneous noise from the amplifier usually dominates receiver shot and thermal noises, it is assumed here that the photodiodes are ideal square-law photo-detectors. In this case, the signal after the balanced detector at the sample instant tk can be calculated as i h
2
2 y˜ (tk ) = xk + nk H1 + |n⊥ H1 |2 − xk + nk H2 + |n⊥ H2 |2

T ∗ + n⊥ H1 H1 T ∗ n⊥T ∗ = xk + nk H1 H1 T ∗ xk + nk i h

T ∗ (5.14) − xk + nk H2 H2 T ∗ xk + nk + n⊥ H2 H2 T ∗ n⊥T ∗ ,

where the vectors e and e T ∗ are left out since their elements are equal to one for t = tk . Furthermore, if the electrical filter with the transfer function He ( f ) is included by defining the elements of the transfer matrix Q as

136

5 System Simulation Aspects

Q p,q = He





q−p , T0

(5.15)

the signal arising at the decision gate after electrical filtering and sampling can be expressed as

T ∗ y(tk ) = xk + nk H1 QH1 T ∗ xk + nk + n⊥ H1 QH1 T ∗ n⊥T ∗

T ∗ − n⊥ H2 QH2 T ∗ n⊥T ∗ − xk + nk H2 QH2 T ∗ xk + nk  
T ∗
= xk + nk H1 QH1 T ∗ − H2 QH2 T ∗ xk + nk   +n⊥ H1 QH1 T ∗ − H2 QH2 T ∗ n⊥T ∗ .

(5.16)

The receiver matrix A = H1 QH1 T ∗ − H2 QH2 T ∗ reflects the special properties of a DPSK receiver composed of DLIs. For particular DPSK receivers and their different branches, different DLI phase shifts are appropriate and determine the values of the matrices H1 , H2 and A. As regards DBPSK, the DLI phase shift is set to ϕ DL I = 0◦ . The procedure of semi-analytical BER estimation for higher-order DPSK formats and Star QAM is briefly discussed in Sect. 5.4.2. In the case of 2ASK, the receiver matrix is simply given by A = HQHT ∗ [11]. With the intention of writing the photocurrent y(tk ) as a sum of weighted squared random variables, an eigendecomposition of the matrix A can be performed. Due to the definition of the electrical filter matrix Q, the matrix A is a hermitian matrix, whose eigenvalues are real. That way, the matrix A can be expressed as A = U3UT ∗ ,

(5.17)

where U is a unitary matrix whose columns contain the eigenvectors of the matrix A, and 3 is a diagonal matrix whose diagonal elements are given by the real-valued eigenvalues λ p of the matrix A. When furthermore imposing the vectors bk = xk U and zk/⊥ = nk/⊥ U with their elements bk, p and z p,k/⊥ , respectively, the photocurrent given by (5.16) can be rewritten as

T ∗ y(tk ) = xk + nk U3UT ∗ xk + nk + n⊥ U3UT ∗ n⊥T ∗

T ∗ + z⊥ 3z⊥T ∗ = bk + zk 3 bk + zk =

L X

=

L X

p=1

L 2
2 X λ p z p,⊥ λ p bk, p + z p,k + p=1

L  2 X  2 λ p Re bk, p + z p,k + λ p I m bk, p + z p,k | {z } p=1 | {z } p=1

+

L X

non-central χ 2

non-central χ 2

L  2 X  2 λ p Re z p,⊥ + λ p I m z p,⊥ . | {z } p=1 | {z } p=1 central χ 2

central χ 2

(5.18)

5.4 Semi-Analytical BER Estimation for DBPSK Direct Detection

137

The photocurrent described by (5.18) can be interpreted as a weighted sum of squared Gaussian random variables. Half of the summands (the terms containing signal and noise) are given by the square of Gaussian random variables with nonzero mean. The statistics of the sum of n squared Gaussian random variables are known as a non-central χ 2 -distribution with n degrees of freedom [15]. The remaining summands are given by the square of zero mean Gaussian random variables and exhibit a central χ 2 -distribution. The PDFs of the non-central and central χ 2 distribution with n degrees of freedom can be found in [10, 15]. The quested overall PDF of y(tk ) can be obtained by the convolution of the PDFs of the particular summands. However, it is easier to determine the moment generating functions (MGF) of the particular PDFs (the MGF is defined as the conjugate complex Laplace transform of the PDF [10]), multiply the particular MGFs and calculate the PDF of y(tk ) from the overall MGF by the conjugate complex inverse Laplace transform. The noise in front of the optical receiver filter is assumed here to be AWGN, so that the elements of nk/⊥ are independent Gaussian random variables with zero mean and equal variances σ 2 , and the elements of zk/⊥ are Gaussian and of equal variance σ 2 as well because the matrix U consists of a set of orthonormal eigenvectors. In this case, by employing the known MGFs for χ 2 -distributed random variables [15], the overall MGF of y(tk ) can be derived as [4, 9, 11]   2 sλ p |bk, p | exp L Y 1−2sλ p σ 2 (5.19) 8 yk (s) = (1 − 2sλ p σ 2 )2 p=1

with s = jω. When considering colored Gaussian noise at the receiver input (which is not further regarded here), the elements of nk/⊥ have different variances σ p2 and the elements of zk/⊥ have different variances σˆ p2 . These can be substituted for the constant σ 2 in (5.19), provided that they are known. The photocurrent PDF can be obtained from the MGF (5.19) by the conjugate complex inverse Laplace transform  ∗ 1 p yk (y) = L−1 8 yk (s) = 2π j

Z

u 0 + j∞

u 0 − j∞

8 yk (s)e−sy ds,

(5.20)

2 + 2 where u 0 must be in the range −1/ max |2λ− p σ | < u 0 < 1/ max |2λ p σ | to ensure −/+

the convergence of the integral [2, 4] and λ p denote the negative / positive eigenvalues of the receiver matrix A. The PDF given by (5.20) reflects the exact statistics of the photocurrent appearing at the decision gate. The probability of an error at the sample time tk conditional upon the b-bit data sequence {an }, with n = (1..b), can be calculated for the DBPSK receiver, when setting the decision threshold to yth , by R u th  p yk (y)dy, an = 1 P {y(tk ) < yth } = R−∞ P (ek |{an }) = . (5.21) ∞ P {y(tk ) > yth } = u th p yk (y)dy, an = 0

138

5 System Simulation Aspects

The integrals of (5.21) can be approximately solved by the so-called “saddlepoint approximation”. Details of this integration method can be found in the literature, for instance in [4, 9]. The saddlepoint approximation for the calculation of the conditional probabilities in (5.21) is given as ±

e9 yk (u 0 ) P {y(tk ) ≷ yth } ≃ ± q , ) 2π 9 y′′k (u ± 0

(5.22)

′′

where 9 yk (s) = ln 8 yk (s)−ln(s)−s · yth , 9 yk (s) is the second derivative of 9 yk (s), − and u + 0 > 0 and u 0 < 0 are the saddle points on the real s-axis which must be used for the “>” or “<” sign, respectively. With (5.21) and (5.22), the BER can be finally estimated as b

BER =

1X P (ek |{an }) . b

(5.23)

n=1

5.4.2 Extension to Higher-Order DPSK and Star QAM A DQPSK direct detection receiver composed of DLIs consists of two independent branches (the in-phase and quadrature branch), both having the same configuration as a DBPSK receiver (see Sect. 3.2.1). By setting the phase shifts of the DLIs in these branches to −45◦ and −135◦ , respectively, the in-phase and quadrature components of DQPSK signals can be obtained by performing binary decisions at zero. The error probability must then be estimated separately in the in-phase and quadrature branches. Individual receiver matrices A result for the two branches due to the different DLI phase shifts. Because the BER has to be calculated twice—once for every component—the simulation time enlarges in comparison to the DBPSK receiver. The overall BER is finally obtained by averaging the BER values calculated in the in-phase and quadrature branches. Semi-analytical BER estimation can also be applied to high-order DPSK and Star QAM formats. As shown in Sect. 3.2.1, arbitrary DPSK signals can be detected by using a multiple DLI receiver composed of N ph /2 DLIs with N ph /2 individual phase shifts, where N ph is equal to M for MDPSK formats and represents the number of phase states. The multiple DLI receiver exhibits nearly the same theoretical BER performance as the direct detection IQ receiver with only two DLIs and arg-decision. The direct application of semi-analytical BER estimation to the IQ receiver with arg-decision is problematic because a nonlinear operation (arg) is performed before decision. To calculate the BER of the multiple DLI receiver, an individual receiver matrix A must be adopted to every DLI branch. N ph /2 different receiver matrices have to be evaluated and N ph /2 individual error probabilities arise. Every error probability is defined as the probability of an erroneous semicircle decision. The overall BER is finally obtained through an appropriate aggregation of

5.4 Semi-Analytical BER Estimation for Higher-Order DPSK and Star QAM

139

the individual error probabilities [9]. For the 8DPSK receiver, for instance, four error probabilities are calculated. A symbol error rate can then be derived based on these four values. When defining the probability of an erroneous decision as P(yk ), k ∈ {1, 2, 3, 4}, the probability of a symbol error is given by Psym = P(y1 ) + P(y2 ) + P(y3 ) + P(y4 ) +P(y1 )P(y2 ) + P(y1 )P(y4 ) + P(y2 )P(y3 ) + P(y3 )P(y4 ) +P(y1 )P(y2 )P(y3 ) + P(y1 )P(y3 )P(y4 ) +P(y1 )P(y2 )P(y4 ) + P(y2 )P(y3 )P(y4 ) +P(y1 )P(y2 )P(y3 )P(y4 ) (5.24) The first line represents the dominant fraction of the symbol error probability for reasonably small error probabilities, because all other terms contain products of the error probabilities. Neglecting these product terms (taking only one erroneous decision per symbol into account) is equivalent to considering only symbol errors corresponding to false decisions of neighboring symbols. When the bit mapping is chosen as Gray coded, one symbol error corresponds to one bit error. Therefore, the BER for the multiple DLI receiver can finally be approximated by N ph /2 1 X P(yk ). BER ≈ m

(5.25)

k=1

As discussed in Sect. 3.2.1, a direct detection IQ receiver with just two DLIs, whose phase shifts in the in-phase and quadrature arms are adjusted to ϕ DL I I = 0◦ and ϕ DL I Q = −90◦ , is sufficient for detecting the in-phase and quadrature components of arbitrary high-order DPSK signals. For this receiver, the error probability must be estimated separately in the in-phase and quadrature branches. Individual receiver matrices A result for the two branches due to the different DLI phase shifts. Since the levels of the in-phase and quadrature photocurrents represent the projection of the symbol states to the in-phase and quadrature axis, multiple decisions on multi-level electrical signals become necessary for DPSK formats with more than four phase states such as 8DPSK or 16DPSK, as described in Sect. 3.2.3. Figure 3.7 illustrates in this section how thresholds must be positioned within the in-phase and quadrature eyes for 8DPSK. It can be observed that just one fixed threshold at zero is not sufficient, but that instead two thresholds per branch are necessary. For every threshold, an individual error probability has to be evaluated. Because the appropriate threshold depends on the particular received symbol, the received signal power and the filter transfer functions, the thresholds at each sample time tk must be adapted. More precisely, the integration interval must be properly chosen when determining the error probability by integration over the PDF. Finally, the overall BER is obtained through an appropriate aggregation of the individual error probabilities, which can be done in a similar way as illustrated for the multiple DLI receiver in (5.24) and (5.25), where P(yk ) then represents the probability of an erroneous decision at the different thresholds in the in-phase and quadrature arms.

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5 System Simulation Aspects

In the case of Star QAM, the error probability corresponding to the bits which encode the phase information can be determined in the same way as for the DPSK format with the same number of phase states. When the Star QAM signals have only two amplitude levels, just one additional bit for which the error probability has to be calculated from the signal in the intensity detection branch is encoded in the additional amplitude modulation. The same BER estimation procedure can then be employed as for 2ASK systems. The receiver matrix A for 2ASK receivers was derived in [11] and simplifies to A = HQHT ∗ . Of course, the threshold in the intensity detection branch must be optimized due to the dependence of the signal-ASE noise on the received signal power. Using the semi-analytical BER estimation described in the last sections, the BER of direct detection receivers can be estimated very accurately and quickly without a large number of bits needing to be simulated. The method presented here takes any deterministic signal distortions and arbitrary pulse shaping into account (this information is contained in the received signal samples), as well as the exact structure and transfer characteristic of the receiver with its filters and interferometers. However, application possibilities are limited to the appearance of stationary Gaussian noise with zero mean in front of the receiver—only in this case the photocurrent can be described as a sum of χ 2 -distributed random variables with known MGF. This prohibits an exact characterization of multi-span systems taking into consideration all relevant transmission effects, as for instance the nonlinear phase noise. The exact noise statistics at the decision gates of homodyne receivers with differential and synchronous detection are not derived here. As shown in [13], optical pre-amplified direct detection receivers are mathematically equivalent with heterodyne receivers with delay demodulation under certain conditions. Moreover, homodyne phase diversity DPSK receivers are shown to have the same performance than heterodyne DPSK receivers in [12]. Therefore, the semi-analytical BER estimation for direct detection can probably also be used for BER evaluation in systems with homodyne differential detection. In digital coherent receivers with homodyne synchronous detection, the noise statistics are altered by equalization and digital phase estimation. Further research is necessary to enable semi-analytical BER estimation for those complex receiver structures.

References 1. Agrawal, G.P.: Nonlinear Fiber Optics. Academic Press (3. Edition, 2001) 2. Bronstein, I., et al.: Taschenbuch der Mathematik. Harry Deutsch Verlag, Frankfurt a. M. (2001) 3. Coelho, L.D.: Numerical optimization of fiber optic communication systems with advanced modulation formats at 40Gbit/s channel data rate. Master´s thesis, Munic University of Technology (2005)

References

141

4. Forestieri, E.: Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and postdetection filtering. IEEE Journal of Lightwave Technology 18(11), 1493–1503 (2000) 5. Gnauck, A.H., Winzer, P.J.: Optical phase-shift-keyed transmission. IEEE Journal of Lightwave Technology 23(1), 115–130 (2005) 6. Jeruchim, M.C., et al.: Simulation of Communication Systems - Modeling, Methodology and Techniques. Kluwer Academic/Plenum Publishers (2000) 7. Kac, M., Siegert, A.J.F.: On the theory of noise in radio receivers with square law detectors. J. Appl. Phys. 18, 383–397 (1947) 8. Lee, J.S., Shim, C.S.: Bit error rate analysis of optically preamplified receivers using an eigenfunction expansion method in optical frequency domain. IEEE Journal of Lightwave Technology 12, 1224–1229 (1994) ¨ 9. N¨olle, M.: Ubertragungseigenschaften von h¨oherwertigen optischen DPSK und QAM Modulationsformaten mit Direktempfang auf Basis eines semi-analytischen BitfehlerratenSch¨atzverfahrens. Diplomarbeit, Technische Universit¨at Berlin (2007) 10. Papoulis, A.: Probability, Random Variables, and Stochastic Processes. McGraw-Hill, Inc. (1984) 11. Randel, S.: Analysis of fibre-optic transmission systems with wavelength-division multiplex at 160 Gb/s data rate per channel. Ph.D. thesis, Technische Universit¨at Berlin (2005) 12. Siuzdak, J., van Etten, W.: BER evaluation for phase and polarization diversity optical homodyne receivers using noncoherent ASK and DPSK demodulation. IEEE Journal of Lightwave Technology 7(4), 584–599 (1989) 13. Tonguz, O.K., Wagner, R.E.: Equivalence between preamplified direct detection and heterodyne receivers. IEEE Photonics Technology Letters 3(9), 835–837 (1991) 14. Wang, J., Kahn, J.M.: Impact of chromatic and polarization-mode dispersions on DPSK systems using interferometric demodulation and direct detection. IEEE Journal of Lightwave Technology 22(2), 362–371 (2004) 15. Whalen, A.D.: Detection of Signals in Noise. Academic Press (1971) 16. Wickham, L.K., et al.: Bit pattern length dependence of intrachannel nonlinearities in pseudolinear transmission. IEEE Photonics Technology Letters 16(6), 1591–1593 (2004)

Chapter 6

Fiber Propagation Effects

Abstract During fiber transmission, optical signals are distorted by several linear and nonlinear degradation effects. This chapter provides a brief description of the most important fiber degradation effects such as fiber attenuation, chromatic dispersion, Kerr nonlinearities, nonlinear scattering effects, polarization mode dispersion and nonlinear phase noise, laying the foundations for understanding the specific behavior of high-order modulation formats in relation to various transmission impairments, discussed in detail later on in Chap. 7 and Chap. 8.

In the previous chapters, only the time dependency of the electrical field was of interest. In the case of fiber propagation, the time and location dependent complex electrical field must be examined. For propagation in z-direction and when neglecting the initial phase and the phase noise, the electrical field can be described by E s (z, t) = x(z, t) · e− jβ0 z+ jωs t ,

(6.1)

√ where x(z, t) = Ps · a(z, t) · e jϕ(z,t) represents the slowly varying time and location dependent complex envelope of the monochromatic electrical field with the propagation constant β0 at the angular optical frequency ωs . The evolution of x(z, t) along an optical fiber can be described by the so-called generalized nonlinear Schroedinger equation [11], which is given by α ∂ x(z, t ′ ) β2 ∂ 2 x(z, t ′ ) β3 ∂ 3 x(z, t ′ ) = − x(z, t ′ ) + j + ∂z ∂t ′2 {z 6 ∂t ′3 } | 2 {z } | 2 attenuation

chromatic dispersion

2 − jγ x(z, t ′ ) x(z, t ′ ), {z } |

(6.2)

Kerr nonlinearities

with the retarded time scale t ′ = t − τgr · z, where τgr · z represents the accumulated group delay. The generalized nonlinear Schroedinger equation takes into account the fiber attenuation described by the attenuation coefficient α, the effect of chromatic M. Seimetz, High-Order Modulation for Optical Fiber Transmission, Springer Series in Optical Sciences 143, DOI 10.1007/978-3-540-93771-5 6, c Springer-Verlag Berlin Heidelberg 2009

143

144

6 Fiber Propagation Effects

dispersion characterized by β2 and β3 , as well as the fiber nonlinearities caused by the intensity dependence of the refractive index (Kerr effect), whose strength is defined by the nonlinear propagation coefficient γ . Equation (6.2) can be solved numerically by applying the split-step Fourier method [1]. With the split-step Fourier method, the fiber is divided into multiple segments with step size 1z. Knowing the complex envelope x(z, t ′ ) at location z, it is possible to calculate x(z + 1z, t ′ ) at location z + 1z. The linear and nonlinear parts of (6.2) are treated separately. Whereas the Kerr nonlinearities are handled in the time domain, attenuation and chromatic dispersion are considered in the frequency domain employing the Fast Fourier Transform (FFT). Long computation times can arise for high optical powers, which necessitate small step sizes. In the following sections, fiber attenuation, chromatic dispersion and Kerr nonlinearities are more closely examined. Afterwards, additional effects such as nonlinear scattering effects, polarization mode dispersion and nonlinear phase noise are briefly discussed. Because the latter three effects are not further detailed in Chap. 7 and Chap. 8, their principal impact on the transmission of high-order modulation formats is already presented here.

6.1 Fiber Attenuation When neglecting the chromatic dispersion and the Kerr nonlinearities in (6.2), the complex envelope of the electrical field at the output of an optical fiber of length l is given by α

x(z = l, t ′ ) = x(z = 0, t ′ ) · e− 2 ·l ,

(6.3)

where x(z = 0, t ′ ) denotes the complex electrical field envelope at the fiber input. For the optical power it holds P(z = l, t ′ ) = x(z = l, t ′ ) · x(z = l, t ′ )∗ = P(z = 0, t ′ ) · e−α·l .

(6.4)

The attenuation coefficient α has the unit 1/km. Commonly, the fiber loss is expressed in units of dB/km with αd B · L = 10 · lg

P(z = 0, t ′ ) , P(z = l, t ′ )

(6.5)

where the attenuation coefficient in decibels αd B is related to α approximately as αd B ≈ 4.343 · α · dB. The two main sources of loss in silica optical fibers are material absorption and Rayleigh scattering. When observing the wavelength band between 800 nm1600 nm used for optical communication systems, the Rayleigh scattering, caused by the orderless molecular structure of glass and the resulting random fluctuations

6.2 Chromatic Dispersion

145

of the refractive index, is the dominant loss factor in the low-wavelength range, whereas the molecular infrared absorption limits the utilizable wavelength window to wavelengths smaller than 1600 nm. Apart from the negligible waveguide loss of pure silica, further loss factors are the ultraviolet absorption (caused by lifting electrons to higher energy levels) and absorption due to material impurities (for instance the OH absorption). In spite of all these effects, a minimum loss of αd B < 0.2 dB/km can be achieved for silica fibers at λ = 1550 nm when employing appropriate manufacturing processes. Although the loss depends on the wavelength of light (the exact wavelength dependency of αd B can be looked up for instance in [11]), αd B can be assumed to be constant within the modulation bandwidth of a single channel for current data rates such as 40 Gbit/s. The attenuation of fiber links can be compensated for by the use of optical amplifiers, for instance EDFAs. Because EDFAs are very broadband, many channels of a WDM signal can be amplified simultaneously by a single EDFA. To be able to bridge longer distances, several sections can be cascaded, each consisting of a fiber link and an optical amplifier (multi-span transmission). Unfortunately, each optical amplifier adds noise with a power spectral density given by (3.25) and degrades the OSNR. This noise accumulation is one of the major reasons for the limitation of the reachable transmission lengths in transparent optical networks.

6.2 Chromatic Dispersion The frequency dependence of the group delay in optical fibers is denoted as chromatic dispersion and caused by the frequency dependence of the refractive index (material dispersion) and the frequency dependent wave guidance in the fiber core and fiber cladding (waveguide dispersion). Mathematically, the effect of chromatic dispersion can be described by expanding the frequency dependent propagation constant β(ω) into a Taylor series at ωs = 2πc/λs β(ω) =

ω c

1 · n(ω) = β0 + β1 (ω − ωs ) + β2 (ω − ωs )2 2 1 3 + β3 (ω − ωs ) + ... 6

(6.6)

In (6.6), β0 is the propagation constant at ω = ωs and β1 = dβ(ω)/dω ω=ωs is equal to the group delay per length unit, τgr (ω), at ω = ωs . The parameters β2 and β3 qualify the chromatic dispersion as well as the chromatic dispersion slope at ω = ωs , respectively, and are given by dτgr (ω) d 2 β(ω) β2 = = , (6.7) dω ω=ωs dω2 ω=ωs

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6 Fiber Propagation Effects

β3 =

d 3 β(ω) dω3 ω=ωs

d 2 τgr (ω) = dω2

(6.8)

. ω=ωs

Distortion free transmission can only be achieved if τgr (ω) is constant within the modulation bandwidth, which is the case for βi = 0 for i ≥ 2. Mostly, the dispersion and the dispersion slope are specified as the first and second derivatives of the group delay on the wavelength, denoted here as Dλ and Sλ , respectively. By using the relation dλ = −dω · λ2 /(2πc), Dλ and Sλ can be calculated from β2 and β3 at λ = λs as dτgr (λ) 2π · c = − 2 · β2 , (6.9) Dλ = dλ λ=λs λs d 2 τgr (λ) Sλ = dλ2

λ=λs

=



2π · c λ2s

2

· β3 +

4π · c · β2 . λ3s

(6.10)

To examine the impact of the chromatic dispersion on the signal propagation along the fiber, the fiber input electrical field E s (z = 0, t) can be Fourier transformed and multiplied with the transfer function of the fiber in the frequency domain to obtain the Fourier transform of the signal at location z E s (z, jω) = E s (z = 0, jω) · e− jβ(ω)z ,

(6.11)

where β(ω) is given by (6.6). To further work out the propagation of the complex envelope x(z, t ′ ) with the retarded time scale t ′ = t − τgr · z, the Fourier transform of x(z, t ′ ) can be calculated by using the time shift theorem as Z +∞ j·τgr ·z x(z, j) = e x(z, t)e− jt dt, (6.12) −∞

with  = ω − ωs . Resolving (6.1) for x(z, t), and then inserting the result in (6.12), leads to x(z, j) = e j·τgr ·z · e jβ0 ·z · E s (z, jω).

(6.13)

With E s (z, jω) given by (6.11) and E(z = 0, jω) = x(z = 0, j), it is finally obtained 1

2

1

3

x(z, j) = x(z = 0, j) · e− j 2 β2 z · e− j 6 β3 z , which can be rewritten as differential equation as   ∂ x(z, j) 1 1 = x(z, j) · − j β2 2 − j β3 3 . ∂z 2 6

(6.14)

(6.15)

6.3 Kerr Nonlinearities

147

Transforming (6.15) back to the time domain with ∂/∂t ′ = j yields the differential equation β2 ∂ 2 x(z, t ′ ) β3 ∂ 3 x(z, t ′ ) ∂ x(z, t ′ ) = j + . ∂z 2 6 ∂t ′2 ∂t ′3

(6.16)

The terms on the right side of (6.16) are identically to the dispersion terms in the generalized nonlinear Schroedinger equation given by (6.2). For standard single mode fibers (SSMF), the dispersion coefficient Dλ is typically zero for λ = 1310 nm and increases up to about 16 ps/(nm·km) at λ = 1550 nm. This means that two spectral components in the λ = 1550 nm range, which are separated by 1 nm, experience a delay difference of 16 ps per kilometer. This causes a broadening of the transmitted pulses and leads to inter-symbol interference. The possible influencing of the waveguide dispersion can be used to develop special fibers, for instance the dispersion shifted fiber (DSF) with Dλ = 0 at λ = 1550 nm or the dispersion compensating fiber (DCF). The latter can be used to fully compensate for the chromatic dispersion of fiber links for single channel transmission or even for broadband dispersion compensation across the whole WDM band. In the latter case, an appropriate compensation of the dispersion slope additionally becomes important. Whereas the chromatic dispersion can in principle be ideally compensated for for point-to-point links, an adaptive compensation becomes necessary in flexible routed optical networks. For high symbol rates exceeding 40 Gbaud, length fluctuations caused by temperature can necessitate an adaptive dispersion compensator to compensate for the steadily changing amount of accumulated dispersion [7]. As shown in Sect. 3.5.3, digital coherent receivers provide the opportunity for performing adaptive dispersion compensation efficiently in the electrical domain.

6.3 Kerr Nonlinearities The Kerr nonlinearities of an optical fiber imply all the nonlinear effects originating from the intensity dependence of the refractive index. For a better understanding of the reason for this intensity dependence, it is useful to look at the electric flux density D, which is related to the electrical field as D = ǫ0 E + P,

(6.17)

where ǫ0 is the vacuum permittivity and P represents the electric polarization which reflects the material properties of the medium and can be divided into a linear and nonlinear part as P = P L + P N L . The linear part of the electric polarization is given by P L = ǫ0 χ1 E, where χ1 denotes the linear susceptibility. Without consideration of the nonlinear electrical polarization it holds D = ǫ0 ǫr E, with the relative permittivity of the medium defined as ǫr = 1 + χ1 . When considering only third-order nonlinear effects which

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6 Fiber Propagation Effects

is generally sufficient for non-doped silica fibers [1, 2, 8], the nonlinear electric polarization is given by P N L = ǫ0 χ3 E3 ,

(6.18)

The parameter χ3 represents the third-order nonlinear susceptibility. An optical wave with an electrical field described by (6.1), propagating in an optical fiber with an effective core area Ae f f [1], exhibits a field intensity within the fiber core of |x(z, ˜ t)|2 = |x(z, t)|2 /Ae f f (in units of W/m2 ). The electrical field given by (6.1) p p normalized to Ae f f is denoted here as E˜ s (z, t) = E s (z, t)/ Ae f f and has the unit √ W /m. It can be written as a real-valued signal by adding the conjugate complex (c.c.) component (in nonlinear optics, one must calculate with real-valued signals because Re[z 1 · z 2 ] 6= Re[z 1 ] · Re[z 2 ], with z 1 and z 2 being complex numbers). Using these definitions, the nonlinear polarization can be calculated by 3 1 1 ˜ E s (z, t) + E˜ s∗ (z, t) 2 2 i 1 h 3 = ǫ0 χ3 · · x˜ (z, t) · e− j3β0 z+ j3ωs t + c.c. 8 h i 3 ˜ t) · e− jβ0 z+ jωs t + c.c. . ˜ t)|2 · x(z, + ǫ0 χ3 · · |x(z, 8

PN L (z, t) = ǫ0 χ3 ·



(6.19)

When neglecting the component at 3 · ωs and returning to complex notation, the electric flux density under consideration of the linear and nonlinear electrical polarization becomes 3 ˜ t)|2 · E˜ s (z, t) D(z, t) = ǫ0 E˜ s (z, t) + ǫ0 χ1 E˜ s (z, t) + ǫ0 χ3 · |x(z, 4   3 2 = ǫ0 · 1 + χ1 + χ3 · |x(z, ˜ t)| · E˜ s (z, t), (6.20) 4 where the term in brackets can be interpreted as an effective relative permittivity ǫr,e f f (x). ˜ The refractive index is then given by r q 3 n(x) ˜ = ǫr,e f f (x) ˜ t)|2 .(6.21) ˜ t)|2 = n 0 + n 2 · |x(z, ˜ = 1 + χ1 + χ3 · |x(z, 4 It can be observed that√the refractive index becomes intensity-dependent for χ3 6= 0. The parameter n 0 = 1 + χ1 denotes the linear refractive index and n 2 is the socalled “nonlinear index coefficient” in units of m2 /W. It can be shown that it is true that n 2 = 3χ3 /8n 0 by expanding the square root in (6.21) in a power series. In the same way as for the refractive index, the propagation constant becomes dependent on the intensity of the light. For the final derivation of the term describing the Kerr nonlinearities in the generalized nonlinear Schroedinger equation (6.2) it is referred to in [1].

6.3 Kerr Nonlinearities

149

The relation between the nonlinear propagation coefficient γ in W−1 m−1 used in (6.2) and the nonlinear index coefficient n 2 is derived in [1] and given by γ =

n 2 · ωs . c · Ae f f

(6.22)

Having understood the origin of the Kerr nonlinearities, let us now look at their effect on signal propagation. When neglecting attenuation and chromatic dispersion, the simple solution of (6.2) is ′

2

x(z, t ′ ) = x(z = 0, t ′ ) · e− jγ ·|x(z=0,t )| z .

(6.23)

Obviously, the intensity dependence of the refractive index leads to a phase modulation of the information signal with the intensity-dependent nonlinear phase shift 2 ϕ N L (z, x, t ′ ) = −γ · x(z = 0, t ′ ) z. The phase modulation causes a broadening of the signal spectrum but does not directly influence the amplitude of the complex envelope. Only the interaction with the chromatic dispersion induces a conversion of the phase modulation into an amplitude modulation and thus an indirect impact 2 of the Kerr effect on the signal power x(z, t ′ ) detected in IM-DD systems. In the case of phase and quadrature amplitude modulation, however, the nonlinear phase shift has a direct influence on the signal information as illustrated in more detail later on in Sect. 7.1.6 and Sect. 7.3.5. When neglecting chromatic dispersion but including fiber attenuation and observing a multi-channel transmission system composed of two channels with the electrical fields E 1 (z, t ′ ) = x1 (z, t ′ ) · e− jβ0,ω1 z+ jω1 t , E 2 (z, t ′ ) = x2 (z, t ′ ) · e− jβ0,ω2 z+ jω2 t , (6.24) the totally induced nonlinear phase shifts of the complex field envelopes of the two channels at ω1 and ω2 are given by [1, 2] 2 2 i 1 − e−αz h x1 (z = 0, t ′ ) + 2 x2 (z = 0, t ′ ) , (6.25) ϕ N L (z, x1 , x2 , t ′ ) ω = −γω1 1 α 2 2 i 1 − e−αz h ϕ N L (z, x1 , x2 , t ′ ) ω = −γω2 x2 (z = 0, t ′ ) + 2 x1 (z = 0, t ′ ) , (6.26) 2 α

with ω1 and ω2 representing the angular frequencies, γω1 and γω2 the nonlinear propagation coefficients, and x1 (z = 0, t ′ ) and x2 (z = 0, t ′ ) the complex envelopes at the fiber input of the two channels, respectively, and assuming same attenuation coefficients
α for both channels. In (6.25) and (6.26), the quantity le f f (z) = 1 − e−α·z /α, which was introduced in Sect. 5.1, can be interpreted as an effective length and indicates that an attenuation free fiber of length le f f would induce the same nonlinear phase shift.

