Preface ........................................................ xv
Author ........................................................ xix
Abbreviations ................................................. xxi
1 Overview of Optical Fiber Communications and DSP-Based
Transmission Systems ....................................... 1
1.1 Introduction ............................................... 1
1.2 From Few Mb/s to Tb/s: Transmission and Receiving for
Optical Communications Systems ............................. 3
1.2.1 Guiding Lightwaves over the Last 40 Years ........... 3
1.2.2 Guiding Lightwaves: Single Mode, Multimode, and
Few Mode ............................................ 8
1.2.3 Modulation Formats: Intensity to Phase Modulation,
Direct to External Modulation ....................... 8
1.2.4 Coherent and Incoherent Receiving Techniques ........ 9
1.2.5 Digital Processing in Advanced Optical
Communication Systems .............................. 10
1.3 Digital Modulation Formats ................................ 11
1.3.1 Modulation Formats ................................. 11
1.3.2 Pulse Shaping and Modulations for High Spectral
Efficiency ......................................... 13
1.3.2.1 Partial Response .......................... 13
1.3.2.2 Nyquist Pulse Shaping ..................... 15
1.4 Optical Demodulation: Phase and Polarization Diversity
Technique ................................................. 18
1.5 Organization of the Book Chapters ......................... 23
References ................................................ 24
2 Optical Fibers: Guiding and Propagation Properties ........ 25
2.1 Optical Fibers: Circular Optical Waveguides ............... 25
2.1.1 General Aspects .................................... 25
2.1.2 Optical Fiber: General Properties .................. 26
2.1.2.1 Geometrical Structures and Index Profile .. 26
2.1.3 Fundamental Mode of Weakly Guiding Fibers .......... 29
2.1.3.1 Solutions of the Wave Equation for
Step-Index Fiber .......................... 30
2.1.3.2 Single and Few Mode Conditions ............ 31
2.1.3.3 Gaussian Approximation: Fundamental Mode
Revisited ................................. 36
2.1.3.4 Cut-Off Properties ........................ 38
2.1.3.4 Power Distribution ........................ 40
2.1.3.6 Approximation of Spot-Size r0 of a
Step-Index Fiber .......................... 41
2.1.4 Equivalent-Step Index Description .................. 41
2.2 Nonlinear Optical Effects ................................. 42
2.2.1 Nonlinear Self-Phase Modulation Effects ............ 42
2.2.2 Self-Phase Modulation .............................. 43
2.2.3 Cross-Phase Modulation ............................. 44
2.2.4 Stimulated Scattering Effects ...................... 45
2.2.4.1 Stimulated Brillouin Scattering ........... 46
2.2.4.2 Stimulated Raman Scattering ............... 47
2.2.4.3 Four-Wave Mixing Effects .................. 48
2.3 Signal Attenuation in Optical Fibers ...................... 49
2.3.1 Intrinsic or Material Absorption Losses ............ 49
2.3.2 Waveguide Losses ................................... 50
2.3.3 Attenuation Coefficient ............................ 52
2.4 Signal Distortion in Optical Fibers ....................... 53
2.4.1 Material Dispersion ................................ 55
2.4.2 Waveguide Dispersion ............................... 58
2.4.2.1 Alternative Expression for Waveguide
Dispersion Parameter ...................... 61
2.4.2.2 Higher-Order Dispersion ................... 62
2.4.3 Polarization Mode Dispersion ....................... 63
2.5 Transfer Function of Single-Mode Fibers ................... 65
2.5.1 Linear Transfer Function ........................... 65
2.5.2 Nonlinear Fiber Transfer Function .................. 72
2.5.3 Transmission Bit Rate and the Dispersion Factor .... 77
2.6 Fiber Nonlinearity Revisited .............................. 78
2.6.1 SPM, XPM Effects ................................... 78
2.6.2 SPM and Modulation Instability ..................... 80
2.6.3 Effects of Mode Hopping ............................ 81
2.6.4 SPM and Intra-Channel Nonlinear Effects ............ 81
2.6.5 Nonlinear Phase Noises ............................. 86
2.7 Special Dispersion Optical Fibers ......................... 87
2.8 SMF Transfer Function: Simplified Linear and Nonlinear
Operating Region .......................................... 88
