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Dedication
by Le Nguyen Binh
Advanced Digital Optical Communications, 2nd Edition
Cover Page
Half title page
Copyright page
Dedication
Contents
Preface
Acknowledgments
Author
Acronyms
Chapter 1 Introduction
1.1 Digital Optical Communications and Transmission Systems: Challenging Issues
1.2 Enabling Technologies
1.2.1 Modulation Formats and Optical Signal Generation
1.2.1.1 Binary Level
1.2.1.2 Binary and Multilevel
1.2.1.3 In-Phase and Quadrature-Phase Channels
1.2.1.4 External Optical Modulation
1.2.2 Advanced Modulation Formats
1.2.3 Incoherent Optical Receivers
1.2.4 DSP-Coherent Optical Receivers
1.2.5 Transmission of Ultra-Short Pulse Sequence
1.2.6 Electronic Equalization
1.2.6.1 Feed-Forward Equalizer
1.2.6.2 Decision Feedback Equalization
1.2.6.3 Minimum Mean Square Error Equalization
1.2.6.4 Placement of Equalizers
1.2.6.5 MLSE Electronic Equalizers
1.2.7 Ultra-Short Pulse Transmission
1.3 Organization of the Book Chapters
References
Chapter 2 Optical Fibers
2.1 Overview
2.2 Optical Fiber: General Properties
2.2.1 Geometrical Structures and Index Profile
2.2.2 Fundamental Mode of Weakly Guiding Fibers
2.2.2.1 Solutions of the Wave Equation for Step-Index Fiber
2.2.2.2 Single-Mode and Few-Mode Conditions
2.2.2.3 Gaussian Approximation: Fundamental Mode Revisited
2.2.2.4 Cutoff Properties
2.2.2.5 Power Distribution
2.2.2.6 Approximation of Spot Size r0 of Step-Index Fiber
2.2.3 Equivalent Step-Index Description
2.3 Nonlinear Effects
2.3.1 Nonlinear Self-Phase Modulation Effects
2.3.2 Self-Phase Modulation
2.3.3 Cross-Phase Modulation
2.3.4 Stimulated Scattering Effects
2.3.4.1 Stimulated Brillouin Scattering
2.3.4.2 Stimulated Raman Scattering
2.3.4.3 Four-Wave Mixing Effects
2.4 Signal Attenuation in Optical Fibers
2.4.1 Intrinsic or Material Absorption Losses
2.4.2 Waveguide Losses
2.4.3 Attenuation Coefficient
2.5 Signal Distortion through Optical Fibers
2.5.1 Material Dispersion
2.5.2 Waveguide Dispersion
2.5.2.1 Alternative Expression for Waveguide Dispersion Parameter
2.5.2.2 Higher-Order Dispersion
2.5.3 Polarization-Mode Dispersion
2.6 Transfer Function of Single-Mode Fibers
2.6.1 Linear Transfer Function
2.6.2 Nonlinear Fiber Transfer Function
2.6.3 Transmission Bit Rate and the Dispersion Factor
2.7 Fiber Nonlinearity Revisited
2.7.1 SPM and XPM Effects
2.7.2 SPM and Modulation Instability
2.7.3 Effects of Mode Hopping
2.7.4 SPM and Intrachannel Nonlinear Effects
2.7.5 Nonlinear Phase Noises in Cascaded Multispan Optical Link
2.8 Special Dispersion Optical Fibers
2.9 SMF Transfer Function: Simplified Linear and Nonlinear Operating Region
2.10 Numerical Solution: Split-Step Fourier Method
2.10.1 Symmetrical SSFM
2.10.1.1 Modeling of PMD
2.10.1.2 Optimization of Symmetrical SSFM
2.11 Concluding Remarks
References
Chapter 3 Optical Transmitters
3.1 Optical Modulators
3.1.1 Phase Modulators
3.1.2 Intensity Modulators
3.1.2.1 Phasor Representation and Transfer Characteristics
3.1.2.2 Chirp-Free Optical Modulators
3.1.3 Structures of Photonic Modulators
3.1.4 Operating Parameters of Optical Modulators
3.2 Return-to-Zero Optical Pulses
3.2.1 Generation
3.2.2 Phasor Representation
3.2.2.1 Phasor Representation of CSRZ Pulses
3.2.2.2 Phasor Representation of RZ33 Pulses
3.3 Differential Phase Shift Keying
3.3.1 Background
3.3.2 Optical DPSK Transmitter
3.4 Generation of Modulation Formats
3.4.1 Amplitude–Modulation ASK-NRZ and ASK-RZ
3.4.1.1 Amplitude–Modulation OOK-RZ Formats
3.4.1.2 Amplitude–Modulation CSRZ Formats
3.4.2 Discrete Phase Modulation NRZ Formats