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6 Fiber Propagation Effects

Two important propagation effects can be explained from (6.25) and (6.26). Firstly, the propagating channels are phase modulated as a result of the intensity change of their own channel which is denoted as self phase modulation (SPM). Secondly, the phases of the channels are shifted due to the intensity fluctuations of the neighboring channels. The latter effect is referred to as cross phase modulation (XPM) and is twice as effective as SPM. However, the XPM efficiency is reduced for non-parallel polarizations of the channels and due to chromatic dispersion because the channels propagate with different group velocities and XPM occurs only in the time intervals in which the propagating pulses are superimposed. A third effect, which can not be deduced from (6.25) and (6.26), is four wave mixing (FWM). It describes the generation of new waves at other frequencies by raising the total electrical field of a WDM signal to the third power, according to (6.18). When considering the interaction of three waves with the frequencies f i , f j and f k to compose a fourth wave
at f i jk = f i + f j − f k , a total number 3 2 of N F W M = 1/2 · N W D M − N W D M new mixing products is generated, where N W D M corresponds to the number of WDM channels. In standard WDM systems with equidistantly arranged channel spacings, the mixing products fall directly into the spectral bands of the WDM channels. As for XPM, the efficiency of FWM is decreased due to chromatic dispersion. Nevertheless, FWM can be a limiting effect when using fibers with low dispersion and for narrow channel spacings. In single-channel systems, the SPM is the only Kerr nonlinearity which must be considered. The SPM is often further partitioned into different intra-channel effects, depending on whether the effects are caused by the own pulse or the neighboring pulses. These effects are then denoted as intra-channel XPM (I-XPM) and intrachannel FWM (I-FWM). The exact impact of SPM on the signal quality has to be determined by examining the SPM as a combined effect with attenuation and chromatic dispersion. Whereas chromatic dispersion can be compensated for very efficiently, SPM-induced signal distortions are one of the main limiting factors for single-channel multi-span fiber-optic transmission systems for high fiber input powers, just as the amplifier noise limits the transmission reach attainable with low fiber input powers. As shown in Chap. 8, an optimal fiber input power can be found as a trade-off of noise and SPM effect. The robustness against SPM of various high-order modulation formats is discussed in Sect. 7.1.5, Sect. 7.2.3 and Sect. 7.3.4.

6.4 Other Propagation Effects The next subsections show how some other effects, namely nonlinear scattering effects, polarization mode dispersion and nonlinear phase noise, influence the signal propagation in optical fibers for high-order modulation formats. This is briefly discussed here rather than later because these effects are not part of the system performance characterization in Chap. 7 and Chap. 8.

6.4 Polarization Mode Dispersion

151

6.4.1 Nonlinear Scattering Effects Nonlinear scattering effects such as stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS), which manifest themselves as an intensity dependent attenuation of the signal wave, are not considered in the generalized nonlinear Schroedinger equation given by (6.2). SBS induces a reflected optical wave, whose frequency is reduced by about 10 GHz with respect to the frequency of the signal wave, and becomes relevant if the optical power exceeds some milliwatts within a bandwidth of 100 MHz [8]. Therefore, modulation formats with a more constant power spectral density allow for higher fiber input powers—without being especially impaired by SBS—than modulation formats with unsuppressed carrier, especially when low-linewidth lasers [2] are used. SRS takes effect only for high optical powers greater than 500 mW [8] and causes an energy transfer to other frequencies. The main part of the scattered power is contained in the peak of the Raman gain spectrum which is located at an about 13.2 THz lower frequency. For this reason, SRS-induced crosstalk must be considered particularly in WDM systems with a high number of channels.

6.4.2 Polarization Mode Dispersion A fiber mode can be interpreted as a solution for the wave equations which satisfies the boundary conditions at theq core-cladding interface [9]. For proper dimensioning

of the fiber with (2π/λs ) · r · n 2cor e − n 2clad < 2.405, where r represents the core radius and n cor e and n clad are the refractive indices of the core and the cladding, respectively, only a single mode is supported, denoted as the fundamental mode. A fiber in which only the fundamental mode can propagate is termed as a single mode fiber. However, this notation is basically imprecise, since two linearly independent solutions for the wave equation, which would have the same propagation constant in an ideal perfectly circularly symmetric fiber, correspond to the fundamental mode. When assuming the fundamental mode as a transverse field, the two solutions are orthogonally polarized in the x-y-plane (for propagation in the z-direction) and denoted as the principle states of polarization (PSP). Because fibers are not perfectly circularly symmetric in practice (this property is denominated as “birefringence”), both PSPs have slightly different propagation constants which leads to signal distortions when the energy of the propagating signal is split between the two PSPs. This effect is denoted as polarization mode dispersion (PMD). The statistic for the group delay difference of both PSPs, caused by random changes in birefringence occurring along the fiber, follows a Maxwell distribution. The mean value of the group delay difference 1τ P M D for a fiber of length l with the PMD-parameter P M D is given by [1, 10, 11] √ h1τ P M D i = P M D · l. (6.27)

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6 Fiber Propagation Effects

√ For good fibers, the PMD-parameter has values of about P M D = 0.1 ps/ km. √ Since h1τ P M D i scales with l, the PMD effect is very weak for those fibers for current data rates such as 40 Gbits/s, even for large distances. In commercially deployed fiber networks, however, particular fibers can show high birefringence, so that the PMD can be a limiting propagation effect, especially for data rates equal to or higher than 40 Gbit/s. The application of high-order modulation formats offers a way to relax the requirements on the fiber birefringence, because a certain group delay difference has a smaller impact on neighboring pulses for reduced symbol rates implicating longer pulse durations.

6.4.3 Nonlinear Phase Noise Another effect with influence on the transmission behavior of optical high-order modulation signals for multi-span long-haul transmission is the nonlinear phase noise. When looking at the complex plane, the complex noise of the optical amplifiers n k/⊥ (t) leads to amplitude and phase fluctuations of the transmitted signals. These phase fluctuations are induced directly and can be referred to as “linear phase noise”. However, the amplitude fluctuations also have influence on the optical phase, since they are converted to phase fluctuations during transmission through the Kerr effect. This additional phase noise is denoted as “nonlinear phase noise” and can be induced by SPM or XPM depending on whether it is caused by the amplitude noise of the own channel or other channels. The corruption of the optical phase due to the nonlinear phase noise was investigated in [4] for the first time. In [6] the variance of the nonlinear phase shift for multi-span transmission at high SNR is derived. It is given by σϕ2N L ≈

2 · hϕ N L i2 , 3 · SN R

(6.28)

with the mean nonlinear phase shift hϕ N L i ≈ −γ · |x(z = 0, t)|2 · N F S · le f f ,

(6.29)

where N F S corresponds to the number of fiber spans, having an effective length of le f f each, and |x(z = 0, t)|2 represents the power launched into the fiber in each span. Thereby, the effect of chromatic dispersion is neglected. The SNR in (6.28) is defined over a bandwidth matched to the signal’s symbol rate r S and related to the OSNR of (5.10) by SN R = 2 · OSN R ·

E s,avg Ps,avg 1f , = = rS No 2 · NF S · σ 2

(6.30)

6.4 Nonlinear Phase Noise

153

where E s,avg is the average energy per symbol and σ 2 represents the variance of the linear amplifier noise n k/⊥ (t) per fiber span per dimension. Furthermore, it has been shown in [6] that the variance of the nonlinear phase noise can significantly be reduced by using a compensator which rotates the received phase proportionally to the received optical power scaled with the factor α N L . This factor is optimized for α N L ≈ −γ · le f f (N F S + 1) /2. This way, the variance of the nonlinear phase shift can be reduced to σϕ2N L ,Comp ≈

hϕ N L i2 , 6 · SN R

(6.31)

which permits the doubling of the transmission distance in systems limited by the nonlinear phase noise and makes it less likely that the nonlinear phase noise becomes the dominant transmission impairment. As illustrated in [5, 12], compensation of the nonlinear phase noise can be performed using a simple optical phase modulator in front of the receiver or by electronic means. For an initial estimation of the impact of the nonlinear phase noise on optical systems with high-order phase modulation, the ratio between the variance of the nonlinear phase noise σϕ2N L and the variance of the phase error due to the linear noise σϕ2L can be examined. As derived in [5], σϕ2L is given for high SNR by σϕ2L ≈

1 . 2 · SN R

(6.32)

The ratio between σϕ2N L and σϕ2L can be easily calculated by using (6.28), (6.29) and (6.32). It can be interpreted as a measure for whether the nonlinear phase noise gets dominant over the linear noise. This happens for σϕ2N L σϕ2L

=

4 4 · hϕ N L i2 = · γ 2 · |x(z = 0, t)|4 · N F2 S · le2f f > 1. 3 3

(6.33)

As can be observed from (6.33), the nonlinear phase noise becomes more dominant for higher fiber input powers and longer transmission lengths. So far, the optimum fiber input powers for high-order modulation formats associated with multi-span transmission are largely unknown. Since the attainable transmission lengths can be expected to be lower for high-order modulation formats, it can be presumed that the nonlinear phase noise may become a less dominant effect. In the case of quadrature amplitude modulation, similar conclusions concerning the nonlinear phase noise are valid as for high-order phase modulation. However, an additional problem occurs here due to SPM. Symbols with different power levels experience different mean nonlinear phase shifts, so that QAM signal constellations are additionally distorted. Therefore, a compensation of the mean nonlinear phase shift becomes essential to avoid a severe performance degradation due to SPM. This effect, as well as its compensation, is discussed in Sect. 7.1.6 and Sect. 7.3.5. Moreover, (6.28) and (6.29) show that the nonlinear phase shift variance is smaller for

154

6 Fiber Propagation Effects

symbols with less power, so that the nonlinear phase noise is more critical for symbols on outer intensity rings. An exact investigation of the impact of the nonlinear phase noise on optical systems with high-order modulation is beyond the scope of this book, but an important issue for future research. Recent work [3] tries to integrate the nonlinear phase noise into tools for semi-analytical BER estimation. This should help us to learn more about the exact influence and the critical nature of this effect.

References 1. Agrawal, G.P.: Nonlinear Fiber Optics. Academic Press (3. Edition, 2001) 2. Coelho, L.D.: Numerical optimization of fiber optic communication systems with advanced modulation formats at 40Gbit/s channel data rate. Master´s thesis, Munic University of Technology (2005) 3. Coelho, L.D., et al.: Numerical and experimental investigation of the effect of dispersion on nonlinear phase noise in RZ-DPSK systems. In: Proceedings of European Conference on Optical Communication (ECOC), vol. 5, pp. 195–196 (2007) 4. Gordon, J.P., Mollenauer, L.F.: Phase noise in photonic communication systems using linear amplifiers. Optics Letters 15(23), 1351–1353 (1990) 5. Ho, K.P.: Phase-Modulated Optical Communication Systems. Springer (2005) 6. Ho, K.P., Kahn, J.M.: Electronic compensation technique to mitigate nonlinear phase noise. IEEE Journal of Lightwave Technology 22(3), 779–783 (2004) 7. Kato, T., et al.: Temperature dependence of chromatic dispersion in various types of optical fiber. Optics Letters 25(16), 1156–1158 (2000) 8. Petermann, K.: Einf¨uhrung in die optische Nachrichtentechnik. Vorlesungsskript, Technische Universit¨at Berlin (2003) 9. Ramaswami, R., Sivarajan, K.: Optical Networks: A Practical Perspective. Morgan Kaufmann (2. Edition, 2001) 10. Rohde, M., et al.: Robustness of DPSK direct detection transmission format in standard fiber WDM systems. Electronics Letters 36, 1483–1484 (1999) 11. Voges, E., Petermann, K.: Optische Kommunikationstechnik. Springer Verlag, Berlin / Heidelberg (2002) 12. Xu, C., Liu, X.: Postnonlinearity compensation with data-driven phase modulators in phaseshift keying transmission. Optics Letters 27(18), 1619–1621 (2002)

Chapter 7

Back-to-Back and Single-Span Transmission

Abstract This chapter discusses the system performance of high-order modulation formats for back-to back and single-span transmission. The individual strengths and drawbacks of phase and quadrature amplitude modulation formats in relation to important system parameters such as noise performance, optimal receiver filter bandwidths, laser linewidth requirements, chromatic dispersion tolerances and self phase modulation tolerances are identified—for systems with direct detection, homodyne differential detection and homodyne synchronous detection. Moreover, the influence of the signal characteristics of different transmitter configurations on system performance is illustrated for NRZ and RZ pulse shapes. Clear performance tendencies are ascertained and help the reader understand the consequences resulting from migration to high-order modulation formats, as well as the impact of the choice of particular system configurations.

Each modulation format shows a specific performance in relation to system impairments due to its individual properties. Euclidean distances and signal characteristics already determine the particular behavior for back-to-back transmission. When optical high-order modulation signals are propagated along the fiber, their individual characteristics—for instance the signal shape in the time domain, the shape of the spectrum and the spectral width—result in a particular robustness or vulnerability in relation to selected fiber degradation effects. In this chapter, the system performance of high-order modulation formats for the back-to-back case and for single-channel single-span transmission without optical amplifier noise on the link is detailed. This allows for tendencies concerning the influence of single parameters on the system performance to be highlighted. Considered parameters are noise performance, optimum optical and electrical receiver filter bandwidths, laser linewidth requirements, chromatic dispersion tolerances and self phase modulation tolerances. This isolated examination of single parameters gives a first indication of the transmission behavior for multi-span transmission over long distances which is discussed later on in Chap. 8.

M. Seimetz, High-Order Modulation for Optical Fiber Transmission, Springer Series in Optical Sciences 143, DOI 10.1007/978-3-540-93771-5 7, c Springer-Verlag Berlin Heidelberg 2009

155

156

7 Back-to-Back and Single-Span Transmission

The illustration of system performance provided in this chapter is based on results from computer simulations at a fixed data rate of 40 Gbit/s (the symbol rates are then reduced to 40/m Gbaud). In many cases, the results can be scaled also to other data rates. A wide range of modulation formats is considered. The discussion of systems with direct detection and homodyne differential detection involves binary amplitude modulation (2ASK), various phase modulation formats up to 16-ary phase modulation and the Star 16QAM. With homodyne synchronous detection, arbitrary modulation formats can be conveniently received, and the Square 16QAM as well as the Square 64QAM are additionally included. Throughout the whole chapter, NRZ and RZ pulse shapes are regarded, where a duty cycle of 50% is assumed for the RZ pulses. A rise time of 1/4 of the symbol duration is fixed for the electrical driving signals of all transmitters examined here. As quality measures for system performance, the eye opening penalty (defined in Sect. 5.2), the BER—determined by Monte Carlo simulations and semi-analytical BER estimation as described in Sect. 5.3 and Sect. 5.4—and the receiver sensitivity penalty / OSNR penalty are used. This enables a system characterization at BER=10−9 for direct detection via semi-analytical BER estimation, whereas a BER reference of 10−4 is used for systems with homodyne detection which are explored by Monte Carlo simulations. For BER determination, the decision thresholds are assumed to be optimally centered between the signal states but not to be optimized for non-uniformly distributed distortions of different symbols which may appear. Solely for ASK and the intensity detection branch for Star 16QAM, the threshold level is optimized with respect to the optimum BER for direct detection to take the power dependence of the signal-ASE noise into account. The sample time is always assumed to be located in the middle of the symbols. The window length T0 for semi-analytical BER estimation is properly chosen according to the system memory length. The de Bruijn bit sequences and de Bruijn symbol sequences used as data sequences are appropriate to take the inter-symbol interference caused by the receiver filters and the examined transmission effects into account.

7.1 Systems with Direct Detection In this section, the system properties of high-order modulation formats for direct detection are addressed. Firstly, back-to-back OSNR requirements are shown for 3 dB filter bandwidths of Bopt = 2.5 · r S (optical receiver filter) and Bel = 0.75 · r S (electrical receiver filter) in Sect. 7.1.1. Afterwards, optimal filter bandwidths are illustrated for all examined modulation formats in Sect. 7.1.2. The laser linewidth requirements for interferometric direct detection are considered as an important aspect in Sect. 7.1.3. Afterwards, the robustness and sensitivity of the different formats against fiber transmission impairments is detailed by discussing chromatic dispersion tolerances and SPM tolerances in Sect. 7.1.4 and Sect. 7.1.5, respectively. Since QAM formats exhibit a very poor SPM tolerance, a compensation of the mean nonlinear phase shift can become necessary. Two simple compensation schemes and

7.1 Back-to-Back OSNR Requirements for Direct Detection

157

their performance gains are illustrated in Sect. 7.1.6. Finally, the system characteristics of high-order modulation formats for direct detection are summarized in Sect. 7.1.7.

7.1.1 OSNR Requirements The back-to-back optical signal-to-noise ratio (OSNR) requirements can be determined using the system setup depicted in Fig. 7.1. DD receiver with optical pre-amplification

TX

BPF

RX

PRX,avg OSNR (noise bandwidth 0.1nm)

Fig. 7.1 Setup for determination of the back-to-back OSNR requirements

The OSNR is specified here between the optical pre-amplifier and the optical receiver filter and given by the average signal power Ps,avg divided by the noise power in both polarizations Pn = 2· N0 ·1 f = 2· N0 ·1λ· f s2 /c as defined in (5.10). The noise bandwidth is set here to 1λ = 0.1 nm. According to (3.25), the two-sided power spectral density of the optical pre-amplifier noise per polarization is given by N0 = n sp (G − 1) · h · f s ≈ F/2 · (G − 1) · h · f s , where the approximation is true for high amplifier gain G [10] and F represents the noise figure of the optical preamplifier. The amplifier noise (Signal-ASE noise and ASE-ASE noise) is assumed to be the dominant noise source, so the shot-noise and the thermal noise of the receiver are neglected. The amplifier gain is given by G = Ps,avg /PR X,avg , where PR X,avg represents the average optical power received in front of the optical pre-amplifier. The OSNR behind the optical pre-amplifier can be calculated as OSN R =

Ps,avg PR X,avg ≈ , Pn F · h · fs · 1 f

(7.1)

where the approximation in (7.1) is valid for high gain. By taking the logarithm of both sides in (7.1), the OSNR in decibels can be related to the received power for 1λ = 0.1 nm and f s = 193.1 THz by O S N Rd B = 58 dBm + PR X,avg,d Bm − Fd B , with PR X,avg,d Bm = 10 lg(PR X,avg /1 mW) and Fd B = 10 lg F. This way, the receiver sensitivities can easily be calculated from the OSNR requirements presented in the following paragraphs. Figure 7.2 shows the OSNR requirements of all examined modulation formats for NRZ (a) and RZ (b) at 40 Gbit/s when the serial transmitter structure (transmitters shown in Fig. 2.7 and Fig. 2.12) and direct detection receivers (depicted in Fig. 3.4

158

7 Back-to-Back and Single-Span Transmission

and Fig. 3.5) with arg-decision (Fig. 3.6a) are employed. As receiver filters, secondorder Gaussian optical bandpass filters and fifth-order electrical Bessel filters are adopted, with 3 dB bandwidths of Bopt = 2.5 · r S and Bel = 0.75 · r S , respectively. 1E-2 a

1E-3

BER

1E-4

16DPSK

1E-5 2ASK

1E-6

Star 16QAM (ASK-8DPSK) RR 1.6

DBPSK

1E-7

DQPSK

1E-8

8DPSK NRZ

1E-9 10

12

14

16

18

20

22

24

26

28

OSNR [dB] 1E-2 b

1E-3 1E-4

BER

2ASK

1E-5

16DPSK

1E-6

DBPSK

1E-7

Star 16QAM (ASK-8DPSK) RR 1.6

DQPSK

1E-8

8DPSK RZ

1E-9 10

12

14

16

18

20

22

24

26

28

OSNR [dB] Fig. 7.2 Back-to-back OSNR requirements of direct detection receivers for NRZ (a) and RZ (b) at r B = 40 Gbit/s for receiver filter 3 dB bandwidths of Bopt = 2.5 · r S and Bel = 0.75 · r S when the serial transmitter structure and arg-decision are employed, lines: semi-analytical BER estimation, symbols: results from MC simulations, RR: ring ratio

7.1 Back-to-Back OSNR Requirements for Direct Detection

159

The lines were calculated by semi-analytical BER estimation, whereas the symbols represent results of MC simulations. Both are in excellent agreement. As regards performances, RZ outperforms NRZ for all formats because the distances between the symbols are greater for the same average power (higher peak-to-average power ratio). Generally, the OSNR requirements are roughly determined by the Euclidean distances. Therefore, phase modulation formats with an increasing number of bits per symbol exhibit increasing OSNR requirements and Star QAM formats feature a better noise performance than DPSK formats with the same number of symbols. The best OSNR performance of all the formats examined here features the DBPSK. When comparing the DPSK formats with 2ASK, DQPSK requires a lower OSNR than 2ASK, but 8DPSK is significantly worse. The comparison of the two 16-ary formats Star 16QAM (ASK-8DPSK) and 16DPSK shows that the Star 16QAM requires a significantly lower OSNR than the 16DPSK and its performance is almost as good as for 8DPSK in a comparison at the same data rate. However, the very poor performance of NRZ-16DPSK can be somewhat improved when employing a broader optical receiver filter as shown later on in Sect. 7.1.2.

Optimum Ring Ratio for Star 16QAM The curves for Star 16QAM in Fig. 7.2 are illustrated for the optimum ring ratio, which defines the ratio of the amplitudes of the outer and inner circle. The optimum ring ratio arises if same error rate performances are obtained in the intensity and phase detection branches—yielding a minimum overall BER. Figure 7.3a depicts the BER for different ring ratios for a fixed OSNR (20.46dB for NRZ, 18.46dB for RZ) when the serial transmitter structure and arg-decision are used. The BER is minimized for a ring ratio of about 1.6. When the parallel transmitter and IQdecision are employed, the optimum ring ratios are 1.65 for NRZ and 1.6 for RZ as can be observed from Fig. 7.3b. Serial transmitter, arg-decision

Parallel transmitter, IQ-decision

1E-2

1E-2

a

b 1E-3 BER

BER

1E-3

Star 16QAM NRZ @ OSNR = 20.46dB

1E-4 1E-5

1E-4 1E-5

Star 16QAM RZ @ OSNR = 18.46dB

1E-6 1,2

Star 16QAM RZ @ OSNR = 18.46dB

1,4

1,6 Ring Ratio

1,8

Star 16QAM NRZ @ OSNR = 20.46dB

2,0

1E-6 1,2

1,4

1,6 Ring Ratio

1,8

2,0

Fig. 7.3 Ring ratio optimization for Star 16QAM when employing the serial transmitter and argdecision (a) / the parallel transmitter and IQ-decision (b)

160

7 Back-to-Back and Single-Span Transmission

Influence of the Transmitter Configuration and Decision Technique In Sect. 2.4.4 and Sect. 2.5, the output signals of the serial and parallel transmitters for DPSK and Star QAM were shown to exhibit different properties with respect to their signal shapes, symbol transitions and chirp characteristics. Furthermore, two decision techniques (arg-decision and IQ-decision) were described in Sect. 3.2.3 and expected to show a different noise performance due to the different positioning of the thresholds. To illustrate the influence of the transmitter structure and the decision method on the back-to-back OSNR requirements, a performance comparison is shown in Fig. 7.4, exemplarily for 8DPSK. TX / RX comparison 8DPSK

1E-2 Se. / IQ NRZ

1E-3

Se. / arg NRZ

BER

1E-4

Fig. 7.4 Impact of the transmitter configuration and decision method on the OSNR performance of 8DPSK for direct detection.

Pa. / IQ NRZ

1E-5 Pa. / arg NRZ

1E-6 1E-7 1E-8

Both TX, arg-dec., RZ Both TX, IQ-dec., RZ

1E-9 16 17 18 19 20 21 22 23 24 25 OSNR [dB]

Looking at RZ pulse shape, it makes no difference whether the serial or the parallel transmitter is used because power is decreased during the symbol transitions and the signal shapes are nearly identical. For NRZ, however, the use of the serial transmitter leads to a worse OSNR performance. This is caused by the smaller peakto-average power ratio and the higher chirp which results in larger distortions at the optical receiver filter. When comparing the decision techniques, arg-decision shows a better performance than IQ-decision, since the thresholds are optimally placed between the symbols for arg-decision, whereas the distances between the thresholds and the symbols are smaller for IQ-decision. The tendencies shown here for 8DPSK are also valid for other formats.

7.1.2 Optimal Receiver Filter Bandwidths In Sect. 7.1.1, the OSNR requirements were illustrated for fixed 3 dB receiver filter bandwidths of Bopt = 2.5 · r S and Bel = 0.75 · r S , conjointly defined for all formats. In this section, the optimal receiver filter bandwidths are discussed. These were calculated using semi-analytical BER estimation and are shown in the contour diagrams of Fig. 7.5—all together in a single figure to simplify the comparison of the different formats and configurations, and to recognize the tendencies.

7.1 Optimal Receiver Filter Bandwidths for Direct Detection ASK NRZ 3.5

2.5

3

Bopt / rS

1.5

2.5

0.5

2

1

2 0.2

0.5

1 0.6

0.7

0.8

0.2

0.4

1.5

16.5

0.5 0.5

0.2

15.6

0.5

1.5

1

2.5

18.4

1.5

1

2

19.0

0.4

0.2

2.5 0.5

1.5

3

0.2

2.5

2

2.5 1

2

0.6 0.8

3

1.5

3.5

0.4

3

3

2

DBPSK Se. TX, RZ

3.5

2

1

1

ASK RZ

DBPSK Se. TX, NRZ

3.5

161

0.6

0.4

1.5

1

0.9

1

1.1

1 0.6

DQPSK Se. TX, NRZ 3.5

2.5

0.8

1

1.2

1.4

1.6

1.8

1 0.6

0.7

DQPSK Pa. TX, NRZ 3

0.8

0.9

1

1.1

1 0.6

DQPSK Se. TX, RZ

3.5

0.8

1

1.5

Bopt / rS

2.5

2 0.5

1

1.2

1.4

3.2

1.6

1.8

17.4 1

1 0.6

0.8

1

1.2

1.4

1.6

1 0.6

0.8

1

1.2

1.4

1.6

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2.5

1.5

1.7

1.9

1.2 0.5

1

0.7

0.9

Bopt / rS

1.3

1.5

1.7

1.9

0.4

0.8

3.2

0.6

1.6

1.2 0.7

0.9

1.1

1.3

1.5

1.7

1.9

1.2 0.7

0.9

1.1

1.3

1.5

3.2

1

2.4

1.5

3.2 0.6

2.8

0.4

0.4

2

0.5

2.4

1.5

2

2

22.8 5

0.5

22.0

21.8

2.4

0.2

1.3

1.5

1.7

1.9

0.2

1.2 0.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

1

1.2 0.9

4.5

1

1.5

1.7

1.9

1.2 0.7

1.7

1.9

1 0.8 0.6

26.0

0.2

0.4

2.6

0.4

0.2

0.8

2

2

1.7

1.9

1.4 0.7

22.0

2.2

1

0.4 5

1.8

1.6

1.5

1.5

3

3

1.3

1.3

3.4

0.2

1

2.2

Bel / rS

1.1

0.6

2

1.1

0.9

0.6

2.4

4

0.9

0.8

1

Star 16QAM Se. / arg, RZ

0.4

2.8

1.5

2.6

5

1.3

16DPSK Se. / arg, RZ

0.5 3.5

1.1

2

24.5

3 1.5 2

2.4

1.6

3.2 0.5

3 2.5

2.8

0.4 0.6

1

1

3.4

28.6 0.5

0.2

0.4

0.6

1.6

Star 16QAM Se. / arg, NRZ

3.6

2

0.2 0.8

1

1.6 5

1.1

1.9

0.6

2.8

1.5

0.9

1.7

8DPSK Pa. / IQ, RZ

0.4

16DPSK Se. / arg, NRZ

Bopt / rS

0.4

0.8

1

2.5

0.5

1.6

1.2 0.7

0.2

2

0.6

8DPSK Se. / IQ, RZ

2.8

2

3.2

1.1

3.5

2

1

1.2 0.7

0.4 0.2

1.5

1

2.5

2

1.8

2.4

21.2

2

2

8DPSK Pa. / IQ, NRZ 4

3

0.5

1.6

1

3.2

2.4

2.8

1.6 5

1

1.4

0.2

1.6

24.3

1.2

3.2

0.6

2.4

1

0.5

8DPSK Se. / IQ, NRZ

2.8

1

0.6

2

1.3

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8DPSK Pa. / arg, RZ

21.1

2

1.1

1 0.6

2

1.6

0.9

1.8

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5

1.2 0.7

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8DPSK Se. / arg, RZ

2.8

22.3

2

1.8

1.5

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1.5

3.2

2.8

3

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3.2

1 1.5

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2

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0.2

17.2

4

2.5

0.5

2 1.5

8DPSK Pa. / arg, NRZ

3.5

23.6

2.4

0.4

2.5

0.2

17.1

1 1

1.5

0.8

3

0.6

2.5

1.5

1

1.5

2

2.5

8DPSK Se. / arg, NRZ

2.8

0.4

0.2

5

Bopt / rS

2

1.5

2.5

2

1 0.6

0.2

0.8

0.6

0.2

0.5

1.5

1.8

1 1

19.1

3

1.6

3.5

3

0.5

2.5

1.4

0.8

3

2

1.2

DQPSK Pa. TX, RZ

3.5 3.5 3

3

0.6

0.8

0.8

0.9

1.1

Bel / rS

1.3

1.2 0.7

1

1.8

1.6

0.9

1.1

1.3

Bel / rS

1.5

1.7

1.9

1.4 1.1

0.2

1.3

1.5

1.7

1.9

Bel / rS

Fig. 7.5 Optimal receiver filter bandwidths for direct detection at r B = 40 Gbit/s for second-order Gaussian optical bandpass filters and fifth-order electrical Bessel filters; The stars indicate the points with minimum required OSNR and are labeled with the minimum OSNR value at a BER of 10−9 . The contour lines are labeled with the OSNR penalty at a BER of 10−9 with respect to the minimum OSNR. RZ duty cycle: 50%

162

7 Back-to-Back and Single-Span Transmission

The stars in Fig. 7.5 indicate points with optimized filter bandwidths and are labeled with the minimum OSNR value at a BER of 10−9 . The contour lines are labeled with the OSNR penalty at a BER of 10−9 with respect to the minimum OSNR value for optimized filter bandwidths. It can be concluded that NRZ signals are much more sensitive to filter bandwidth variations than signals with RZ pulse shape. In the case of RZ, the contour lines are labeled in steps of 0.2 (compared to steps of 0.5 for NRZ) and high deviations from the optimum electrical receiver bandwidths can be tolerated without significant penalties, as well as deviations of the optical receiver bandwidth down to a certain minimum value which depends on each modulation format and increases with the modulation format order. Moreover, there are only minor differences between systems with serial and parallel transmitters for RZ. For NRZ, the optimal receiver filter bandwidths are strongly dependent on the transmitter configuration used and the parallel transmitter proves to be much more tolerant than the serial transmitter as regards bandwidth deviations of the optical filter—especially for the higher-order formats, as becomes apparent from the results for 8DPSK. When the serial transmitter is used in combination with NRZ, an optical bandwidth should be chosen that is not too small, since the signals become very vulnerable to narrow optical filtering with increasing order of the phase modulation. This can be observed by comparing the contour plots of NRZ-DQPSK, NRZ8DPSK and NRZ-16DPSK for the serial transmitter configuration. In Table 7.1, the optimum optical and electrical receiver filter bandwidths are summarized for all modulation formats and system configurations examined here. Table 7.1 Optimum receiver filter bandwidths for back-to-back in systems with direct detection Modulation Format (Configuration)

Bel /r S , Bopt /r S for NRZ

Bel /r S , Bopt /r S for RZ

2ASK

0.7, 1.4

0.7, 2.4

DPBSK

1.3, 1.4

1.3, 2.2

DQPSK (Se./arg) DQPSK (Pa./arg)

0.9, 2.4 0.7, 1.4

1.1, 2.2 0.7, 2.4

8DPSK (Se./arg) 8DPSK (Se./IQ) 8DPSK (Pa./arg) 8DPSK (Pa./IQ)

0.9, 3.2 0.9, 3.0 0.7, 2.4 0.7, 2.0

1.1, 2.4 1.1, 2.4 0.7, 2.6 0.9, 2.4

16DPSK (Se./arg)

0.9, 3.4

1.3, 2.6

Star 16QAM (Se./arg) Star 16QAM (Pa./arg)

0.9, 3.2 0.7, 2.4

1.5, 2.2 0.7, 2.6

In Fig. 7.6, the BER is illustrated over the OSNR for optimized filter bandwidths, again assuming for all formats the use of the serial transmitter structure and argdecision. When these curves are compared with the curves for fixed optical and electrical receiver filter bandwidths of Bopt = 2.5 · r S and Bel = 0.75 · r S depicted in Fig. 7.2, it becomes apparent that the differences are nearly negligible for RZ

7.1 Optimal Receiver Filter Bandwidths for Direct Detection

163

pulse shape, whereas significant improvements are obtained for NRZ-ASK / NRZDBPSK and especially for the NRZ-16DPSK format which is very sensitive to too narrow optical filtering. 1E-2

1E-2

a

1E-3

1E-4

2ASK

1E-5 DQPSK

Star 16QAM RR 1.6

1E-6 1E-7

16DPSK

1E-5

Star 16QAM RR 1.6

2ASK

1E-6 DQPSK

1E-7

DBPSK

1E-8

BER

BER

1E-4

b

1E-3

16DPSK

1E-8

8DPSK NRZ

1E-9 10 12 14 16 18 20 22 24 26 28 OSNR [dB]

DBPSK 8DPSK RZ

1E-9 10 12 14 16 18 20 22 24 26 28 OSNR [dB]

Fig. 7.6 OSNR requirements for direct detection receivers for NRZ (a) and RZ (b) at a data rate of r B = 40 Gbit/s for optimal receiver filter bandwidths when the serial transmitter structure and arg-decision are employed, calculated by semi-analytical BER estimation

The conclusions concerning the comparison of different transmitter and decision schemes drawn in Sect. 7.1.1 are just as valid for optimized filter bandwidths, as can be observed from the 8DPSK curves in Fig. 7.7. These can be compared to the curves for non-optimized bandwidths shown in Fig. 7.4. TX / RX comparison 8DPSK, opt. BW

1E-2 Se. / IQ NRZ

1E-3

Se. / arg NRZ

1E-4 BER

Pa. / IQ NRZ

Fig. 7.7 Performance comparison of different transmitter structures and decision schemes for 8DPSK when optimal receiver filter bandwidths are applied

1E-5 Pa. / arg NRZ

1E-6 1E-7 1E-8

Both TX, arg-dec., RZ Both TX, IQ-dec., RZ

1E-9 16 17 18 19 20 21 22 23 24 25 OSNR [dB]

Although the back-to-back OSNR requirements are shown here for a fixed data rate of 40 Gbit/s, they can also be scaled to other data rates. When quadrupling the data rate, for instance, the fourfold amount of noise power falls into the detection bandwidth and the fourfold signal power PR X,avg is required at the receiver input to obtain the same BER. With the OSNR definition of (7.1), this corresponds to a required OSNR which is 6 dB higher. Alternatively, the system noise performance can be expressed in a form that is independent of the data rate by illustrating the

164

7 Back-to-Back and Single-Span Transmission

BER with respect to the SNR defined in (6.30). In that case, the relative distances between the curves of different modulation formats change.