2.9 Numerical Solution: Split-Step Fourier Method ............. 95
2.9.1 Symmetrical Split-Step Fourier Method .............. 95
2.9.1.1 Modeling of Polarization Mode Dispersion .. 97
2.9.1.2 Optimization of Symmetrical SSFM .......... 98
2.10 Nonlinear Fiber Transfer Functions and Compensations
in Digital Signal Processing .............................. 99
2.10.1 Cascades of Linear and Nonlinear Transfer
Functions in Time and Frequency Domains ........... 101
2.10.2 Volterra Nonlinear Transfer Function and
Electronic Compensation ........................... 103
2.10.3 Inverse of Volterra Expansion and Nonlinearity
Compensation in Electronic Domain ................. 104
2.10.3.1 Inverse of Volterra Transfer Function .... 106
2.10.3.2 Electronic Compensation Structure ........ 108
2.10.3.3 Remarks .................................. 111
2.10.4 Back-Propagation Techniques for Compensation of
Nonlinear Distortion .............................. 111
2.11 Concluding Remarks ....................................... 114
References ............................................... 115
3 External Modulators for Coherent Transmission and
Reception ................................................ 121
3.1 Introduction ............................................. 121
3.2 External Modulation and Advanced Modulation Formats ...... 122
3.2.1 Electro-Absorption Modulators ..................... 122
3.2.2 Electro-Optic Modulators .......................... 124
3.2.2.1 Phase Modulators ......................... 125
3.2.2.2 Intensity Modulators ..................... 125
3.2.2.3 Phasor Representation and Transfer
Characteristics .......................... 127
3.2.2.4 Bias Control ............................. 128
3.2.2.5 Chirp-Free Optical Modulators ............ 129
3.2.2.6 Structures of Photonic Modulators ........ 130
3.2.2.7 Typical Operational Parameters ........... 131
3.2.3 ASK Modulation Formats and Pulse Shaping .......... 131
3.2.3.1 Return-to-Zero Optical Pulses ............ 131
3.2.3.2 Phasor Representation .................... 134
3.2.3.3 Phasor Representation of CSRZ Pulses ..... 135
3.2.3.4 Phasor Representation of RZ33 Pulses ..... 136
3.2.4 Differential Phase Shift Keying ................... 137
3.2.4.1 Background ............................... 137
3.2.4.2 Optical DPSK Transmitter ................. 138
3.3 Generation of Modulation Formats ......................... 140
3.3.1 Amplitude Modulation ASK-NRZ and ASK-RZ ........... 140
3.3.2 Amplitude Modulation Carrier-Suppressed RZ
Formats ........................................... 141
3.3.3 Discrete Phase Modulation NRZ Formats ............. 141
3.3.3.1 Differential Phase Shift Keying .......... 141
3.3.3.2 Differential Quadrature Phase Shift
Keying ................................... 143
3.3.3.3 Non Return-to-Zero Differential Phase
Shift Keying ............................. 143
3.3.3.4 Return-to-Zero Differential Phase Shift
Keying ................................... 143
3.3.3.4 Generation of M-Ary Amplitude
Differential Phase Shift Keying (M-Ary
ADPSK) Using One MZIM .................... 144
3.3.3.6 Continuous Phase Modulation PM-NRZ
Formats .................................. 146
3.3.3.7 Linear and Nonlinear MSK ................. 147
3.4 Photonic MSK Transmitter Using Two Cascaded Electro-
Optic Phase Modulators ................................... 151
3.4.1 Configuration of Optical MSK Transmitter Using
Mach-Zehnder Intensity Modulators: I-Q Approach ... 153
3.4.2 Single-Side Band Optical Modulators ............... 155
3.4.3 Optical RZ-MSK .................................... 156
3.4.4 Multi-Carrier Multiplexing Optical Modulators ..... 156
3.4.5 Spectra of Modulation Formats ..................... 159
3.5 I-Q Integrated Modulators ................................ 164
3.5.1 Inphase and Quadrature Phase Optical Modulators ... 164
3.5.2 IQ Modulator and Electronic Digital Multiplexing
for Ultra-High Bit Rates .......................... 167
3.6 DAC for DSP-Based Modulation and Transmitter ............. 168
3.6.1 Fujitsu DAC ....................................... 168
3.6.2 Structure ......................................... 170
3.6.2.1 Generation of I and Q Components ......... 171
3.7 Remarks ............................................. 173
References ............................................... 176
4 Optical Coherent Detection and Processing Systems ........ 179
4.1 Introduction ............................................. 179