3.4.2.1 Differential Phase Shift Keying
3.4.2.2 Differential Quadrature Phase Shift Keying
3.4.2.3 Generation of M-ary Amplitude Differential Phase Shift Keying Using One MZIM
3.4.3 Continuous Phase Modulation PM-NRZ Formats
3.4.3.1 Linear and Nonlinear MSK
3.4.3.2 MSK as a Special Case of CPFSK
3.4.3.3 MSK as ODQPSK
3.4.3.4 Configuration of Photonic MSK Transmitter Using Two Cascaded Electro-Optic Phase Modulators
3.4.3.5 Configuration of Optical MSK Transmitter Using Mach–Zehnder Intensity Modulators: I–Q Approach
3.4.4 Single-Sideband Optical Modulators
3.4.4.1 Operating Principles
3.4.4.2 Optical RZ MSK
3.4.5 Multicarrier Multiplexing Optical Modulators
3.4.6 Spectra of Modulation Formats
3.5 Spectral Characteristics of Digital Modulation Formats
3.6 I–Q Integrated Modulators
3.6.1 In-Phase and Quadrature-Phase Optical Modulators
3.6.2 I–Q Modulator and Electronic Digital Multiplexing for Ultra-High Bit Rates
3.7 Digital-to-Analog Converter for DSP-Based Modulation and Transmitter
3.7.1 Fujitsu DAC
3.7.2 Structure
3.7.3 Generation of I and Q Components
3.8 Concluding Remarks
3.9 Problems on Transmitter (Tx) for Advanced Modulation Formats for Long-Haul Transmission Systems
References
Chapter 4 Optical Receivers and Transmission Performance: Fundamentals
4.1 Introduction
4.2 Digital Optical Receivers
4.2.1 Photonic and Electronic Noise
4.2.1.1 Electronic Noise of Receiver
4.2.1.2 Shot Noise
4.2.1.3 Thermal Noise
4.2.1.4 ASE Noise of Optical Amplifier
4.2.1.5 Optical Amplifier Noise Figure
4.2.1.6 Electronic Beating Noise
4.2.1.7 Accumulated ASE Noise in Cascaded Optical Amplifiers
4.3 Performance Evaluation of Binary Amplitude Modulation Format
4.3.1 Received Signals
4.3.1.1 Case 1: OFF or a Transmitted 0 Is Received
4.3.1.2 Case 2: ON Transmitted 1 Received
4.3.2 Probability Distribution Functions
4.3.3 Receiver Sensitivity
4.3.4 OSNR and Noise Impact
4.3.4.1 Optical Signal-to-Noise Ratio
4.3.4.2 Determination of the Impact of Noise
4.4 Quantum Limit of Optical Receivers under Different Modulation Formats
4.4.1 Direct Detection
4.4.2 Coherent Detection
4.4.3 Coherent Detection with Matched Filter
4.4.3.1 Coherent ASK Systems
4.4.3.2 Coherent Phase and Frequency Shift Keying Systems
4.5 Binary Coherent Optical Receiver
4.6 Noncoherent Detection for Optical DPSK and MSK
4.6.1 Photonic Balanced Receiver
4.6.2 Optical Frequency Discrimination Receiver
4.7 Transmission Impairments
4.7.1 Chromatic Dispersion
4.7.2 Chromatic Linear Dispersion
4.7.3 Polarization-Mode Dispersion
4.7.4 Fiber Nonlinearity
4.8 MATLAB® and Simulink® Simulator for Optical Communications Systems
4.8.1 Fiber Propagation Model
4.8.1.1 Nonlinear Schrödinger Equation
4.8.1.2 Symmetrical Split-Step Fourier Method
4.8.1.3 Modeling of PMD
4.8.1.4 Optimizing the Symmetrical SSFM
4.8.1.5 Fiber Propagation in Linear Domain
4.8.2 Nonlinear Effects via Fiber Propagation Model
4.8.2.1 SPM Effects
4.8.2.2 XPM Effects
4.8.2.3 FWM Effects
4.8.2.4 SRS Effects
4.8.2.5 SBS Effects
4.9 Performance Evaluation
4.9.1 BER from Monte Carlo Method
4.9.2 BER and Q Factor from Probability Distribution Functions
4.9.3 Histogram Approximation
4.9.4 Optical SNR
4.9.5 Eye Opening Penalty
4.9.6 Statistical Evaluation Techniques
4.9.6.1 Multi-Gaussian Distributions via Expectation Maximization Theorem
4.9.6.2 Selection of Number of Gaussian Distributions for MGD Fitting
4.9.7 Generalized Pareto Distribution
4.9.7.1 Selection of Threshold for GPD Fitting
4.9.7.2 Validation of Novel Statistical Methods
4.9.8 Novel BER Statistical Techniques
4.9.8.1 MGDs and EM Theorem
4.10 Effects of Source Linewidth