7.1.3 Laser Linewidth Requirements This section gives an insight into the laser linewidth requirements of direct detection systems with high-order modulation. In the case of negligible influence of the optical receiver filter, an analytical formula for calculation of the BER of DBPSK systems under consideration of the laser linewidth 1νs is presented in [4] as BER =

∞ S N R · e−S N R X (−1)n 1 − · 2 2 2n + 1 n=0      SN R S N R 2 −(2n+1)2 π 1νs TS , ·e · In + In+1 2 2

(7.2)

where In represents the n-th order modified Bessel function of the first kind. However, the phase-noise statistics of light are modified by optical filtering. In [15], an analytical method is described for taking the statistics of filtered DBPSK signals with phase noise into account. The influence of different optical receiver filters on the phase noise statistics is illustrated in [1], where a semi-analytical BER estimation method for DQPSK systems was proposed under consideration of the laser phase noise. The laser linewidth requirements presented here were calculated by MC simulations, where the laser phase noise is modeled as a random walk process as described in Sect. 2.1.1, assuming a white power spectral density of the frequency noise and a Lorentzian line-shape. Within a symbol duration of TS , the optical signal phase exhibits a Gaussian distributed random phase change of 1ϕn s (t), whose variance is given by h1ϕn2s (TS )i = 2π 1νs TS . 1E-3

1E-3

a

∆ν / rB = 3.75e-3

b

∆ν / rB = 25e-3

BER

BER

∆ν / rB = 20e-3

1E-4 ∆ν / rB = 0

∆ν / rB = 15e-3

∆ν / rB = 2.5e-3

1E-4 ∆ν / rB = 0

∆ν / rB = 1.25e-3 ∆ν / rB = 5e-3 ∆ν / rB = 0.625e-3

1E-5 11

RZ-DBPSK

12

13 14 15 OSNR [dB]

16

17

1E-5 14

NRZ-DQPSK

15

16 17 18 OSNR [dB]

19

20

Fig. 7.8 BER performance of RZ-DBPSK (a) and NRZ-DQPSK (b) considering laser phase noise

7.1 Laser Linewidth Requirements for Direct Detection

165

In Fig. 7.8, the BER is shown against the OSNR for back-to-back, considering different linewidth-to-data-rate ratios, exemplarily for RZ-DBPSK (a) and NRZDQPSK (b). The receiver filters are assumed to be second-order Gaussian optical bandpass filters and third-order electrical Bessel filters with 3 dB bandwidths of Bopt = 2.5 · r S and Bel = 0.75 · r S . The laser phase noise leads to BER floors which are a function of the ratio of the laser linewidth to the data rate. It should be noted that the laser linewidth requirements are much more stringent when calling for a BER of 10−9 instead of 10−4 due to the appearance of the BER floors. From the BER curves, the OSNR penalties at a BER of 10−4 can be derived. These are defined by the differences of the required OSNR at a BER of 10−4 for the inspected curves and the reference curve for zero linewidth, and illustrated with respect to the linewidth-to-data-rate ratio for all modulation formats examined here in Fig. 7.9 for NRZ (a) and RZ (b). 4

a

Penalty @ BER=10 [dB]

Star 16QAM

3

-4

-4

Penalty @ BER=10 [dB]

4

2 DQPSK

16DPSK

DBPSK

1 8DPSK

0 -5 10

-4

NRZ -3

-2

10 10 10 Linewidth / data rate

-1

10

b 3 Star 16QAM

2

DBPSK DQPSK

16DPSK

1 0 -5 10

RZ

8DPSK -4

-3

-2

10 10 10 Linewidth / data rate

-1

10

Fig. 7.9 OSNR penalties at a BER of 10−4 with respect to the linewidth-to-data-rate ratio for various modulation formats for NRZ (a) and RZ (b) pulse shapes.

When comparing the phase modulation formats, the linewidth requirements increase with an increasing number of phase states. This is reasonable, since a certain level of laser phase noise becomes more critical for smaller phase distances. Additionally, the reduction of the symbol rate makes the laser phase noise more critical for modulation formats with a higher number of bits per symbol. This way, the slightly worse performance of Star 16QAM compared with 8DPSK can be explained. With regard to the pulse shapes, differences between NRZ and RZ are relatively small. It can be concluded that the linewidth requirements for direct detection are quite relaxed. Even for NRZ-16DPSK, which shows the most stringent requirements on the laser phase noise of the formats discussed here, the required linewidth-to-datarate ratio is 2.6 · 10−5 . This corresponds to 1νs =1 MHz at r B =40 Gbit/s.

166

7 Back-to-Back and Single-Span Transmission

7.1.4 Chromatic Dispersion Tolerances The last sections have discussed the influence of some performance parameters for the back-to-back case. In the following sections, system parameters for single-span optical fiber transmission are highlighted. Next, the chromatic dispersion tolerances are presented. These can be determined by sending the optical signals over a dispersive single mode fiber, without using any dispersion compensation. Other disturbing effects such as laser phase noise and Kerr nonlinearities are neglected. Figure 7.10 shows the chromatic dispersion tolerances at r B = 40 Gbit/s of all modulation formats discussed here for direct detection. In Fig. 7.10 is assumed that serial transmitters and arg-decision are employed, as well as optical and electrical filters with 3 dB bandwidths of Bopt = 2.5 · r S and Bel = 0.75 · r S , respectively. As performance measures, two different quality criteria are used. The OSNR penalties at a BER of 10−9 were calculated by semi-analytical BER estimation (the OSNR values for zero dispersion serve as a reference). Additionally, eye opening penalties are illustrated which are shown separately for the intensity detection and phase detection branches for Star 16QAM.

3

-9

2ASK DBPSK 8DPSK, 16DPSK, Star 16QAM

DQPSK

2 1

NRZ

0 -320

-160 0 160 Dispersion [ps/nm]

320

4

c

2ASK

3

DBPSK

2

DQPSK, 8DPSK, 16DPSK

1

Star 16QAM Phase

Star 16QAM Int.

NRZ

0 -320

Penalty @ BER=10 [dB]

4

a

-160 0 160 Dispersion [ps/nm]

320

Eye Opening Penalty [dB]

Eye Opening Penalty [dB]

-9

Penalty @ BER=10 [dB]

4

b

2ASK, DBPSK

3 DQPSK

2

8DPSK 16DPSK

1 Star 16QAM

0 -320

RZ

-160 0 160 Dispersion [ps/nm]

320

4

d

2ASK, DBPSK

3 DQPSK

8DPSK

2 16DPSK

1

Star 16QAM Phase

Star 16QAM Int.

RZ

0 -320

-160 0 160 Dispersion [ps/nm]

320

Fig. 7.10 Chromatic dispersion tolerances of various modulation formats for direct detection at 40 Gbit/s when using the serial transmitters and arg-decision; The two upper diagrams show the OSNR penalties at a BER of 10−9 against the chromatic dispersion for NRZ (a) and RZ (b). The bottom diagrams (c, d) illustrate the eye opening penalties.

7.1 Chromatic Dispersion Tolerances for Direct Detection

167

The principal tendencies for the chromatic dispersion tolerances for the migration to high-order modulation formats become clear when looking at the diagrams for RZ pulse shape (Fig. 7.10b/d). For a comparison at a fixed data rate, the chromatic dispersion tolerances increase with the order of the modulation format due to the reduced symbol rates and the narrowed spectral widths. However, it becomes apparent from Fig. 7.10a/c that this is not valid without exception for NRZ when employing the serial transmitter structure, since the advantage of the smaller bandwidth for the high-order formats is neutralized by detrimental chirp characteristics of the transmitter output signals. Generally, RZ outperforms NRZ for all the non-binary modulation formats. In the case of binary modulation, the smaller bandwidth of the NRZ signals compared with RZ is the reason for superior NRZ performance, whereas for high-order modulation formats the reduced chirp of the RZ signals becomes the dominant influencing factor and yields significantly higher chromatic dispersion tolerances for RZ. Both 16-ary formats, RZ-16DPSK and RZ-Star 16QAM, show by far the highest dispersion tolerances of all the formats observed here. When accepting an OSNR penalty of 2 dB at BER=10−9 , a dispersion of about 290 ps/nm can be tolerated and the EOP for 320 ps/nm is about 1dB. For Star 16QAM, the EOP in the intensity detection branch is slightly worse than in the phase detection branch for—with respect to OSNR—the optimum ring ratio of 1.6 (see Fig. 7.10c/d). For other ring ratios this relation can change as discussed in [13]. It can be concluded from a comparison of the OSNR penalties and the eye opening penalties that the EOP overestimates the acceptable residual dispersion compared to the OSNR penalties at BER=10−9 . To better illustrate the disturbing effect of chromatic dispersion, the IQ diagrams and the phase and intensity eyes for Star 16QAM are depicted in Fig. 7.11 for zero dispersion (a) and 320 ps/nm dispersion (b). a

Dispersion 0ps/nm

b

Dispersion 320 ps/nm

NRZ

RZ

IQ-Plot

Phase eye

Intensity eye

IQ-Plot

Phase eye

Fig. 7.11 Effect of chromatic dispersion on Star 16QAM signals

Intensity eye

168

7 Back-to-Back and Single-Span Transmission

Impact of the Transmitter Configuration and the Decision Scheme The signal shapes, symbol transitions and chirp characteristics are different for the output signals of the serial and parallel transmitters (see Sect. 2.4.4 and Sect. 2.5) and have a significant influence on the obtainable chromatic dispersion tolerance. In Fig. 7.12, this influence is illustrated for 8DPSK (a) and Star 16QAM (b), just as the impact of the decision method (see Sect. 3.2.3) is. TX / RX comparison Star 16QAM

TX / RX comparison 8DPSK

4 Se. / arg NRZ

-9

a 3

Penalty @ BER=10 [dB]

-9

Penalty @ BER=10 [dB]

4

Pa. / IQ NRZ Se. / arg RZ

2 Pa. / IQ RZ

1 0 -320

-160 0 160 Dispersion [ps/nm]

320

b 3

Se. / arg NRZ Pa. / arg NRZ Se. / arg RZ

2 Pa. / arg RZ

1 0 -320

-160 0 160 Dispersion [ps/nm]

320

Fig. 7.12 Impact of the transmitter configuration and decision method on the chromatic dispersion tolerances at 40 Gbit/s for direct detection. a 8DPSK. b Star 16QAM.

Unlike the decision technique, which does not significantly affect the attainable dispersion tolerance, the transmitter configuration has a substantial effect. The serial transmitters show higher penalties than the parallel transmitters due to the disadvantageous chirp characteristics. These tendencies are consistent with the signal characteristics discussed in Sect. 2.4.4 and Sect. 2.5 and illustrated in Fig. 2.11 and Fig. 2.14, respectively. The product of the chirp and the intensity was introduced in these sections as an intuitive measure for the chirp influence on the transmission performance and the parallel transmitter was already expected to exhibit a better transmission behavior than the serial transmitter.

7.1.5 Self Phase Modulation Tolerances Self phase modulation (SPM) tolerances for single-span transmission can be determined using the system setup shown in Fig. 7.13. The optical signals are transmitted over a single dispersive and nonlinear fiber link with a length of l = 80 km. The dispersion parameter and the nonlinear index coefficient of the SMF at the optical carrier frequency f s = 193.1 THz are assumed here to be Dλ = 16 ps/(nm·km) and n 2 = 2.6 · 10−20 m2 /W (Ae f f = 80 · 10−12 m2 ), respectively, and the dispersion slope is assumed to be zero (Sλ = 0). The chromatic dispersion is compensated for

7.1 Self Phase Modulation Tolerances for Direct Detection

169

behind the link by a dispersion compensating fiber (degree of compensation: 100%) which is assumed to be linear. The average fiber input power PT X,avg is varied. SMF

DCF

80km

100% CD-comp.

TX

RX

BPF

PTX

OSNR (noise bandwidth 0.1nm)

Fig. 7.13 Single-span system setup for determination of self phase modulation tolerances

In Fig. 7.14, the SPM tolerances of all examined formats are depicted for a data rate of 40 Gbit/s, where the use of serial configurations at the transmitter side is assumed, as well as the application of second-order Gaussian optical bandpass filters and third-order electrical Bessel filters—with 3 dB bandwidths of Bopt = 2.5 · r S and Bel = 0.75 · r S —and arg-decision at the receiver end. 4 NRZ

Penalty @ BER=10 [dB]

a

8DPSK

-9

3 2ASK Star 16QAM

2

DQPSK

1

16DPSK

DBPSK

0 0

3 6 9 12 Fiber input power [dBm]

15

4 NRZ

3

c

8DPSK

Star 16QAM Int.

Eye Opening Penalty [dB]

Eye Opening Penalty [dB]

-9

Penalty @ BER=10 [dB]

4

2ASK

2 1

16DPSK Star 16QAM Phase

DQPSK

DBPSK

0 0

3 6 9 12 Fiber input power [dBm]

15

RZ

16DPSK

3

b

2ASK 8DPSK

2

DQPSK DBPSK

1

Star 16QAM

0 0

3 6 9 12 Fiber input power [dBm]

15

4 RZ

2ASK, Star 16QAM Int.

3

d

16DPSK

2 8DPSK

1 0 0

Star 16QAM Phase

DBPSK, DQPSK

3 6 9 12 Fiber input power [dBm]

15

Fig. 7.14 SPM tolerances of various modulation formats for direct detection at 40 Gbit/s when serial transmitters and arg-decision are used; The two upper diagrams show the OSNR penalties at a BER of 10−9 against the fiber input power for NRZ (a) and RZ (b). The bottom diagrams (c, d) illustrate the eye opening penalties.

170

7 Back-to-Back and Single-Span Transmission

Figure 7.14a/b illustrates the OSNR penalties (with respect to the linear case), and Fig. 7.14c/d illustrates the eye opening penalties. It can be seen that RZ-DPSK signals exhibit higher tolerable fiber input powers than NRZ-DPSK signals due to their better chirp characteristics. Higher chirp leads to a greater influence of the chromatic dispersion and thus to a stronger interaction between chromatic dispersion and SPM. A comparison of the different DPSK formats shows that the SPM tolerance decreases with an increasing number of symbols which is equivalent to a decrease in the phase distances. Moreover, DPSK formats exhibit higher SPM tolerances than ASK formats. For instance, even RZ-16DPSK shows a similar SPM performance to RZ-2ASK. Whereas the Star 16QAM gives a considerably better performance than the 16DPSK with respect to noise and a similar chromatic dispersion tolerance, the SPM tolerance of Star 16QAM is very poor for NRZ and RZ. For RZ-16DPSK, an OSNR penalty of less than 2 dB is observed for 11 dBm fiber input power. In contrast, a fiber input power of about 5.5 dBm yields an OSNR penalty of 2 dB for RZ-Star 16QAM. In the case of NRZ, this performance difference can not be detected because the NRZ-16DPSK is highly sensitive against chirp when the serial transmitter is employed. As becomes apparent from the EOP diagrams shown in Fig. 7.14c/d, the remarkably bad SPM tolerance of Star QAM formats is caused by a poor performance in the phase detection branch. The reasons for this effect, as well as solutions for a possible performance improvement using appropriate SPM compensators, are illustrated in detail in Sect. 7.1.6. Another possibility for enhancing the poor SPM tolerance of Star 16QAM in the phase detection branch which is simultaneously associated with a performance degradation in the intensity detection branch, is to modify the ring ratio as shown in Fig. 7.15. However, this is not an ideal solution because the OSNR performance becomes worse in this case [13].

4

a

RR 4

3 RR 2

2 1 0 0

RR 1.41 RR 1.19

3 6 9 12 Fiber input power [dBm]

RZ-Star 16QAM, intensity detection branch

Eye Opening Penalty [dB]

Eye Opening Penalty [dB]

RZ-Star 16QAM, phase detection branch

15

4

b 3

RR 1.19 RR 1.41 RR 2

2 1 RR 4

0 0

3 6 9 12 Fiber input power [dBm]

15

Fig. 7.15 Influence of the ring ratio (RR) on the SPM tolerance in the phase detection branch (a) and the intensity detection branch (b) for RZ-Star 16QAM

7.1 Nonlinear Phase Shift Compensation for Direct Detection

171

Influence of the Transmitter Configuration and the Decision Scheme A comparison of the SPM tolerances of 8DPSK and Star 16QAM for different transmitter configurations and decision techniques is depicted in Fig. 7.16a and Fig. 7.16b, respectively. TX / RX comparison 8DPSK

TX / RX comparison Star 16QAM

4 Penalty @ BER=10 [dB]

a Se. / arg NRZ Se. / IQ NRZ

3

Pa. / arg NRZ

-9

-9

Penalty @ BER=10 [dB]

4

Se. TX, arg + IQ RZ

2 Pa. / IQ NRZ

1 0 0

Pa. TX, arg + IQ RZ

3 6 9 12 Fiber input power [dBm]

15

b 3

Se. / arg NRZ

2 Pa. / arg NRZ

1 0 0

Se. / arg RZ Se. / IQ RZ

3 6 9 12 Fiber input power [dBm]

15

Fig. 7.16 Impact of the transmitter configuration and decision method on the SPM tolerances at 40 Gbit/s for direct detection for 8DPSK (a) and Star 16QAM (b)

As can be seen from Fig. 7.16a, DPSK systems with serial transmitters exhibit a worse SPM tolerance than DPSK systems with parallel transmitters. This difference appears more distinctly for NRZ. A comparison of the decision methods shows no strong differences. The SPM performance is very poor throughout all system configurations for Star 16QAM, as shown in Fig. 7.16b. The reasons for this effect and its compensation are discussed in Sect. 7.1.6.

7.1.6 Nonlinear Phase Shift Compensation Section 6.3 showed that an optical signal experiences a SPM-induced nonlinear 2 phase shift of ϕ N L (z, x, t ′ ) = −γ · le f f (z) · x(z = 0, t ′ ) = −γ · le f f (z) · PT X (t ′ ) when it propagates in a fiber (under negligence of the chromatic dispersion). Obviously, the nonlinear phase shift depends on the instantaneous fiber input power PT X (t ′ ). For DPSK formats, the power levels of the different symbols are equal (in the idealized case) and every symbol gets the same nonlinear phase shift during transmission. Since phase differences are evaluated for differential demodulation, these nonlinear phase shifts have no influence on information recovery and the determined modulation phase differences are still correct. In contrast, symbols with different power levels experience different nonlinear phase shifts for QAM formats. Therefore, the modulation phase differences are incorrect after differential detection when two consecutive symbols with different power levels are detected. This effect

172

7 Back-to-Back and Single-Span Transmission

reflects an inherent problem of optical QAM transmission that leads to performance degradation even when not taking the interaction between SPM and chromatic dispersion into account. The distortion of a RZ-Star 16QAM signal after differential detection is shown in the electrical IQ diagram on the right side of Fig. 7.17b for an average fiber input power of PT X,avg = 8 dBm after transmission over a non-dispersive fiber of length l = 80 km (le f f ≈ 21.17 km for αd B = 0.2 dB/km) with n 2 = 2.6 · 10−20 m2 /W and Ae f f = 80 · 10−12 m2
, which corresponds to a nonlinear propagation coefficient of γ = 2π f s n 2 / c Ae f f = 1.31 W−1 km−1 for f s = 193.1 THz. a 16DPSK DD

w/o SPM

w. SPM

b Star 16QAM DD

w/o SPM

w. SPM

Fig. 7.17 Effect of the SPM-induced nonlinear phase shift on differentially detected 16DPSK (a) and Star 16QAM (b) signals

The SPM-induced nonlinear phase shift has no influence on the differential detection of (idealized) DPSK signals, as can be observed from Fig. 7.17a. In the case of Star 16QAM, however, the detected symbols are positioned on three different circles after differential detection as explained in Sect. 3.2.3. It becomes apparent from the right part of Fig. 7.17b that the middle circle (corresponding to the case of detecting consecutive symbols with different power levels) is significantly corrupted by SPM-induced phase errors which are equal to the differences of the nonlinear phase shifts experienced by two consecutive symbols with different power levels. The phase distortions caused by non-zero nonlinear phase shift differences can be significantly reduced by using relatively simple compensation schemes—at least in the case of single-span transmission. When taking only SPM and attenuation into account and neglecting chromatic dispersion and any other effects disturbing the signal intensity, the intensity shape of the fiber output signal can be assumed to be equal to the one of the fiber input signal. The nonlinear phase shift can then be calculated from the instantaneous fiber output power. When the same parameter values are assumed as specified above, it holds ϕ N L (t ′ ) = −γ · le f f (z) · PT X (t ′ ) = −γ · le f f (z) · PR X (t ′ ) · 10

αd B ·l 10

≈ 1104 · PR X (t ′ ).

(7.3)

Under these simplified conditions, the phase distortions can be ideally compensated for using the fiber output signal if the fiber and system parameters are known. In practice, the compensation is not ideal because the intensity shape of the propagating signal changes along the fiber, for instance due to chromatic dispersion.

7.1 Nonlinear Phase Shift Compensation for Direct Detection

173

In Fig. 7.18, two different compensation schemes are illustrated, both of which may compensate for nonlinear phase shift. Both schemes can also be used to reduce the variance of the nonlinear phase noise. a

b

Optical compensation of NL phase shift

Electrical compensation of NL phase shift

Intensity

-

PM TS

3dB

ROTATE

In-phase Quadrature

Fig. 7.18 Schemes for compensation of the nonlinear phase shift for QAM formats. a Compensation with a phase modulator (PM) in the optical domain in front of the QAM receiver before differential detection. b Compensation in the electrical domain after differential detection.

Figure 7.18a shows a simple optical compensator, proposed in [4, 13, 18] and typically placed in front of the QAM receiver. The nonlinear phase shift is rotated back by an optical phase modulator before differential detection. The electrical driving current of the phase modulator is proportional to the fiber output power and must be adjusted according to the system parameters to ensure appropriate compensation of the accumulated nonlinear phase shift. Care has to be taken that the delays of the upper and the lower paths are equal. SPM compensation can also be accomplished in the electrical domain after differential detection as depicted in Fig. 7.18b. In this case, a corrective electrical signal proportional to the difference of the nonlinear phase shifts of two consecutive symbols is generated from the received photocurrent in the intensity detection branch and is used to rotate back the phase of the symbols received in the phase detection branch. The efficiency of the optical compensator for Star 16QAM is illustrated in Fig. 7.19. The electrical compensator exhibits nearly the same performance.

-9

Penalty @ BER=10 [dB]

4

Fig. 7.19 Enhancement of the SPM tolerance by nonlinear phase shift compensation for Star 16QAM systems with serial transmitter and arg-decision

RZ uncompensated

RZ compensated

3 2 1 0 0

NRZ uncompensated

NRZ compensated

3 6 9 12 Fiber input power [dBm]

15

174

7 Back-to-Back and Single-Span Transmission

It can be observed that the SPM tolerance can be significantly improved by compensating for the nonlinear phase shift. For NRZ, the enhancement of the SPM tolerance is smaller than for RZ, simply caused by the fact that the SPM tolerance for NRZ is worse than for RZ anyway. A comparison of Fig. 7.19 with Fig. 7.14a shows that the SPM tolerance for NRZ-Star 16QAM with compensation is even in the same range as the SPM tolerance for NRZ-8DPSK. In the case of RZ-Star 16QAM, a fiber input power which is more than 5 dB higher can be tolerated thanks to the nonlinear phase shift compensation and the same performance can be reached as for RZ-16DPSK. To better illustrate the effect of compensation, the received NRZ-Star 16QAM IQ diagrams, phase eyes and intensity eyes are depicted in Fig. 7.20 for a fiber input power of PT X,avg = 8 dBm and three different cases: without SPM (a), with SPM without compensation (b) and with SPM when using the compensation (c). Without compensation, the phase eye is completely closed due to SPM, whereas the intensity eye is only slightly distorted. By using the nonlinear phase shift compensation, the phase eye can be clearly opened and the SPM tolerance improves significantly.

a w/o SPM

b w. SPM, w/o compensation

c w. SPM, w. compensation IQ-Plot

Phase eye

Intensity eye

Fig. 7.20 Effect of nonlinear phase shift compensation for NRZ-Star 16QAM

The nonlinear phase shift compensation schemes shown in this section are quite effective for single-span transmission. But even if the chromatic dispersion is completely compensated for before nonlinear phase shift compensation, the interaction between chromatic dispersion and SPM prevents a complete compensation of the nonlinear phase shift. So there is the potential to obtain even higher performance gains with compensation techniques which better take the mutation of the signal intensity during transmission into account and more accurately estimate the nonlinear phase shift accumulated for each symbol. Potentially, compensation efficiency can be enhanced using digital equalization. The compensation of the nonlinear phase shift for multi-span long-haul transmission is discussed later on in Chap. 8.

7.1 Parameter Summary Direct Detection

175

7.1.7 Parameter Summary Table 7.2 summarizes the performance parameters of 40 Gbit/s direct detection systems, considering all high-order modulation discussed in the previous sections and NRZ / RZ pulse shapes. The OSNR requirements given in Table 7.2 are valid for the optimized receiver filter bandwidths specified in Table 7.1. The shown receiver sensitivities imply a pre-amplifier noise figure of Fd B = 3 dB and are calculated from the OSNR requirements by PR X,avg,d Bm = O S N Rd B − 58 d Bm + Fd B as described in Sect. 7.1.1. Moreover, Table 7.2 lists the laser linewidth requirements, the chromatic dispersion tolerances and the SPM tolerances. The last two parameters are specified by eye opening penalties as well as by OSNR penalties. All given parameter values are valid for direct detection systems with serial transmitter configurations and arg-decision. Table 7.2 Performance parameters of various modulation formats for direct detection at 40 Gbit/s for NRZ / RZ. The given parameter values are valid for direct detection systems with serial transmitters and arg-decision. Ph: Phase, Int: Intensity, Comp: Nonlinear phase shift compensation Modulation Format

2ASK

DBPSK

DQPSK

8DPSK

16DPSK Star 16QAM

O S N Rd B [dB] @ BER=10−4

15.2 / 14.7

12.9 / 12.1

14.8 / 13.1

19.1 / 16.8

23.8 / 21.5

19.6 / 17.3

PR X,avg,d Bm [dBm] @ BER=10−4

-39.8 / -40.3

-42.1 / -42.9

-40.2 / -41.9

-35.9 / -38.2

-31.2 / -33.5

-35.4 / -37.7

O S N Rd B [dB] @ BER=10−9

19.0 / 18.4

16.5 / 15.6

19.1 / 17.1

23.6 / 21.2

28.6 / 26.0

24.4 / 22.0

PR X,avg,d Bm [dBm] @ BER=10−9

-36.0 / -36.6

-38.5 / -39.4

-35.9 / -37.9

-31.4 / -33.8

-26.4 / -29.0

-30.6 / -33.0

1ν/r B @ Pen. 2 dB (10−4 )

-/ -

1.8e-2 / 1.6e-2

1.7e-3 / 1.6e-3

2.6e-4 / 3.2e-4

2.6e-5 / 4.5e-5

2e-4 / 2.3e-4

1ν [MHz], 40 Gbit/s, @ Pen. 2 dB (10−4 )

-/ -

720 / 640

68 / 64

10.4 / 12.8

1.0 / 1.8

8.0 / 9.2

Disp. Tol. [ps/nm] @ Pen 2 dB (10−9 )

48 / 40

64 / 35

77 / 123

111 / 205

115 / 280

114 / 290

Disp. Tol. [ps/nm] @ EOP 2 dB

86 / 37

84 / 42

118 / 151

118 / 302

118 / >320

Ph 193 / >320 Int 160 / >320

SPM Tol. [dBm] @ Pen. 2 dB (10−9 )

8.9 / 11.9

>15 / >15

10.7 / >15

6.2 / 13.8

2.9 / 11.3

4.4 / 5.5 Comp 6.5 / 11.0

SPM Tol. [dBm] @ EOP 2 dB

10.3 / 13.2

>15 / >15

12.6 / >15

9.1 / 15.0

7.4 / 13.8

Ph 6.1 / 6.0 Comp 7.8 / 11.1 Int 11.8 / 12.9

176

7 Back-to-Back and Single-Span Transmission

The migration to high-order modulation formats with more bits per symbol results in higher spectral efficiencies, higher dispersion tolerances and higher PMD tolerances (as discussed in Sect. 6.4.2). But they come along with higher OSNR requirements and worse SPM tolerances. Both are critical parameters when attainable distances of many thousand kilometers for multi-span long-haul transmission are considered. This point is further detailed in Chap. 8. The laser linewidth requirements increase with a growing number of phase states and when reducing the symbol rate. They remain above one megahertz for all shown modulation formats at 40 Gbit/s and are therefore relatively uncritical for direct detection. As regards the single-channel single-span system configurations described in this chapter, RZ features a significantly better system performance than NRZ for all system parameters discussed here (except for the linewidth requirements which are comparatively independent of the pulse shape). However, this may no longer be valid for systems where optical signals are narrowly filtered and the signal characteristics undergo a significant change, for instance in WDM systems with small channel spacings. In particular, the performance differences between NRZ and RZ become significant in systems where the serial transmitter configuration is employed. Performance differences are smaller for the parallel transmitter structure, as can be observed from the comparison of different system configurations for 8DPSK summarized in Table 7.3. Table 7.3 Comparison of different 8DPSK system configurations for direct detection at 40 Gbit/s for NRZ / RZ pulse shapes Configuration

8DPSK Se./arg

8DPSK Se./IQ

8DPSK Pa./arg

8DPSK Pa./IQ

O S N Rd B [dB] @ BER=10−4

19.1 / 16.8

19.7 / 17.5

17.8 / 16.8

18.3 / 17.5

O S N Rd B [dB] @ BER=10−9

23.4 / 21.2

24.2 / 21.9

22.3 / 21.1

22.8 / 21.8

1ν/r B @ Pen. 2 dB (10−4 )

2.6e-4 / 3.2e-4

-/ -

-/ -

2.9e-4 / 2.6e-4

1ν [MHz], 40 Gbit/s, @ Pen. 2 dB (10−4 )

10.4 / 12.8

-/ -

-/ -

11.4 / 10.5

Disp. Tol. [ps/nm] @ Pen. 2 dB (10−9 )

111 / 205

-/ -

-/ -

160 / 274

Disp. Tol. [ps/nm] @ EOP 2 dB

118 / 302

138 / 269

212 / >320

230 / 302

SPM Tol. [dBm] @ Pen. 2 dB (10−9 )

6.2 / 13.8

6.1 / 13.8

8.3 / 14.3

9.3 / 14.6

SPM Tol. [dBm] @ EOP 2 dB

9.1 / 15.0

9.0 / 14.5

10.0 / >15

10.1 / 15.0

7.2 Systems with Homodyne Differential Detection

177

Each modulation format has its own benefits and drawbacks. When evaluating the benefits of particular formats, it can be said that the application of the DBPSK format instead of 2ASK leads to an improved OSNR performance and to a significant enhancement of the SPM tolerance at almost the same chromatic dispersion tolerance. The DQPSK format seems to be a very attractive candidate for future networks. The OSNR requirements for DQPSK are still more relaxed than for 2ASK and only slightly higher than for DBPSK. However, the chromatic dispersion tolerance can be enhanced by almost a factor of four for RZ pulse shape without reducing the SPM tolerance to a great extent. When migrating to even higher-order modulation formats, the spectral efficiency and the dispersion tolerance can be further enhanced. However, this results in stricter OSNR requirements. Furthermore, SPM tolerances decrease. A comparison of the two 16-ary modulation formats discussed here—16DPSK and Star 16QAM—shows clear advantages for Star 16QAM as regards its OSNR requirements. On the other hand, the SPM tolerance of QAM formats in the phase detection branch is very poor, and a compensation of the mean nonlinear phase shift becomes necessary to avoid a significant performance degradation due to SPM.