4.2 Coherent Receiver Components ............................. 181
4.3 Coherent Detection ....................................... 182
4.3.1 Optical Heterodyne Detection ...................... 185
4.3.1.1 ASK Coherent System ...................... 187
4.3.1.2 PSK Coherent System ...................... 189
4.3.1.3 Differential Detection ................... 190
4.3.1.4 FSK Coherent System ...................... 191
4.3.2 Optical Homodyne Detection ........................ 192
4.3.2.1 Detection and OPLL ....................... 193
4.3.2.2 Quantum Limit Detection .................. 194
4.3.2.3 Linewidth Influences ..................... 195
4.3.3 Optical Intradyne Detection ....................... 200
4.4 Self-Coherent Detection and Electronic DSP ............... 201
4.5 Electronic Amplifiers: Responses and Noises .............. 203
4.5.1 Introduction ...................................... 203
4.5.2 Wideband TIAs ..................................... 205
4.5.2.1 Single Input/Single Output .............. 205
4.5.2.2 Differential Inputs, Single/
Differential Output ..................... 205
4.5.3 Amplifier Noise Referred to Input ................. 206
4.6 Digital Signal Processing Systems and Coherent Optical
Reception ................................................ 208
4.6.1 DSP-Assisted Coherent Detection ................... 208
4.6.1.1 DSP-Based Reception Systems .............. 209
4.6.2 Coherent Reception Analysis ....................... 211
4.6.2.1 Sensitivity .............................. 211
4.6.2.2 Shot-Noise-Limited Receiver Sensitivity .. 215
4.6.2.3 Receiver Sensitivity under Nonideal
Conditions ............................... 216
4.6.3 Digital Processing Systems ........................ 217
4.6.3.1 Effective Number of Bits ................. 218
4.6.3.2 Impact of ENOB on Transmission
Performance .............................. 226
4.6.3.3 Digital Processors ....................... 228
4.7 Concluding Remarks ....................................... 228
4.8 Appendix: A Coherent Balanced Receiver and Method
for Noise Suppression .................................... 231
4.8.1 Analytical Noise Expressions ...................... 233
4.8.2 Noise Generators .................................. 235
4.8.3 Equivalent Input Noise Current .................... 236
4.8.4 Pole-Zero Pattern and Dynamics .................... 238
4.8.5 Responses and Noise Measurements .................. 242
4.8.5.1 Rise-Time and 3 dB Bandwidth ............. 242
4.8.5.2 Noise Measurement and Suppression ........ 244
4.8.5.3 Requirement for Quantum Limit ............ 245
4.8.5.4 Excess Noise Cancellation Technique ...... 246
4.8.5.5 Excess Noise Measurement ................. 247
4.8.6 Remarks ........................................... 248
4.8.7 Noise Equations ................................... 249
References ............................................... 252
5 Optical Phase Locking .................................... 255
5.1 Overview of Optical Phase Lock Loop ...................... 255
5.2 Optical Coherent Detection and Optical PLL ............... 258
5.2.1 General PLL Theory ................................ 258
5.2.1.1 Phase Detector ........................... 259
5.2.1.2 Loop Filter .............................. 260
5.2.1.3 Voltage-Controlled Oscillator ............ 261
5.2.1.4 A Second-Order PLL ....................... 261
5.2.2 PLL ............................................... 263
5.2.3 OPLL .............................................. 265
5.2.3.1 Functional Requirements .................. 265
5.2.3.2 Nonfunctional Requirements .............. 265
5.2.4 Digital LPF Design ............................... 266
5.2.4.1 Fixed-Point Arithmetic ................... 266
5.2.4.2 Digital Filter ........................... 268
5.2.4.3 Interface Board .......................... 270
5.2.4.4 FPGA Implementation ...................... 272
5.2.4.5 Indication of Locking State .............. 272
5.2.4.6 OPLL Hardware Details .................... 273
5.3 Performances: Simulation and Experiments ................. 274
5.3.1 Simulation ........................................ 274
5.3.2 Experiment: Digital Feedback Control .............. 275
5.3.2.1 Noise Sources ............................ 278
5.3.2.2 Quality of Locking State ................. 278
5.3.2.3 Limitations .............................. 280
5.3.3 Simulation and Experiment Test Bed: Analog