4.11 Concluding Remarks
4.12 Problems
Appendix 4A: Sellmeier’s Coefficients for Different Core Materials
Appendix 4B: Total Equivalent Electronic Noise
References
Chapter 5 Optical Coherent Detection and Processing Systems
5.1 Introduction
5.2 Coherent Receiver Components
5.3 Coherent Detection
5.3.1 Optical Heterodyne Detection
5.3.1.1 ASK Coherent System
5.3.1.2 PSK Coherent System
5.3.1.3 Differential Detection
5.3.1.4 FSK Coherent System
5.3.2 Optical Homodyne Detection
5.3.2.1 Detection and Optical PLL
5.3.2.2 Quantum Limit Detection
5.3.2.3 Linewidth Influences
5.3.3 Optical Intradyne Detection
5.4 Self-Coherent Detection and Electronic DSP
5.5 Electronic Amplifiers: Responses and Noise
5.5.1 Introduction
5.5.2 Wideband TIAs
5.5.2.1 Single Input, Single Output
5.5.2.2 Differential Inputs, Single/Differential Output
5.5.3 Amplifier Noise Referred to Input
5.6 Digital Signal Processing Systems and Coherent Optical Reception
5.6.1 DSP-Assisted Coherent Detection
5.6.1.1 DSP-Based Reception Systems
5.6.2 Coherent Reception Analysis
5.6.2.1 Sensitivity
5.6.2.2 Shot-Noise-Limited Receiver Sensitivity
5.6.2.3 Receiver Sensitivity under Nonideal Conditions
5.6.3 Digital Processing Systems
5.6.3.1 Effective Number of Bits
5.6.3.2 Digital Processors
5.7 Concluding Remarks
References
Chapter 6 Differential Phase Shift Keying Photonic Systems
6.1 Introduction
6.2 Optical DPSK Modulation and Formats
6.2.1 Generation of RZ Pulses
6.2.2 Phasor Representation
6.2.3 Phasor Representation of CSRZ Pulses
6.2.4 Phasor Representation of RZ33 Pulses
6.2.5 Discrete Phase Modulation—DPSK
6.2.5.1 Principles of DPSK and Theoretical Treatment of DPSK and DQPSK Transmission
6.2.5.2 Optical DPSK Transmitter
6.2.6 DPSK-Balanced Receiver
6.3 DPSK Transmission Experiment
6.3.1 Components and Operational Characteristics
6.3.2 Spectra of Modulation Formats
6.3.3 Dispersion Tolerance of Optical DPSK Formats
6.3.4 Optical Filtering Effects
6.3.5 Performance of CSRZ-DPSK over a Dispersion-Managed Optical Transmission Link
6.3.6 Mutual Impact of Adjacent 10G and 40G DWDM Channels
6.4 DQPSK Modulation Format
6.4.1 DQPSK
6.4.2 Offset DQPSK Modulation Format
6.4.2.1 Influence of the Minimum Symbol Distance on Receiver Sensitivity
6.4.2.2 Influence of Self-Homodyne Detection on Receiver Sensitivity
6.4.3 MATLAB® and Simulink® Model
6.4.3.1 Simulink® Model
6.4.3.2 Eye Diagrams
6.5 Comparisons of Different Formats and ASK and DPSK
6.5.1 BER and Receiver Sensitivity
6.5.1.1 RZ-ASK and NRZ-ASK
6.5.1.2 RZ-DPSK and NRZ-DQPSK
6.5.1.3 RZ-ASK and NRZ-DQPSK
6.5.2 Dispersion Tolerance
6.5.3 PMD Tolerance
6.5.4 Robustness toward Nonlinear Effects
6.5.4.1 Robustness toward SPM
6.5.4.2 Robustness toward Cross-Phase Modulation
6.5.4.3 Robustness toward Four-Wave Mixing
6.5.4.4 Robustness toward Stimulated Raman Scattering
6.5.4.5 Robustness toward Stimulated Brillouin Scattering
6.6 Concluding Remarks
Appendix 6A: MATLAB® and Simulink® Model for DQPSK Optical System
References
Chapter 7 Multilevel Amplitude and Phase Shift Keying Optical Transmission
7.1 Introduction
7.2 Amplitude and Differential Phase Modulation
7.2.1 ASK Modulation
7.2.1.1 NRZ-ASK Modulation
7.2.1.2 RZ-ASK Modulation
7.2.1.3 CSRZ-ASK Modulation
7.2.2 Differential Phase Modulation
7.2.3 Comparison of Different Amplitude and Phase Optical Modulation Formats
7.2.4 Multilevel Optical Transmitter Using Single Dual-Drive MZIM Transmitter
7.3 MADPSK Optical Transmission
7.3.1 Performance Evaluation
7.3.2 Implementation of MADPSK Transmission Models
7.3.3 Transmitter Model
7.3.4 Receiver Model
