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Digital Processing

Book Description

With coherent mixing in the optical domain and processing in the digital domain, advanced receiving techniques employing ultra-high speed sampling rates have progressed tremendously over the last few years. These advances have brought coherent reception systems for lightwave-carried information to the next stage, resulting in ultra-high capacity global internetworking. Digital Processing: Optical Transmission and Coherent Receiving Techniques describes modern coherent receiving techniques for optical transmission and aspects of modern digital optical communications in the most basic lines.

The book includes simplified descriptions of modulation techniques for such digital transmission systems carried by light waves. It discusses the basic aspects of modern digital optical communications in the most basic lines. In addition, the book covers digital processing techniques and basic algorithms to compensate for impairments and carrier recovery, as well as noise models, analysis, and transmission system performance.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright Page
  5. Table of Contents
  6. Preface
  7. Author
  8. Abbreviations
  9. 1 Overview of Optical Fiber Communications and DSP-Based Transmission Systems
    1. 1.1 Introduction
    2. 1.2 From Few Mb/s to Tb/s: Transmission and Receiving for Optical Communications Systems
      1. 1.2.1 Guiding Lightwaves over the Last 40 Years
      2. 1.2.2 Guiding Lightwaves: Single Mode, Multimode, and Few Mode
      3. 1.2.3 Modulation Formats: Intensity to Phase Modulation, Direct to External Modulation
      4. 1.2.4 Coherent and Incoherent Receiving Techniques
      5. 1.2.5 Digital Processing in Advanced Optical Communication Systems
    3. 1.3 Digital Modulation Formats
      1. 1.3.1 Modulation Formats
      2. 1.3.2 Pulse Shaping and Modulations for High Spectral Efficiency
        1. 1.3.2.1 Partial Response
        2. 1.3.2.2 Nyquist Pulse Shaping
    4. 1.4 Optical Demodulation: Phase and Polarization Diversity Technique
    5. 1.5 Organization of the Book Chapters
    6. References
  10. 2 Optical Fibers: Guiding and Propagation Properties
    1. 2.1 Optical Fibers: Circular Optical Waveguides
      1. 2.1.1 General Aspects
      2. 2.1.2 Optical Fiber: General Properties
        1. 2.1.2.1 Geometrical Structures and Index Profile
      3. 2.1.3 Fundamental Mode of Weakly Guiding Fibers
        1. 2.1.3.1 Solutions of the Wave Equation for Step-Index Fiber
        2. 2.1.3.2 Single and Few Mode Conditions
        3. 2.1.3.3 Gaussian Approximation: Fundamental Mode Revisited
        4. 2.1.3.4 Cut-Off Properties
        5. 2.1.3.5 Power Distribution
        6. 2.1.3.6 Approximation of Spot-Size r0 of a Step-Index Fiber
      4. 2.1.4 Equivalent-Step Index Description
    2. 2.2 Nonlinear Optical Effects
      1. 2.2.1 Nonlinear Self-Phase Modulation Effects
      2. 2.2.2 Self-Phase Modulation
      3. 2.2.3 Cross-Phase Modulation
      4. 2.2.4 Stimulated Scattering Effects
        1. 2.2.4.1 Stimulated Brillouin Scattering
