Kumar Impact of Nonlinearities on Fiber Optic Communications

1. Auflage 2011
ISBN: 978-1-4419-8139-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 7, 544 Seiten

Reihe: Optical and Fiber Communications Reports

This book covers the recent progress in fiber-optic communication systems with a main focus on the impact of fiber nonlinearities on the system performance. Over the past few years, there has been significant progress in coherent communication systems mainly because of the advances in digital signal processing techniques. This has led to renewed interest in fiber linear and nonlinear impairments and techniques to mitigate them in electrical domain. In this book, the reader will find all the important topics of fiber optic communication systems in one place with in-depth coverage by the experts of each subtopics. Pioneers from each of the sub-topics have been invited to contribute. Each chapter will have a section on fundamentals, review of literature survey and the recent developments. The reader will benefit from this approach since many of the conference proceedings and journal articles mainly focus on the authors' research work without spending space on preliminaries.

Autoren/Hrsg.

Kumar, Shiva

Inhaltsverzeichnis

1;Preface;6
2;Contents;10
3;Contributors;12
4;Chapter 1:Coherent, Self-Coherent, and DifferentialDetection Systems;14
4.1;1.1 Introduction;14
4.2;1.2 Recent Advances in Fiberoptic Communication Systems;15
4.2.1;1.2.1 40-Gb s-1 Transmission;15
4.2.2;1.2.2 100-Gb s-1 Transmission;17
4.2.3;1.2.3 200-Gb s-1 Transmission and Beyond;18
4.2.4;1.2.4 From Research Demonstration to Commercial Reality;19
4.3;1.3 Self-Coherent and Differential Detection-Based Systems;20
4.3.1;1.3.1 Upgrading 10-Gb s-1-Based DWDM System to 40-Gb s-1 DBPSK and DQPSK;20
4.3.1.1;1.3.1.1 SE Consideration;21
4.3.1.2;1.3.1.2 Transmission Distance Consideration;22
4.3.1.3;1.3.1.3 CD and PMD Consideration;22
4.3.1.4;1.3.1.4 Nonlinear Tolerance Consideration;22
4.3.1.5;1.3.1.5 Overall Comparison;28
4.3.2;1.3.2 Self-Coherent Detection;28
4.3.2.1;1.3.2.1 Principle of Digital Self-Coherent Detection;30
4.3.2.2;1.3.2.2 Receiver Sensitivity Enhancement via Data-Aided MSPE;31
4.3.2.3;1.3.2.3 Unified Detection of m-ary DPSK;32
4.3.2.4;1.3.2.4 More Advanced DSCD Signal Processing;33
4.4;1.4 DCD-Based Systems;34
4.4.1;1.4.1 Digital Coherent Detection;34
4.4.2;1.4.2 State-of-the-Art DCD Demonstrations;38
4.4.2.1;1.4.2.1 100-Gb s-1 DCD-Based Field Trials;38
4.4.2.2;1.4.2.2 High-Capacity Transmission;39
4.4.2.3;1.4.2.3 High SE Transmission;39
4.4.2.4;1.4.2.4 448-Gb s-1 RGI-CO-OFDM Transmission;41
4.4.2.5;1.4.2.5 1-Tb s-1 NGI-CO-OFDM Transmission;44
4.5;1.5 Concluding Remarks;47
4.6;References;49
5;Chapter 2:Optical OFDM Basics;56
5.1;2.1 Introduction;56
5.2;2.2 Historical Perspective of OFDM;57
5.3;2.3 OFDM Fundamentals;58