7.3.5 Transmission Fiber and Dispersion Compensation Fiber Model
7.3.6 Transmission Performance
7.3.6.1 Signal Spectrum, Signal Constellation, and Eye Diagram
7.3.6.2 BER Evaluation
7.3.6.3 ASK Subsystem Error Probability
7.3.6.4 DQPSK Subsystem Error Probability Evaluation
7.3.6.5 MADPSK System BER Evaluation
7.3.6.6 Chromatic DT
7.3.6.7 Critical Issues
7.3.6.8 Offset Detection
7.4 Star 16-QAM Optical Transmission
7.4.1 Introduction
7.4.2 Design of 16-QAM Signal Constellation
7.4.3 Signal Constellation
7.4.4 Optimum Ring Ratio for Star Constellation
7.4.4.1 Square 16-QAM
7.4.4.2 Offset-Square 16-QAM
7.4.5 Detection Methods
7.4.5.1 Direct Detection
7.4.5.2 Coherent Detection
7.4.6 Transmitter Design
7.4.7 Receiver for 16-Star QAM
7.4.7.1 Coherent Detection Receiver without Phase Estimation
7.4.7.2 Coherent Detection Receiver with Phase Estimation
7.4.7.3 Direct Detection Receiver
7.4.7.4 Coherent Receiver without Phase Estimation
7.4.7.5 Remarks
7.4.8 Other Multilevel and Multi-Subcarrier Modulation Formats for 100 Gbps Ethernet Transmission
7.4.8.1 Multilevel Modulation
7.4.8.2 Optical Orthogonal Frequency Division Multiplexing
7.4.8.3 100 Gbps 8-DPSK–2-ASK 16-Star QAM
7.4.9 Concluding Remarks
7.4.9.1 Offset MADPSK Modulation
7.4.9.2 MAMSK Modulation
7.4.9.3 Star QAM Coherent Detection
References
Chapter 8 Continuous Phase Modulation Format Optical Systems
8.1 Introduction
8.2 Generation of Optical MSK-Modulated Signals
8.3 Detection of M-ary CPFSK-Modulated Optical Signal
8.3.1 Optical MSK Transmitter Using Parallel I–Q MZIMs
8.3.1.1 Linear MSK
8.3.1.2 Weakly Nonlinear MSK
8.3.1.3 Strongly Nonlinear MSK
8.3.2 Optical MSK Receivers
8.4 Optical Binary Amplitude MSK Format
8.4.1 Generation
8.4.2 Optical MSK
8.5 Numerical Results and Discussion
8.5.1 Transmission Performance of Linear and Nonlinear Optical MSK Systems
8.5.2 Transmission Performance of Binary Amplitude Optical MSK Systems
8.6 Concluding Remarks
References
Chapter 9 Frequency Discrimination Reception for Optical Minimum Shift Keying
9.1 Introduction
9.2 ONFDR Operational Principles
9.3 Receiver Modeling
9.4 Receiver Design
9.4.1 Optical Filter Passband
9.4.2 Center Frequency of the Optical Filter
9.4.3 Optimum ODL
9.5 ONFDR Optimum Bandwidth and Center Frequency
9.6 Receiver Performance: Numerical Validation
9.7 ONFDR Robustness to Chromatic Dispersion
9.7.1 Dispersion Tolerance
9.7.2 10 Gbps Transmission
9.7.3 Robustness to PMD of ONFDR
9.7.4 Resilience to Nonlinearity (SPM) of ONFDR
9.7.5 Transmission Limits of OFDR-Based Optical MSK Systems
9.8 Dual-Level Optical MSK
9.8.1 Generation Scheme
9.8.2 Incoherent Detection Technique
9.8.3 Optical Power Spectrum
9.8.4 Receiver Sensitivity
9.8.5 Remarks
9.9 Concluding Remarks
References
Chapter 10 Partial Responses and Single-Sideband Optical Modulation
10.1 Partial Responses: DBM Formats
10.1.1 Introduction
10.1.2 DBM Formatter
10.1.3 40 Gbps DB Optical Fiber Transmission Systems
10.1.4 Electro-Optic Duobinary Transmitter
10.1.5 DB Encoder
10.1.6 External Modulator
10.1.7 DB Transmitters and Precoder
10.1.8 Alternative Phase DB Transmitter
10.1.9 Fiber Propagation
10.2 DB Direct Detection Receiver
10.3 System Transmission and Performance
10.3.1 DB Encoder
10.3.2 Transmitter
10.3.3 Transmission Performance
10.3.4 Alternating-Phase and Variable-Pulse-Width DB: Experimental Setup and Transmission Performance
10.3.4.1 Transmission Setup
10.3.4.2 Test Bed for Variable-Pulse-Width Alternating-Phase DBM Optical Transmission
10.3.4.3 CSRZ-DPSK Experimental Transmission Platform and Transmission Performance
10.3.5 Remarks