        2. 2.2.4.2 Stimulated Raman Scattering
        3. 2.2.4.3 Four-Wave Mixing Effects
    3. 2.3 Signal Attenuation in Optical Fibers
      1. 2.3.1 Intrinsic or Material Absorption Losses
      2. 2.3.2 Waveguide Losses
      3. 2.3.3 Attenuation Coefficient
    4. 2.4 Signal Distortion in Optical Fibers
      1. 2.4.1 Material Dispersion
      2. 2.4.2 Waveguide Dispersion
        1. 2.4.2.1 Alternative Expression for Waveguide Dispersion Parameter
        2. 2.4.2.2 Higher-Order Dispersion
      3. 2.4.3 Polarization Mode Dispersion
    5. 2.5 Transfer Function of Single-Mode Fibers
      1. 2.5.1 Linear Transfer Function
      2. 2.5.2 Nonlinear Fiber Transfer Function
      3. 2.5.3 Transmission Bit Rate and the Dispersion Factor
    6. 2.6 Fiber Nonlinearity Revisited
      1. 2.6.1 SPM, XPM Effects
      2. 2.6.2 SPM and Modulation Instability
      3. 2.6.3 Effects of Mode Hopping
      4. 2.6.4 SPM and Intra-Channel Nonlinear Effects
      5. 2.6.5 Nonlinear Phase Noises
    7. 2.7 Special Dispersion Optical Fibers
    8. 2.8 SMF Transfer Function: Simplified Linear and Nonlinear Operating Region
    9. 2.9 Numerical Solution: Split-Step Fourier Method
      1. 2.9.1 Symmetrical Split-Step Fourier Method
        1. 2.9.1.1 Modeling of Polarization Mode Dispersion
        2. 2.9.1.2 Optimization of Symmetrical SSFM
    10. 2.10 Nonlinear Fiber Transfer Functions and Compensations in Digital Signal Processing
      1. 2.10.1 Cascades of Linear and Nonlinear Transfer Functions in Time and Frequency Domains
      2. 2.10.2 Volterra Nonlinear Transfer Function and Electronic Compensation
      3. 2.10.3 Inverse of Volterra Expansion and Nonlinearity Compensation in Electronic Domain
        1. 2.10.3.1 Inverse of Volterra Transfer Function
        2. 2.10.3.2 Electronic Compensation Structure
        3. 2.10.3.3 Remarks
      4. 2.10.4 Back-Propagation Techniques for Compensation of Nonlinear Distortion
    11. 2.11 Concluding Remarks
    12. References
  11. 3 External Modulators for Coherent Transmission and Reception
    1. 3.1 Introduction
    2. 3.2 External Modulation and Advanced Modulation Formats
      1. 3.2.1 Electro-Absorption Modulators
      2. 3.2.2 Electro-Optic Modulators
        1. 3.2.2.1 Phase Modulators
        2. 3.2.2.2 Intensity Modulators
        3. 3.2.2.3 Phasor Representation and Transfer Characteristics
        4. 3.2.2.4 Bias Control
        5. 3.2.2.5 Chirp-Free Optical Modulators
        6. 3.2.2.6 Structures of Photonic Modulators
        7. 3.2.2.7 Typical Operational Parameters
      3. 3.2.3 ASK Modulation Formats and Pulse Shaping
        1. 3.2.3.1 Return-to-Zero Optical Pulses
        2. 3.2.3.2 Phasor Representation
        3. 3.2.3.3 Phasor Representation of CSRZ Pulses
        4. 3.2.3.4 Phasor Representation of RZ33 Pulses
      4. 3.2.4 Differential Phase Shift Keying
        1. 3.2.4.1 Background
        2. 3.2.4.2 Optical DPSK Transmitter
    3. 3.3 Generation of Modulation Formats
      1. 3.3.1 Amplitude Modulation ASK-NRZ and ASK-RZ
      2. 3.3.2 Amplitude Modulation Carrier-Suppressed RZ Formats