Feedback Control .................................. 281
5.3.3.1 Simulation: Analog Feedback Control
Loop ..................................... 281
5.3.3.2 Laser Beating Experiments ................ 288
5.3.3.3 Loop Filter Design ....................... 289
5.3.3.4 Closed-Loop Locking of LO and Signal
Carrier: Closed-Loop OPLL ................ 290
5.3.3.5 Monitoring of Beat Signals ............... 291
5.3.3.6 High-Resolution Optical Spectrum
Analysis ................................. 293
5.3.3.7 Phase Error and LPF Time Constant ........ 293
5.3.3.8 Remarks .................................. 295
5.4 OPLL for Superchannel Coherent Receiver .................. 296
5.5 Concluding Remarks ....................................... 298
References ............................................... 299
6 Digital Signal Processing Algorithms and Systems
Performance .............................................. 301
6.1 Introduction ............................................. 301
6.2 General Algorithms for Optical Communications Systems .... 304
6.2.1 Linear Equalization ............................... 305
6.2.1.1 Basic Assumptions ........................ 306
6.2.1.2 Zero-Forcing Linear Equalization
(ZF-LE) .................................. 307
6.2.1.3 ZF-LE for Fiber as a Transmission
Channel .................................. 308
6.2.1.4 Feedback Transversal Filter .............. 310
6.2.1.5 Tolerance of Additive Gaussian Noises .... 310
6.2.1.6 Equalization with Minimizing MSE in
Equalized Signals ........................ 312
6.2.1.7 Constant Modulus Algorithm for Blind
Equalization and Carrier Phase Recovery .. 314
6.2.2 Nonlinear Equalizer or DFEs ....................... 319
6.2.2.1 DD Cancellation of ISI ................... 319
6.2.2.2 Zero-Forcing Nonlinear Equalization ...... 321
6.2.2.3 Linear and Nonlinear Equalization of a
Factorized Channel Response .............. 323
6.2.2.4 Equalization with Minimizing MSE in
Equalized Signals ........................ 324
6.3 MLSD and Viterbi ......................................... 324
6.3.1 Nonlinear MLSE .................................... 325
6.3.2 Trellis Structure and Viterbi Algorithm ........... 326
6.3.2.1 Trellis Structure ........................ 326
6.3.2.2 Viterbi Algorithm ........................ 327
6.3.3 Optical Fiber as a Finite State Machine ........... 328
6.3.4 Construction of State Trellis Structure ........... 328
6.3.5 Shared Equalization between Transmitter and
Receivers ......................................... 329
6.3.5.1 Equalizers at the Transmitter ............ 329
6.3.5.2 Shared Equalization ...................... 332
6.4 Maximum a Posteriori Technique for Phase Estimation ...... 333
6.4.1 Method ............................................ 333
6.4.2 Estimates ......................................... 334
6.5 Carrier Phase Estimation ................................. 339
6.5.1 Remarks ........................................... 339
6.5.2 Correction of Phase Noise and Nonlinear Effects ... 340
6.5.3 Forward Phase Estimation QPSK Optical Coherent
Receivers ......................................... 341
6.5.4 CR in Polarization Division Multiplexed
Receivers: A Case Study ........................... 342
6.5.4.1 FO Oscillations and Q-Penalties .......... 343
6.5.4.2 Algorithm and Demonstration of Carrier
Phase Recovery ........................... 345
6.6 Systems Performance of MLSE Equalizer-MSK Optical
Transmission Systems ..................................... 348
6.6.1 MLSE Equalizer for Optical MSK Systems ............ 348
6.6.1.1 Configuration of MLSE Equalizer in
Optical Frequency Discrimination
Receiver ................................. 348
6.6.1.2 MLSE Equalizer with Viterbi Algorithm .... 349
6.6.1.3 MLSE Equalizer with Reduced-State
Template Matching ........................ 351
6.6.2 MLSE Scheme Performance ........................... 351
6.6.2.1 Performance of MLSE Schemes in 40 Gb/s
Transmission Systems ..................... 351
6.6.2.2 Transmission of 10 Gb/s Optical MSK
Signals over 1472 km SSMF Uncompensated
Optical Link ............................. 352
6.6.2.3 Performance Limits of Viterbi-MLSE
Equalizers ............................... 355
6.6.2.4 Viterbi-MLSE Equalizers for PMD
Mitigation ............................... 359
6.6.2.5 On the Uncertainty and Transmission
Limitation of Equalization Process ....... 364
References ............................................... 365