5.3.1;2.3.1 Orthogonality Between OFDM Subcarriers and Subbands;59
5.3.2;2.3.2 Discrete Fourier Transform Implementation of OFDM;63
5.3.3;2.3.3 Cyclic Prefix for OFDM;64
5.3.4;2.3.4 Spectral Efficiency for Optical OFDM;66
5.3.5;2.3.5 Peak-to-Average Power Ratio for OFDM;68
5.3.6;2.3.6 Flavors of Optical OFDM;71
5.4;2.4 Coherent Optical OFDM Systems;72
5.4.1;2.4.1 Principle for CO-OFDM;73
5.4.2;2.4.2 OFDM Digital Signal Processing;75
5.4.2.1;2.4.2.1 Window Synchronization;75
5.4.2.2;2.4.2.2 Frequency Offset Synchronization;76
5.4.2.3;2.4.2.3 Channel Estimation;77
5.4.2.4;2.4.2.4 Phase Estimation;78
5.4.3;2.4.3 Polarization-Diversity Multiplexed OFDM;78
5.4.4;2.4.4 Real-Time Coherent Optical OFDM;79
5.4.4.1;2.4.4.1 Real-Time Window Synchronization;80
5.4.4.2;2.4.4.2 Real-Time Frequency Offset Synchronization;81
5.4.4.3;2.4.4.3 Real-Time Channel Estimation;83
5.4.4.4;2.4.4.4 Real-Time Phase Estimation;84
5.4.5;2.4.5 Experimental Demonstrations for CO-OFDM, from 100Gb s-1 to 1Tb s-1, from Offline to Real-Time;84
5.5;2.5 Promising Research Direction and Future Expectations;92
5.6;2.6 Conclusion;95
5.7;References;95
6;Chapter 3:Nonlinear Impairments in Coherent OpticalOFDM Systems and Their Mitigation;99
6.1;3.1 Introduction;99
6.2;3.2 Rigorous OFDM Transmission Model;102
6.2.1;3.2.1 Interpolation and Digital Frequency Up-Shifting;103
6.2.2;3.2.2 OFDM Analog-Like Tx Model;106
6.3;3.3 Fiber Channel Model: Third-Order Volterra Description of the FWM/XPM Impairment;107
6.3.1;3.3.1 Complex Representation;107
6.3.2;3.3.2 Fiber Channel Model;107
6.3.3;3.3.3 Linear + SPM/XPM Propagation of the Subcarriers;109
6.3.4;3.3.4 VTF for the FWM Among the Subcarriers;111
6.4;3.4 OFDM Receiver: Linear and Nonlinear Modeling;116
6.4.1;3.4.1 Rx Processing;116
6.4.2;3.4.2 Aliasing of NL Components in a Baud-Rate OFDM Receiver;118
6.4.3;3.4.3 Oversampling the NL Output;119
6.5;3.5 Derivation of the FWM VTF: OPI Model of Third-Order NL+CD Propagation;120
6.5.1;3.5.1 OPI Approach;120
6.5.2;3.5.2 Quasilinear Propagation Transfer Function;121
6.5.3;3.5.3 Virtual Backpropagated Fields;122
6.5.4;3.5.4 OPI Derivation of the VTF of a General Inhomogeneous Fiber Link;123
6.5.5;3.5.5 Homogeneous Fiber Link;126
6.5.6;3.5.6 Single Homogeneous Span;127
6.5.7;3.5.7 ``Regular' Multispan Link;128
6.5.8;3.5.8 Irregular Inhomogenenous Links;130
6.5.9;3.5.9 Dispersion-Unmanaged ``Regular' Spans Revisited;132
6.5.10;3.5.10 Phased-Array Effect Tends to Reduce FWM Build-up;133
6.5.11;3.5.11 The Effect of Dispersion-Compensation Fiber: Dispersion-Managed Links;135
6.5.12;3.5.12 Intermod Statistics: Power Propagation Over a ``Regular' Spans Link;136
6.5.13;3.5.13 The FWM Power for Dispersion-Managed Links;138
6.6;3.6 OFDM Link Performance;139
6.6.1;3.6.1 Angular Variance;140
6.6.2;3.6.2 Q-Factor, Symbol Error Rate, BER;142
6.7;3.7 PA Effect for Dispersion-Unmanaged Regular Multispan Links;143
6.7.1;3.7.1 Compounding Multiple PAs;144