      3. 3.3.3 Discrete Phase Modulation NRZ Formats
        1. 3.3.3.1 Differential Phase Shift Keying
        2. 3.3.3.2 Differential Quadrature Phase Shift Keying
        3. 3.3.3.3 Non Return-to-Zero Differential Phase Shift Keying
        4. 3.3.3.4 Return-to-Zero Differential Phase Shift Keying
        5. 3.3.3.5 Generation of M-Ary Amplitude Differential Phase Shift Keying (M-Ary ADPSK) Using One MZIM
        6. 3.3.3.6 Continuous Phase Modulation PM-NRZ Formats
        7. 3.3.3.7 Linear and Nonlinear MSK
    4. 3.4 Photonic MSK Transmitter Using Two Cascaded Electro-Optic Phase Modulators
      1. 3.4.1 Configuration of Optical MSK Transmitter Using Mach–Zehnder Intensity Modulators: I-Q Approach
      2. 3.4.2 Single-Side Band Optical Modulators
      3. 3.4.3 Optical RZ-MSK
      4. 3.4.4 Multi-Carrier Multiplexing Optical Modulators
      5. 3.4.5 Spectra of Modulation Formats
    5. 3.5 I-Q Integrated Modulators
      1. 3.5.1 Inphase and Quadrature Phase Optical Modulators
      2. 3.5.2 IQ Modulator and Electronic Digital Multiplexing for Ultra-High Bit Rates
    6. 3.6 DAC for DSP-Based Modulation and Transmitter
      1. 3.6.1 Fujitsu DAC
      2. 3.6.2 Structure
        1. 3.6.2.1 Generation of I and Q Components
    7. 3.7 Remarks
    8. References
  12. 4 Optical Coherent Detection and Processing Systems
    1. 4.1 Introduction
    2. 4.2 Coherent Receiver Components
    3. 4.3 Coherent Detection
      1. 4.3.1 Optical Heterodyne Detection
        1. 4.3.1.1 ASK Coherent System
        2. 4.3.1.2 PSK Coherent System
        3. 4.3.1.3 Differential Detection
        4. 4.3.1.4 FSK Coherent System
      2. 4.3.2 Optical Homodyne Detection
        1. 4.3.2.1 Detection and OPLL
        2. 4.3.2.2 Quantum Limit Detection
        3. 4.3.2.3 Linewidth Influences
      3. 4.3.3 Optical Intradyne Detection
    4. 4.4 Self-Coherent Detection and Electronic DSP
    5. 4.5 Electronic Amplifiers: Responses and Noises
      1. 4.5.1 Introduction
      2. 4.5.2 Wideband TIAs
        1. 4.5.2.1 Single Input/Single Output
        2. 4.5.2.2 Differential Inputs, Single/Differential Output
      3. 4.5.3 Amplifier Noise Referred to Input
    6. 4.6 Digital Signal Processing Systems and Coherent Optical Reception
      1. 4.6.1 DSP-Assisted Coherent Detection
        1. 4.6.1.1 DSP–Based Reception Systems
      2. 4.6.2 Coherent Reception Analysis
        1. 4.6.2.1 Sensitivity
        2. 4.6.2.2 Shot-Noise-Limited Receiver Sensitivity
        3. 4.6.2.3 Receiver Sensitivity under Nonideal Conditions
      3. 4.6.3 Digital Processing Systems
        1. 4.6.3.1 Effective Number of Bits
        2. 4.6.3.2 Impact of ENOB on Transmission Performance
        3. 4.6.3.3 Digital Processors
    7. 4.7 Concluding Remarks
    8. 4.8 Appendix: A Coherent Balanced Receiver and Method for Noise Suppression
      1. 4.8.1 Analytical Noise Expressions
      2. 4.8.2 Noise Generators
      3. 4.8.3 Equivalent Input Noise Current
      4. 4.8.4 Pole-Zero Pattern and Dynamics
      5. 4.8.5 Responses and Noise Measurements
        1. 4.8.5.1 Rise-Time and 3 dB Bandwidth
        2. 4.8.5.2 Noise Measurement and Suppression