7.2 Systems with Homodyne Differential Detection This section discusses the performance of systems with homodyne differential detection. As for direct detection, the recovery of phase information is accomplished by evaluating the phase differences of two consecutive symbols. Thus, the same modulation formats can be received and the same data recovery schemes can be employed at the receiver as for direct detection. Under certain conditions, systems with homodyne differential detection exhibit a similar or even the same performance as systems with direct detection. This can be analytically explained based on the theory presented in [16] and [14]. The coming sections present results from computer simulations. A similar behavior of systems with direct detection and homodyne differential detection is thereby identified, regarding a wide range of modulation formats. Exemplarily, systems with homodyne phase diversity receivers (see Sect. 3.4.1) are discussed. However, receivers with digital differential demodulation described in Sect. 3.4.2 show a nearly the same performance. Next, noise performances are detailed in Sect. 7.2.1—for shot-noise limited detection and amplifier noise limited detection. Afterwards, the laser linewidth requirements for homodyne differential detection are illustrated in Sect. 7.2.2. Chromatic dispersion and SPM tolerances are briefly presented by eye opening penalties in Sect. 7.2.3. In Sect. 7.2.4, the properties of systems with homodyne differential detection are summarized.

178

7 Back-to-Back and Single-Span Transmission

7.2.1 Noise Performance The traditional way of characterizing the noise performance of coherent receivers is to determine the shot-noise limits. The transmitters and receivers are directly connected as depicted in Fig. 7.21a. Amplifier noise is not present. The shot-noise is assumed to be the dominant noise source, whereas the thermal noise is neglected (which can be done for sufficiently large LO powers). However, optical transmission systems with coherent detection and optical amplification on the link or in front of the receiver are no longer shot-noise limited, but limited by the amplifier noise. Then, the dominant noise component usually is the LO-ASE noise, as discussed in Sect. 3.3.2 and shown in [3]. In the case of amplifier noise limited detection, the noise performance of coherent receivers can be characterized by the OSNR requirements in the same way as for direct detection receivers. This can be done using the setup depicted in Fig. 7.21b. a

Shot-noise limited detection (quantum limit η = 1)

Coherent RX

TX

η=1 PRX,avg

b

Amplifier-noise limited detection (with FdB = 3dB)

TX

BPF FdB = 3dB

Coherent RX Shot-noise negligible

PRX,avg OSNR (0.1nm, both polarizations)

Fig. 7.21 Characterization of the receiver noise performance for shot-noise limited homodyne detection (a) and amplifier noise limited homodyne detection (b) in the quantum limit for η = 1 and for Fd B = 3 dB; The required receiver input powers PR X,avg for a given BER are the same for both configurations when using a quadrature receiver.

For η = 1/n sp = 2/F, both configurations illustrated in Fig. 7.21 exhibit the same receiver performance and require the same power PR X,avg at the indicated points to obtain a certain BER—when using a homodyne quadrature receiver and neglecting the influence of the optical filtering in Fig. 7.21b. At first view, this is a surprise because shot-noise limited homodyne detection is known to be 3 dB superior in noise performance in comparison with homodyne detection limited by amplifier noise [3, 4]. But this is no longer valid when using a quadrature receiver, where the optical power is equally split between the in-phase and quadrature branches and the SNR degrades by 3 dB in each branch for shot-noise limited detection, leading to a performance equivalent to that of amplifier noise limited

7.2 Noise Performances for Homodyne Differential Detection

179

detection. Due to this equivalence, the OSNR requirements at the reference point behind the optical amplifier for amplifier noise limited detection can be calculated from the necessary receiver input powers PR X,avg for shot-noise limited detection by O S N Rd B = 58 dBm + PR X,avg,d Bm − Fd B with η = 2/F. The receiver sensitivities for direct detection systems are specified for Fd B = 3 dB in Table 7.2. For a fair comparison with these results, the receiver sensitivities of the homodyne receivers for amplifier noise limited detection are also specified here for Fd B = 3 dB. This corresponds to an equivalent shot-noise limited system in the quantum limit with η = 1 and a responsivity of R = 1.25 at f s = 193.1 THz. In the following paragraphs, the back-to-back receiver sensitivities at BER=10−4 , which are defined as the necessary receiver input powers PR X,avg to obtain a BER of 10−4 , are discussed by looking at the shot-noise limited case. These receiver sensitivities can easily be scaled to the OSNR requirements for the amplifier noise limited case as described in the previous paragraph. The BER versus the receiver input power for shot-noise limited detection in the quantum limit for η = 1 at 40 Gbit/s is shown in Fig. 7.22 for all considered formats, regarding NRZ (a) and RZ (b) pulse shapes. Thereby, it is assumed that third-order electrical Bessel lowpass filters are used at two different locations of the receiver depicted in Fig. 3.15. Two filters with an electrical 3 dB bandwidth of BW D M = 1.25·r S are placed behind the two outputs of the quadrature optical frontend (in front of the electronic network) in the in-phase and quadrature arms. These filters are typically used to select desired channels of WDM signals. Two more electrical filters with Bel = 0.75·r S are located in the in-phase and quadrature arms behind the electronic circuit. In the case of Star 16QAM, the receiver configuration depicted in Fig. 3.17 with amplitude detection based on direct detection is observed here. Noise performances shown in Fig. 7.22 are valid for system configurations with serial transmitters and arg-decision. 1E-2

1E-2

a Star 16QAM RR 1.65

1E-3 16DPSK

DBPSK 2ASK

1E-4

16DPSK

BER

1E-3 BER

b

2ASK 8DPSK

1E-4

8DPSK

Star 16QAM RR 1.65

DQPSK DBPSK DQPSK

1E-5 -45

NRZ

-42 -39 -36 -33 -30 Received power [dBm]

-27

1E-5 -45

RZ

-42 -39 -36 -33 -30 Received power [dBm]

-27

Fig. 7.22 BER against receiver input power for homodyne phase diversity differential detection for NRZ (a) and RZ (b) at r B = 40 Gbit/s for Bel = 0.75 · r S when employing the serial transmitter structures and arg-decision

The comparison of the receiver sensitivities for homodyne phase diversity differential detection illustrated in Fig. 7.22 with the receiver sensitivities of direct detection receivers listed in Table 7.2 shows sizable similarities. As already mentioned

180

7 Back-to-Back and Single-Span Transmission

above, this can be analytically explained based on the theory presented in [16] and [14]. Optical pre-amplified direct detection receivers are shown in [16] to be mathematically equivalent to shot-noise limited heterodyne receivers with delay demodulation for η = 1/n sp = 2/F when ignoring the amplifier noise from the orthogonal polarization. When the noise from the orthogonal polarization is included, an additional penalty of about 0.4 dB arises for direct detection [4]. Moreover, homodyne phase diversity DBPSK receivers are shown to have the same performance as heterodyne DBPSK receivers in [14]. Homodyne two-branch ASK phase diversity receivers with squarers are 0.25 dB worse than ideal ASK heterodyne detectors [14]. The results from Monte Carlo simulations presented here show that the system equivalence also holds true for the high-order formats. Small differences in the noise performances of both receiver schemes arise here due to the different filters which have been employed. Almost identical performance values can be observed for RZ, whereas for NRZ, the receiver sensitivities of the direct detection receivers are partly better because the electrical filter bandwidths have not been optimized for homodyne phase diversity differential detection. Furthermore—for shot-noise limited detection—a sensitivity degradation of about 3 dB can be detected for Star 16QAM homodyne differential detection compared with direct detection, caused by the power splitting of the signal into the phase and intensity detection branches and the smaller optical powers at the balanced detector inputs. However, this disadvantage disappears for amplifier noise limited detection and for the alternative receiver structure shown in Fig. 3.16. The optimum ring ratios for the homodyne phase diversity Star 16QAM receivers are in the same range as for the Star 16QAM direct detection receivers and correspond to a value of about 1.6. As regards the comparison of systems with different transmitter configurations and decision schemes shown in Fig. 7.23 for Star 16QAM, the same conclusions as for the direct detection receivers can be drawn. Arg-decision leads to an improved noise performance in comparison with IQ-decision due to better placed thresholds. This can be observed from the curves for RZ pulse shape in Fig. 7.23. In the case of NRZ, the worse chirp behavior of the serial transmitter neutralizes the advantage of the arg-decision scheme. TX / RX comparison Star 16QAM

1E-2 Se. / arg NRZ

1E-3 BER

Pa. / IQ NRZ

Fig. 7.23 Impact of the transmitter configuration and decision scheme on the noise performance of homodyne phase diversity receivers in the case of Star 16QAM

1E-4

Se. / arg RZ

Pa. / IQ RZ

1E-5 -37

-36 -35 -34 -33 -32 Received power [dBm]

-31

7.2 Linewidth Requirements for Homodyne Differential Detection

181

7.2.2 Laser Linewidth Requirements In the case of direct detection as well as homodyne differential detection, the differential demodulation is impaired by the laser phase noise. Whereas the linewidth of the signal laser is relevant for the differential demodulation in the optical domain for direct detection, for homodyne differential detection the beat-linewidth, which is given by the sum of the linewidths of the signal laser and the LO, is the determining parameter for the electrical differential demodulation. Thus, when assuming the same linewidths for the signal laser and the LO, the linewidth requirements on each laser are doubled. The receiver sensitivity penalties at BER=10−4 (with respect to the phase noise free system) versus the ratio of the linewidth per laser and the data rate are illustrated for all formats discussed here in Fig. 7.24. They were calculated by Monte Carlo simulations, where the 3 dB bandwidths of the electrical third-order Bessel receiver filters are assumed to be BW D M = 1.25 · r S and Bel = 0.75 · r S . For simplicity, the same linewidths are assumed for the signal laser and the LO. 4

a

Penalty @ BER=10 [dB]

3

-4

-4

Penalty @ BER=10 [dB]

4

Star 16QAM

DBPSK

2 DQPSK

16DPSK

1 0 -6 10

8DPSK NRZ -5

-4

-3

-2

-1

10 10 10 10 10 Linewidth per laser / data rate

b 3

Star 16QAM DBPSK

2 16DPSK

DQPSK

1 0 -6 10

RZ

8DPSK -5

-4

-3

-2

-1

10 10 10 10 10 Linewidth per laser / data rate

Fig. 7.24 Receiver sensitivity penalties at BER=10−4 versus the linewidth-to-data-rate ratio for homodyne phase diversity differential detection for NRZ (a) and RZ (b) pulse shapes

The laser phase noise becomes more critical with an increasing number of phase states and with a reduction of the symbol rate, just like for direct detection. The absolute values show that the requirements on the linewidth of each laser are twice as high as for the signal laser for direct detection. Nevertheless, they are still relatively relaxed, even for 8DPSK and Star 16QAM, where the linewidth per laser must be in the range of some megahertz at 40 Gbit/s. Solely for NRZ-16DPSK, the laser linewidth is required to be in the sub-MHz range at 40 Gbit/s (400 kHz for a receiver sensitivity penalty smaller than 2 dB). Again it should be borne in mind that the laser linewidth requirements become much more stringent when calling for a BER of 10−9 instead of 10−4 due to the appearance of the BER floors.

182

7 Back-to-Back and Single-Span Transmission

7.2.3 Transmission Parameter Tolerances Direct detection and homodyne phase diversity detection are both based on differential demodulation. Thus, the same signals can be received and the same data recovery techniques can be employed. When the same signals are propagated along the fiber, the received signals are equally distorted by inter-symbol interference caused by chromatic dispersion and SPM. In principle, differences in the receiver structure can lead to a different impact of these deterministic signal distortions on the system performance. As discussed in Sect. 7.2.1, based on the analysis performed in [16] and [14], direct detection receivers with optical pre-amplification have been demonstrated to be mathematically equivalent to homodyne phase diversity receivers with differential detection under certain conditions. This equivalence includes the sensitivity against deterministic signal distortions caused by chromatic dispersion and SPM. The identical sensitivity against deterministic signal distortions can be also understood from the description of the receivers given in Chap. 3. The inphase / quadrature photocurrents of the direct detection receiver and the homodyne phase diversity receiver are given by (3.35) / (3.36) and (3.79) / (3.81), respectively, the only difference between them being a constant factor. Figure 7.25 shows some simulation results for systems with homodyne phase diversity differential detection at 40 Gbit/s. These demonstrate the identical performance of systems with direct detection and homodyne differential detection in relation to chromatic dispersion (a) and SPM (b), and can be compared with Fig. 7.10d concerning the chromatic dispersion tolerances and with Fig. 7.14d with respect to the SPM tolerances. Only minor differences arise caused by the different filters used in each of the two receiver schemes.

a

2ASK, DBPSK

3 DQPSK

8DPSK

2 16DPSK

1 0 -320

Star 16QAM Phase

Star 16QAM Int.

RZ

-160 0 160 Dispersion [ps/nm]

320

Phase Diversity SPM Tolerance RZ

Eye Opening Penalty [dB]

Eye Opening Penalty [dB]

Phase Diversity CD Tolerance RZ

4

4 2ASK, Star 16QAM Int.

b 3

16DPSK

2 8DPSK

1 0 0

Star 16QAM Phase

DBPSK, DQPSK

RZ

3 6 9 12 Fiber input power [dBm]

15

Fig. 7.25 Chromatic dispersion tolerances (a) and SPM tolerances (b) of various modulation formats at 40 Gbit/s for homodyne phase diversity differential detection and RZ pulse shape.

By the way, the same compensators as for direct detection (see Sect. 7.1.6) can be used to compensate for the mean nonlinear phase shift and to improve the poor SPM tolerance of QAM formats.

7.2 Parameter Summary Homodyne Differential Detection

183

7.2.4 Parameter Summary In Table 7.4, some performance parameters of 40 Gbit/s systems with homodyne phase diversity differential detection are summarized, regarding all high-order modulation formats discussed in the previous sections and NRZ / RZ pulse shapes. The given parameter values imply the application of the serial transmitter configurations, as well as arg-decision at the receiver. Table 7.4 Performance parameters of various modulation formats for homodyne phase diversity differential detection at 40 Gbit/s for NRZ / RZ. The given parameter values are valid for systems with serial transmitters, arg-decision and Bel = 0.75·r S . Ph: Phase, Int: Intensity, Comp: Nonlinear phase shift compensation Modulation Format

2ASK

DBPSK

DQPSK

8DPSK

16DPSK Star 16QAM

PR X,avg,d Bm [dBm] @ BER=10−4

-38.7 / -40.5

-41.5 / -43.1

-39.8 / -41.8

-35.4 / -38.2

-27.2 / -33.5

-31.4 / -34.4

O S N Rd B [dB] @ BER=10−4

16.3 / 14.5

13.5 / 11.9

15.2 / 13.2

19.6 / 16.8

27.8 / 21.5

20.6 / 17.6

1ν/r B @ Pen. 2 dB (10−4 )

-/ -

8e-3 / 7.8e-3

8.4e-4 / 8.6e-4

1.2e-4 / 1.5e-4

1e-5 / 2.9e-5

7.6e-5 / 1.3e-4

1ν [MHz], 40 Gbit/s, @ Pen. 2 dB (10−4 )

-/ -

320 / 312

33.6 / 34.4

5.0 / 6.0

0.4 / 1.2

3.0 / 5.2

Disp. Tol. [ps/nm] @ EOP 2 dB

87 / 39

86 / 43

124 / 156

124 / 316

150 / >320

Ph 222 / >320 Int 168 / >320

SPM Tol. [dBm] @ EOP 2 dB

10.4 / 13.1

>15 / >15

13.0 / >15

10.0 / 15.0

8.6 / 13.8

Ph 6.4 / 5.8 Comp 8.5 / 11.1 Int 11.8 / 12.8

Systems with homodyne differential detection are very similar in terms of performance to systems with direct detection. This similarity becomes apparent after a comparison of Table 7.4 with Table 7.2. The values for PR X,avg,d Bm in Table 7.4 specify the receiver sensitivities at BER=10−4 for shot-noise limited detection in the quantum limit with η = 1. These are equivalent to the required receiver input powers for amplifier noise limited detection with Fd B = 3 dB when a quadrature receiver is used. Therefore, the OSNR requirements for obtaining a BER of 10−4 for amplifier noise limited detection, given in the third row of Table 7.4, can be calculated from the receiver sensitivities for shot-noise limited detection by O S N Rd B = 55 dBm + PR X,avg,d Bm . In the case of shot-noise limited detection, a 3 dB poorer receiver sensitivity compared with direct detection can be observed for Star 16QAM caused by the optical power splitting before photo-detection within the receiver illustrated in Fig. 3.17. This disadvantage disappears in the case of amplifier noise limited detection or when the receiver structure shown in Fig. 3.16 is used instead.

184

7 Back-to-Back and Single-Span Transmission

The linewidth requirements listed in Table 7.4 correspond to a receiver sensitivity penalty of 2 dB at BER=10−4 . They would be more stringent at BER=10−9 . The linewidth requirements on each laser are doubled compared with direct detection when the same linewidths are assumed for the signal laser and the LO, since the effective phase noise taking effect on the electrical differential demodulation process is determined by the beat-linewidth. The transmission parameter tolerances are specified here by the eye opening penalties and are almost identical with direct detection. Minor differences to systems with direct detection only arise here due to the use of different filters in each of the two receiver schemes. A performance comparison of two different 8DPSK system configurations with homodyne phase diversity differential detection is presented in Table 7.5. The same conclusions can be drawn as for direct detection. Arg-decision leads to a receiver sensitivity improvement compared with IQ-decision. Systems with a parallel transmitter outperform systems with a serial transmitter in relation to the noise performances and the dispersion and SPM tolerances for NRZ. Table 7.5 Comparison of different 8DPSK system configurations for homodyne phase diversity differential detection at 40 Gbit/s for NRZ / RZ pulse shapes Configuration

8DPSK Se./arg

8DPSK Pa./IQ

PR X,avg,d Bm [dBm] @ BER=10−4

-35.4 / -38.2

-35.9 / -37.4

O S N Rd B [dB] @ BER=10−4

19.6 / 16.8

19.1 / 17.6

1.2e-4 / 1.5e-4

1.3e-4 / 1.5e-4

5.0 / 6.0

5.2 / 6.0

Disp. Tol. [ps/nm] @ EOP 2 dB

124 / 316

246 / 307

SPM Tol. [dBm] @ EOP 2 dB

10.0 / 15.0

10.6 / 15.0

1ν/r B @

Pen. 2 dB (10−4 )

1ν [MHz], 40 Gbit/s, @ Pen. 2 dB

(10−4 )

The benefits and drawbacks of particular modulation formats were already discussed for the direct detection receivers in Sect. 7.1.7 and are also true for homodyne differential detection. Since systems with direct detection and homodyne differential detection exhibit very similar performances, the question may arise of which system should be used. At this point, general considerations comparing systems with direct and coherent detection come into play. Systems with direct detection do not require a LO and frequency synchronization. On the other hand, coherent detection offers enhanced possibilities for electronic equalization and allows the selection of WDM channels with high selectivity using a tunable LO.

7.3 Noise Performances for Homodyne Synchronous Detection

185

7.3 Systems with Homodyne Synchronous Detection This section describes the performance of systems with homodyne synchronous detection in the case that receivers with digital phase estimation according to Sect. 3.5.3 are used. A wide range of modulation formats is regarded. Since arbitrary modulation formats can be received with those receivers, the Square 16QAM and the Square 64QAM are additionally included in the discussion. The receiver sensitivities at BER=10−4 for the shot-noise limited case and the OSNR requirements for the amplifier noise limited case are presented in Sect. 7.3.1, assuming an ideal carrier recovery. In the same section, a performance comparison is carried out for the different Square 16QAM transmitters which are described in Sect. 2.6. A special focus is laid on the laser linewidth requirements for homodyne phase estimation receivers. These are characterized by the receiver sensitivity penalties at BER=10−4 and illustrated in Sect. 7.3.2, considering the phase estimation schemes described in Sect. 3.5.3. Besides, the impact of the block length on the phase noise requirements is shown. Subsequently, the influence of chromatic dispersion and SPM on the performance of systems with homodyne synchronous detection is detailed in Sect. 7.3.3 and Sect. 7.3.4, respectively. Section 7.3.5 demonstrates that the SPM-induced nonlinear phase shift leads to drastic distortions of the QAM signal constellations and highlights improvement of the SPM performance by nonlinear phase shift compensation for Star 16QAM, Square 16QAM and Square 64QAM. In Sect. 7.3.6, systems with homodyne synchronous detection are finally discussed and the most important performance parameters are summarized.

7.3.1 Noise Performance The noise performance of homodyne receivers with digital phase estimation at a data rate of r B = 40 Gbit/s is illustrated for a wide range of formats in Fig. 7.26. 1E-2

1E-2

a Star 16QAM RR 1.8 QPSK

1E-4

RZ

1E-3 16PSK

8PSK

1E-4

8PSK Square 16QAM

BER

BER

1E-3

b

NRZ

Square 64QAM

1E-5 -46 -44 -42 -40 -38 -36 -34 -32 Received power [dBm]

Square 16QAM QPSK

Star 16QAM RR 1.8

16PSK

Square 64QAM

1E-5 -46 -44 -42 -40 -38 -36 -34 -32 Received power [dBm]

Fig. 7.26 BER against received power for homodyne receivers with digital phase estimation for NRZ (a) and RZ (b) at r B = 40 Gbit/s for Bel = 0.75 · r S and shot-noise limited detection in the quantum limit with η = 1, when assuming serial transmitters and ideal carrier synchronization

186

7 Back-to-Back and Single-Span Transmission

The curves in Fig. 7.26 assume shot-noise limited detection in the quantum limit with η = 1 and an ideal carrier synchronization, as well as the use of serial transmitter configurations, arg-decision for MPSK / Star QAM formats and IQ-decision for Square QAM formats. One of the advantages of homodyne synchronous detection compared with direct detection and homodyne differential detection is its superior noise performance. From the theory, a performance gain of 0.5 dB / 2.3 dB / 3 dB / 3 dB can be expected for synchronously detected BPSK / QPSK / 8PSK / 16PSK in comparison with differentially detected DBPSK / DQPSK / 8DPSK / 16DPSK, respectively [6, 11, 17]. The comparison of Fig. 7.26 with the receiver sensitivities for direct detection and homodyne differential detection listed in Table 7.2 and Table 7.4, respectively, shows a performance difference of a little less than usually obtained when comparing synchronous and differential detection. The reason for this is the differential coding used to resolve the phase ambiguity of the digital phase estimation. The “differentially encoded MPSK” (DEMPSK)—as it is often referred to—can not achieve the performance limits of the ideal synchronous MPSK and leads to a penalty of about 0.5 dB [2, 17]. A further sensitivity degradation, which is not considered in Fig. 7.26, must be borne in mind for including the phase estimation in the receiver performance. As shown in Sect. 7.3.2, this penalty is caused if the laser phase noise necessitates an averaging over small block lengths. In that case, the noise performance improvement of homodyne synchronous phase estimation receivers compared with differential detection receivers is relatively small. On the other hand, Square QAM formats exhibit the best noise performance for a given number of bits per symbol and can only be detected conveniently by synchronous detection. The noise performance of RZ-Square 16QAM is in the same range as for RZ-8PSK. RZ-Square 64QAM shows nearly the same performance as RZ-16PSK. Moreover, it should be noted that Fig. 7.26 implies the use of electrical thirdorder Bessel filters with a 3 dB bandwidth of Bel = 0.75 · r S , conjointly defined for all formats. These are located in the in-phase and quadrature arms behind the outputs of the balanced detectors. Especially for NRZ and some high-order formats, performance can be improved by optimizing the receiver filter bandwidths. The noise performances presented here are the results of numerical calculations and characterize specific system configurations under consideration of the transmitter setups, filtering, data recovery and signal shape. In Appendix B, they are compared with results calculated using theoretical BER formulas, well known from the literature [4, 11, 17] and reflecting the matched filtering case. As described in Sect. 7.2.1, receiver sensitivities for the shot-noise limited case can be easily scaled to the OSNR requirements for the amplifier noise limited case by O S N Rd B = PR X,avg,d Bm + 55 dBm when a pre-amplifier noise figure of Fd B = 3 dB and the use of a quadrature receiver are assumed. However, this relation becomes imprecise when an optical filter is included into the system, located behind the optical pre-amplifier in front of the optical quadrature frontend. Figure 7.27 illustrates the OSNR requirements for amplifier noise limited detection if an optical receiver filter with Bopt = 2.5 · r S is additionally considered.

7.3 Noise Performances for Homodyne Synchronous Detection 1E-2

187

1E-2

a

NRZ

1E-3 Square 16QAM

1E-4

QPSK

Star 16QAM RR 1.8

8PSK

BER

BER

1E-3

16PSK

Star 16QAM RR 1.8

8PSK

RZ

b

1E-4

Square 16QAM

Square 64QAM 16PSK

Square 64QAM QPSK

1E-5 10

12

14

16 18 20 OSNR [dB]

22

24

1E-5 10

12

14

16 18 20 OSNR [dB]

22

24

Fig. 7.27 OSNR requirements at r B =40 Gbit/s for homodyne phase estimation receivers, amplifier noise limited detection, Bopt = 2.5 · r S and Bel = 0.75 · r S , assuming the use of serial transmitters and an ideal carrier synchronization. a NRZ. b RZ.

From Fig. 7.26 and 7.27, a performance improvement can be observed for most formats when employing an optical receiver filter with a 3 dB bandwidth of Bopt = 2.5 · r S . The required OSNR for BER=10−4 for NRZ-8PSK without optical filtering can be calculated by O S N Rd B = −38.1 dBm + 55 dBm=16.9 dB and is decreased to 16.1 dB by the optical filtering, for instance. However, the OSNR performance degrades when the optical filter bandwidth is not appropriately adapted to the modulation format used, as shown here for Square 64QAM (20.0 dB / 18.6 dB without optical filtering in comparison with 21.7 dB / 20.7 dB with optical filtering for NRZ / RZ). Ideally, the optical and electrical filter bandwidths should be optimized for each format individually to obtain the best OSNR performances, in the same way as discussed for the direct detection receivers in Sect. 7.1.2.

Optimum Star 16QAM Ring Ratio / Square 16QAM Transmitter Comparison The optimum ring ratio for Star 16QAM in the case of homodyne synchronous detection corresponds to a value of about 1.8. This becomes apparent from Fig. 7.28a. In contrast to direct detection, where the Star 16QAM constellation comprises three different rings after differential detection and the noise power depends on the symbol amplitude, the optimum ring ratio can be easily understood for coherent synchronous detection. If the amplitude of the outer circle is normalized to one, the amplitude of the inner circle is given by 1/R R, so the Euclidean distance between the two rings—relevant for the error probability of amplitude decision—is given by d1 = 1 − 1/R R. By adopting simple geometry, the Euclidean distance between two p √ symbols on the inner ring can be shown to be d2 = 2 − 2/R R. Best overall BER performance is obtained for equal error probabilities for phase and amplitude decision, occurring for d1 = d2 . From this condition, an optimum ring ratio of R R ≈ 1.77 can easily be derived. Figure 7.28b illustrates the impact of the transmitter configuration on the noise performance for Square 16QAM systems. All transmitters exhibit nearly the same

188

7 Back-to-Back and Single-Span Transmission Optimal Star 16QAM Ring Ratio

TX Comparison Square 16QAM

1E-2

1E-2

a

b Star 16QAM NRZ @ PRX = -37dBm

1E-3 BER

BER

1E-3

Serial + Enhanced IQ + Tandem QPSK, NRZ

1E-4

Conv. IQ, NRZ

1E-4 All TX, RZ

1E-5 1,5

Star 16QAM RZ @ PRX = -39dBm

Se. / arg

1,6

1,7

1,8 1,9 2,0 Ring ratio

2,1

2,2

1E-5 -43 -42 -41 -40 -39 -38 -37 -36 -35 Received Power [dBm]

Fig. 7.28 a Optimal Star 16QAM ring ratio for homodyne synchronous detection. b Impact of the transmitter configuration on the noise performance for Square 16QAM.

performance for RZ. The conventional IQ transmitter shows a performance improved by 1 dB compared with the serial / enhanced IQ / Tandem-QPSK transmitters for NRZ. This is attributable primarily to the higher peak-to-average power ratio.

7.3.2 Laser Linewidth Requirements This section discusses the laser linewidth requirements of systems with homodyne phase estimation receivers for shot-noise limited back-to-back transmission. Thereby, the feed forward (FF) M-th power block scheme and the closed loop (CL) M-th power block scheme (both described in Sect. 3.5.3) are considered, as well as different averaging schemes denoted as field averaging, normalized field averaging and argument averaging and defined by (3.96), (3.99) and (3.103), respectively. As a quality criterion, the receiver sensitivity penalty at BER=10−4 is used, where the receiver input powers required for the phase noise free systems without phase estimation are taken as power references. The linewidth requirements are specified by the linewidth per laser and assume the same linewidths for the signal laser and the LO, so that the required beat-linewidths 1νe f f = 1νs + 1νlo can be easily obtained by doubling the given values. Bessel low-pass filters with a 3 dB bandwidth of Bel = 0.75 · r S are located in the in-phase and quadrature arms of the receiver. Comparison of Different Phase Estimation Schemes for NRZ-QPSK In Fig. 7.29, different phase estimation schemes are compared for NRZ-QPSK and a block length of N = 8. The curves for the closed loop scheme are shown for the limit of zero processing delay with D = 1. It can be observed that normalized field averaging, where the amplitudes of the phasors are normalized to one before being summed, shows a slightly better performance than field averaging, since the

7.3 Linewidth Requirements for Homodyne Synchronous Detection Fig. 7.29 Comparison of different phase estimation concepts for NRZ-QPSK at r B = 40 Gbit/s, assuming a block length of N = 8 and zero processing delay (D = 1)

189

CL no proc. delay Arg averaging

-4

Penalty @ BER=10 [dB]

3

2 FF + CL no proc. delay Field averaging

1 FF + CL no proc. delay Norm. field averaging

0 0

2 4 6 8 Linewidth per laser [MHz]

10

phase error is estimated more accurately. It can be expected that this performance difference is even higher when the signals are additionally distorted by inter-symbol interference caused by fiber propagation effects. Compared with field averaging, argument averaging exhibits an improved performance for smaller linewidths. On the other hand, the receiver performance degrades faster for higher linewidths. For zero processing delay, the CL scheme performs identically to the FF scheme when the same averaging mechanism is employed. When considering practical implementation, however, the accumulated phase error (which should be available from the last block for the calculation of the phase error of the current block in the ideal case) is only available after a processing delay of D block lengths for the CL scheme. The processing delay has an effect comparable to the loop delay in optical phase locked loops and leads to a drastic reduction of the phase noise tolerance. For NRZ-QPSK this is shown for field averaging in Fig. 7.30a and for argument averaging in Fig. 7.30b. 3

a

Penalty @ BER=10 [dB]

CL, field averaging

b

2

1

0 0

Proc. delay 8ns Proc. delay 4ns

Proc. delay 2ns

0,2 0,4 0,6 0,8 1,0 Linewidth per laser [MHz]

1,2

CL, arg averaging Proc. delay 8ns

-4

-4

Penalty @ BER=10 [dB]

3

2 Proc. delay 4ns

1

0 0

Proc. delay 2ns

0,2 0,4 0,6 0,8 1,0 Linewidth per laser [MHz]

1,2

Fig. 7.30 Degradation of the phase noise tolerance due to the processing delay for NRZ-QPSK at r B = 40 Gbit/s for the M-th power CL block scheme, a block length of N = 8 and processing delays of 2 ns (D = 5), 4 ns (D = 10) and 8 ns (D = 20). a Field averaging. b Argument averaging.

At 40 Gbit/s, the duration of a QPSK symbol is TS = 50 ps and the block duration is 400 ps for N = 8, so that processing delays of 2 ns / 4 ns / 8 ns correspond to

190

7 Back-to-Back and Single-Span Transmission

D = 5 / 10 / 20 blocks, respectively. The crucial influence of the processing delay on the performance of the CL scheme is clarified by comparing the linewidth requirements for a receiver sensitivity penalty of 2 dB at BER=10−4 for zero processing delay, shown in Fig. 7.29, with the diagrams of Fig. 7.30. For zero processing delay, the linewidths required for NRZ-QPSK are about 6 MHz and 10 MHz for argument averaging and field averaging, respectively. When taking loop delay into account, the linewidth requirements increase drastically to 1070 kHz / 470 kHz / 270 kHz for field averaging and to 1320 kHz / 550 kHz / 260 kHz for argument averaging for processing delays of 2 ns / 4 ns / 8 ns, respectively. For comparison, the linewidths required for a receiver sensitivity penalty of 1 dB at BER=10−10 of QPSK receivers with OPLL, derived in [9] and listed in Table 3.1, are 3.86 MHz for zero loop delay and 143 kHz / 72 kHz / 36 kHz for loop delays of 2 ns / 4 ns / 8 ns, respectively. When considering the higher BER reference of 10−10 and the lower penalty reference of 1 dB, the requirements are in a comparable range. Therefore, higher phase noise tolerances—compared with receivers with OPLL—can only be achieved using digital phase estimation receivers when feed forward schemes are used for phase estimation or processing delay can be kept small.