6.7.2;3.7.2 The NLT is set by Bandwidth2xLengthxGVD;144
6.7.3;3.7.3 A Simple Q-Factor Performance Lower Bound for Dispersion Unmanaged Links;145
6.8;3.8 Overview of NLC Methods;148
6.9;3.9 Baud-Rate Sampled Version of the B-NLPR NLC;150
6.10;3.10 Volterra DF-Based NLC: Principle of Operation;152
6.11;3.11 Volterra DF NLC: Complete Block Diagram, Overall Characteristics and Performance;156
6.12;3.12 Baud-Rate Sampling Principles for the Volterra DF NLC;158
6.13;3.13 Low Error Propagation for the Volterra DF NLC;160
6.14;3.14 The Role of Higher-Order (5th, 7th, …) Nonlinearities;162
6.15;3.15 ``XPM Undo and Derotate' Decoupling XPM and FWM Mitigation in the Volterra DF NLC;163
6.16;3.16 Volterra DF NLC Performance Simulations (Q-Factor and BER);165
6.17;3.17 Computational Complexity vs. NL Tolerance Performance Trade-Offs;166
6.18;3.18 Discussion: Volterra DF NLC vs. BP – Suggested Roadmap for Future NLC;168
6.19;3.19 Conclusions;170
6.20;3.20 Appendix A: Derivation of the Analog-Like OFDM Transmitter Model;172
6.21;3.21 Appendix B: Volterra NL Systems Formalism Extending to Third-Order;174
6.22;3.22 Appendix C: Sampling and Nonlinearity Effects in the OFDM Receiver;178
6.22.1;3.22.1 Nyquist Sampling the Linear Component Under Samples the NL Component;178
6.22.2;3.22.2 AA Filtering;180
6.23;References;185
7;Chapter 4:Systems with Higher-Order Modulation;188
7.1;4.1 Introduction;188
7.2;4.2 Higher-Order Modulation Formats;189
7.3;4.3 Signal Generation;192
7.3.1;4.3.1 External Optical Modulators;192
7.3.2;4.3.2 Higher-Order PSK/DPSK and QAM Transmitters;194
7.3.2.1;4.3.2.1 Transmitters Based on Multi-Level Driving Signals;194
7.3.2.2;4.3.2.2 Transmitters Based on Binary Driving Signals;196
7.4;4.4 Signal Detection;199
7.4.1;4.4.1 Direct Detection Receivers;199
7.4.2;4.4.2 Homodyne Receivers;201
7.4.2.1;4.4.2.1 Receivers with Homodyne Synchronous Detection;202
7.4.2.2;4.4.2.2 Receivers with Homodyne Differential Detection;205
7.4.2.3;4.4.2.3 2×4 90 Hybrid Optical Front-end;206
7.5;4.5 Trends in System Performance;208
7.6;4.6 Long-Haul Transmission;211
7.6.1;4.6.1 System Experiments with Optical Inline CD Compensation;212
7.6.2;4.6.2 System Experiments with Electrical CD Compensation;216
7.6.3;4.6.3 System Simulations with Nonlinear Phase Shift Compensation;220
7.7;4.7 Issues of Future Research;224
7.8;References;226
8;Chapter 5:Power-Efficient Modulation Schemes;229
8.1;5.1 Introduction;229
8.1.1;5.1.1 Optical Coherent Modulation: Background;230
8.2;5.2 Definitions and System Model;232
8.2.1;5.2.1 The Four-Dimensional Optical Signal;232
8.2.2;5.2.2 Digital Transmission Over a Noisy Channel;233
8.2.3;5.2.3 Symbol Error Rates and Sphere Packing;235
8.3;5.3 N-Dimensional Sphere Packing Results;237
8.3.1;5.3.1 Sphere Packings: Background;237
8.3.2;5.3.2 Results: Sensitivity vs. Spectral Efficiency;239
8.3.3;5.3.3 Specific Formats;241