        3. 4.8.5.3 Requirement for Quantum Limit
        4. 4.8.5.4 Excess Noise Cancellation Technique
        5. 4.8.5.5 Excess Noise Measurement
      6. 4.8.6 Remarks
      7. 4.8.7 Noise Equations
    9. References
  13. 5 Optical Phase Locking
    1. 5.1 Overview of Optical Phase Lock Loop
    2. 5.2 Optical Coherent Detection and Optical PLL
      1. 5.2.1 General PLL Theory
        1. 5.2.1.1 Phase Detector
        2. 5.2.1.2 Loop Filter
        3. 5.2.1.3 Voltage-Controlled Oscillator
        4. 5.2.1.4 A Second-Order PLL
      2. 5.2.2 PLL
      3. 5.2.3 OPLL
        1. 5.2.3.1 Functional Requirements
        2. 5.2.3.2 Nonfunctional Requirements
      4. 5.2.4 Digital LPF Design
        1. 5.2.4.1 Fixed-Point Arithmetic
        2. 5.2.4.2 Digital Filter
        3. 5.2.4.3 Interface Board
        4. 5.2.4.4 FPGA Implementation
        5. 5.2.4.5 Indication of Locking State
        6. 5.2.4.6 OPLL Hardware Details
    3. 5.3 Performances: Simulation and Experiments
      1. 5.3.1 Simulation
      2. 5.3.2 Experiment: Digital Feedback Control
        1. 5.3.2.1 Noise Sources
        2. 5.3.2.2 Quality of Locking State
        3. 5.3.2.3 Limitations
      3. 5.3.3 Simulation and Experiment Test Bed: Analog Feedback Control
        1. 5.3.3.1 Simulation: Analog Feedback Control Loop
        2. 5.3.3.2 Laser Beating Experiments
        3. 5.3.3.3 Loop Filter Design
        4. 5.3.3.4 Closed-Loop Locking of LO and Signal Carrier: Closed-Loop OPLL
        5. 5.3.3.5 Monitoring of Beat Signals
        6. 5.3.3.6 High-Resolution Optical Spectrum Analysis
        7. 5.3.3.7 Phase Error and LPF Time Constant
        8. 5.3.3.8 Remarks
      4. 5.4 OPLL for Superchannel Coherent Receiver
    4. 5.5 Concluding Remarks
    5. References
  14. 6 Digital Signal Processing Algorithms and Systems Performance
    1. 6.1 Introduction
    2. 6.2 General Algorithms for Optical Communications Systems
      1. 6.2.1 Linear Equalization
        1. 6.2.1.1 Basic Assumptions
        2. 6.2.1.2 Zero-Forcing Linear Equalization (ZF-LE)
        3. 6.2.1.3 ZF-LE for Fiber as a Transmission Channel
        4. 6.2.1.4 Feedback Transversal Filter
        5. 6.2.1.5 Tolerance of Additive Gaussian Noises
        6. 6.2.1.6 Equalization with Minimizing MSE in Equalized Signals
        7. 6.2.1.7 Constant Modulus Algorithm for Blind Equalization and Carrier Phase Recovery
      2. 6.2.2 Nonlinear Equalizer or DFEs
        1. 6.2.2.1 DD Cancellation of ISI
        2. 6.2.2.2 Zero-Forcing Nonlinear Equalization
        3. 6.2.2.3 Linear and Nonlinear Equalization of a Factorized Channel Response
        4. 6.2.2.4 Equalization with Minimizing MSE in Equalized Signals
    3. 6.3 MLSD and Viterbi
      1. 6.3.1 Nonlinear MLSE
      2. 6.3.2 Trellis Structure and Viterbi Algorithm
        1. 6.3.2.1 Trellis Structure
        2. 6.3.2.2 Viterbi Algorithm
      3. 6.3.3 Optical Fiber as a Finite State Machine
      4. 6.3.4 Construction of State Trellis Structure
      5. 6.3.5 Shared Equalization between Transmitter and Receivers
        1. 6.3.5.1 Equalizers at the Transmitter
        2. 6.3.5.2 Shared Equalization