Linewidth Requirements for the Feed Forward M-th Power Block Scheme The contour plots in Fig. 7.31 show the receiver sensitivity penalties at BER=10−4 with respect to the linewidth per laser and the block length N at 40 Gbit/s for the feed forward M-th power block scheme, regarding NRZ and RZ pulse shapes and a wide range of modulation formats. Field averaging according to (3.96) is assumed to be used for the MPSK formats, whereas normalized field averaging according to (3.99) is applied to Star 16QAM because phasors with different amplitudes are averaged. As described in Sect. 3.5.3, a class partitioning is performed for the Square QAM formats before the phase error estimate is calculated by (3.101). All the Class I symbols are used for phase error estimation in the case of Square 16QAM, but only the eight symbols on the inner and outer rings are used for the calculation of the phase error estimate in the case of Square 64QAM. The block lengths are varied in steps of 2n (n = 0, 1, 2, ..). Obviously, a certain minimum block length is necessary to obtain a satisfactory performance. For the PSK formats, block lengths of at least four are required for receiver sensitivity penalties smaller than 2 dB, even for zero linewidth. When implying the phase estimation scheme with class partitioning considered here, significantly higher block lengths are needed for Square QAM formats, since only a part of the symbols of each block are used for determination of the phase error estimate. For block lengths of 32 and 512, the penalty is still greater than 2 dB for Square 16QAM and Square 64QAM, respectively. For zero linewidth, the receiver performance can be improved almost up to the limit of ideal carrier recovery when increasing the block length towards infinity. With increasing linewidth, the optimum block lengths are getting smaller because they are determined by a trade-off between the shot-noise (or amplifier noise) and the phase noise.

7.3 Linewidth Requirements for Homodyne Synchronous Detection QPSK Se. TX, NRZ

8PSK Se. / arg, NRZ

32

4

20 1.5

1

3 2.5

12

2

8

1.5

1

2

2

3

2

16

0.5

4

5

6

7

8

1

8

0.2

QPSK Se. TX, RZ

Block Length N

4

3

1.5

12 8

1.5

1 1.5

4 1

2

3

4

5

2

7

2.5

20

1

16

8

2

0.5 1.5

12 8

1 1.5 2.5

0.2

0.4

0.6

Star 16QAM Se. / arg, NRZ

0.8

4

Block Length N

2 1

1.5

12 8

0.5

192 5 2.5

128

1

0.2

1.5

64 2.5

0.4

0.6

0.8

1 0

1

1.5

8

1.5

1.5 2 2.5

50

100

3.5 4

2

2.5

3

3

3072

1

4

3 2.5 1.5

1024

2

50

2 3

4 5

100

150

1 0

200

500

1000

Square 64QAM Conv. IQ, RZ 4096

1.5

0.5

3

128

0.4

1.5 2.5

1.5

0.2

2.5

1

64

1

4 1 0

1

192

0.6

2

0.8

Linewidth per laser [MHz]

1

1 0

5

4 3.5

2 3

Block Length N

Block Length N

Block Length N

2

12 8

2000

0.5

5 4.5

2.5 0.5

1500

Linewidth per laser [Hz]

0.5

3

16

200

3.5

2048

3.5

Square 16QAM Conv. IQ, RZ

4

1

150

4.5

3.5

20

3

Square 64QAM Conv. IQ, NRZ

256

4.5

24

2

12

Linewidth per laser [kHz]

Star 16QAM Se. / arg, RZ 28

1

5

Linewidth per laser [MHz]

32

4.5

3

1.5

1.5

2

2.5

16

4096

1

4

3

20

5

2.5

16

4 3.5

0.5

3

20

200

Linewidth per laser [kHz]

Square 16QAM Conv. IQ, NRZ

3.5

24

150

4.5

1 0

1

256 4.5

100

24

Linewidth per laser [MHz]

32

3

5

50

4

2

1 0

9 10

2.5

28

3

Linewidth per laser [MHz]

28

2

16PSK Se. / arg, RZ

3.5

4

2

6

2

8

32

4

24

2.5

1.5

Linewidth per laser [kHz]

Block Length N

Block Length N

2.5

1 0.5

3

12

0.6

28

5

4.5

20

1.5

8PSK Se. / arg, RZ

24 3.5

3.5

1 0

1

4

2

16 1

4 0.8

4.5

20

2.5

32

28

Block Length N

0.4

24

Linewidth per laser [MHz]

32

1 0

1.5

1.5 2

3

1 0

9 10

1.5

12

Linewidth per laser [MHz]

1 0

1

4

2.5

1

2.5

20

1.5

4

5

3

Block Length N

16 0.5

28

3.5

24

Block Length N

Block Length N

Block Length N

32

28 2.5

24

16

16PSK Se. / arg, NRZ

32

28

1 0

191

4.5

2.5

3

100

1 4 3.5

2048 3

1.5

1024

2

2.5

1000

1500

2

3

3 3.5

4

5

50

3072

150

Linewidth per laser [kHz]

200

1 0

500

5

2000

Linewidth per laser [Hz]

Fig. 7.31 Receiver sensitivity penalties at BER=10−4 versus the linewidth per laser and the block length N for homodyne phase estimation receivers employing the feed forward M-th power block scheme at r B = 40 Gbit/s, for various modulation formats and NRZ and RZ pulse shapes

192

7 Back-to-Back and Single-Span Transmission

For accepting a receiver sensitivity penalty of 2 dB at BER=10−4 and searching for the block length with the greatest linewidth tolerable, the optimal block lengths in steps of 2n (n = 0, 1, 2, ..) are N = 8 for the PSK formats and Star 16QAM, N = 64 for Square 16QAM and N = 1024 for Square 64QAM. For a clearer illustration, the receiver sensitivity penalties at BER=10−4 versus the linewidth per laser are illustrated for selected block lengths in Fig. 7.32, exemplarily for NRZ8PSK (a) and RZ-Square 16QAM (b). NRZ-8PSK linewidth requirements

RZ-Square 16QAM linewidth requirements

4

a

N=16

2

-4

3

Penalty @ BER=10 [dB]

-4

Penalty @ BER=10 [dB]

4

N=4 N=8

1 FF, field averaging

0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 Linewidth per laser [MHz]

b

N=128

3 N=32

2

N=64

1 FF, norm. field averaging

0 0

50 100 150 200 Linewidth per laser [kHz]

250

Fig. 7.32 Receiver sensitivity penalties at BER=10−4 versus the linewidth per laser for selected block lengths N at r B = 40 Gbit/s, when employing the FF M-th power block scheme, illustrated for NRZ-8PSK (a) and RZ-Square 16QAM (b)

Higher block lengths should be used when the linewidth requirements for a particular modulation format can easily be fulfilled. However, smaller block lengths are necessary to achieve a better system performance when the laser phase noise becomes a critical parameter. For RZ-Square 16QAM, for instance, a receiver sensitivity penalty of about 1 dB can be obtained with lasers possessing a linewidth in the 50 kHz range by choosing N = 128. However, if the laser linewidths are around 100 kHz, a block length of N = 64 is the appropriate choice to obtain the best performance. As already discussed in Sect. 7.3.1, the penalty caused by the phase estimation degrades the overall receiver performance and reduces the performance gain of synchronous detection compared with differential detection. As mentioned above, the optimal block lengths are specified here in steps of just 2n (n = 0, 1, 2, ..) and the term “optimal block length” is defined here by the block length allowing for the greatest tolerable linewidth at a receiver sensitivity penalty of 2 dB for the phase estimation. In this context, the optimal block lengths are N = 8 for the MPSK formats and for Star 16QAM, N = 64 for Square 16QAM and N = 1024 for Square 64QAM. The receiver sensitivity penalties versus the linewidth per laser to data rate ratio for optimal block lengths—calculated with Monte Carlo simulations— are summarized for all modulation formats discussed here in Fig. 7.33 for NRZ (a) and RZ (b) pulse shapes. The comparison of the modulation formats shows that the linewidth requirements increase with an increasing number of phase states. In spite of having a

7.3 Linewidth Requirements for Homodyne Synchronous Detection Penalty @ BER=10 [dB]

3

a

QPSK

2

1

16PSK Square 16QAM 8PSK Star 16QAM

0 -8 10

-7

b

QPSK Square 16QAM

-4

Square 64QAM

-4

Penalty @ BER=10 [dB]

3

193

NRZ, FF field averaging -6

-5

-4

-3

10 10 10 10 10 Linewidth per laser / data rate

2 Square 64QAM

1

16PSK 8PSK Star 16QAM

0 -8 10

-7

RZ, FF field averaging -6

-5

-4

-3

10 10 10 10 10 Linewidth per laser / data rate

Fig. 7.33 Receiver sensitivity penalties at BER=10−4 versus the linewidth-to-data-rate ratio for homodyne receivers with feed forward M-th power digital phase estimation and field averaging (PSK) / normalized field averaging (Star 16QAM, Square QAM), for optimal block lengths and NRZ (a) and RZ (b) pulse shapes

smaller symbol rate, the Star 16QAM exhibits the same performance as the 8PSK in Fig. 7.33 because normalized field averaging is assumed to be used here only for QAM formats, leading to a slight performance improvement compared with field averaging as illustrated in Fig. 7.29 for QPSK. When the feed forward phase estimation algorithm based on class partitioning described in Sect. 3.5.3 is implemented, the Square QAM formats require lower linewidths for a certain number of bits per symbol due to the higher block lengths necessary. For instance, the phase distances for 16PSK (22.5◦ ) are smaller than the smallest phase distance for Square 16QAM (26.6◦ ), but the RZ-Square 16QAM is nevertheless more phase noise sensitive than the RZ-16PSK, since larger block lengths are needed. The previous paragraphs have shown that—for current data rates—the laser phase noise becomes a critical parameter for 16PSK, Square 16QAM and Square 64QAM, even when employing the feed forward M-th power block scheme which is not impaired by processing delay. Square QAM formats in particular require low linewidths when only some of the symbols are used for calculation of the phase error estimate. The laser linewidths must be in the range of 240 kHz / 120 kHz / 1 kHz for RZ-16PSK / RZ-Square 16QAM / RZ-Square 64QAM at 40 Gbit/s. These requirements can be fulfilled with high-spec lasers for the lab, but not with lasers currently available for commercial use. The Star 16QAM features the most relaxed phase noise requirements of the 16-level formats. These are around 1 MHz at 40 Gbit/s. To enable a commercial application of modulation formats such as the Square 16QAM or the 16PSK, the development of commercial lasers with linewidths in the range of 100 kHz is necessary or else more sophisticated phase estimation schemes must be adopted. The linewidth requirements for Square QAM formats can possibly be relaxed by the application of decision directed techniques [5], or by the use of enhanced feed forward algorithms which allow to incorporate all constellation points into the calculation of the phase error estimate [8, 12]. Moreover, it should be noted that the optimal block lengths shown here are valid for the back-to-back case, considering only the trade-off between shot-noise and

194

7 Back-to-Back and Single-Span Transmission

phase noise effects. In practical transmission systems, fiber degradation effects such as XPM necessitate a further optimization of phase estimation block lengths.

7.3.3 Chromatic Dispersion Tolerances

-4

a 3 QPSK, 8PSK, 16PSK, Square 16QAM

2

Square 64QAM

0

NRZ

-320

Eye Opening Penalty [dB]

Star 16QAM

1

-160 0 160 Dispersion [ps/nm]

320

4

c

Square 16QAM

3 QPSK

8PSK, 16PSK

2 1

Penalty @ BER=10 [dB]

4

Star 16QAM, Int.+Ph. Square 64QAM

0 -320

NRZ

-160 0 160 Dispersion [ps/nm]

320

4

b 3 QPSK

2 Square 64QAM

1

16PSK, Square 16QAM, Star 16QAM

0

8PSK

RZ

-320

Eye Opening Penalty [dB]

-4

Penalty @ BER=10 [dB]

Next, the chromatic dispersion tolerances of optical fiber transmission systems with homodyne phase estimation receivers are discussed, provided that no electrical dispersion compensation is implemented at the receiver. They are specified here by the receiver sensitivity penalties at BER=10−4 , assuming digital phase estimation with the optimum block lengths for back-to-back highlighted in Sect. 7.3.2, as well as by the eye opening penalties for ideal carrier synchronization. In Fig. 7.34, chromatic dispersion tolerances at r B = 40 Gbit/s are shown for a wide range of formats. The diagrams imply the use of serial structures at the transmitter and the use of electrical Bessel filters with 3 dB bandwidths Bel = 0.75 · r S at the receiver.

-160 0 160 Dispersion [ps/nm]

320

4

d 3 QPSK

2 Square 64QAM

16PSK, Square 16QAM, Star 16QAM

8PSK

1 0 -320

RZ

-160 0 160 Dispersion [ps/nm]

320

Fig. 7.34 Chromatic dispersion tolerances for systems with homodyne detection and digital phase estimation at r B = 40 Gbit/s when using the serial transmitter structures; The two upper diagrams show the receiver sensitivity penalties at BER=10−4 against the chromatic dispersion for NRZ (a) and RZ (b) when employing digital phase estimation with the optimal block lengths. The bottom diagrams (c, d) illustrate the eye opening penalties for ideal carrier synchronization.

7.3 Dispersion Tolerances for Homodyne Synchronous Detection

195

The receiver sensitivity penalties at BER=10−4 and the eye opening penalties show very similar results, so the EOP can be used as a good first performance criterion when MC simulations with high computational effort must be avoided. A comparison of the eye opening penalties discovered here with the eye opening penalties for differential detection listed in Table 7.2 and Table 7.4 indicates slightly higher dispersion tolerances for homodyne synchronous detection. In the same way as for differential detection, the dispersion tolerances for RZ increase with the order of the modulation format due to the smaller symbol rates and reduced spectral widths. In the case of NRZ, the detrimental chirp characteristics neutralize the advantage of the reduced spectral widths for the high-order formats, especially when serial transmitter configurations are employed. RZ signals are less distorted by chromatic dispersion than NRZ signals. This difference becomes significant for high-order formats in particular. For Square 64QAM, the curves in Fig. 7.34 are shown for the conventional IQ transmitter and the performance would be worse for NRZ if a serial transmitter structure was used.

Influence of the Transmitter Configuration for Square 16QAM The impact of the configuration of the transmitter on the chromatic dispersion tolerance is illustrated in Fig. 7.35 for some of the Square 16QAM transmitters introduced in Sect. 2.6.

-4

Penalty @ BER=10 [dB]

TX comparison Square 16QAM

Fig. 7.35 Impact of the transmitter configuration on the chromatic dispersion tolerance for Square 16QAM at r B = 40 Gbit/s

4 3

Serial + Enhanced IQ + Tandem QPSK, NRZ

2 Conv. IQ, NRZ

1 All TX, RZ

0 -320

-160 0 160 Dispersion [ps/nm]

320

All transmitter types show nearly the same performance for RZ. For NRZ, the usage of the conventional IQ transmitter significantly improves the dispersion tolerance in comparison with the serial transmitter, the enhanced IQ transmitter and the Tandem-QPSK transmitter. This could be expected as a result of the discussion of signal properties in Sect. 2.6.7. The product of the chirp and the normalized intensity was shown to be small there for the conventional IQ transmitter. For the other configurations, chirp appears simultaneously with high power levels and leads to a higher influence of chromatic dispersion.

196

7 Back-to-Back and Single-Span Transmission

Vivid Illustration of the Chromatic Dispersion on Signal Shape A vivid illustration of the impact of the chromatic dispersion on the signal quality of optical high-order modulation signals is provided in Fig. 7.36 and Fig. 7.37. Dispersion 0ps/nm Original IQ-Plot

Ideal in-phase eye

Dispersion 320ps/nm IQ-Plot before PE

IQ-Plot after PE+LPF

In-phase eye after PE+LPF

QPSK Pa./IQ NRZ

QPSK Se./IQ NRZ

QPSK Se./IQ RZ

8PSK Se./arg NRZ

8PSK Se./arg RZ

16PSK Se./arg NRZ

16PSK Se./arg RZ

Fig. 7.36 Impact of chromatic dispersion on PSK signals at r B = 40 Gbit/s, representation with time scales adapted to the particular symbol rates; PE: phase estimation, LPF: low-pass filter

7.3 Dispersion Tolerances for Homodyne Synchronous Detection Dispersion 0ps/nm Original IQ-Plot

Ideal in-phase eye

197

Dispersion 320ps/nm IQ-Plot before PE

IQ-Plot after PE+LPF

In-phase eye after PE+LPF

Star 16QAM Se./arg NRZ

Star 16QAM Se./arg RZ

Square 16QAM Se. TX NRZ

Square 16QAM Conv. IQ TX NRZ

Square 16QAM Enh. IQ TX NRZ

Square 16QAM Enh. IQ TX RZ

Square 64QAM Conv. IQ TX NRZ

Square 64QAM Conv. IQ TX RZ

Fig. 7.37 Impact of chromatic dispersion on QAM signals at r B = 40 Gbit/s, representation with time scales adapted to the particular symbol rates; PE: phase estimation, LPF: low-pass filter

198

7 Back-to-Back and Single-Span Transmission

The undistorted electrical eyes and IQ diagrams of various PSK and QAM signals for r B = 40 Gbit/s are depicted on the left side in Fig. 7.36 and 7.37, respectively, and compared to the distorted eyes and IQ diagrams after an accumulated dispersion of 320 ps (three diagrams on the right in each figure). Thereby, the time scales of the eye diagrams are adapted to the particular symbol rates. The distorted IQ diagrams are shown before phase estimation where they are partly rotated by a constant phase offset, as well as after phase estimation and electrical low-pass filtering with a thirdorder Bessel filter with a 3 dB bandwidth of Bel = 0.75 · r S . The averaging of the phase estimation is performed over the entire number of symbols, so that the constellation diagrams are rotated back only by the constant phase offset. The distorted eye diagrams after 320 ps accumulated dispersion are more clearly opened for the high-order formats and for RZ pulse shape. Moreover, it can be observed from the IQ diagrams for QPSK and Square 16QAM that the specific chirp characteristics of different transmitters lead to individually different signal distortions. The parallel transmitter, the conventional IQ transmitter and all RZ transmitters tend to result in equally distributed distortions of the symbols. In contrast, the intensity of the distortions is symbol dependent for systems employing the serial transmitter structure and NRZ pulse shape.

7.3.4 Self Phase Modulation Tolerances The SPM tolerances of high-order modulation formats in systems with homodyne synchronous detection and digital phase estimation receivers can be identified using the same system setup as for direct detection. As shown in Fig. 7.13, the optical signals are transmitted over a dispersive and nonlinear fiber link with a length of l = 80 km. The data rate is r B = 40 Gbit/s and the 3 dB bandwidth of the electrical receiver filters is assumed to be Bel = 0.75 · r S . The SMF parameters are specified by Dλ = 16 ps/(nm·km), Sλ = 0 and n 2 = 2.6 · 10−20 m2 /W. Chromatic dispersion is compensated for by ideal dispersion compensation behind the link. The average fiber input power is varied and the receiver sensitivity penalties at BER=10−4 and the eye opening penalties are determined. In Fig. 7.38, the receiver sensitivity penalties (a, b) and the eye opening penalties (c, d) versus fiber input power are shown for the case of using the serial configurations on the transmitter side, except for Square 64QAM where the use of the conventional IQ transmitter is assumed. The same principal tendencies can be observed as for differential detection. The SPM tolerance of PSK formats decreases with increasing modulation format order and thus smaller phase distances. Signals with RZ pulse shape tolerate higher fiber input powers than NRZ signals due to the more beneficial chirp characteristics. All QAM formats show very poor SPM performance, since symbols on different circles experience different nonlinear phase shifts. This leads to drastic deformations of the signal constellations as further illustrated in Sect. 7.3.5.

199

a 3 Square 64QAM

-4

Square 16QAM 8PSK

2 Star 16QAM

1

QPSK

0 16PSK

-1 -6

NRZ

-3 0 3 6 9 12 Fiber input power [dBm]

4

c 3 2 1 0 -6

Square 16QAM, Star 16QAM, Phase

Square 64QAM

16PSK

8PSK

Star 16QAM, Int. QPSK NRZ

-3 0 3 6 9 12 Fiber input power [dBm]

15

4

b

Square 16QAM

3 2 1

Square 64QAM

16PSK

Star 16QAM

8PSK QPSK

0 RZ

-1 -6

15

Eye Opening Penalty [dB]

Eye Opening Penalty [dB]

-4

Penalty @ BER=10 [dB]

4

Penalty @ BER=10 [dB]

7.3 Nonlinear Phase Shift Compensation

-3 0 3 6 9 12 Fiber input power [dBm]

15

4

d

Square 16QAM

3

Star 16QAM, Phase

2 Square 64QAM

1

Star 16QAM, Int.

16PSK 8PSK QPSK

RZ

0 -6

-3 0 3 6 9 12 Fiber input power [dBm]

15

Fig. 7.38 SPM tolerances of various modulation formats for homodyne detection with digital phase estimation at 40 Gbit/s when using the serial transmitter structures; the two upper diagrams show the receiver sensitivity penalties at BER=10−4 against the fiber input power for NRZ (a) and RZ (b). The bottom diagrams (c, d) illustrate the eye opening penalties.

7.3.5 Nonlinear Phase Shift Compensation During fiber propagation, an optical signal experiences an intensity dependent SPMinduced nonlinear phase shift as described in Sect. 6.3 and discussed for direct detection receivers in Sect. 7.1.6. QAM symbols have different intensity levels. Therefore, the intensity dependent nonlinear phase shift causes drastic deformations of the received QAM signal constellations. This effect is shown in Fig. 7.39 for Star 16QAM and Square 16QAM after transmission over a dispersive nonlinear fiber with a length of l = 80 km and Dλ = 16 ps/(nm·km) and γ = 1.31 W−1 km−1 , where it is assumed that the chromatic dispersion is compensated for ideally behind the link and the average input power launched into the fiber is PT X,avg = 8 dBm. It can be observed that symbols with different power levels undergo different degrees of phase rotation. The resulting distortions of the signal constellations can not be compensated for by phase estimation solely, which just rotates back the entire constellation (or more precisely: all symbols within a block) by the phase error as shown in Fig. 7.39b, but must be compensated for by an additional nonlinear phase shift compensator to enable further use of simple decision techniques. For Square 16QAM, for instance, the optimal decision boundaries are spiral-like when

200

7 Back-to-Back and Single-Span Transmission Star 16QAM NRZ

Square 16QAM Square 16QAM NRZ RZ

Star 16QAM RZ

a w/o compensation w/o PE

b w/o compensation w. PE

c w. compensation w. PE

Fig. 7.39 Deformation of the signal constellations of Star 16QAM and Square 16QAM caused by the SPM-induced nonlinear phase shift, assuming a fiber length of l = 80 km and an average fiber input power of PT X,avg = 8 dBm. a Without (w/o) phase estimation (PE) and w/o nonlinear phase shift compensation. b With (w.) PE and w/o compensation. c With PE and compensation.

not employing compensation, whereas the usual straight-line decision boundaries can be used after nonlinear phase shift compensation. Further investigation concerning QAM signal detection impaired by SPM—also under consideration of the nonlinear phase noise—is presented in [7]. The distortions caused by the SPM-induced nonlinear phase shift can be compensated for using the optical compensator depicted in Fig. 7.18a, which can be placed in front of the coherent receiver. The obtainable improvements of the SPM tolerance for Star 16QAM and Square 64QAM are illustrated in Fig. 7.40. Square 64QAM, conventional IQ TX

2 1 0 0

a

NRZ uncompensated RZ uncompensated

-4

3

4 Penalty @ BER=10 [dB]

-4

Penalty @ BER=10 [dB]

Star 16QAM, serial TX, arg-decision

4

RZ compensated NRZ compensated

3 6 9 12 Fiber input power [dBm]

15

b 3

RZ uncompensated

NRZ uncompensated

NRZ compensated

2 RZ compensated

1 0 -6

-3 0 3 6 9 12 Fiber input power [dBm]

15

Fig. 7.40 Enhancement of the SPM tolerance by nonlinear phase shift compensation for Star 16QAM (a) and Square 64QAM (b), l = 80 km, r B = 40 Gbit/s

7.3 Nonlinear Phase Shift Compensation

201

As regards the single-span system configuration discussed here, it can be seen in Fig. 7.40 that SPM tolerance can be greatly enhanced for both formats shown. With compensation, the performance for NRZ-Star 16QAM is nearly in the same range as for NRZ-8PSK and the SPM tolerance can be increased by more than 5 dB for RZ-Star 16QAM. In the case of Square 64QAM, the performance gain is even higher—almost 10 dB for NRZ and RZ pulse shapes.

Discussion of the Impact of the Transmitter Configuration for Square 16QAM A comparison of the SPM tolerances of Square 16QAM systems comprising different transmitter structures is shown in Fig. 7.41. TX comparison Square 16QAM

-4

Penalty @ BER=10 [dB]

4

Fig. 7.41 SPM tolerances for Square 16QAM when using different transmitter types, with and without nonlinear phase shift compensation, l = 80 km, r B = 40 Gbit/s

3 2 1 0 0

All TX, NRZ uncompensated

All TX, RZ uncompensated

All TX RZ compensated

Serial + enhanced IQ NRZ compensated

Conv. IQ NRZ compensated

3 6 9 12 Fiber input power [dBm]

15

The SPM tolerance of all Square 16QAM system configurations is very poor without the compensation. When using the compensation, a performance gain of more than 6 dB can be achieved for RZ and the conventional IQ transmitter shows a higher robustness against SPM than the other transmitters for NRZ. The nonlinear phase shift compensation scheme discussed here turns out to be quite effective for the single-span system configuration examined in this chapter. Later on in Chap. 8, its application to multi-span transmission systems is briefly shown. It should also be borne in mind that the nonlinear phase noise (see Sect. 6.4) must be considered for multi-span transmission. Alternatively or additionally to the compensation scheme described here, signal distortions through the SPM-induced mean nonlinear phase shift can potentially be reduced by means of digital equalization in the electrical part of the receiver, for instance using decision directed adaptive equalization schemes, or by applying predistortion techniques on the transmitter side.

202

7 Back-to-Back and Single-Span Transmission

7.3.6 Parameter Summary Some performance parameters of 40 Gbit/s systems with homodyne synchronous detection and digital phase estimation receivers are summarized in Table 7.6, regarding all high-order modulation discussed before and NRZ / RZ pulse shapes. The given parameter values are valid for systems using serial transmitter configurations (except for Square 64QAM where the use of the conventional IQ transmitter is assumed), arg-decision for the PSK formats and Star 16QAM, IQ-decision for Square QAM and electrical Bessel filters with Bel = 0.75·r S in the in-phase and quadrature branches of the receiver. Table 7.6 Performance parameters of 40 Gbit/s systems with homodyne synchronous detection and digital phase estimation receivers, regarding various modulation formats and NRZ / RZ pulse shapes. The given parameter values are valid for systems with serial transmitter structures (except for Square 64QAM where the use of the conventional IQ transmitter is assumed), arg-decision for the PSK formats and Star 16QAM, IQ-decision for Square QAM and Bel = 0.75 · r S . Modulation Format

QPSK

8PSK

16PSK St.16QAM Sq.16QAM Sq.64QAM

PR X,avg,d Bm [dBm] @ BER=10−4

-42.0 / -43.8

-38.1 / -40.4

-32.6 / -36.1

-36.6 / -38.9

-37.8 / -40.0

-34.9 / -36.3

O S N Rd B [dB], BER=10−4 w/o optical filter

13.0 / 11.2

16.9 / 14.6

22.4 / 18.9

18.4 / 16.1

17.2 / 15.0

20.1 / 18.7

O S N Rd B [dB], BER=10−4 opt. filter, Bopt = 2.5 · r S

12.5 / 11.0

16.1 / 14.2

22.4 / 19.0

17.8 / 15.8

16.6 / 14.8

21.7 / 20.7

1ν/r B , FF @ Pen. 2 dB (10−4 )

2.5e-4 / 2.8e-5 / 2.7e-6 / 3.5e-5 / 2.5e-4 3.7e-5 6.2e-6 3.8e-5

2.9e-6 / 2.9e-6

3.7e-8 / 2.8e-8

1ν [kHz], 40 Gbit/s, FF @ Pen. 2 dB (10−4 )

10000 / 1120 / 10000 1480

108 / 248

1400 / 1520

116 / 116

1.5 / 1.1

Optimal N (steps 2n )

8/ 8

8/ 8

8/ 8

8/ 8

64 / 64

1024 / 1024

Disp. Tol. [ps/nm] @ Pen. 2 dB (10−4 )

184 / 150

172 / 294

190 / >320

248 / >320

176 / >320

>320 / >320

Disp. Tol. [ps/nm] @ EOP 2 dB

143 / 179

179 / >320

188 / >320

233 / >320

284 / >320

>320 / >320

SPM Tol. [dBm] @ Pen. 2 dB (10−4 )

13.8 / >15

10.0 / 15.0

7.9 / 13.4

7.6 / 6.1

4.9 / 4.1

-0.7 / -2.6

SPM Tol. w. comp. [dBm] @ Pen. 2 dB (10−4 )

-/ -

-/ -

-/ -

9.2 / 11.5

7.3 / 10.5

8.7 / 7.0

SPM Tol. [dBm] @ EOP 2 dB

13.0 / >15

9.6 / >15

8.0 / 14.1

6.3 / 7.1

6.0 / 6.4

2.5 / 0.7

7.3 Parameter Summary Homodyne Synchronous Detection

203

The receiver sensitivities at BER=10−4 for shot-noise limited detection with η = 1 , as well as the OSNR requirements for a BER of 10−4 for amplifier noise limited detection (with and without consideration of the influence of an optical receiver filter with Bopt = 2.5·r S ), are summarized in the first three rows of Table 7.6. When these values are compared with the parameters of systems with differential detection listed in Table 7.2 and Table 7.4, it can be seen that systems with homodyne synchronous detection have the principal advantage of superior noise performance in comparison with systems with direct and homodyne differential detection. The performance gain depends on the modulation format used. It is about 2 dB on average and slightly smaller than usual since differential coding is employed to resolve the phase ambiguity arising at the carrier synchronization. It should be borne in mind that a further penalty, caused by the phase estimation for averaging over small block lengths, must be considered when the linewidth requirements are in a critical range for a particular modulation format. In this case, similar noise performance can be obtained in systems with differential detection which feature simpler implementation and more relaxed linewidth requirements. Even when employing feed forward phase estimation which can be practically implemented without impairment from processing delay, the laser linewidth requirements become critical at r B = 40 Gbit/s for 16PSK, Square 16QAM and Square 64QAM. The particular requirements on laser linewidth for systems which estimate the phase using the feed forward M-th power block scheme (with class partitioning for Square QAM formats, as described in Sect. 3.5.3) are listed in Table 7.6. This scheme is a candidate for practical employment in the near future due to its relatively simple implementation. Potentially, the laser phase noise requirements can be further relaxed by using symbol-to-symbol phase correction, Wiener filtering and—for Square QAM, in particular—decision-directed phase estimation schemes or enhanced phase estimation algorithms which allow to incorporate all constellation points into the calculation of the phase error estimate [8]. The chromatic dispersion and self phase modulation tolerances of the different modulation formats can be also found in Table 7.6. The same tendencies arise as for systems with differential detection. The migration to higher-order modulation formats with more bits per symbol results in higher dispersion tolerances and worse SPM tolerances. SPM tolerance is very poor for all QAM formats, but can be greatly improved by nonlinear phase shift compensation. RZ signals show a more beneficial system behavior than NRZ signals in relation to all criteria shown (except for the linewidth requirements which are almost identical)—at least for the single-channel single-span system configurations without narrow optical filtering at the transmitter or the transmission link discussed in this chapter. A comparison of system performance when employing different Square 16QAM transmitter configurations is presented in Table 7.7. Nearly the same performances values can be observed for the different transmitters in the case of RZ pulse shape. For NRZ, the conventional IQ transmitter features a superior system performance with respect to its robustness against noise, chromatic dispersion and SPM (with nonlinear phase shift compensation) in comparison with the other transmitters. The improved performance for RZ pulse shape in comparison with NRZ pulse shape

204

7 Back-to-Back and Single-Span Transmission

Table 7.7 Properties of Square 16QAM systems for homodyne detection with digital phase estimation at 40 Gbit/s for NRZ / RZ when using different transmitter configurations Transmitter Type

Serial

Conv. IQ

Enh. IQ

Tand.-QPSK

PR X,avg,d Bm [dBm], BER=10−4

-37.8 / -40.0

-38.8 / -40.1

-37.9 / -40.0 -37.7 / -39.9

Disp. Tol. [ps/nm], Pen. 2 dB (10−4 )

176 / >320

>320 / >320 184 / >320

198 / >320

SPM Tol. [dBm], Pen. 2 dB (10−4 )

4.9 / 4.1

5.1 / 4.2

5.1 / 4.2

-/-

SPM Tol. w. comp., Pen. 2 dB (10−4 )

7.3 / 10.5

9.6 / 10.5

7.2 / 10.4

-/-

becomes particularly noticeable for the serial transmitter, the enhanced IQ transmitter and the Tandem-QPSK transmitter, but also for the conventional IQ transmitter, to a reduced extent. In this chapter, tendencies concerning the influence of single parameters on system performance were highlighted looking at the back-to-back case and single-span transmission and considering a wide range of high-order modulation formats. The tendencies observed give a first indication of the transmission behavior of particular formats for multi-span transmission over long distances. Independently from the detection scheme used, the migration to higher-order modulation formats with more bits per symbol has the advantage of higher chromatic dispersion and PMD tolerances. On the other hand, two main parameters limiting the distances attainable in multi-span long-haul transmission systems are becoming more critical: noise performance and Kerr nonlinearities. Therefore, it can be expected that the achievable transmission lengths are reduced when migrating to higher-order formats. This issue is discussed further in Chap. 8.