8.3.3.1;5.3.3.1 Two-Dimensional Constellations, N=2 ;242
8.3.3.2;5.3.3.2 Four-Dimensional Constellations, N=4;245
8.4;5.4 Symbol- and Bit-Error Rates ;251
8.5;5.5 Sensitivities and Nonlinearities;254
8.5.1;5.5.1 Fundamental Sensitivity Limits;255
8.5.2;5.5.2 Nonlinear Effects ;256
8.5.2.1;5.5.2.1 Power Efficiency;257
8.5.2.2;5.5.2.2 Nonlinear Robustness;258
8.5.2.3;5.5.2.3 XPM-Induced Crosstalk;258
8.5.2.4;5.5.2.4 Relevance of Maximum Energy Optimization;258
8.6;5.6 Summary and Outlook;260
8.7;References;261
9;Chapter 6:A Unified Theory of Intrachannel Nonlinearityin Pseudolinear Transmission;263
9.1;6.1 Introduction;263
9.2;6.2 Basic Formalism;264
9.3;6.3 First-Order Perturbation Theory;265
9.4;6.4 Sequence of Gaussian Pulses;268
9.5;6.5 Coherent and Direct Detection;269
9.6;6.6 Effect of the Symmetry of the Dispersion Profile;273
9.7;6.7 Pseudo-Random Sequence in DPSK and DQPSK;274
9.7.1;6.7.1 FWM Terms Afwm and Bfwm, and Correlation Terms Acorr,fwm and Bcorr,fwm;277
9.7.2;6.7.2 Cross-Phase Modulation Term Axpm and Correlation Term Bcorr,xpm;277
9.8;6.8 Pseudo-Random Sequence in IMDD;278
9.9;6.9 Continuous Approximation;279
9.10;6.10 Numerical Examples;281
9.11;6.11 Total Receiver Noise;286
9.12;6.12 Discussion;289
9.13;6.13 Information Rate for DPSK and DQPSK Transmission;290
9.14;6.14 Timing Jitter Between Two Pulses;292
9.15;6.15 Timing Jitter in a Pseudo-Random Sequence;295
9.16;6.16 Conclusions;300
9.17;References;300
10;Chapter 7:Analysis of Nonlinear Phase Noisein Single-Carrier and OFDM Systems;302
10.1;7.1 Introduction;302
10.2;7.2 Linear Phase Noise;304
10.3;7.3 Gordon–Mollenauer Phase Noise;307
10.4;7.4 Phase Noise in Dispersive Nonlinear Fiberoptic Single Carrier System;311
10.4.1;7.4.1 Results and Discussion;316
10.5;7.5 Phase Noise in OFDM Systems;320
10.5.1;7.5.1 SPM and XPM Induced Nonlinear Phase Noise;321
10.5.2;7.5.2 FWM-Induced Nonlinear Phase Noise;323
10.5.3;7.5.3 Total Phase Noise;326
10.5.4;7.5.4 Results and Discussions;326
10.6;7.6 Conclusions;331
10.7;References;332
11;Chapter 8:Cross-Phase Modulation-Induced NonlinearPhase Noise for Quadriphase-Shift-KeyingSignals;334
11.1;8.1 Introduction;334
11.2;8.2 Gaussian-Distributed Phase Error;335
11.2.1;8.2.1 DQPSK Signals;336
11.2.2;8.2.2 QPSK Signals;336
11.3;8.3 XPM-Induced Nonlinear Phase Noise;338
11.3.1;8.3.1 Pump-Probe Model;338
11.3.2;8.3.2 XPM from Phase-Modulated Channels;340
11.3.3;8.3.3 XPM from On-Off Keying Channels;341
11.4;8.4 XPM-Induced Nonlinear Phase Noise to DQPSK Signals;341
11.5;8.5 XPM-Induced Nonlinear Phase Noise for QPSK Signals;343
11.5.1;8.5.1 Feedforward Carrier Recovery;343
11.5.2;8.5.2 Performance of QPSK Signals;345
11.6;8.6 Conclusion;348
11.7;References;349
12;Chapter 9:Nonlinear Polarization Scatteringin Polarization-Division-Multiplexed CoherentCommunication Systems;351
12.1;9.1 Introduction;351
12.2;9.2 Analytical Theory;352