10.4 DWDM VSB Modulation-Format Optical transmission
10.4.1 Transmission System
10.4.2 VSB Filtering and DWDM Channels
10.4.3 Transmission Dispersion and Compensation Fibers
10.4.4 Transmission Performance
10.4.4.1 Effects of Channel Spacing on Q Factor
10.4.4.2 Effects of GVD on Q Factor
10.4.4.3 Effects of Filter Passband on the Q Factor
10.5 Single-Sideband Modulation
10.5.1 Hilbert Transform SSB MZ Modulator Simulation
10.5.2 SSB Demodulator Simulation
10.6 Concluding Remarks
References
Chapter 11 OFDM Optical Transmission Systems
11.1 Introduction
11.1.1 Principles of oOFDM: OFDM as a Multicarrier Modulation Format
11.1.1.1 Spectra
11.1.1.2 Orthogonality
11.1.1.3 Subcarriers and Pulse Shaping
11.1.1.4 OFDM Receiver
11.1.2 FFT- and IFFT-Based OFDM Principles
11.2 Optical OFDM Transmission Systems
11.2.1 Impacts of Nonlinear Modulation Effects on Optical OFDM
11.2.2 Dispersion Tolerance
11.2.3 Resilience to PMD Effects
11.3 OFDM and DQPSK Formats for 100 Gbps Ethernet
11.4 Concluding Remarks
References
Chapter 12 Digital Signal Processing in Optical Transmission Systems under Self-Homodyne Coherent Reception
12.1 Introduction
12.2 Electronic Digital Processing Equalization
12.3 System Representation of Equalized Transfer Function
12.3.1 Generic Equalization Formulation
12.3.1.1 Signal Representation and Channel Pure Phase Distortion
12.3.1.2 Equalizers at Receiver
12.3.1.3 Equalizers at the Transmitter
12.3.1.4 Equalization Shared between Receiver and Transmitter
12.3.1.5 Performance of FFE and DFE
12.3.2 Impulse and Step Responses of the Single-Mode Optical Fiber
12.4 Electrical Linear Double-Sampling Equalizers for Duobinary Modulation Formats for Optical Transmission
12.5 MLSE Equalizer for Optical MSK Systems
12.5.1 Configuration of MLSE Equalizer in OFDR
12.5.2 MLSE Equalizer with Viterbi Algorithm
12.5.3 MLSE Equalizer with Reduced-State Template Matching
12.6 MLSE Scheme Performance
12.6.1 Performance of MLSE Schemes in 40 Gbps Transmission
12.6.2 Transmission of 10 Gbps Optical MSK Signals over 1472 km SSMF Uncompensated Optical Link
12.6.3 Performance Limits of Viterbi-MLSE Equalizers
12.6.4 Viterbi-MLSE Equalizers for PMD Mitigation
12.6.5 The Uncertainty and Transmission Limitation of the Equalization Process
12.7 Nonlinear MLSE Equalizers for MSK Optical Transmission Systems
12.7.1 Nonlinear MLSE
12.7.2 Trellis Structure and Viterbi Algorithm
12.7.2.1 Trellis Structure
12.7.2.2 Viterbi Algorithm
12.7.3 Optical Fiber as an FSM
12.8 Uncertainties in Optical Signal Transmission
12.8.1 Uncertainty in ASK Modulation Optical Receiver without Equalization
12.8.2 Uncertainty in MSK Optical Receiver with Equalization
12.9 Electronic Dispersion Compensation of Modulation Formats
12.10 Concluding Remarks
References
Chapter 13 DSP-Based Coherent Optical Transmission Systems
13.1 Introduction
13.2 Quadrature Phase Shift Keying Systems
13.2.1 Carrier Phase Recovery
13.2.2 112G QPSK Coherent Transmission Systems
13.2.3 I–Q Imbalance Estimation Results
13.2.4 Skew Estimation
13.2.5 Fractionally Spaced Equalization of CD and PMD
13.2.6 Linear and Nonlinear Equalization, and Back Propagation Compensation of Linear and Nonlinear Phase Distortion
13.3 16QAM Systems
13.4 Terabits/Second Superchannel Transmission Systems
13.4.1 Overview
13.4.2 Nyquist Pulse and Spectra
13.4.3 Superchannel System Requirements
13.4.3.1 Transmission Distance
13.4.3.2 CD Tolerance
13.4.3.3 PMD Tolerance
13.4.3.4 SOP Rotation Speed
13.4.3.5 Modulation Format
13.4.3.6 Spectral Efficiency
13.4.4 System Structure
13.4.4.1 DSP-Based Coherent Receiver