References 1. Avlonitis, N.S., Yeatman, E.M.: Performance evaluation of optical DQPSK using saddle point approximation. IEEE Journal of Lightwave Technology 24(3), 1176–1185 (2006) 2. Cai, Y., Pilipetskii, A.N.: Comparison of two carrier phase estimation schemes in optical coherent detection systems. In: Proceedings of Optical Fiber Communication Conference (OFC), OMP5 (2007) 3. Desurvire, E.: Erbium-Doped Fiber Amplifiers. John Wiley & Sons, Inc. (1994) 4. Ho, K.P.: Phase-Modulated Optical Communication Systems. Springer (2005) 5. Ip, E., Kahn, J.M.: Feedforward carrier recovery for coherent optical communications. IEEE Journal of Lightwave Technology 25(9), 2675–2692 (2007) 6. Kahn, J.M., Ho, K.P.: Spectral efficiency limits and modulation/detection techniques for DWDM systems. IEEE Journal of Selected Topics in Quantum Electronics 10(2), 259–272 (2004) 7. Lau, A.P.T., Kahn, J.M.: Signal design and detection in presence of nonlinear phase noise. IEEE Journal of Lightwave Technology 25(10), 3008–3016 (2007) 8. Louchet, H., et al.: Improved DSP algorithms for coherent 16-QAM transmission. In: Proceedings of European Conference on Optical Communication (ECOC), Tu.1.E.6 (2008)

References

205

9. Norimatsu, S., Iwashita, K.: Linewidth requirements for optical synchronous detection systemes with nonnegligible loop delay time. IEEE Journal of Lightwave Technology 10(3), 341–349 (1992) 10. Petermann, K.: Einf¨uhrung in die optische Nachrichtentechnik. Vorlesungsskript, Technische Universit¨at Berlin (2003) 11. Proakis, J.G.: Digital Communications. McGraw-Hill (2001) 12. Rice, F.: Bounds and algorithms for carrier frequency and phase estimation. Ph.D. thesis, University of South Australia (2002) 13. Seimetz, M., et al.: Optical systems with high-order DPSK and Star QAM modulation based on interferometric direct detection. IEEE Journal of Lightwave Technology 25(6), 1515–1530 (2007) 14. Siuzdak, J., van Etten, W.: BER evaluation for phase and polarization diversity optical homodyne receivers using noncoherent ASK and DPSK demodulation. IEEE Journal of Lightwave Technology 7(4), 584–599 (1989) 15. Smith, P., et al.: Optical heterodyne binary-DPSK systems: A review of analysis and performance. IEEE Journal on Selected Areas in Communications 13(3), 557–568 (1995) 16. Tonguz, O.K., Wagner, R.E.: Equivalence between preamplified direct detection and heterodyne receivers. IEEE Photonics Technology Letters 3(9), 835–837 (1991) 17. Xiong, F.: Digital Modulation Techniques. Artech House, Inc. (2000) 18. Xu, C., Liu, X.: Postnonlinearity compensation with data-driven phase modulators in phaseshift keying transmission. Optics Letters 27(18), 1619–1621 (2002)

Chapter 8

Multi-Span Long-Haul Transmission

Abstract This chapter outlines some current activities performed in the author’s research group and aimed at identifying the performance and the distances attainable in optical multi-span long-haul transmission systems with high-order modulation. Firstly, some system experiments are presented which investigate achievable distances with 8PSK and Star 16QAM when using homodyne synchronous detection. In these experiments, system configurations with optical inline CD compensation as well as electrical CD compensation at the receiver are considered. Subsequently, the transmission lengths which have been achieved with different modulation formats are compared, showing that they are significantly reduced when migrating to higher-order formats. Finally, system degradation by the SPM-induced mean nonlinear phase shift in multi-span QAM transmission is highlighted and the efficiency of possible compensation schemes is shown.

Chapter 7 illustrated the behavior of a wide range of modulation formats in relation to particular impairments for single-span transmission. This allows tendencies concerning the properties for multi-span long-haul transmission to be preestimated. However, achievable transmission distances and long-haul transmission performance of a particular modulation format can be only evaluated precisely for the specific system in which it is operated, since several degradation effects interact with each other within the whole system. Optical multi-span long-haul transmission systems, which are typically composed of multiple transmission sections each containing a fiber—usually with a length of about 80 km—and optical amplifiers compensating for fiber attenuation, are mainly limited by amplifier noise and fiber nonlinearities. Chromatic dispersion can be compensated for within each span (inline CD compensation) or electrically at the receiver. In Chap. 7, it was shown for single-span transmission that noise and self phase modulation become more critical in the case of high-order modulation. Thus, the attainable transmission lengths for multi-span transmission can be expected to be reduced when migrating to higher-order formats.

M. Seimetz, High-Order Modulation for Optical Fiber Transmission, Springer Series in Optical Sciences 143, DOI 10.1007/978-3-540-93771-5 8, c Springer-Verlag Berlin Heidelberg 2009

207

208

8 Multi-Span Long-Haul Transmission

Already installed long-haul fiber transmission systems are mainly based on onoff keying and differential binary phase shift keying. Currently, quadrature phase keying is on the way towards a commercial deployment. Even higher-order formats are not yet adopted in commercially deployed systems. But the imminent need for optical data transmission capacity feeds the interest in system concepts allowing for high spectrally efficient transmission by the use of higher-order modulation formats and motivates the current research activities in this field. This chapter presents some initial research results of the research group of the author dealing with the multi-span transmission behavior of some high-order modulation formats and the achievable transmission lengths. Section 8.1 presents re-circulating fiber loop experiments which identify the transmission distances attainable with RZ-8PSK. In these experiments, system configurations with optical inline CD compensation and electrical CD compensation at the receiver are considered. In Sect. 8.2, multi-span transmission experiments with RZ-Star 16QAM are described. They highlight the limitation of transmission lengths due to noise, implementation imperfections of the system practically investigated and signal distortions caused by the SPM-induced nonlinear phase shift. Subsequently, transmission distances achieved with RZ-QPSK, RZ-8PSK and RZStar 16QAM are compared in Sect. 8.3. Finally, system degradation by the SPMinduced mean nonlinear phase shift in multi-span QAM transmission is illustrated on the basis of RZ-Star 16QAM in Sect. 8.4, and the efficiency of some possible compensation schemes is shown.

8.1 8PSK Multi-Span Transmission Experiments The next two subsections present some experimental results which have been published in [5] and [1]. Section 8.1.1 describes a RZ-8PSK multi-span transmission experiment with optical inline CD compensation and homodyne synchronous detection. In Sect. 8.1.2, distances experimentally achieved with RZ-8PSK are illustrated in the case of employing electrical CD compensation at the receiver.

8.1.1 Optical Inline CD Compensation In Fig. 8.1, the schematic of the experimental system setup with optical inline CD compensation used in [5] is shown. For RZ-8PSK signal generation, the parallel transmitter structure (see Sect. 2.4.2) is employed. The CW light is emitted by an external cavity laser with a linewidth specified as 100 kHz. A Mach-Zehnder modulator is used for RZ pulse carving. Afterwards, the optical IQ modulator generates an optical QPSK signal and the consecutive phase modulator accomplishes a π/4 phase modulation for constitution of the 8PSK constellation. The transmitted data signal is a 211 de Bruijn sequence

8.1 8PSK Experiments with Optical Inline CD Compensation

RZ Transmitter

Fig. 8.1 Experimental system setup for the 30 Gbit/s coherent RZ-8PSK multi-span long-haul transmission experiment with inline chromatic dispersion compensation performed in [5]

209 90°

MZM

MZM

ECL

MZM PM MZM

LO

t SSMF 4 km

Pulse Pat.Gen.

DATA DATA

Transmission Link

8PSK

3 dB

EDFA

SSMF 80 km

Loop

DCF 13 km

EDFA

Data

EDFA Pol.-ctrl.

90°Hybrid

LO

Bal. Det. Bal. Det.

Digital Storage Oscillosc. 40 GSa/s

Offline Processing

Receiver

EDFA

which is given to the modulator inputs with different delays. The system symbol rate is r S = 10 Gbaud, corresponding to a data rate of r B = 30 Gbit/s. The transmission link is based on a re-circulating loop with an adjustable number of sections. Each section consists of 80 km SSMF and about 13 km DCF which fully compensates for the SSMF dispersion. The fiber parameters are measured for the SSMF as αd B = 0.2 dB/km, Dλ = 16.8 ps/(nm·km), Sλ = 0.0585 ps/(nm2 · km) and γ = 0.99 W−1 km−1 , as well as αd B = 0.56 dB/km, Dλ = −104.3 ps/(nm·km), Sλ = −0.217 ps/(nm2 ·km) and γ = 5.1 W−1 km−1 for the DCF. Erbium doped fiber amplifiers are used to compensate for the fiber loss and for controlling the launch powers into the SSMF and DCF. The noise power of the optical amplifiers is reduced by optical filters. The signal can be sent to the receiver after being transmitted over a desired number of cascaded sections by the use of acousto-optical switches. At the receiver end, the RZ-8PSK signal is interfered with the light of a local oscillator (Plo =10 dBm) in a Li N bO3 2×4 90◦ hybrid. For experimental simplicity, the LO light is taken from the transmitter laser to avoid an automatic frequency control loop. In the back-to-back case where the transmitter is directly connected to the receiver, the received information signal and the LO signal are de-correlated by a 4 km long SSMF. The polarization is controlled manually in front of the inputs of the 2 × 4 90◦ hybrid. The hybrid output signals are detected by two balanced detectors and the in-phase and quadrature photocurrents are digitized using a 40 GSa/s digital storage oscilloscope. Finally, data is recovered off-line by applying an 8-th power digital phase estimation algorithm (N =8) and an appropriate data recovery circuit, including a differential decoder to remove the 8-fold phase ambiguity.

210

8 Multi-Span Long-Haul Transmission

1E-2

a 1E-3 BER

Experiment Simulation

1E-4

RZ-8PSK, 30Gbit/s

1E-5 8

10

12 14 OSNR [dB]

16

18

Norm. power in 0.01nm [dBm]

For system characterization, the noise loaded back-to-back performance was measured in [5] and compared with Monte Carlo simulations. As can be observed from Fig. 8.2a, an OSNR of about 13 dB was required in the experiment for a BER of 10−3 . The Monte Carlo simulation for RZ-8PSK at r B = 30 Gbit/s for the system configuration with the parallel transmitter and arg-decision indicates a required OSNR of about 11.5 dB. The difference of about 1.5 dB must be considered an implementation penalty when using off-the-shelf components. Furthermore, the measured optical signal spectrum at the transmitter output is depicted in Fig. 8.2b. The 20 dB bandwidth of the optical 30 Gbit/s RZ-8PSK signal can be seen to be approximately 0.2 nm (25 GHz). 0

b -10 -20 -30 -40 RZ-8PSK, 30Gbit/s

1550,4

1550,6 1550,8 1551,0 Wavelength [nm]

1551,2

Fig. 8.2 Measured back-to-back OSNR performance (a) and optical signal spectrum at the transmitter output (b) in the 30 Gbit/s RZ-8PSK multi-span transmission experiment performed in [5]

To determine the possible transmission lengths of 30 Gbit/s RZ-8PSK on widely used SSMF and DCF spans, the optical RZ-8PSK signal was sent over the recirculating fiber loop. The launch powers into the SSMF and DCF (PS M F and PDC F , respectively) were varied. In Fig. 8.3a, the measured BER is shown versus the transmission length for different values of PS M F and PDC F . Reach with inline CD compensation

SSMF input power optimization at 960km

1E-2

1E-2 PSMF = -6.0dBm PDCF = -7.6dBm

BER

PSMF = -1.0dBm PDCF = -6.6dBm

PSMF = -0.7dBm PDCF = -2.2dBm

1E-4

a 1E-5 0

1E-4

RZ-8PSK, 30Gbit/s

480 960 1440 1920 Transmission length [km]

PDCF ≈ PSMF - 5dB

1E-3 BER

1E-3

2400

1E-5 -8

b

RZ-8PSK, 30Gbit/s

-6 -4 -2 0 2 SSMF input power [dBm]

4

Fig. 8.3 BER vs. transmission distance (a) and power optimization at 960 km (b) in the RZ-8PSK experiments with inline chromatic dispersion (CD) compensation performed in [5]

8.1 8PSK Experiments with Optical Inline CD Compensation

211

First, PDC F was chosen about 1.5 dB below PS M F and best BER performance was obtained for PS M F = −0.7 dBm. When decreasing PDC F , the bridgeable transmission distance can be further increased, but only slightly. Figure 8.3b shows the influence of SSMF launch power variation on the BER at a fixed transmission length of 960 km when PDC F is chosen about 5 dB below PS M F . Optimal performance was obtained for PS M F = −1 dBm and PDC F = −6.6 dBm. In this case, the trade-off between noise and nonlinearities allows for the largest transmission distances. For a BER of about 10−3 which allows for error free transmission when using forward error correction coding, a transmission distance of 1360 km (17 cascaded sections) could be achieved, choosing the optimum launching condition. The plotted BER values were calculated for evaluating 2.304.000 bits and averaging over 6 realizations. In Fig. 8.4, the IQ diagrams for back-to-back and after 960 km are shown as displayed by the digital storage oscilloscope when employing synchronous sampling, taking four samples per symbol and showing 2048 samples. NRZ-8PSK, BtB

NRZ-8PSK, 960km

RZ-8PSK, BtB

RZ-8PSK, 960km

Fig. 8.4 Received 8PSK IQ diagrams for back-to-back and after 960 km for NRZ and RZ pulse shapes, as displayed by the digital storage oscilloscope when employing synchronous sampling, taking four samples per symbol and showing 2048 samples

The IQ diagrams for NRZ in Fig. 8.4 were obtained by bypassing the pulse carver of the transmitter. They show the typical symbol transitions of the parallel transmitter structure. The received RZ-8PSK constellation diagrams from selecting one sample per symbol in the middle of the symbols are depicted in Fig. 8.5 for the back-to-back case before (a) and after (b) phase estimation and at 1200km after phase estimation (c) by displaying 65.536 received symbols.

Fig. 8.5 Received RZ-8PSK constellation diagrams for back-to-back before (a) and after (b) digital phase estimation (PE) and at 1200 km after phase estimation (c)

a

b

c

BtB, before PE

BtB, after PE

1200km, after PE

212

8 Multi-Span Long-Haul Transmission

8.1.2 Electrical CD Compensation at the Receiver A great advantage of the homodyne IQ receiver in comparison with the direct detection receiver is its capability to efficiently compensate for transmission impairments in the electrical domain. All information parameters of the optical signal are accessible after detection. The accumulated chromatic dispersion can be compensated for by convolution of the received complex signal with the inverse fiber impulse response using a complex finite impulse response (FIR) filter. The transfer function of this filter—when neglecting the dispersion slope—is given by He (ω) = e j0.5·β2 ·ω

2 ·N

F S ·l

(8.1)

,

where β2 represents the fiber dispersion, N F S the number of cascaded transmission sections and l the fiber length in each section. To discover the attainable transmission lengths without optical inline compensation of chromatic dispersion, the DCF and the EDFA in front of the DCF were removed from the transmission section shown in Fig. 8.1 in the experiments described in [1], and the raw data was electrically equalized off-line by an ideal FIR filter before digital phase estimation within the receiver. For practical filter implementation, the equalization performance will be limited, for instance by the number of taps. In Fig. 8.6b, the BER against the launch power into the SSMF (PS M F ) after transmission through 1680 km is shown. An optimum value of PS M F ≈ −3.5 dBm was measured which is about 2.5 dB below the optimum value for inline chromatic dispersion compensation. Reach with electrical CD compensation at RX

SSMF input power optimization at 1680km

1E-2

1E-2

a

b PSMF = -1.0dBm

1E-3 BER

BER

1E-3

1E-4

1E-4

PSMF = -3.5dBm

RZ-8PSK, 30Gbit/s

1E-5 960

1440 1920 2400 2880 Transmission length [km]

3360

1E-5 -8

RZ-8PSK, 30Gbit/s

-6 -4 -2 0 SSMF input power [dBm]

2

Fig. 8.6 BER vs. distance (a) and power optimization at 1680 km (b) in the RZ-8PSK experiments with electrical chromatic dispersion (CD) compensation at the receiver conducted in [1]

In Fig. 8.6a, the BER against the transmission length is shown for two different values of PS M F . When choosing the optimum launching condition, a maximum transmission distance of 2800 km (35 cascaded sections) for a target BER of 10−3 could be achieved. This is approximately twice the maximum transmission distance compared with optical inline dispersion compensation and can be explained by an

8.2 Single-Channel Star 16QAM Experiments with Inline CD Compensation

213

improvement of OSNR, caused by the noise reduction through the removal of the EDFA-amplified DCF and measured to have an increase of about 1 dB at a transmission distance of 1440 km. Moreover, the accumulated fiber nonlinearities decrease due to the removal of the DCF and lower optimum launch power into the SSMF. From another point of view, the amplifier spacing can be enlarged to achieve the same transmission performance as for inline dispersion compensation at a certain distance. This can result in cost savings. It can be concluded from the outlined 8PSK experiments that a distance of 1360 km could be bridged with RZ-8PSK transmission and homodyne detection at 30 Gbit/s for a target BER of 10−3 when employing optical inline dispersion compensation with DCF modules. The maximum transmission distance could be doubled to approximately 2800 km by replacing optical inline CD compensation with electrical CD compensation at the receiver.

8.2 Star 16QAM Multi-Span Transmission Experiments Next, in Sect. 8.2.1, a multi-span transmission experiment with Star 16QAM and optical inline compensation of chromatic dispersion is described which has been published in [6]. It investigates the transmission performance of Star 16QAM single-channel systems for single-polarization and polarization division multiplexing (PDM) and highlights the limitation of attainable transmission lengths due to amplifier noise and SPM-induced signal distortions. Subsequently, a Star 16QAM WDM experiment is presented in Sect. 8.2.2. Five WDM channels are transmitted over more than 1000 km and demodulated with the aid of enhanced electronic equalization at the receiver.

8.2.1 Single-Channel Experiments Figure 8.7 illustrates the schematic of the experimental setup for investigation of Star 16QAM multi-span transmission systems with optical inline CD compensation and polarization division multiplexing used in [6]. The main part of the transmitter is equal to the RZ-8PSK transmitter employed in the 8PSK experiments described in Sect. 8.1. Another Mach-Zehnder modulator is used for Star 16QAM signal generation. By changing the driving and bias voltages of this modulator, different ring ratios can be adjusted. The system symbol rate is r S = 10 Gbaud, resulting in a data rate of 40 Gbit/s for single-polarization and 80 Gbit/s for polarization division multiplexing. Polarization division multiplexed transmission is investigated by splitting the signal with a polarization beam splitter, delaying one polarization component, and afterwards adding both polarization components in a polarization beam combiner (PBC).

214

8 Multi-Span Long-Haul Transmission 8PSK

QPSK

Transmitter

RZ LO

ECL

Star 16QAM

MZM

90°

MZM

PM

MZM

t

t

3 dB PBS

t

3 dB PBC

MZM EDFA

t

1

Pulse DATA Pat.Gen. DATA

Transmission Link

SSMF 4 km

3

2

3 dB

EDFA

SSMF 80 km

DCF 13 km

Loop

EDFA

EDFA

EDFA

PBS

90°LO Hybrid

3 dB

Data

90°LO Hybrid

Bal. Det. Bal. Det. Bal. Det.

Digital Storage Oscillosc. 50 GSa/s

Offline Processing

Receiver

Data

Bal. Det.

Fig. 8.7 Experimental system setup for the 80 Gbit/s coherent RZ-Star 16QAM multi-span transmission experiment with inline chromatic dispersion compensation and polarization division multiplexing performed in [6]

The transmission link is based on a re-circulating fiber loop with an adjustable number of sections and optical inline CD compensation in each section. It has the same configuration as in the experiment described in Sect. 8.1.1. In the case of PDM experiments, the signal launched into the receiver is split by a PBS first. Afterwards, both polarization components are interfered with the LO light (which is again taken from the transmitter laser to avoid an automatic frequency control loop) in two 2 × 4 90◦ hybrids. The hybrid output signals are detected by a pair of balanced detectors and the photocurrents are digitized using a 50 GSa/s digital storage oscilloscope. Data is then recovered off-line by applying digital phase estimation (using the feedforward block scheme with rectangular time domain filtering and averaging over 8 symbols) and appropriate data recovery. Further electrical equalization of transmission impairments was not performed in this experiment. Figure 8.8a depicts the transmission lengths achieved with 10 Gbaud RZ-Star 16QAM in the experiments, showing the measured BER versus the transmission length for launched powers into the SSMF (PSS M F ) as specified there. In all cases, the power launched into the DCF (PDC F ) was chosen as 5 dB below PS M F . The influence of SSMF launch power variation on the BER at fixed transmission lengths of 800 km (single-polarization) and 320 km (PDM) is shown in Fig. 8.8b and indicates

8.2 Single-Channel Star 16QAM Experiments with Inline CD Compensation

215

optimal SSMF input powers of -4 dBm for single-polarization and 0 dBm for PDM. Even when applying the optimal launch powers, the transmission distance was limited to about 600 km for single-polarization and 400 km for PDM case. Reach with inline CD compensation

SSMF input power optimization

1E-2

1E-1

a

PDM, RR 1.8 PSMF = 0dBm

b Single Pol., RR 1.8 at 800km

1E-3 BER

BER

1E-2 Single Pol., RR 1.9 PSMF = -1dBm

1E-4

1E-3 Single Pol., RR 1.9 PSMF = -4dBm

PDM, RR 1.8 at 320km

RZ-Star 16QAM

1E-5 0

200 400 600 800 Transmission length [km]

1000

1E-4 -8

RZ-Star 16QAM

-6 -4 -2 0 2 SSMF input power [dBm]

4

Fig. 8.8 BER vs. transmission distance (a) and power optimization (b) in the RZ-Star 16QAM experiments with inline chromatic dispersion compensation conducted in [6], r S = 10 Gbaud.

Compared with RZ-8PSK, transmission distances are considerably reduced for RZ-Star 16QAM. The reasons for that are the following: Firstly, the Euclidean distances between the symbols for Star 16QAM are smaller (the required OSNR at BER=10−3 for the single-polarization system in the experiment was 16.5 dB for RZStar 16QAM, but only about 13.5 dB for RZ-8PSK) and ISI effects appearing within the transmitter impaired system performance. In the practical transmitter setup, every new modulation stage can lead to higher ISI caused by pattern effects and thus to higher implementation penalties. Secondly, symbols with different power levels experience different SPM-induced mean nonlinear phase shifts as observable for the single-polarization case from the constellation diagram received after 560 km, shown on the right side of Fig. 8.9. Symbols on different rings have obtained different phase rotations. When these phase shifts are not being compensated for, they limit attainable transmission lengths even for ISI- and noise-free systems. Received constellation diagrams for single-polarization

Back-to-back

400km

560km

Fig. 8.9 Received Star 16QAM constellation diagrams for back-to-back, after 400 km and after 560 km in the experiments conducted in [6] for the single-polarization case

216

8 Multi-Span Long-Haul Transmission

Figure 8.10b illustrates how BER performance can be improved when the relative nonlinearity-induced phase difference of both rings is compensated for. After 720 km, optimum BER performance is obtained when symbols on the inner ring are rotated by about -0.19 rad. Using the mean nonlinear phase shift compensation, achievable distances can probably be increased to about 1000 km for singlepolarization (see Fig. 8.10a), whereas the performance gain was only small for PDM where other impairments such as polarization crosstalk limited the performance of the system investigated in [6]. Star 16QAM reach with /without compensation

NL phase shift compensation at 720km

1E-2

1E-2

a

PDM, with comp.

b

BER

Single Pol., w/o comp.

BER

1E-3

PDM, w/o comp.

1E-3

1E-4 Single Pol., with comp. RZ-Star 16QAM

1E-5 0

200 400 600 800 Transmission length [km]

1000

Single-polarization

1E-4 -0,4

RZ-Star 16QAM

-0,3 -0,2 -0,1 Phase shift inner ring [rad]

0,0

Fig. 8.10 a BER versus distance for single-polarization and PDM RZ-Star 16QAM systems with / without nonlinear phase shift compensation. b BER improvement through mean nonlinear phase shift compensation at 720 km for single-polarization RZ-Star 16QAM. r S = 10 Gbaud.

An important performance parameter which must be optimized in Star QAM systems is the ring ratio. Figure 8.11 illustrates the BER dependence on the ring ratio for single-polarization RZ-Star 16QAM, measured in [6]. After 400 km, the optimum ring ratio is about 1.77, which is consistent with the theory (see Sect. 7.3.1). In the case of back-to-back, a higher ring ratio was optimal in the experiment. This can be explained by the ISI-induced radial distortions of the constellation points due to pattern effects which can be recognized in the left diagram of Fig. 8.9. Star 16QAM ring ratio optimization

1E-2 At 400km

BER

1E-3

Fig. 8.11 Experimental optimization of the Star 16QAM ring ratio for back-to-back transmission and at 400 km for the single-polarization case, performed in [6]

1E-4 1E-5 1E-6

Back-to-back

RZ-Star 16QAM Single-polarization

1E-7 1,6 1,7 1,8 1,9 2,0 2,1 2,2 2,3 2,4 Ring ratio

8.2 Star 16QAM WDM Experiments with Electrical CD Compensation

217

8.2.2 WDM Experiments

Fig. 8.12 Measured fivechannel WDM RZ-Star 16QAM power spectra within 0.1 nm at the transmitter output and after transmission over 1200 km for the 40 Gbit/s single-polarization system

Power in 0.1nm [dBm]

Another RZ-Star 16QAM transmission experiment which uses electrical dispersion compensation at the receiver has been performed in the WDM systems group of the Fraunhofer Institute for Telecommunications, Heinrich-Hertz-Institut, in collaboration with VPIsystems GmbH. Five 10 Gbaud RZ-Star 16QAM WDM channels were transmitted over 720 km / 1200 km SSMF with / without PDM on a 50 GHz frequency grid centered at 1550.92 nm. The central channel was demodulated with the aid of enhanced electronic equalization at the receiver. The system setup employed in the experiment is very similar to the singlechannel experimental setup shown in Fig. 8.7, but upgraded to WDM at some locations. The transmitter consists of five external cavity lasers which are coupled by a set of 3 dB couplers. The transmission section within the re-circulating fiber loop is composed of three 80 km SSMF spans without inline dispersion compensating modules. Erbium doped fiber amplifiers are used to compensate for the loop loss and control the launch powers into the fiber spans. The noise power of the amplifiers is reduced by optical bandpass filters and a gain equalizer controls the gain of each WDM channel. At the receiver, the central channel is selected by an optical bandpass filter and then split by a polarization beam splitter in the case of PDM. Afterwards, both polarization components are interfered with the LO light in two 2 × 4 90◦ hybrids which are followed by four balanced detectors. In the electrical domain, the photocurrents are digitized and processed by digital equalization. Chromatic dispersion is compensated for by using a filter that is implemented in the frequency domain. Thereafter, an enhanced constant modulus algorithm—denoted as multiple moduli algorithm (MMA) and published in [3] where it was applied to Square 16QAM—is used to compensate for residual transmission impairments such as nonlinearities and polarization crosstalk. After equalization, feed forward M-th power phase estimation is used to compensate for laser phase noise. Finally, decoding and error counting are performed. Figure 8.12 shows the measured WDM spectra at the output of the transmitter and after transmission over 1200 km for a fiber launch power of -1 dBm / channel. 0 -5 -10 At 1200km -15 -20 -25 Transmitter -30 output -35 -40 Single-polarization WDM RZ-Star 16QAM -45 1548 1549 1550 1551 1552 1553 1554 Wavelength [nm]

218

8 Multi-Span Long-Haul Transmission

BER values of the central channel were measured after different numbers of loop round trips. Figure 8.13a shows BER versus transmission distance when using only the non-adaptive frequency domain equalizer to compensate for chromatic dispersion. Applying this approach, transmission distances of 480 km / 950 km were achieved for 80 Gbit/s / 40 Gbit/s RZ-Star-16QAM with / without PDM (assuming a BER reference of 10−3 ). In Fig. 8.13b, the BER is shown for the case that an additional MMA equalizer with 9 taps per complex filter structure is employed. Using this additional equalizer, transmission distance could be extended to about 800 km and 1400 km for 80 Gbit/s and 40 Gbit/s RZ-Star 16QAM with and without PDM, respectively. CD compensation in frequency domain

Additional adaptive MMA equalization

1E-2

1E-2

a

b

PDM

PDM

1E-3 BER

BER

1E-3 Single-polarization

1E-4

1E-4 Single-polarization

WDM RZ-Star 16QAM

WDM RZ-Star 16QAM

1E-5 0

400 800 1200 Transmission length [km]

1600

1E-5 0

400 800 1200 Transmission length [km]

1600

Fig. 8.13 BER versus transmission distance for 80 Gbit/s and 40 Gbit/s WDM RZ-Star-16QAM with and without PDM, using only frequency domain CD compensation (a) and MMA equalization additionally (b).

It can be concluded from the RZ-Star 16QAM experiments described in the last two sections that distances of 600 km and 400 km over a link with optical inline CD compensation could be bridged at 10 Gbaud without and with PDM, respectively, achieving a BER lower than 10−3 . By employing compensation of the nonlinear phase shift, distances could be increased to about 1000 km for single-polarization. It can be expected that even higher transmission distances can be achieved in systems with inline CD compensation when transmitter performance is further improved and additional electronic distortion equalization at the receiver is used. In the five-channel WDM experiment with electrical CD compensation at the receiver described in the last paragraphs, 80 Gbit/s and 40 Gbit/s WDM RZ-Star 16QAM transmission has been demonstrated over 800 km and 1400 km for PDM and singlepolarization, respectively. This was possible by applying enhanced electronic distortion equalization techniques.

8.3 Comparison of Transmission Distances

219

8.3 Comparison of Transmission Distances Based on the results obtained in the experiments described in Sect. 8.1 and Sect. 8.2, transmission distances at 10 Gbaud achieved experimentally with RZ-QPSK, RZ8PSK and RZ-Star 16QAM are compared in this section. Results for RZ-QPSK, which have not been shown in the last sections, are attained using the same experimental setup as illustrated for RZ-8PSK in Fig. 8.1. At the transmitter, simply the π/4 phase modulation of the phase modulator must be switched off. At the receiver end, the quadrature optical frontend remains unchanged and just the phase estimation and the data recovery must be adapted. A first indicator for the transmission length achievable with a particular modulation format is the back-to-back noise performance. In Fig. 8.14, the back-to-back OSNR requirements measured in [6] for RZ-QPSK, RZ-8PSK and RZ-Star 16QAM are compared for single-polarization (Fig. 8.14a) and PDM (Fig. 8.14b). OSNR requirements single-polarization

OSNR requirements for PDM

1E-2

1E-2

a

b RZ-Star 16QAM

RZ-Star 16QAM

1E-3 RZ-8PSK

1E-4

RZ-8PSK

1E-4 RZ-QPSK

1E-5 6

BER

BER

1E-3

8

10 12 14 16 18 20 22 24 OSNR [dB]

RZ-QPSK

1E-5 10 12 14 16 18 20 22 24 26 28 OSNR [dB]

Fig. 8.14 Back-to-back OSNR requirements of RZ-QPSK, RZ-8PSK and RZ-Star 16QAM measured in [6] for single-polarization (a) and polarization division multiplexing (b), assuming a common symbol rate of r S = 10 Gbaud.

To obtain a BER of 10−3 , an OSNR of about 16.5 dB and 20.0 dB was required for RZ-Star 16QAM in the case of single-polarization and PDM, respectively. The measured OSNR penalty at BER=10−3 is 2-3 dB and 9 dB compared with RZ-8PSK and RZ-QPSK, respectively. The difference in the required OSNR between RZ-Star 16QAM and RZ-QPSK is larger than expected from numerical simulation (7.5 dB, as shown in Sect. 7.3.1), since in the practical transmitter setup the modulation stage performing the 45◦ phase modulation led to an implementation penalty caused by pattern effects of the electrical driving signals. OSNR requirements increase by about 3 dB when upgrading from single-polarization to PDM. Transmission distances achieved in [6] with RZ-QPSK, RZ-8PSK and RZ-Star 16QAM in multi-span transmission systems with optical inline CD compensation are compared in Fig. 8.15 for single-polarization (a) and PDM (b), assuming a common symbol rate of r S = 10 Gbaud for all formats.

220

8 Multi-Span Long-Haul Transmission Reach comparison single-polarization

Reach comparison for PDM

1E-2

1E-2

a

b

RZ-Star 16QAM w/o NL PS comp.

1E-3

1E-3 BER

RZ-QPSK

BER

RZ-Star 16QAM w/o NL PS comp.

RZ-8PSK

1E-4

RZ-8PSK

Opt. Inline CD comp.

Opt. Inline CD comp.