12.3;9.3 Nonlinear Polarization Scattering in PDM-QPSK Coherent Transmission Systems;356
12.3.1;9.3.1 System Model;357
12.3.2;9.3.2 42.8-Gb/s PDM-QPSK Systems;359
12.3.3;9.3.3 112-Gb/s PDM-QPSK Systems;362
12.3.4;9.3.4 Hybrid OOK and PDM-QPSK Systems;365
12.4;9.4 Nonlinear Polarization Scattering Mitigation Techniques;366
12.4.1;9.4.1 Time Interleaved RZ-PDM Modulation Format;367
12.4.1.1;9.4.1.1 Coherent ILRZ-PDM-QPSK Systems;368
12.4.1.2;9.4.1.2 Direct-Detection ILRZ-PDM Systems;369
12.4.2;9.4.2 PGD Dispersion Compensators;373
12.4.3;9.4.3 Adding PMD into the System;375
12.5;9.5 Conclusion;376
12.6;References;377
13;Chapter 10:Multicanonical Monte Carlofor Simulation of Optical Links;380
13.1;10.1 Introduction;380
13.2;10.2 Monte Carlo Techniques;381
13.2.1;10.2.1 Conventional Monte Carlo Estimation;382
13.2.2;10.2.2 Importance Sampling;383
13.2.3;10.2.3 Uniform Weight Importance Sampling;385
13.3;10.3 Multicanonical Monte Carlo ;387
13.3.1;10.3.1 MMC Adaptation;387
13.3.2;10.3.2 Smoothed MMC;389
13.3.3;10.3.3 Example: Chi-Square Distribution;392
13.3.4;10.3.4 Drawing Warped Samples: Markov Chain Monte Carlo;394
13.4;10.4 Implementation Issues;396
13.4.1;10.4.1 Minimizing Rejections;396
13.4.1.1;10.4.1.1 Discretization of the Output Space;396
13.4.1.2;10.4.1.2 Exploration of the Input Space;396
13.4.2;10.4.2 Input Vector Correlations;396
13.4.3;10.4.3 Choice of Number of Cycles vs. Samples per Cycle;397
13.4.4;10.4.4 Dealing with System Memory;398
13.5;10.5 Examples;399
13.5.1;10.5.1 Example: Bit Patterning in SOAs;399
13.5.1.1;10.5.1.1 SOA Memory;399
13.5.1.2;10.5.1.2 SOA Modeling;399
13.5.1.3;10.5.1.3 MMC Platform;402
13.5.1.4;10.5.1.4 Results;403
13.5.2;10.5.2 Example: Spectral Efficiency in SS-WDM;404
13.5.2.1;10.5.2.1 Use of Forward Error Correction;404
13.5.2.2;10.5.2.2 Modeling SOA Noise Suppression;405
13.5.2.3;10.5.2.3 Multi-Channel MMC Platform;406
13.5.2.4;10.5.2.4 Parallelization of MMC;407
13.5.2.5;10.5.2.5 Simulation Results;409
13.5.3;10.5.3 Example: Nonlinear Interaction Between Signal and Noise in Very-Long-Haul Dispersion-Managed Amplified Optical Links;410
13.5.3.1;10.5.3.1 Received ASE Statistics;411
13.5.3.2;10.5.3.2 Transmission Test;413
13.5.4;10.5.4 Further Examples in the Literature;415
13.6;10.6 Conclusions;416
13.7;10.7 Appendix: MCMC Fundamentals;417
13.8;References;419
14;Chapter 11:Optical Regenerators for NovelModulation Schemes;421
14.1;11.1 Introduction;421
14.2;11.2 Regeneration of Binary Phase-Shift Keying Signals;423
14.2.1;11.2.1 DPSK Signal Regeneration Using Amplitude Regenerators;423
14.2.1.1;11.2.1.1 DPSK Regenerator Using a Straight-Line Phase Modulator;423
14.2.1.2;11.2.1.2 DPSK Regenerator Using MZI Phase Modulator;424
14.2.1.3;11.2.1.3 Experiment Using Fiber-Based Amplitude Regenerator;427
14.2.1.4;11.2.1.4 Logic Alteration by the Regenerator and Its Compensation;432