7 DSP-Based Coherent Optical Transmission Systems .......... 369
7.1 Introduction ............................................. 369
7.2 QPSK Systems ............................................. 371
7.2.1 Carrier Phase Recovery ............................ 371
7.2.2 112 G QPSK Coherent Transmission Systems .......... 371
7.2.3 I-Q Imbalance Estimation Results .................. 374
7.2.4 Skew Estimation ................................... 375
7.2.5 Fractionally Spaced Equalization of CD and PMD .... 377
7.2.6 Linear and Nonlinear Equalization and Back-
Propagation Compensation of Linear and Nonlinear
Phase Distortion .................................. 377
7.3 16 QAM Systems ........................................... 381
7.4 Tera-Bits/s Superchannel Transmission Systems ............ 385
7.4.1 Overview .......................................... 385
7.4.2 Nyquist Pulse and Spectra ......................... 386
7.4.3 Superchannel System Requirements .................. 388
7.4.4 System Structure .................................. 389
7.4.4.1 DSP-Based Coherent Receiver .............. 389
7.4.4.2 Optical Fourier Transform-Based
Structure ................................ 394
7.4.4.3 Processing ............................... 395
7.4.5 Timing Recovery in Nyquist QAM Channel ............ 398
7.4.6 128 Gb/s 16 QAM Superchannel Transmission ......... 399
7.4.7 450 Gb/s 32 QAM Nyquist Transmission Systems ...... 401
7.4.8 DSP-Based Heterodyne Coherent Reception Systems ... 403
7.5 Concluding Remarks ....................................... 406
References ............................................... 407
8 Higher-Order Spectrum Coherent Receivers ................. 409
8.1 Bispectrum Optical Receivers and Nonlinear Photonic
Pre-processing ........................................... 409
8.1.1 Introductory Remarks .............................. 409
8.1.2 Bispectrum ........................................ 411
8.1.3 Bispectrum Coherent Optical Receiver .............. 412
8.1.4 Triple Correlation and Bispectra .................. 412
8.1.4.1 Definition ............................... 412
8.1.4.2 Gaussian Noise Rejection ................. 413
8.1.4.3 Encoding of Phase Information ............ 413
8.1.4.4 Eliminating Gaussian Noise ............... 413
8.1.5 Transmission and Detection ........................ 414
8.1.5.1 Optical Transmission Route and
Simulation Platform ...................... 414
8.1.5.2 Four-Wave Mixing and Bispectrum
Receiving ................................ 415
8.1.5.3 Performance .............................. 415
8.2 NL Photonic Signal Processing Using Higher-Order
Spectra .................................................. 419
8.2.1 Introductory Remarks .............................. 419
8.2.2 FWM and Photonic Processing ....................... 420
8.2.2.1 Bispectral Optical Structures ............ 420
8.2.2.2 The Phenomena of FWM ..................... 422
8.2.3 Third-Order Nonlinearity and Parametric FWM
Process ........................................... 424
8.2.3.1 NL Wave Equation ......................... 424
8.2.3.2 FWM Coupled-Wave Equations ............... 425
8.2.3.3 Phase Matching ........................... 427
8.2.3.4 Coupled Equations and Conversion
Efficiency ............................... 427
8.2.4 Optical Domain Implementation ..................... 428
8.2.4.1 NL Wave Guide ............................ 428
8.2.4.2 Third-Harmonic Conversion ................ 429
8.2.4.3 Conservation of Momentum ................. 429
8.2.4.4 Estimate of Optical Power Required for
FWM ...................................... 429
8.2.5 Transmission Models and NL Guided Wave Devices .... 430
8.2.6 System Applications of Third-Order Parametric
Nonlinearity in Optical Signal Processing ......... 431
8.2.6.1 Parametric Amplifiers .................... 431
8.2.6.2 Wavelength Conversion and NL Phase
Conjugation .............................. 436
8.2.6.3 High-Speed Optical Switching ............. 437
8.2.6.4 Triple Correlation ....................... 442
8.2.6.5 Remarks .................................. 448
8.2.7 NL Photonic Pre-Processing in Coherent Reception
Systems ........................................... 449
8.2.8 Remarks ........................................... 455
References ............................................... 456
Index ......................................................... 459
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