13.4.4.2 Optical Fourier Transform–Based Structure
13.4.4.3 Processing
13.4.5 Timing Recovery in Nyquist QAM Channel
13.4.6 128 Gbps 16QAM Superchannel Transmission
13.4.7 450 Gbps 32QAM Nyquist Transmission Systems
13.4.8 DSP-Based Heterodyne Coherent Reception Systems
13.5 Concluding Remarks
References
Chapter 14 DSP Algorithms and Coherent Transmission Systems
14.1 Introduction
14.2 General Algorithms for Optical Communications Systems
14.2.1 Equalization of DAC-Limited Bandwidth for Tbps Transmission
14.2.1.1 Motivation
14.2.1.2 Experimental Setup and Bandwidth-Limited Equalization
14.2.2 Linear Equalization
14.2.2.1 Basic Assumptions
14.2.2.2 Zero-Forcing Linear Equalization
14.2.2.3 ZF-LE for Fiber as Transmission Channel
14.2.2.4 Feedback Transversal Filter
14.2.2.5 Tolerance to Additive Gaussian Noises
14.2.2.6 Equalization with Minimizing MSE in Equalized Signals
14.2.2.7 Constant Modulus Algorithm for Blind Equalization and Carrier Phase Recovery
14.2.3 NLE or DFE
14.2.3.1 DD Cancellation of ISI
14.2.3.2 Zero-Forcing Nonlinear Equalization
14.2.3.3 Linear and Nonlinear Equalization of Factorized Channel Response
14.2.3.4 Equalization with Minimizing MSE in Equalized Signals
14.3 Maximum A Posteriori Technique for Phase Estimation
14.3.1 Method
14.3.2 Estimates
14.4 Carrier Phase Estimation
14.4.1 Remarks
14.4.2 Correction of Phase Noise and Nonlinear Effects
14.4.3 Forward Phase Estimation QPSK Optical Coherent Receivers
14.4.4 Carrier Recovery in Polarization Division Multiplexed Receivers: A Case Study
14.4.4.1 FO Oscillations and Q Penalties
14.4.4.2 Algorithm and Demonstration of Carrier Phase Recovery
14.4.4.3 Modified Gardner Phase Detector for Nyquist Coherent Optical Transmission Systems
14.5 Systems Performance of MLSE Equalizer–MSK Optical Transmission Systems
14.5.1 MLSE Equalizer for Optical MSK Systems
14.5.1.1 Configuration of MLSE Equalizer in Optical Frequency Discrimination Receiver
14.5.1.2 MLSE Equalizer with Viterbi Algorithm
14.5.1.3 MLSE Equalizer with Reduced-State Template Matching
14.5.2 MLSE Scheme Performance
14.5.2.1 Performance of MLSE Schemes in 40 Gbps Transmission Systems
14.5.2.2 Transmission of 10 Gbps Optical MSK Signals over 1472 km SSMF Uncompensated Optical Links
14.5.2.3 Performance Limits of Viterbi-MLSE Equalizers
14.5.2.4 Viterbi-MLSE Equalizers for PMD Mitigation
14.5.2.5 Uncertainty and Transmission Limitation of the Equalization Process
14.6 Adaptive Joint CR and Turbo Decoding for Nyquist Terabit Optical Transmission in the Presence of Phase Noise
14.6.1 Motivation
14.6.2 Terabit Experiment Setup and Algorithm Principle
References
Chapter 15 Optical Soliton Transmission System
15.1 Introduction
15.2 Fundamentals of Nonlinear Propagation Theory
15.3 Numerical Approach
15.3.1 Beam Propagation Method
15.3.2 Analytical Approach—ISM
15.3.2.1 Soliton N = 1 by Inverse Scattering
15.3.2.2 Soliton N = 2 by Inverse Scattering
15.4 Fundamental and Higher-Order Solitons
15.4.1 Soliton Evolution for N = 1, 2, 3, 4, and 5
15.4.2 Soliton Breakdown
15.5 Interaction of Fundamental Solitons
15.5.1 Two Solitons’ Interaction with Different Pulse Separation
15.5.2 Two Solitons’ Interaction with Different Relative Amplitude
15.5.3 Two Solitons’ Interaction under Different Relative Phases
15.5.4 Triple Solitons’ Interaction under Different Relative Phases
15.5.5 Triple Solitons’ Interaction with Different Relative Phases and r = 1.5
15.6 Soliton Pulse Transmission Systems and ISM
15.6.1 ISM Revisited
15.6.1.1 Step 1: Direct Scattering
15.6.1.2 Step 2: Evolution of the Scattering Data
15.6.1.3 Step 3: Inverse Spectral Transform