1E-5 0

RZ-QPSK

1E-4

1000 2000 3000 Transmission length [km]

4000

1E-5 0

1000 2000 3000 Transmission length [km]

4000

Fig. 8.15 Transmission distances achieved in [6] with RZ-QPSK, RZ-8PSK and RZ-Star 16QAM for multi-span transmission with optical inline CD compensation for single-polarization (a) and PDM (b), assuming a common symbol rate of r S = 10 Gbaud.

The experimental results presented in Fig. 8.15 assume optimized launch powers into the SSMF and DCF and demonstrate that the attainable transmission distances are considerably reduced when migrating from QPSK to 8PSK, and even more when applying Star 16QAM. This is primarily caused by the more stringent OSNR requirements of the higher-order formats, as well as by their reduced tolerance against nonlinear effects. However, it should be noted that the curves for RZ-Star 16QAM in Fig. 8.15 are shown without compensation of the mean nonlinear phase shift. Distances for Star 16QAM can be increased when the relative nonlinearity-induced phase difference of both rings is compensated for, as described in Sect. 8.2.1 and further discussed in Sect. 8.4. Moreover, distances for all formats can potentially be increased by means of adaptive electrical equalization within the coherent receiver, which has not been employed in the experiments conducted in [6]. As illustrated for RZ-8PSK and RZ-Star 16QAM in Sect. 8.1.2 and Sect. 8.2.2, longer transmission distances are possible when optical inline CD compensation is replaced with electrical CD compensation within the coherent receiver. Transmission distances experimentally achieved with optical inline CD compensation and electrical CD compensation at r S = 10 Gbaud are compared in Fig. 8.16a for the single-polarization case, exemplarily for RZ-QPSK and RZ-8PSK. 1E-2 RZ-8PSK, inline comp.

1E-3 BER

Fig. 8.16 Reach comparison of RZ-QPSK and RZ8PSK at r S = 10 Gbaud for single-polarization multi-span transmission with optical inline CD compensation and electronic CD compensation, based on the experiments performed in [1, 5].

1E-4

1E-5 0

RZ-QPSK, inline comp. RZ-8PSK, el. comp. RZ-QPSK, el. comp.

1000 2000 3000 4000 5000 6000 Transmission distance [km]

8.4 Nonlinear Phase Shift Compensation in Systems with Inline CD Compensation

221

8.4 Nonlinear Phase Shift Compensation As explained in Sect. 7.1.6 and Sect. 7.3.5 for single-span systems and briefly discussed in Sect. 8.2.1 for RZ-Star 16QAM multi-span systems, optical QAM transmission inherently suffers from performance degradation caused by different SPMinduced mean nonlinear phase shifts experienced by symbols with different power levels. This section clarifies the influence of this effect in multi-span transmission systems and points out differences between system configurations with optical inline CD compensation (Sect. 8.4.1) and electrical CD compensation at the receiver (Sect. 8.4.2), regarding the single-polarization and PDM case. Possible compensation schemes and their efficiency for Star 16QAM are discussed on the basis of results from numerical simulations obtained in [4].

8.4.1 Systems with Optical Inline CD Compensation Figure 8.17 shows the RZ-Star 16QAM multi-span system setup with optical inline CD compensation employed in [4] for simulative investigation of the singlepolarization case. The RZ-Star 16QAM signal is generated by using the parallel RZStar 16QAM transmitter structure described in Sect. 2.5. The transmission link consists of N F S sections, each being composed of 80 km SSMF, 13 km DCF (fully compensating for the chromatic dispersion of the SSMF) and optical amplifiers (OA) with a noise figure of 5.6 dB. An additional attenuation of 10 dB was used in each section to better emulate the behavior of an experimental re-circulating fiber loop test bed. At the receiver side, the signal is detected by a homodyne phase estimation receiver which is described in detail in Sect. 3.5.3.

MZM RZ

3dB

3dB -90°

A/D

PM

MZM

2x4 90° Hybrid

MZM

A/D LO

Transmission Link PSMF OA

Data Recovery

CW

Electr. CD Comp.

MZM

Phase Estimation

Star 16QAM Homodyne Receiver

RZ-Star 16QAM Transmitter

× NFS Inline CD compensation

PDCF

SSMF 80 km

OA

DCF 13 km

10dB OA

Comp. Case A

10dB

α Comp. Case B

Fig. 8.17 Single-polarization RZ-Star 16QAM multi-span system setup used in [4] to investigate different schemes for compensation of the SPM-induced mean nonlinear phase shift.

222

8 Multi-Span Long-Haul Transmission

In the case of PDM, the transmitter is doubled and both polarizations are multiplexed in a polarization beam combiner before the PDM signal is launched into the fiber. Moreover, the receiver frontend is enhanced as shown in Fig. 8.7. SPM-induced signal distortions are different for single-polarization and PDM systems, as illustrated in Fig. 8.18 for RZ-Star 16QAM transmission over a single non-dispersive noise-free transmission section with nonlinear propagation coefficients of the SSMF and DCF given by γ S M F = 1.43 W−1 km−1 and γ DC F = 5.84 W−1 km−1 , respectively, and for fiber input powers of PS M F = 6 dBm and PDC F = 1 dBm. a

b

Single-polarization

PDM

Fig. 8.18 Effect of the SPMinduced mean nonlinear phase shift on RZ-Star 16QAM signals in single-polarization systems (a) and for PDM (b).

It can be observed from the single-polarization case (Fig. 8.18a) that symbols with different power levels undergo different degrees of phase rotation. In the case of PDM, distortions are different due to nonlinear cross-polarization effects (see Fig. 8.18b). As already discussed in Chap. 7 for single-span transmission systems, the resulting distortions of the signal constellations must be compensated for by a nonlinear phase shift compensator. Without compensation, attainable transmission lengths for multi-span QAM transmission are strongly limited. This was already demonstrated in the experiments described in Sect. 8.2.1. For comparison, some results for PDM systems at 10 Gbaud determined by computer simulations in [4] are illustrated in Fig. 8.19. These are valid for optimized fiber input powers and indicate that the transmission distances achieved experimentally for 8PSK in [5] and Star 16QAM in [6] can potentially be increased by additional practical system optimization. Nevertheless, attainable transmission distances for RZ-Star 16QAM are limited to about 800 km at BER=10−3 due to the SPM-induced mean nonlinear phase shift and significantly reduced in comparison to RZ-8PSK. 1E-1 1E-2 BER

Fig. 8.19 Transmission distances attainable for PDM RZ-Star 16QAM in comparison to RZ-8PSK and RZ-QPSK at 10 Gbaud when nonlinear phase shift compensation is not employed. Results were determined by computer simulations in [4].

RZ-Star 16QAM

1E-3 RZ-QPSK RZ-8PSK

1E-4 PDM

1E-5 0

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The distortions caused by the SPM-induced mean nonlinear phase shift can be partly compensated for using the simple optical compensator depicted in Fig. 7.18a. The optical phase is rotated back proportionally to the instantaneous power at the compensator input. The proportionality factor depends on the link parameters and the location where the compensator is placed within the system. In multi-span transmission systems with inline CD compensation, the compensator could principally be placed behind each fiber in each span (denoted here as “Case A”), but this is not a very practical approach. Another, more practical option is to place the compensator only in front of the coherent receiver (denoted here as “Case B”). Both compensation schemes are indicated in Fig. 8.17. It should be noted, that in both cases compensation is not ideal, since the intensity shape of the propagating signal changes along the fiber and interaction between chromatic dispersion and SPM prevents a complete compensation of the mean nonlinear phase shift. Moreover, the compensator depicted in Fig. 7.18a does not work ideally for PDM where distortions due to cross-polarization effects necessitate a more complex compensator for achieving best performance. Furthermore, the nonlinear phase noise (see Sect. 6.4.3) should be considered additionally in practical systems and an appropriate scaling factor α N L should be found to reduce the variance of the nonlinear phase shift [2]. Nevertheless, both compensation schemes presented here, which use only the simple compensator shown in Fig. 7.18a, lead to a significant transmission reach enhancement. This is illustrated in the case of RZ-Star 16QAM transmission for single-polarization in Fig. 8.20a and for PDM in Fig. 8.20b, assuming optimized launched powers into the SSMF and DCF. Reach enhancement single-polarization

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Fig. 8.20 Enhancement of transmission reach for RZ-Star 16QAM at 10 Gbaud for single polarization (a) and PDM (b) using different schemes of nonlinear phase shift compensation based on the optical compensator depicted in Fig. 7.18a.

In single-polarization systems, the transmission lengths attainable with RZ-Star 16QAM at 10 Gbaud can be increased from 900 km to about 1500 km when placing the compensator only at the receiver (Case B) and almost doubled to 1750 km when using a compensator behind each fiber (Case A). However, compensation with this simple optical compensator does not work equally effective for PDM where

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transmission distances are increased to 1100 km and 1200 km for Case B with scaling factors of α N L = 1 and α N L = 0.85, respectively, and to 1400 km for Case A (with α N L = 0.85). It can be observed from Fig. 8.20b that scaling factors not equal to one are optimal for PDM due to nonlinear cross-polarization effects. Nonlinear phase noise was neglected in these investigations.

8.4.2 Systems with Electrical CD Compensation When chromatic dispersion is not compensated for periodically in each transmission section but solely by an electrical CD compensation module within the receiver (see Fig. 8.17; the DCF and the optical amplifier in front of the DCF are then removed from the transmission link), the mean nonlinear phase shift difference between symbols with different power levels is smaller because the symbol power levels become indistinguishable after certain transmission distances due to chromatic dispersion. In Fig. 8.21a and Fig. 8.21b, the received constellation diagrams before digital phase estimation within the receiver in systems with inline CD compensation after 960 km are shown for SSMF input powers of -5 dBm (optimal) and -1 dBm, respectively. The mean nonlinear phase shift difference between symbols of the different intensity rings can be clearly seen as the limiting degradation effect. On the contrary, the relative nonlinearity-induced phase difference of both rings is smaller in systems without optical inline CD compensation. This becomes apparent from the constellation diagram depicted in Fig. 8.21c which is received at 1600 km after electrical CD compensation when an optimal SSMF input power of -1 dBm is chosen. Optical inline CD compensation

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Even without nonlinear phase shift compensation, transmission distances of 1700 km (single-polarization) and 1500 km (PDM) can be bridged in systems with electrical CD compensation at the receiver, as illustrated in Fig. 8.22. These distances are similar to or even greater than in systems with optical inline CD compensation which additionally use nonlinear phase shift compensation.

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Transmission distances in systems with electrical CD compensation at the receiver can be further increased by compensating for the small relative phase difference of both rings observable in Fig. 8.21c. Alternatively or additionally, signal distortions through the SPM-induced mean nonlinear phase shift can be reduced by means of adaptive digital equalization within the receiver or by applying predistortion techniques on the transmitter side. Both techniques are also applicable to systems with optical inline CD compensation. In summary, the SPM-induced mean nonlinear phase shift limits achievable distances for optical Star 16QAM transmission in multi-span systems with optical inline CD compensation when it is not being compensated for. However, transmission distances can be increased from 900 km / 800 km (without compensation) to 1750 km / 1400 km for single-polarization / PDM using the nonlinear phase shift compensation described above. The SPM-induced mean nonlinear phase shift is less critical in systems with electrical CD compensation at the receiver, in which distances of 1700 km / 1500 km can be attained even without nonlinear phase shift compensation. The research results which have been described in this chapter are just a first small step towards the characterization of high-order modulation formats with respect to their properties for optical multi-span transmission. On the one hand, spectral efficiencies can be increased by the application of high-order modulation formats, but on the other hand, transmission distances are decreased—to evaluate to what exact extent is an important issue of future research. Currently, more and more research groups become interested in this field. In their investigations, the transmission lengths and spectral efficiencies attainable in WDM systems are a matter of particular interest. Recently, impressive experimental results have been shown in [9] and [8] where a record spectral efficiency of 4.2 bit/s/Hz and a new record C-band capacity of 17 Tbit/s could be obtained with RZ-8PSK. Moreover, a transmission distance of 315 km has been demonstrated with Square 16QAM in a 10 × 112 Gbit/s WDM environment in [7]. Goals of future research in this field are discussed in detail later on in Sect. 9.4.

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References 1. Freund, R., et al.: 30 Gbit/s RZ-8-PSK transmission over 2800 km standard single mode fibre without inline dispersion compensation. In: Proceedings of Optical Fiber Communication Conference (OFC), OMI5 (2008) 2. Ho, K.P.: Phase-Modulated Optical Communication Systems. Springer (2005) 3. Louchet, H., et al.: Improved DSP algorithms for coherent 16-QAM transmission. In: Proceedings of European Conference on Optical Communication (ECOC), Tu.1.E.6 (2008) 4. Seimetz, M.: System degradation by the SPM-induced mean nonlinear phase shift in optical QAM transmission. In: Proceedings of Optical Fiber Communication Conference (OFC), JWA38 (2009) 5. Seimetz, M., et al.: Coherent RZ-8PSK transmission at 30Gbit/s over 1200km employing homodyne detection with digital carrier phase estimation. In: Proceedings of European Conference on Optical Communication (ECOC), vol. 3, pp. 265–266 (2007) 6. Seimetz, M., et al.: Transmission reach attainable for single-polarization and PolMux coherent Star 16QAM systems in comparison to 8PSK and QPSK at 10Gbaud. In: Proceedings of Optical Fiber Communication Conference (OFC), OTuN2 (2009) 7. Winzer, P., Gnauck, A.H.: 112-Gb/s polarization-multiplexed 16-QAM on a 25-GHz WDM grid. In: Proceedings of European Conference on Optical Communication (ECOC), Th.3.E.5 (2008) 8. Yu, J., et al.: 17 Tb/s (161x114 Gb/s) PolMux-RZ-8PSK transmission over 662km of ultra-low loss fiber using C-band EDFA amplification and digital coherent detection. In: Proceedings of European Conference on Optical Communication (ECOC), Th.3.E.2 (2008) 9. Zhou, X., et al.: 8x114Gb/s, 25-GHz-spaced, PolMux-RZ-8PSK transmission over 640km of SSMF employing digital coherent detection and EDFA-only amplification. In: Proceedings of Optical Fiber Communication Conference (OFC), PDP1 (2008)

Chapter 9

Performance Trends

Abstract This chapter summarizes the major trends in system performance which result from migration to higher-order modulation formats. Tendencies regarding relevant system parameters such as noise performance, laser linewidth requirements, chromatic dispersion tolerances and self phase modulation tolerances are identified. The principal impact of the choice of particular transmitter configurations and receiver schemes on system performance is outlined. Furthermore, the reduction of transmission distances achievable with high-order modulation formats is briefly discussed. Finally, goals for future research in this field are pointed out.

In order to assess the potential application of highly spectral efficient modulation formats in their networks, system designers would like to know how high-order modulation formats typically behave with respect to relevant performance degradation effects and attainable transmission distances. Thus, in addition to system complexity issues which have been detailed in the first part of this book, two major questions which have importance for system design are: How does the system react to transmission impairments? Which transparent optical transmission lengths can be bridged? The second part of the book has provided insight in the system and transmission characteristics of a wide range of phase and quadrature amplitude modulation formats for single-span and multi-span optical fiber transmission and has addressed these questions.

9.1 Migration to Higher-Order Formats—Parameter Trends In Chap. 7, several system parameters of interest such as noise performance, optimal receiver filter bandwidths, laser linewidth requirements, chromatic dispersion tolerances and self phase modulation tolerances have been discussed by looking at back-to-back and single-span system configurations. Concrete parameter values are summarized in Table 7.2, Table 7.4 and Table 7.6 for systems which use direct

M. Seimetz, High-Order Modulation for Optical Fiber Transmission, Springer Series in Optical Sciences 143, DOI 10.1007/978-3-540-93771-5 9, c Springer-Verlag Berlin Heidelberg 2009

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detection, homodyne differential detection and homodyne synchronous detection with digital phase estimation, respectively, assuming the use of serial transmitter configurations (described in Chap. 2). By using this material, the individual system properties and parameter tolerances of particular modulation formats can be rated in comparison with other formats. Clear performance tendencies valuable for system design can be ascertained and these are briefly summarized in the following paragraphs. The migration from traditionally used modulation formats to formats with more bits per symbol leads to a reduction of the symbol rate and narrowed spectral widths. Therefore, higher spectral efficiencies and per fiber capacities can be realized. This is the main motivation for a system upgrade to higher-order modulation. At the same time, migration to higher-order modulation formats strongly influences system performance. Positive effects are the improvement of chromatic dispersion tolerances and an increased robustness against polarization mode dispersion at reduced symbol rates. However, multi-span long-haul optical fiber transmission systems are typically limited by noise and Kerr nonlinearities. These impairments become more critical for higher-order modulation formats, resulting in a reduction of transmission reach. The noise performance degrades significantly for high-order PSK / DPSK formats in particular, whereas self phase modulation has a critical impact on QAM signals in particular, due to the unequal nonlinear phase shifts obtained by symbols with different power levels. The latter effect can partly be compensated for by nonlinear phase shift compensation, but is an inherent problem of optical QAM transmission. Moreover, the laser linewidth requirements increase with an increasing number of phase states and decreasing symbol rates. Currently, they are hardly able to be fulfilled at 40 Gbit/s by lasers for commercial use in case of 16PSK, Square 16QAM and Square 64QAM in systems with homodyne synchronous detection, even when feed forward digital phase estimation is used. Next, the system performance parameters just mentioned are discussed individually in some more detail. Noise performance: Noise performance degrades with an increasing number of bits per symbol as the Euclidean distances between the symbols become smaller. Assuming a fixed data rate, quaternary phase modulation shows a noise performance similar (synchronous detection) or only about 1 dB worse (differential detection) than binary phase modulation. But high performance penalties arise for higherorder phase modulation formats (8PSK requires an OSNR about 3.5 dB higher than QPSK, 16PSK an OSNR about 4.5 dB higher than 8PSK). High-order QAM formats exhibit a significantly better noise performance than high-order phase modulation formats for a certain number of bits per symbol, in particular Square QAM formats. In comparison with 16PSK, Square 16QAM has an OSNR performance gain of about 4 dB, for instance. Laser linewidth requirements: Laser linewidth requirements increase with an increasing number of phase states, since a certain level of laser phase noise is more critical for closer phase distances. In addition, the reduction of the symbol rate makes the laser phase noise more critical for modulation formats with a higher number of bits per symbol. In systems with direct detection, the linewidth requirements

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are relatively relaxed. Even 16DPSK can tolerate a linewidth of about 1 MHz at r B = 40 Gbit/s. In the case of homodyne differential detection, the effective phase noise taking effect on the electrical differential demodulation process is determined by the beat-linewidth. The linewidth requirements on each laser are approximately doubled in comparison with direct detection when the same linewidths are assumed for the signal laser and the LO. In systems with homodyne synchronous detection, the laser phase noise becomes a very critical parameter for high-order formats such as 16PSK, Square 16QAM and Square 64QAM, even when using feed forward digital phase estimation which is not impaired by processing delay. When the feed forward M-th power block scheme described in Sect. 3.5.3 is employed for phase estimation, the required linewidths at 40 Gbit/s are in the range of 240 kHz, 120 kHz and 1 kHz for 16PSK, Square 16QAM and Square 64QAM, respectively. These requirements are not able to be fulfilled with lasers currently available for commercial use. A commercial application of those modulation formats in systems with synchronous detection necessitates the development of low-cost lasers with very low linewidth specifications. Moreover, the application of improved phase estimation schemes offers a way of further relaxing the requirements on laser linewidth. Chromatic dispersion tolerances: The principal tendencies for the chromatic dispersion tolerances of high-order modulation formats become clear when looking at signals with RZ pulse shape. At a fixed data rate, the dispersion tolerances increase with the order of the modulation format due to the reduced symbol rates and the related narrower spectral widths. As regards high-order modulation signals with NRZ pulse shape, the chromatic dispersion tolerances are smaller in comparison to RZ and depend strongly on the chirp behavior of the transmitter. When a chromatic dispersion of 320 ps/nm has been accumulated along the transmission link, the receiver sensitivity penalty at BER=10−4 is still below 1 dB for modulation formats of at least fourth order in systems using homodyne synchronous detection and RZ pulse shape, even when no electrical chromatic dispersion compensation is implemented within the receiver. Self phase modulation tolerances: Generally, the modulation formats tend to result in SPM tolerances which become worse with an increasing number of phase states. Each symbol of an idealized phase modulated signal with constant power would be effected by the same nonlinear phase shift during fiber propagation if there was no other effect than SPM. In this case, the received constellation would be rotated, but not distorted. However, chromatic dispersion and SPM interact during propagation. Power fluctuations induced by chromatic dispersion cause the nonlinear phase shifts obtained by the symbols to become different and the received constellation diagrams to become distorted in amplitude and phase. When QAM signals have been propagated through the fiber, the constellation diagrams are deformed even when the chromatic dispersion is not taken into account, since symbols with different power levels are effected by different mean nonlinear phase shifts. This additional effect on them points to an inherent problem of optical QAM transmission and is the reason for the poor SPM performance of all QAM formats. However, relatively simple techniques can be employed to compensate for this effect.

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Polarization mode dispersion and nonlinear phase noise: The impact of polarization mode dispersion and nonlinear phase noise on the transmission of optical signals with high-order modulation was only briefly discussed in Sect. 6.4. In the same manner as for chromatic dispersion, high-order modulation formats offer a way of relaxing the requirements on polarization mode dispersion since a certain group delay difference has a smaller impact on neighboring pulses for reduced symbol rates and longer pulse durations. Moreover, it was presumed in Sect. 6.4 that nonlinear phase noise may become a less dominant effect for higher-order modulation formats when compared to the linear phase noise because the transmission lengths achievable with higher-order formats are shorter. However, this must be proved by future research.

9.2 Impact of the System Configuration and Pulse Shape The second part of the book has also discussed the impact of the choice of particular system configurations on system performance. Nearly all transmitter and receiver structures described in the first part of this book have been examined in this discussion. This allows the transmitters and receivers to be rated not only on the basis of their complexity and practical feasibility as done in Chap. 4, but also according to aspects of their system performance. Moreover, differences between high-order modulation signals with NRZ and RZ (50% duty cycle) pulse shapes have been exposed. Parameter values of systems with direct detection and homodyne differential detection are summarized in Table 7.3 and Table 7.5, respectively, where various 8PSK / 8DPSK system configurations which comprise different transmitter configurations with individual signal characteristics and different decision schemes are taken into consideration. Parameter values of systems with homodyne synchronous detection considering several Square 16QAM transmitter configurations are given in Table 7.7. In what follows, the major performance tendencies are outlined. Impact of the transmitter configuration and pulse shape: For any modulation format, the transmitter can be composed of different structures. The optical output signals of the respective transmitters exhibit individual properties in signal shape, spectrum, symbol transitions and chirp characteristics. These signal properties have a crucial influence on the overall system performance. Generally, transmitter configurations where optical power is reduced during symbol transitions show a beneficial system behavior. Firstly, noise performance is improved due to higher peakto-average power ratios. Secondly, chromatic dispersion tolerances are increased because chirp does not appear simultaneously with high power levels. Thirdly, the self phase modulation tolerances are enhanced, since power fluctuations induced by chromatic dispersion are less distinct when the impact of chirp is insignificant. Moreover, higher deviations from the optimal bandwidths of the optical and electrical receiver filters can be tolerated. For these reasons, the parallel DPSK / Star QAM transmitter outperforms the serial DPSK / Star QAM transmitter for NRZ

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pulse shape. In the case of Square QAM and NRZ, the conventional IQ transmitter is superior to other Square QAM transmitters where symbol transitions are conducted at higher power levels. Furthermore, RZ signals show a predominantly superior system performance in comparison with NRZ signals and their transmission characteristics are almost independent of the transmitter structure used. All tendencies mentioned here tend to become more significant with increasing modulation format order, because the percentage of unfavorable symbol transitions with high chirp then increases. To sum up, transmitter setups where high chirp appears simultaneously with high power levels should be avoided. However, it should be noted that the conclusions drawn here may no longer be valid in systems where optical signals are narrowly filtered at the transmitter output or the transmission link and where signal characteristics undergo a significant change, for instance in WDM systems with small channel spacings. Impact of the employed receiver concept: Apart from heterodyne detection, which was not dealt with within this book due to high receiver bandwidth requirements, three detection schemes can be employed for the reception of optical highorder modulation signals: direct detection, homodyne differential detection and homodyne synchronous detection. Homodyne synchronous detection with carrier synchronization through digital phase estimation features the principal advantage of an improved noise performance compared with the other two detection schemes. The performance gain depends on the modulation format used and is about 2 dB on average—as long as laser phase noise does not degrade receiver sensitivity. But laser linewidth requirements for homodyne synchronous detection are critical for many of the high-order formats, so differential detection schemes which show more relaxed linewidth requirements can probably achieve similar receiver sensitivities in practice and should then be preferred, since they feature simpler implementation. However, it should be borne in mind that Square QAM formats are conveniently detected only by synchronous techniques and feature the best noise performance for a given number of bits per symbol. The general benefits of coherent detection compared to direct detection can be exploited using homodyne synchronous as well as homodyne differential detection. Transmission impairments such as chromatic dispersion, polarization mode dispersion, and possibly even Kerr nonlinearities, can be compensated for efficiently in the electrical domain. WDM channels can be selected with high selectivity using a tunable local oscillator. The great potential of coherent detection combined with the electronic compensation of chromatic dispersion for transmission reach and cost savings was demonstrated in the multi-span transmission experiments without inline CD compensation described in Chap. 8. However, direct detection has its benefits as well, since it features the most relaxed linewidth requirements and does not require any frequency or phase synchronization or polarization control. Moreover, the positioning of the thresholds for data recovery influences the system noise performance. In systems limited by shot-noise or amplifier noise, the thresholds in circular constellations should optimally be arranged radially to maximize distances between symbol states and thresholds.

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Tolerance to deviations from the optimal receiver filter bandwidths: Optimal receiver filter bandwidths for systems with direct detection in back-to-back configuration have been discussed in Sect. 7.1.2. It has been shown that RZ signals tolerate much higher deviations from the optimum optical and electrical receiver bandwidths than NRZ signals. In the case of NRZ, the parallel transmitter features reduced power during symbol transitions and proves to be more tolerant than the serial transmitter—as far as deviations from the optimal bandwidths of the optical and electrical receiver filters are concerned. When the serial transmitter configuration is used in combination with NRZ pulse carving, the signals become very vulnerable to narrow optical filtering with an increasing order of phase modulation. For instance, an optical bandwidth of at least 3 · r S is then necessary for 16DPSK to avoid high performance penalties. Generally, in more complex systems such as multi-span transmission systems comprising many fiber spans and optical filtering on the link, the optimal receiver filter bandwidths depend on the setup of the whole system and must be optimized for every system configuration individually.

9.3 Reduction of Attainable Transmission Distances In Sect. 9.1, it was discussed that the migration to modulation formats with more bits per symbol leads to higher spectral efficiencies and higher chromatic dispersion and polarization mode dispersion tolerances. At the same time, these are accompanied by inferior noise performance and smaller self phase modulation tolerances. The two latter effects considerably determine the distances achievable for single-channel multi-span long-haul transmission. Thus, systems applying high-order modulation formats show a reduced transmission reach. The evaluation of transmission distances attainable using high-order modulation formats represents an important field of current and future research. Some recent experimental results obtained in the research group of the author have been presented in Chap. 8. These confirm the expected reduction of transmission reach when migrating to higher-order formats. In multi-span transmission systems with optical inline CD compensation, distances of 3700 km / 1360 km / 600 km and 3200 km / 960 km / 400 km could be bridged with RZ-QPSK / RZ-8PSK / RZStar 16QAM for single-polarization and polarization division multiplexing, respectively, assuming a common symbol rate of 10 Gbaud, single-channel transmission and a BER reference of 10−3 . In the case of single-polarization, the transmission distance for RZ-Star 16QAM could be increased to about 1000 km by applying compensation of the mean nonlinear phase shift. Moreover, the transmission lengths can be increased by replacing optical inline CD compensation with an electrical CD compensation at the receiver. This way, transmission distances of > 6000 km / 2800 km / 950 km could be attained for single-polarization RZQPSK / RZ-8PSK / RZ-Star 16QAM. The transmission distance of 950 km for RZStar 16QAM was achieved in a five-channel WDM environment and could even be extended to 1400 km by using adaptive electronic equalization. Results from

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computer simulations indicate that a further extension of transmission reach is possible for the higher-order formats by optimizing the practical system setups. Generally, as regards optical QAM transmission, a compensation of the SPM-induced mean nonlinear phase shift is essential for achieving longer distances. It should be noted that the comparison of transmission distances in this book assumes a common symbol rate for all the modulation formats. The differences detected between transmission distances would have been smaller for comparisons made at the same data rate.

9.4 Goals of Future Research In the future, an extension of network capacities is desirable while maintaining an attractive system reach. Network capacities can be increased by applying high-order modulation formats which provide a higher spectral efficiency. The reduction of transmission distances aligned with this can be mitigated by attention to the practical optimization and high-quality fabrication of the system components required for generating and detecting optical signals with high-order modulation, but also by diminishing transmission impairments such as noise and fiber nonlinearities using low-noise optical amplification and Kerr effect compensation. Future research should cover the following areas: Transmission distances achievable with high-order modulation formats: Analysis of multi-span fiber transmission systems with high-order modulation is still at an early stage. Some initial results, exploring the transmission distances for singlechannel transmission, have been presented in this book. In order to enable transmission of signals with high-order modulation over long distances, more detailed investigations are indispensable. Link configurations must be optimized for optimal fiber input powers and dispersion maps in systems with optical inline chromatic dispersion compensation—individually for any format and for a wide range of formats. A key issue is the development of techniques which will efficiently compensate for fiber nonlinearities. It is necessary to pursue the question of how the inherent phase distortions of QAM signals through the unequal nonlinear phase shifts obtained by symbols with different power levels can best be compensated for in multi-span transmission systems, when single-channel and WDM systems are taken into consideration. Furthermore, the influence of the nonlinear phase noise must be estimated to be able to finally evaluate the question: Which transparent optical transmission lengths can be bridged? Behavior of high-order modulation formats in WDM systems: The transmission lengths and channel spacings achievable with high-order modulation formats in WDM systems are a matter of particular interest. Attention must paid to some aspects which have not been considered in detail within this book: channel filtering, crosstalk and inter-channel nonlinearities. The channel spacing attainable depends on the signal bandwidth and on how narrowly optical signals can be filtered.

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Narrower channel spacing induces higher penalties due to cross phase modulation and four wave mixing. Thus, the system penalty induced by narrow optical filtering and the impact of linear and nonlinear inter-channel crosstalk must be determined for the various modulation formats. Moreover, narrow filtering has an influence on the signal’s transmission properties, so the conclusions drawn within this book concerning the transmission behavior of NRZ and RZ signals may require amendment. Another issue stems from limitation of the maximal power per fiber which is regulated in WDM systems and limited practically by the maximum output power of the optical amplifiers. In the case of higher spectral efficiencies and thus a higher number of channels within a certain bandwidth, the power available for a single channel is reduced—perhaps by too much to provide each channel with the optimal fiber input power determined by a trade-off between noise and fiber nonlinearities. From this point of view, nonlinear fiber effects may play a less important role in highly spectral efficient future networks with high-order modulation formats. Future research should address the question: Which transmission lengths, channel spacings and channel numbers can be obtained in WDM systems? Capacity and spectral efficiency attainable in WDM systems: Theoretically, if the fiber were linear and there were no system degradation through fiber nonlinearities, spectral efficiency could be increased to infinity by applying modulation formats of higher and higher order. Thereby, the expected increase of spectral efficiency would be about the ratio of the data rate to the symbol rate. Increasing noise requirements of the higher-order formats could then be fulfilled by simply launching more and more power into the fiber. However, in practical transmission systems, performance degrades due to fiber nonlinearities when the fiber input power is increased. Theoretical calculations show that spectral efficiencies attainable in WDM fiber transmission systems are upper-bounded. Even if low-noise distributed Raman amplification is assumed and intra-channel nonlinear effects are compensated for by applying reverse propagation, spectral efficiency in one polarization is estimated to be limited to 5 bit/s/Hz and 7 bit/s/Hz for WDM transmission over 2000 km and 1000 km, respectively [3, 4], caused by inter-channel nonlinear effects. A lot of research investigating the properties of practical WDM systems with high-order modulation must be undertaken in order to finally answer the question: Which spectral efficiencies and network capacities can be obtained practically, while maintaining attractive transmission distances? Increase of the capacity-distance product: Whereas it is evident that the spectral efficiency and network capacity can be increased by the application of high-order modulation formats, it has not been clarified yet whether the capacity-distance product can be improved, due to the reduced transmission distances. In [2], experiments with the greatest capacity-distance products have been reviewed. These experiments use binary and quaternary phase modulation and show the trend that the highest system capacities are achieved over the most moderate distances. The stars in Fig. 9.1 indicate capacities and distances attained in the experiments performed in [1, 2, 8]. Moreover, two reference lines are shown in Fig. 9.1, corresponding to constant capacity-distance products of 10 Pbit/s·km and 40 Pbit/s·km. In [1], the second-best

9.4 Goals of Future Research in the Field of High-Order Modulation 12000 41.03 Pbit/s⋅km DBPSK, Cai et al., 2003

10000 Distance [km]

Fig. 9.1 Can the capacitydistance product be increased by the application of highorder modulation formats? The stars indicate results experimentally achieved in [1, 2, 8]. The solid lines are reference lines for constant capacity-distance products.