14.2.2;11.2.2 Noise Reduction of BPSK Signals Based on Noise Averaging;433
14.2.3;11.2.3 Phase-Preserving Amplitude Regeneration;435
14.2.3.1;11.2.3.1 Nonlinear Phase Noise and Its Suppression;435
14.2.3.2;11.2.3.2 Phase-Preserving Amplitude Regenerator;438
14.2.3.3;11.2.3.3 Transmission Experiment Using a Phase-Preserving Amplitude Limiter;440
14.2.4;11.2.4 BPSK Signal Regeneration Using Phase-Sensitive Amplifiers;442
14.2.4.1;11.2.4.1 BPSK Regenerator Using Nonlinear Sagnac Interferometer;442
14.2.4.2;11.2.4.2 BPSK Regenerator Using Two-Pump Degenerate FWM in Fiber;444
14.3;11.3 Regeneration of Quadrature Phase-Shift Keying Signals;446
14.3.1;11.3.1 DQPSK Signal Regeneration Using Differential Demodulation;447
14.3.2;11.3.2 QPSK Signal Regeneration Using Coherent Demodulation;451
14.4;11.4 Discussion and Summary;452
14.5;References;453
15;Chapter 12:Codes on Graphs, Coded Modulationand Compensation of Nonlinear Impairmentsby Turbo Equalization;456
15.1;12.1 Introduction;456
15.2;12.2 Channel Coding Preliminaries;458
15.2.1;12.2.1 Linear Block Codes;464
15.2.1.1;12.2.1.1 Generator Matrix for Linear Block Code;465
15.2.1.2;12.2.1.2 Parity-Check Matrix;466
15.2.1.3;12.2.1.3 Coding Gain;467
15.3;12.3 Codes on Graphs;469
15.3.1;12.3.1 Quasi-cyclic (QC) Binary LDPC Codes;471
15.3.1.1;12.3.1.1 Design of Large Girth Quasi-cyclic LDPC Codes;471
15.3.1.2;12.3.1.2 Decoding of LDPC Codes;472
15.3.1.3;12.3.1.3 BER Performance of LDPC Codes;475
15.4;12.4 Coded Modulation;476
15.4.1;12.4.1 Multilevel Coding and Bit-Interleaved Coded Modulation;477
15.4.2;12.4.2 Polarization-Multiplexed Coded-OFDM;480
15.4.3;12.4.3 Multidimensional Coded Modulation;482
15.5;12.5 LDPC-Coded Turbo Equalization;487
15.5.1;12.5.1 Optimum Detection;487
15.5.2;12.5.2 Multilevel Turbo Equalizer Description;488
15.5.3;12.5.3 Performance of LDPC-Coded Turbo Equalizer;492
15.5.4;12.5.4 Multilevel Turbo Equalizer with Digital Backpropagation;497
15.6;12.6 Information Capacity of Fiber-Optics Systems;499
15.6.1;12.6.1 Channel Capacity of Channels with Memory;500
15.6.2;12.6.2 Calculation of Information Capacity of Multilevel Modulation Schemes by Forward Recursion of BCJR Algorithm;502
15.6.3;12.6.3 Information Capacity of Coherent detection Systems;503
15.7;References;507
16;Chapter 13:Channel Capacity of Non-Linear TransmissionSystems;511
16.1;13.1 Introduction;511
16.2;13.2 Linear Capacity Limits;514
16.2.1;13.2.1 The Shannon Limit;514
16.2.2;13.2.2 Constellation Analysis;515
16.3;13.3 Non-linear Limits;524
16.3.1;13.3.1 Theoretical Information Capacity Limits;524
16.3.2;13.3.2 Comparison of Reported Results with Theoretical Limit;531
16.4;13.4 Increasing the Information Capacity Limit;532
16.4.1;13.4.1 Optical Regeneration;532
16.4.2;13.4.2 Fibre Design;534
16.4.3;13.4.3 Channel Bandwidth;535
16.4.4;13.4.4 Amplifier Noise Figure;536
16.5;13.5 Conclusions;538
16.6;References;538
17;Index;543