15.6.2 ISM Solutions for Solitons
15.6.2.1 Step 1: Direct Scattering Problem
15.6.2.2 Step 2: Evolution of the Scattering Data
15.6.2.3 Step 3: Inverse Scattering Problem
15.6.3 N-Soliton Solution (Explicit Formula)
15.6.4 Special Case A = N
15.6.5 N-Soliton Solution (Asymptotic Form as τ → ±∞)-Soliton Solution (Asymptotic Form as τ → ±∞)
15.6.6 Bound States and Multiple Eigenvalues
15.7 Interaction between Two Solitons in an Optical Fiber
15.7.1 Soliton Pair with Initial Identical Phases
15.7.2 Soliton Pair with Initial Equal Amplitudes
15.7.3 Soliton Pair with Initial Unequal Amplitudes
15.7.4 Design Strategy
15.8 Generation of Bound Solitons
15.8.1 Generation of Bound Solitons in Actively Phase Modulation Mode-Locked Fiber Ring Resonators
15.8.1.1 Introduction
15.8.1.2 Formation of Bound States in an FM MLFL
15.8.1.3 Experimental Setup and Results
15.8.1.4 Simulation of Dynamics of Bound States in an FM MLFL
15.8.2 Active Harmonic MLFL for Soliton Generation
15.8.2.1 Experiment Setup
15.8.2.2 Tunable Wavelength Harmonic Mode-Locked Pulses
15.8.2.3 Measurement of the Fundamental Frequency
15.8.2.4 Effect of the Modulation Frequency
15.8.2.5 Effect of the Modulation Depth/Index
15.8.2.6 Effect of Fiber Ring Length
15.8.2.7 Effect of Pump Power
15.9 Concluding Remarks
References
Chapter 16 Higher-Order Spectrum Coherent Receivers
16.1 Bispectrum Optical Receivers and Nonlinear Photonic Preprocessing
16.1.1 Introductory Remarks
16.1.2 Bispectrum
16.1.3 Bispectrum Coherent Optical Receiver
16.1.4 Triple Correlation and Bispectra
16.1.4.1 Definition
16.1.4.2 Gaussian Noise Rejection
16.1.4.3 Encoding of Phase Information
16.1.4.4 Eliminating Gaussian Noise
16.1.5 Transmission and Detection
16.1.5.1 Optical Transmission Route and Simulation Platform
16.1.5.2 FWM and Bispectrum Receiving
16.1.5.3 Performance
16.2 Nonlinear Photonic Signal Processing Using Higher-Order Spectra
16.2.1 Introductory Remarks
16.2.2 FWM and Photonic Processing for Higher-Order Spectra
16.2.2.1 Bispectral Optical Structures
16.2.2.2 Phenomena of FWM
16.2.3 Third-Order Nonlinearity and Parametric FWM Process
16.2.3.1 Nonlinear Wave Equation
16.2.3.2 FWM Coupled-Wave Equations
16.2.3.3 Phase Matching
16.2.3.4 Coupled Equations and Conversion Efficiency
16.2.4 Optical Domain Implementation
16.2.4.1 Nonlinear Wave Guide
16.2.4.2 Third Harmonic Conversion
16.2.4.3 Conservation of Momentum
16.2.4.4 Estimate of Optical Power Required for FWM
16.2.5 Transmission Models and Nonlinear Guided Wave Devices
16.3 System Applications of Third-Order Parametric Nonlinearity in Optical Signal Processing
16.3.1 Parametric Amplifiers
16.3.1.1 Wavelength Conversion and Nonlinear Phase Conjugation
16.3.1.2 High-Speed Optical Switching
16.3.1.3 Triple Correlation
16.3.1.4 Remarks
16.3.2 Nonlinear Photonic Preprocessing in Coherent Reception Systems
16.4 Concluding Remarks
References
Chapter 17 Temporal Lens and Adaptive Electronic/Photonic Equalization
17.1 Introduction
17.2 Space–Time Duality and Equalization
17.2.1 Space–Time Duality
17.2.1.1 Paraxial Diffraction
17.2.1.2 Governing Nonlinear Schrödinger Equation
17.2.1.3 Diffractive and Dispersive Phases
17.2.1.4 Spatial Lens
17.2.1.5 Time Lens
17.2.1.6 Temporal Imaging
17.2.1.7 Electro-Optic Phase Modulator as a Time Lens
17.2.2 Equalization in Transmission System
17.2.2.1 Equalization with Sinusoidal Driven Voltage Phase Modulator
17.2.2.2 Equalization with Parabolic Driven Voltage Phase Modulator
17.3 Simulation of Transmission and Equalization
17.3.1 Single-Pulse Transmission
17.3.1.1 Equalization of Second-Order Dispersion