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capacity-distance product so far, 41.03 Pbit/s·km, has been demonstrated by transmitting 373 RZ-DPSK channels in the C-band and the L-band at 10 Gbit/s over a transoceanic distance of 11000 km while using hybrid EDFA / Raman amplification and FEC. In [2], the record capacity-distance product of 41.82 Pbit/s·km has been attained, sending 164 PDM-QPSK channels at a channel data rate of 100 Gbit/s over a length of 2550 km while using Raman amplification and coherent detection. Very recently, initial impressive results using RZ-8PSK have been obtained. A record capacity of 17 Tbit/s in the C-band was demonstrated by sending 161 polarization division multiplexed RZ-8PSK WDM channels over 662 km ultra-low loss fiber, with a record spectral efficiency of 4.2 bit/s/Hz [8]. The capacity-distance product thereby achieved is 11.25 Pbit/s·km and four times smaller than the record product of 41.82 Pbit/s·km obtained in [2], due to the comparatively small transmission length. However, latent potential for further practical system optimization and for increasing experience with systems applying high-order modulation leaves the question open: Can the capacity-distance product be improved by applying high-order modulation formats? Utilization of polarization: Polarization information provides an additional degree of freedom in optical fiber transmission systems. Utilizing polarization, the spectral efficiency of any modulation format can be doubled by means of polarization division multiplexing. Here, how far crosstalk between the multiplexed channels degrades the performance of systems applying high-order modulation remains to be clarified in future research. Moreover, the compensation of the SPM-induced nonlinear phase shift for QAM transmission becomes more critical in the case of polarization division multiplexing. In addition to the phase and quadrature amplitude modulation formats discussed within this book, formats exploiting all the parameters of the electrical field and encoding information additionally into the polarization are available for optical transmission, so the question remains: How efficiently can polarization information be exploited in future optical networks? Practical system optimization: For many system experiments with high-order modulation currently performed, the main challenge is still a practical optimization of the system components. Signal distortions caused by pattern effects and accumulating in multiple modulator stages have led to implementation penalties in the Star 16QAM experiment described in Sect. 8.2.1 [6]. In recent Square 16QAM

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9 Performance Trends

experiments limited to distances of some hundred kilometers, an enhanced generation of the multi-level electrical driving signals for the conventional IQ transmitter [7] and an improved practical fabrication of the integrated quad-parallel MZM transmitter [5] are important steps in achieving improved system performance and reach. Thus, in order to compose transmitters performing closely to the theoretical performance limits, it is aimed to develop high-speed integrated optical modulator structures and electrical level generators of high quality. At the receiver end, it is an aim to design practical solutions which integrate the whole optical receiver frontend in a single chip, and to exploit digital signal processing technology to compensate for performance degradation effects and facilitate the recovery of information. So an important question is: What are the performance limits of practically optimized systems employing high-order modulation? Simulative system evaluation: Performance limits of optical fiber transmission systems with high-order modulation can also be explored via computer simulations. But this is not easily accomplished. In Monte Carlo simulations with a high number of bits, the computational effort can become unmanageable when multi-span WDM systems with long transmission distances, high per channel powers and a high number of channels are investigated. Currently available tools for semi-analytical BER estimation can not consider all transmission effects and can not easily be implemented for complex receiver configurations with complicated noise statistics at the decision gates, for instance the homodyne receiver with digital equalization and phase estimation. Furthermore, the data sequence length requirements can not be fulfilled when high magnitudes of accumulated chromatic dispersion lead to intersymbol interference across many symbols—being a particular problem for systems without optical inline CD compensation. This all raises the question: How can the performance of optical multi-span transmission systems with high-order modulation be evaluated exactly via computer simulations? Having finished all this research and answered all the questions posed above, it is possible that the final question may arise: Which is the most favorable modulation format? However, the ultimate modulation format will not be able to be identified. Each modulation format has its own benefits and drawbacks with respect to particular system parameters, so its suitability depends on the respective specifications of the system which it operates in and on the field of application, for instance the network segment which it is intended for. The future will show for which system applications and in which network segments particular high-order modulation formats can most profitably be deployed.

References 1. Cai, J.X., et al.: A DWDM demonstration of 3.73 Tb/s over 11,000 km using 373 RZ-DPSK channels at 10 Gb/s. In: Proceedings of Optical Fiber Communication Conference (OFC), PD22 (2003)

References

237

2. Charlet, G., et al.: Transmission of 16.4Tbit/s capacity over 2550km using PDM QPSK modulation format and coherent receiver. In: Proceedings of Optical Fiber Communication Conference (OFC), PDP3 (2008) 3. Essiambre, R.J., et al.: The capacity of fiber-optic communication systems. In: Proceedings of Optical Fiber Communication Conference (OFC), OTuE1 (2008) 4. Essiambre, R.J., et al.: Exploring capacity limits of fibre-optic communication systems. In: Proceedings of European Conference on Optical Communication (ECOC), We.1.E.1 (2008) 5. Sakamoto, T., et al.: 50-km SMF transmission of 50-Gb/s 16 QAM generated by quad-parallel MZM. In: Proceedings of European Conference on Optical Communication (ECOC), Tu.1.E.3 (2008) 6. Seimetz, M., et al.: Transmission reach attainable for single-polarization and PolMux coherent Star 16QAM systems in comparison to 8PSK and QPSK at 10Gbaud. In: Proceedings of Optical Fiber Communication Conference (OFC), OTuN2 (2009) 7. Winzer, P., Gnauck, A.H.: 112-Gb/s polarization-multiplexed 16-QAM on a 25-GHz WDM grid. In: Proceedings of European Conference on Optical Communication (ECOC), Th.3.E.5 (2008) 8. Yu, J., et al.: 17 Tb/s (161x114 Gb/s) PolMux-RZ-8PSK transmission over 662km of ultra-low loss fiber using C-band EDFA amplification and digital coherent detection. In: Proceedings of European Conference on Optical Communication (ECOC), Th.3.E.2 (2008)

Appendix A

Differential Encoders for 8DPSK / 16DPSK

In this appendix, the logical circuits of the differential encoders for 8DPSK and 16DPSK are specified. In Sect. 2.4.3, differential encoding for DPSK formats is described and the logical relations for the differential encoders of the serial and parallel DQPSK transmitter are derived. In the same manner, the differential encoders for higher-order DPSK transmitters can be obtained. Starting from the constellationdiagrams with the original bit mappings given, which assign the original data bits b1k , b2k , .., bm k to particular symbols, and with symbol assignments specified  at the encoder output mapping the differentially encoded bits d1k , d2k , .., dm k into particular symbols with absolute phase states, the truth tables can be established. Subsequently, the corresponding Karnaugh maps can be evaluated to determine the logical relations of the encoders.

Differential Encoders for 8DPSK Transmitters In the case of 8DPSK, the truth tables of the encoders have 64 rows. When using the bit mappings and symbol assignments as defined in Fig. 2.6 and Fig. 2.9 respectively, the logical circuit  of the serial 8DPSK transmitter, which  relates the current encoder output bits d1k , d2k, d3k to the current data bits b1k , b2k , b3k and the previous encoder output bits d1k−1 , d2k−1 , d3k−1 , is specified by d1k = b1k d1k−1 d2k−1 d3k−1 + b1k b3k d1k−1 d2k−1 + b2k b3k d1k−1 d3k−1

+ b2k d1k−1 d2k−1 d3k−1 + b1k b2k d1k−1 d2k−1 + b2k b3k d1k−1 d3k−1

+ b1k b3k d1k−1 d2k−1 + b1k d1k−1 d2k−1 d3k−1 + b1k b2k d1k−1 d3k−1 + b1k b3k d1k−1 d2k−1 d3k−1 + b1k b3k d1k−1 d2k−1 d3k−1 ,

(A.1)

d2k = b3k d2k−1 d3k−1 + b3k d2k−1 d3k−1 + b1k b2k d2k−1 d3k−1

+ b1k b2k d2k−1 d3k−1 + b1k b2k d2k−1 d3k−1 + b1k b2k d2k−1 d3k−1 , (A.2) 239

240

A Differential Encoders for 8DPSK / 16DPSK

d3k = b1k b2k b3k d3k−1 + b1k b2k b3k d3k−1 + b1k b2k b3k d3k−1

+ b1k b2k b3k d3k−1 + b1k b2k b3k d3k−1 + b1k b2k b3k d3k−1 + b1k b2k b3k d3k−1 + b1k b2k b3k d3k−1 .

(A.3)

Section 2.4.3 has demonstrated that the setup of the differential encoder changes when the parallel transmitter configuration is employed instead of the serial one. When the bit mappings and symbol assignments shown in Fig. 2.6 and Fig. 2.9 are assumed, respectively, the logical relations describing the differential encoder of the parallel 8DPSK transmitter can be derived as d1k = b1k d1k−1 d2k−1 d3k−1 + b2k b3k d1k−1 d3k−1 + b1k b2k d1k−1 d3k−1 + b1k b2k d2k−1 d3k−1 + b1k b3k d2k−1 d3k−1 + b2k b3k d1k−1 d3k−1

+ b1k b3k d2k−1 d3k−1 + b1k b2k d1k−1 d3k−1 + b2k d1k−1 d2k−1 d3k−1 , (A.4)

d2k = b2k d1k−1 d2k−1 d3k−1 + b1k b3k d1k−1 d3k−1 + b1k d1k−1 d2k−1 d3k−1 + b1k b2k d2k−1 d3k−1 + b2k b3k d2k−1 d3k−1 + b1k b3k d1k−1 d3k−1

+ b2k b3k d2k−1 d3k−1 + b1k b2k d1k−1 d3k−1 + b1k d1k−1 d2k−1 d3k−1 , (A.5) d3k = b1k b2k b3k d3k−1 + b1k b2k b3k d3k−1 + b1k b2k b3k d3k−1

+ b1k b2k b3k d3k−1 + b1k b2k b3k d3k−1 + b1k b2k b3k d3k−1 + b1k b2k b3k d3k−1 + b1k b2k b3k d3k−1 .

(A.6)

The relations for the third encoder output bit, given by (A.3) and (A.6), can be seen to be identical.

Differential Encoder for the Serial 16DPSK Transmitter In the case of 16DPSK, the differential encoders are quite complex. Here, only the differential encoder for the serial 16DPSK transmitter is described. The derivation of its logical relations necessitates the evaluation of a truth table with 256 rows. The relation for the encoder output bit d1k , for instance, has 30 OR combined terms, each consisting of 4-7 AND combined inputs. Based on the bit mapping defined in Fig. 2.6 and the symbol assignment shown in Fig. 2.9, the logical circuit of the differential encoder of the  serial 16DPSK trans mitter can be derived and the current encoder output bits d1k , d2k , d3k , d4k can

A Differential Encoders for 8DPSK / 16DPSK

241

 be shown to be related  to the current data bits b1k , b2k , b3k , b4k and the previous encoder output bits d1k−1 , d2k−1 , d3k−1 , d4k−1 with d1k = b1k b2k d1k−1 d2k−1 + b1k b2k d1k−1 d2k−1 + b1k b2k d1k−1 d2k−1

+ b1k b2k d1k−1 d2k−1 + b1k b3k b4k d1k−1 d2k−1 + b2k b3k b4k d1k−1 d2k−1

+ b2k b3k d1k−1 d3k−1 d4k−1 + b2k b4k d1k−1 d2k−1 d3k−1 + b2k d1k−1 d2k−1 d3k−1 d4k−1

+ b1k b3k b4k d1k−1 d2k−1 + b2k b4k d1k−1 d2k−1 d3k−1 + b2k b3k d1k−1 d3k−1 d4k−1 + b2k b3k b4k d1k−1 d2k−1 + b1k b2k d1k−1 d3k−1 d4k−1

+ b1k b2k b4k d1k−1 d2k−1 d3k−1 + b1k b2k b3k d1k−1 d2k−1 d4k−1

+ b1k b3k b4k d1k−1 d2k−1 d4k−1 + b1k b2k b3k d1k−1 d2k−1 d3k−1

+ b1k b4k d1k−1 d2k−1 d3k−1 d4k−1 + b2k b3k b4k d1k−1 d2k−1 d4k−1

+ b1k b2k b4k d1k−1 d2k−1 d3k−1 + b2k b4k d1k−1 d2k−1 d3k−1 d4k−1

+ b1k b2k b3k d1k−1 d2k−1 d4k−1 + b1k b3k b4k d1k−1 d2k−1 d4k−1

+ b1k b2k b3k d1k−1 d2k−1 d3k−1 + b2k b4k d1k−1 d2k−1 d3k−1 d4k−1

+ b1k b4k d1k−1 d2k−1 d3k−1 d4k−1 + b2k b3k b4k d1k−1 d2k−1 d4k−1

+ b1k b2k b4k d1k−1 d2k−1 d3k−1 d4k−1 + b1k b2k b4k d1k−1 d2k−1 d3k−1 d4k−1 ,

(A.7)

d2k = b3k b4k d2k−1 d4k−1 + b3k b4k d2k−1 d4k−1 + b1k b2k b4k d2k−1 d3k−1

+ b1k b2k d2k−1 d3k−1 d4k−1 + b1k b2k b4k d2k−1 d3k−1 + b1k b2k d2k−1 d3k−1 d4k−1 + b2k b3k d2k−1 d3k−1 d4k−1 + b1k b2k b4k d2k−1 d3k−1 + b2k b3k d2k−1 d3k−1 d4k−1

+ b1k b2k d2k−1 d3k−1 d4k−1 + b2k b3k d2k−1 d3k−1 d4k−1 + b1k b2k b4k d2k−1 d3k−1 + b1k b2k d2k−1 d3k−1 d4k−1 + b2k b3k d2k−1 d3k−1 d4k−1

+ b1k b2k b4k d2k−1 d3k−1 d4k−1 + b1k b2k b4k d2k−1 d3k−1 d4k−1

+ b1k b2k b4k d2k−1 d3k−1 d4k−1 + b1k b2k b4k d2k−1 d3k−1 d4k−1 ,

(A.8)

d3k = b4k d3k−1 d4k−1 + b1k b2k b3k d3k−1 d4k−1 + b1k b2k b3k d3k−1 d4k−1

+ b1k b2k b3k d3k−1 d4k−1 + b1k b2k b3k d3k−1 d4k−1 + b1k b2k b3k d3k−1 d4k−1 + b2k b4k d3k−1 d4k−1 + b1k b2k b3k d3k−1 d4k−1

+ b1k b2k b3k d3k−1 d4k−1 + b2k b4k d3k−1 d4k−1

+ b1k b2k b3k d3k−1 d4k−1 ,

(A.9)

242

A Differential Encoders for 8DPSK / 16DPSK

d4k = b1k b2k b3k b4k d4k−1 + b1k b2k b3k b4k d4k−1 + b1k b2k b3k b4k d4k−1

+ b1k b2k b3k b4k d4k−1 + b1k b2k b3k b4k d4k−1 + b1k b2k b3k b4k d4k−1

+ b1k b2k b3k b4k d4k−1 + b1k b2k b3k b4k d4k−1 + b1k b2k b3k b4k d4k−1

+ b1k b2k b3k b4k d4k−1 + b1k b2k b3k b4k d4k−1 + b1k b2k b3k b4k d4k−1 + b1k b2k b3k b4k d4k−1 + b1k b2k b3k b4k d4k−1

+ b1k b2k b3k b4k d4k−1 + b1k b2k b3k b4k d4k−1 .

(A.10)

It can be concluded that the complexity of the differential encoders increases significantly with an increasing order of the phase modulation.

Appendix B

Theoretical BER Formulas

This appendix compiles theoretical BER formulas for systems with direct detection and coherent synchronous detection which are well known from the literature [1–4]. These formulas describe the theoretical SNR requirements of systems with PSK / DPSK and QAM for idealized receivers with matched filtering. With matched filtering, the SNR of the decision samples is maximized, becomes independent of the signal shape and is solely a function of the average symbol energy and the power spectral density of the noise SN R =

E s,avg 1f = 2 · OSN R · . N0 rS

(B.1)

In contrast to the system characterization conducted in Chap. 7, the impact of specific setups used at the transmitter, the pulse shape of the signal, the optical and electrical receiver filters and the data recovery techniques employed at the receiver are not considered here. For some cases, the formulas represent approximations. More details can be found in [1–4].

SNR Requirements of Systems with Direct Detection Equations (B.2)–(B.5) describe the theoretical SNR requirements of direct detection systems with OOK, DBPSK, DQPSK and M-ary DPSK, respectively, assuming the matched filtering case.

BER

OOK

=

  1 −S N R/2 SN R ·e · 1+ , yth = R · Ps,avg /2 2 2

BER

DB PSK

=

  1 −S N R SN R ·e · 1+ 2 4

(B.2)

(B.3)

243

244

B Theoretical BER Formulas

BER

BER

DQ PSK

M DPSK

=

∞ 3 S N R · e−S N R X sin(nπ/4) − · 8 4 n n=1      SN R SN R 2 + I n+1 · I n−1 2 2 2 2

2 · er f c ≈ log2 M

r

π SN R · sin 2 M

!

(B.4)

(B.5)

In (B.4), In is the n-th order modified Bessel function of the first kind. The BER of Star MQAM systems can be estimated from the BER formulas for PSK / DPSK formats by calculating the BER for the inner ring, while assuming the same average power as for the corresponding PSK / DPSK constellation with an equal number of phase states. Moreover, an appropriate pre-factor of 2/log2 M must be assigned. In this calculation, it is not taken into account that the noise levels on the rings are different for direct detection.

SNR Requirements of Systems with Coherent Synchronous Detection In (B.6)–(B.9), the theoretical SNR requirements of systems with coherent synchronous detection for 2ASK, BPSK, MPSK and Square MQAM is specified, assuming amplifier noise limited detection and matched filtering. !

(B.6)

√  1 · er f c SN R 2

(B.7)

√ π 2 · er f c S N R · sin log2 M M

(B.8)

B E R 2AS K

BER

BER

B E R Squar e

M PSK

M Q AM

B PSK

≈

1 = · er f c 2

=

r

SN R 2

s !   2 1 3S N R ≈ · 1− √ · er f c log2 M 2(M − 1) M

(B.9)

References

245

In Table B.1, OSNR requirements for B E R = 10−4 calculated with (B.8), (B.9) and (B.1) are compared with values obtained by computer simulations for the specific system configurations discussed in Sect. 7.3.1. Table B.1 Comparison of OSNR requirements calculated with (B.8), (B.9) and (B.1) with values obtained by computer simulations (sim.) for the system configurations discussed in Sect. 7.3.1, assuming a data rate of r B = 40 Gbit/s and a reference noise bandwidth of 1λ = 0.1 nm. Format

QPSK

8PSK

16PSK

St.16QAM

Sq.16QAM Sq.64QAM

SNR [dB], theory OSNR [dB], theory OSNR [dB], RZ, sim. OSNR [dB], NRZ, sim.

11.8 10.8 11.2 13.0

16.9 14.2 14.6 16.9

22.6 18.6 18.9 22.4

20.0 16.0 16.1 18.4

18.2 14.2 15.0 17.2

24.3 18.5 18.7 20.1

The values calculated with the theoretical BER formulas, reflecting the matched filtering case, show the same relative performance tendencies as observed for the specific system configurations discussed in Sect. 7.3.1. Moreover, it can be seen that the theoretical performance limits of matched filtering are approached more closely in the case of RZ.

References 1. 2. 3. 4.

Ho, K.P.: Phase-Modulated Optical Communication Systems. Springer (2005) Proakis, J.G.: Digital Communications. McGraw-Hill (2001) Schwartz, M.: Information, Transmission, Modulation, and Noise. McGraw-Hill (1990) Xiong, F.: Digital Modulation Techniques. Artech House, Inc. (2000)

Index

Symbols 2 × 4 90◦ hybrid 62, 71, 84 3 × 3 coupler 65, 87 χ 2 -distribution 137 120◦ hybrid 65 180◦ hybrid 61 3 dB coupler 61 A Absorption 144 Access networks 6 Active control loop 64 Additive white Gaussian noise 69, 134 Amplifier noise 69, 82, 134, 145, 157, 207 Amplifier noise limited detection 178, 186 Amplitude shift keying (ASK) 4, 23 Analog-to-digital converter 91, 100 Arg-decision 74, 111 Arg-operation 21 Argument averaging 109, 188 ASE-ASE noise 69, 82 Asynchronous detection 93 Attenuation 143, 144 Attenuation coefficient 144 Automatic frequency control (AFC) 89, 99 Auxiliary phase coding 4 B Back-to-back transmission 155 Balanced detection 62, 70, 80, 84 Balanced OPLL 96 Band-pass filter 60 Bandwidth demands 6 Beat-linewidth 80, 97, 181

Bessel filter 60 Bessel function, modified 164 Birefringence 151 Bit error ratio (BER) 132 theoretical performance 243 Bit mapping 23, 25, 34 rotation symmetric 38, 45, 114 Block length 103, 106, 190 Block-by-block phase correction 102 Boltzmann constant 69 Burst-mode transmission 94 Butterfly equalizer 100 C Capacity 2, 234 Capacity-distance product 2, 7, 234 Carrier recovery data aided 94 decision directed 94, 110 joint-polarization 100 non data aided 94 Carrier synchronization 6, 94 Central Limit Theorem 16 Channel cross-channel interference 91 Channel separation 91 Channel spacing 2, 233 Chirp 16, 32, 167, 170, 195 Chirp-intensity product 33, 36, 55, 168, 195 Chromatic dispersion (CD) 145, 167, 196 Chromatic dispersion compensation electrical 207, 212, 217, 224 optical, inline 207, 208, 213, 221 Chromatic dispersion tolerances direct detection 166, 175 homodyne detection differential detection 182, 183

248 synchronous detection 194, 202 summary 229 Class partitioning 105, 190 Closed loop M-th power block scheme 107 performance 188 Closed loop carrier recovery 94 Coherence time 17 Coherent detection 3, 5, 79 complexity 122 Combination 85 Complex envelope 32, 93, 101 Complexity 3 receiver 122 transmitter 119 Constant modulus algorithm (CMA) 100 Constellation diagram 23 Continuous wave 16 Conventional IQ transmitter 42, 121, 204 Costas loop 95 Cross phase modulation (XPM) 150, 234 intra-channel 150 Crosstalk 233 Cycle slips 104 D Data rate 23 Data recovery 73, 111 Data recovery logic 74, 111, 124 Data sequences 127, 236 Data to phase-lock crosstalk 96 De Bruijn bit sequence 128 De Bruijn symbol sequence 128 Decision boundaries 200 Decision circuit 74, 106, 114 Decision driven OPLL 96 Degree of compensation 169 Delay line frequency discriminator 99 Delay line interferometer (DLI) 61, 135 Demultiplexer 27, 103 Differential decoder 73, 97, 104, 111, 121 Differential detection 66, 73, 86 performance 156, 177 Differential encoder 27, 28, 97, 104, 239 Differential phase shift keying (DPSK) 25 Differential quadrant encoding 37, 113 Differentially encoded PSK (DEPSK) 186 Digital coherent receiver 85, 95, 100, 140 Digital differential demodulation 91, 177 Digital frequency offset estimation 92, 110 Digital phase estimation 6, 95, 99 performance 186, 188, 202 Digital signal processing 6, 91, 99 Digital signal processor (DSP) 99, 103

Index Digital storage oscilloscope 209 Digital subscriber line (DSL) 1 Digital-to-analog converter 40 Direct detection 66 complexity 122 performance 156, 175 Direct detection interference 91 Direct modulation 16 Dispersion compensating fiber (DCF) 147 Dispersion managed fiber 6 Dispersion map 233 Dispersion shifted fiber (DSF) 147 Dispersion slope 145 Distributed feedback (DFB) laser 16 Driving signals 24 Duobinary 4 Duty cycle 22 E Effective core area 148 Effective length 149, 152 Eigendecomposition 136 Eigenvalue 136 Eigenvector 136 Electric flux density 147 Electric polarization 147 Electrical field 16, 79, 143 Electrical field parameters 3, 79, 235 Electronic distortion equalization (EDE) 91, 92, 100 Enhanced IQ transmitter 47, 121, 204 Equalization 6, 95, 100, 174, 225 Equalizer frequency domain 100 time domain 100 Erbium doped fiber amplifier (EDFA) 2, 145 Euclidean distance 37, 159 External cavity laser (ECL) 16 External modulation 16 Eye opening 131 Eye opening penalty (EOP) 131, 167 Eye spreading 24, 47 F Fabry-Perot laser 15 Fast Fourier transform (FFT) 132, 144 Feed forward M-th power block scheme 102 performance 188, 190 Feed forward carrier recovery 94 Field averaging 103, 109, 188 Filters 59 Finite impulse response (FIR) filter 212

Index

249

Forward error correction (FEC) 2, 235 Four wave mixing (FWM) 150, 234 intra-channel 150 Fourier series 134 Fractionally spaced equalizer 100 Free space optics 65 Frequency noise 16 Frequency offset 86, 89, 92, 93, 99, 110 Frequency shift keying (FSK) 86 Frequency synchronization 6, 91, 123 Fundamental mode 151 G Galois fields 128 Gaussian filter 60 Gray coding 23, 25, 34 Group delay 145 H Heterodyne detection 81, 140, 180 Homodyne detection 80 differential detection 86 complexity 123 performance 177, 183 synchronous detection 93, 104, 111 complexity 123 performance 185, 202 Hyperbolic filter 110 I Ideal driving 40, 55 Image-rejection receiver 63, 81 Impulse shaper 22 Initial phase offset 94, 110 Intensity 148 Intensity detection branch 67, 68, 140 Intensity dips 33 Intensity modulation 4, 19 Intensity noise 16 Intensity ripples 56 Inter-symbol interference (ISI) 128, 147 Intermediate frequency (IF) 81 Internet 1, 6 IQ modulator (IQM) 20, 42 IQ receiver with 2 × 4 90◦ hybrid 71 with DLIs 68, 122, 139 IQ-decision 74, 111 K Karhunen-Lo`eve expansion

134

Karnaugh maps 31 Kerr effect 128, 144, 147 L Laplace transform 137 Large-amplitude QPSK 52 Laser 15 Laser linewidth 16 Laser linewidth requirements 5, 98 direct detection 164, 175 homodyne detection differential detection 181, 183 synchronous detection 188, 202 summary 228 Laser phase noise 16, 70, 80, 86, 89, 93 Least mean square (LMS) algorithm 100 Level generator 40, 44, 121 Light emitting diode (LED) 15 Linear phase noise 152 Linewidth-to-data-rate ratio 165, 192 LO-ASE noise 82, 83, 178 Local loop 1 Local oscillator 79 tunable 96, 98 Loop delay 97, 108, 189 Loop filter 96 Low-pass filter 60, 91 M Mach-Zehnder modulator (MZM) 19 Matched filter 60, 186, 243 Material dispersion 145 Maximum length sequence 127 Minimum transmission point 20 Modulator driver 42 Modulators 18 Moment generating function (MGF) 137 Monte Carlo (MC) simulation 132, 159 Multi-level signaling 23 Multi-mode interference (MMI) coupler 64 Multi-parallel MZM transmitter 52 Multi-span transmission 207 Multiple DLI receiver 67, 122, 138 Multiple moduli algorithm (MMA) 217 N Network scenarios 6 Noise figure 157, 221 Non-ideal driving 40, 56 Non-return to zero (NRZ) 4, 21, 176 Nonlinear index coefficient 148 Nonlinear phase noise 140, 152, 173, 230 Nonlinear phase shift 149, 171, 199, 215

250 mean 152 variance 152 Nonlinear phase shift compensation compensators 173 direct detection 171 future research 233 homodyne detection synchronous detection 199, 202 multi-span transmission 216, 221 Nonlinear propagation coefficient 144, 149 Nonlinear scattering effects 151 Nonlinear Schroedinger equation 143, 147 Nonlinearities 128, 144, 147, 207, 234 Normalization 77 Normalized field averaging 105, 107, 188 Normalized symbol coordinates 23 O On-off keying (OOK) 4, 24 Optical phase locked loop (OPLL) 6, 95, 190 Optical quadrature frontend 84 Optical signal to noise ratio (OSNR) 135 Optical time division multiplexing 6 Optical voltage controlled oscillator 98 Optimal receiver filter bandwidths 160, 231 OSNR penalty 165, 167 OSNR requirements 160 direct detection 157, 175 experiments 219 homodyne detection differential detection 178, 183 synchronous detection 185, 202 summary 228 P Parallel DPSK transmitter 27, 33, 120, 176 Parallel Star QAM transmitter 36, 120, 221 Parallelization 103 Pattern effects 215 Peak-to-average power ratio 160, 188 Permittivity 147, 148 Phase ambiguity 37, 104, 111 Phase detection branch 67, 70 Phase detector 96 Phase differential algorithm 110 Phase differentiation 92 Phase diversity receiver 63, 86, 140 performance 177, 180 Phase error 93, 94, 101, 110 Phase locked loop (PLL) 81, 98 Phase locking 6 Phase matching 85

Index Phase modulation 5, 18, 25 Phase modulator 18 Phase offset 81, 99 Phase pre-integration 34 Phase shifter 63, 72 Phase tracking 107, 109 Phase unwrapping 104 Photodiode 68, 135 Planck constant 69 PM-IM conversion 61, 149 PMD-parameter 151 Pockels effect 18 Polarization beam combiner (PBC) 213 Polarization beam splitter (PBS) 65, 85, 213 Polarization control 6, 91, 124 Polarization diversity 85, 124 Polarization division multiplexing (PDM) 6, 81, 85, 100, 124, 213, 219, 235 Polarization information 81, 235 Polarization mode dispersion 151, 230 Polarization modulation 81, 235 Polarization shift keying (POLSK) 81 Polarization states 65 Power spectral density 69, 157 Pre-amplifier 69, 134 Pre-distortion 225 Preamble 94 Principle states of polarization (PSP) 151 Probability density function (PDF) 133, 137 Processing delay 108, 188 Propagation constant 143, 145, 148 Pseudo random binary sequence 127 Pulse carver 22 Pulse shape 4, 21, 176, 230 Push-pull mode 19 Push-push mode 19 Q Quad-parallel MZM transmitter 52, 121 Quadrant ambiguity 37, 97, 113 Quadrature amplitude modulation 5, 34, 37 Quadrature point 19 Quantum efficiency 69 Quantum limit 179 R Raman amplification 2, 7 Raman gain spectrum 151 Random number seed 128, 132 Random walk 16, 81, 104, 164 Rayleigh scattering 144 Re-circulating fiber loop 209, 214

Index Receiver configuration, impact 231 Receiver matrix 136, 138 Receiver sensitivities direct detection 157, 175 homodyne detection differential detection 178, 183 synchronous detection 185, 202 summary 228 Receiver sensitivity 5, 93 Receiver sensitivity penalty 181 Records 6 Rectangular filter 103 Reference bandwidth 135 Refractive index 18, 145, 147 Relative intensity noise (RIN) 17, 91 Responsivity 68 Return to zero (RZ) 4, 21, 176 Reverse propagation 234 Ring ratio 35, 159, 170, 187, 216 Rise time 22, 55 S Saddlepoint approximation 138 Scaling factor 153, 223 Segment change detector 104 Selective gated PLL 98 Self phase modulation (SPM) 150, 174 Self phase modulation tolerances direct detection 168, 175 homodyne detection differential detection 182, 183 synchronous detection 198, 202 summary 229 Semi-analytical BER estimation 133, 140, 159, 236 Serial DPSK transmitter 26, 33, 120, 176 Serial Square QAM transmitter 38, 121, 204 Serial Star QAM transmitter 35, 120 Shot-noise 69, 80, 94, 135 Shot-noise limited detection 178, 186 Signal to noise ratio (SNR) 152 Signal-ASE noise 24, 69, 82 Signal-LO beating 80, 83 Single mode fiber (SMF) 147, 151 Single-ended detection 62 Single-span transmission 155 Sliding window 102 Small-amplitude QPSK 52 SNR requirements, matched filtering 243

251 Spectral efficiency 2, 7, 81, 234 Split-step Fourier 144 Spontaneous emission 16 Spontaneous emission parameter 69 Square QAM 5, 37 Square QAM coder 43, 46, 49, 121 Star QAM 5, 34 Stimulated Brillouin scattering (SBS) 151 Stimulated Raman scattering (SRS) 151 Subcarrier based OPLL 98 Susceptibility 147 Symbol error probability 139 Symbol rate 23 Symbol-to-symbol phase correction 102 System memory length 128 T Tandem-QPSK transmitter 51, 121, 204 Thermal noise 69, 135 Timing recovery Gardner 100 square 100 Training sequence 38, 101, 104 Transmission distances, attainable 8PSK 210, 212 comparison 219, 222 future research 233 records 7 Star 16QAM 215, 218 summary 232 Transmitter configuration, impact 230 Truth table 30 Twisted pair 1 U Uniformity

63, 65

V Voltage controlled oscillator (VCO)

98

W Waveguide dispersion 145, 147 Wavelength division multiplexing (WDM) 2, 217, 233 Wiener filter 103, 110