17.3.1.2 Equalization of TOD
17.3.2 Pulse Train Transmission
17.3.2.1 Second-Order Dispersion
17.3.2.2 Equalization of TOD
17.3.3 Equalization of Timing Jitter and PMD
17.4 Equalization in 160 Gbps Transmission System
17.4.1 System Overview
17.4.1.1 System Configurations
17.4.1.2 Experimental Setup
17.4.2 Simulation Model Overview
17.4.2.1 System Overview
17.4.2.2 Transmitter Block
17.4.2.3 Transmission Link
17.4.2.4 Demultiplexer
17.4.2.5 Equalizer System
17.4.2.6 Errors Calculation
17.4.3 Simulation Results
17.4.3.1 Single-Pulse Transmission
17.4.3.2 160 Gbps Transmission and Equalization
17.5 Concluding Remarks
References
Chapter 18 Comparison of Modulation Formats for Digital Optical Communications
18.1 Identification of Modulation Features for Combating Impairment Effects
18.1.1 Binary Digital Optical Signals
18.1.2 M-ary Digital Optical Signals
18.1.3 Multi-Subcarrier Digital Optical Signals
18.1.4 Modulation Formats and Electronic Equalization
18.2 Amplitude, Phase, and Frequency Modulation Formats in Dispersion-Compensating Span Transmission Systems
18.2.1 ASK—DPSK and DPSK—DQPSK under Self-Homodyne Reception
18.2.1.1 Dispersion Sensitivity of Different Modulation Formats of ASK and DPSK
18.2.2 NRZ-ASK and NRZ-DPSK under Self-Homodyne Reception
18.2.3 RZ-ASK and RZ-DPSK under Self-Homodyne Reception
18.2.4 CSRZ-ASK and CSRZ-DPSK under Self-Homodyne Reception
18.2.5 ASK and DPSK Spectra
18.2.6 ASK and DPSK under Self-Homodyne Reception in Long-Haul Transmission
18.3 Nonlinear Effects in ASK and DPSK under Self-Homodyne Reception in Long-Haul Transmission
18.3.1 Performance of DWDM RZ-DPSK and CSRZ-DPSK
18.3.2 Nonlinear Effects on CSRZ-DPSK and RZ-DPSK
18.3.3 Nonlinear Effects on CSRZ-ASK and RZ-ASK
18.3.4 Continuous Phase versus Discrete Phase Shift Keying under Self-Homodyne Reception
18.3.5 Multi-Subcarrier versus Single/Dual Carrier Modulation under Self-Homodyne Reception
18.3.6 Multilevel versus Binary or I–Q Modulation under Self-Homodyne Reception
18.3.7 Single-Sideband and Partial Response Modulation under Self-Homodyne Reception
18.4 100 G and Tbps Homodyne Reception Transmission Systems
18.4.1 Generation of Multi-Subcarriers
18.4.2 Nyquist Signal Generation Using DAC by Equalization in Frequency Domain
18.4.3 Function Modules of a Nyquist-WDM System
18.4.4 DSP Architecture
18.4.5 Key Hardware Subsystems
18.4.5.1 Recirculating Frequency Shifting
18.4.5.2 Nonlinear Excitation Comb Generation and Multiplexed Laser Sources
18.4.5.3 Experimental Platform for Comb Generators
18.4.6 Non-DCF 1 Tbps and 2 Tbps Superchannel Transmission Performance
18.4.6.1 Transmission Platform
18.4.6.2 Performance
18.4.6.3 Coding Gain of FEC and Transmission Simulation
18.4.6.4 MIMO Filtering Process to Extend Transmission Reach
18.4.7 Multicarrier Scheme Comparison
18.5 Modulation Formats and All-Optical Networking
18.5.1 Advanced Modulation Formats in Long-Haul Transmission Systems
18.5.2 Advanced Modulation Formats in All-Optical Networks
18.5.3 Hybrid 40 Gbps over 10 Gbps Optical Networks: 328 km SSMF + DCF for 320 km Tx—Impact of Adjacent 10 G/40 G Channels
18.6 Ultra-Fast Optical Networks
18.7 Concluding Remarks
References
Annex 1: Technical Data of Single-Mode Optical Fibers
Annex 2: Coherent Balanced Receiver and Method for Noise Suppression
Annex 3: RMS Definition and Power Measurement
Annex 4: Power Budget
Annex 5: Modeling of Digital Photonic Transmission Systems
Index
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To my wife, Phuong, and my son, Lam.
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