    4. 6.4 Maximum a Posteriori Technique for Phase Estimation
      1. 6.4.1 Method
      2. 6.4.2 Estimates
    5. 6.5 Carrier Phase Estimation
      1. 6.5.1 Remarks
      2. 6.5.2 Correction of Phase Noise and Nonlinear Effects
      3. 6.5.3 Forward Phase Estimation QPSK Optical Coherent Receivers
        1. 6.5.4 CR in Polarization Division Multiplexed Receivers: A Case Study
        2. 6.5.4.1 FO Oscillations and Q-Penalties
        3. 6.5.4.2 Algorithm and Demonstration of Carrier Phase Recovery
    6. 6.6 Systems Performance of MLSE Equalizer–MSK Optical Transmission Systems
      1. 6.6.1 MLSE Equalizer for Optical MSK Systems
        1. 6.6.1.1 Configuration of MLSE Equalizer in Optical Frequency Discrimination Receiver
        2. 6.6.1.2 MLSE Equalizer with Viterbi Algorithm
        3. 6.6.1.3 MLSE Equalizer with Reduced-State Template Matching
      2. 6.6.2 MLSE Scheme Performance
        1. 6.6.2.1 Performance of MLSE Schemes in 40 Gb/s Transmission Systems
        2. 6.6.2.2 Transmission of 10 Gb/s Optical MSK Signals over 1472 km SSMF Uncompensated Optical Link
        3. 6.6.2.3 Performance Limits of Viterbi–MLSE Equalizers
        4. 6.6.2.4 Viterbi-MLSE Equalizers for PMD Mitigation
        5. 6.6.2.5 On the Uncertainty and Transmission Limitation of Equalization Process
    7. References
  15. 7 DSP-Based Coherent Optical Transmission Systems
    1. 7.1 Introduction
    2. 7.2 QPSK Systems
      1. 7.2.1 Carrier Phase Recovery
      2. 7.2.2 112 G QPSK Coherent Transmission Systems
      3. 7.2.3 I–Q Imbalance Estimation Results
      4. 7.2.4 Skew Estimation
      5. 7.2.5 Fractionally Spaced Equalization of CD and PMD
      6. 7.2.6 Linear and Nonlinear Equalization and Back-Propagation Compensation of Linear and Nonlinear Phase Distortion
    3. 7.3 16 QAM Systems
    4. 7.4 Tera-Bits/s Superchannel Transmission Systems
      1. 7.4.1 Overview
      2. 7.4.2 Nyquist Pulse and Spectra
      3. 7.4.3 Superchannel System Requirements
      4. 7.4.4 System Structure
        1. 7.4.4.1 DSP-Based Coherent Receiver
        2. 7.4.4.2 Optical Fourier Transform-Based Structure
        3. 7.4.4.3 Processing
      5. 7.4.5 Timing Recovery in Nyquist QAM Channel
      6. 7.4.6 128 Gb/s 16 QAM Superchannel Transmission
      7. 7.4.7 450 Gb/s 32 QAM Nyquist Transmission Systems
      8. 7.4.8 DSP-Based Heterodyne Coherent Reception Systems
    5. 7.5 Concluding Remarks
    6. References
  16. 8 Higher-Order Spectrum Coherent Receivers
    1. 8.1 Bispectrum Optical Receivers and Nonlinear Photonic Pre-Processing
      1. 8.1.1 Introductory Remarks
      2. 8.1.2 Bispectrum
      3. 8.1.3 Bispectrum Coherent Optical Receiver
      4. 8.1.4 Triple Correlation and Bispectra
        1. 8.1.4.1 Definition
        2. 8.1.4.2 Gaussian Noise Rejection
        3. 8.1.4.3 Encoding of Phase Information
        4. 8.1.4.4 Eliminating Gaussian Noise
        5. 8.1.5 Transmission and Detection
        6. 8.1.5.1 Optical Transmission Route and Simulation Platform
        7. 8.1.5.2 Four-Wave Mixing and Bispectrum Receiving
        8. 8.1.5.3 Performance
    2. 8.2 NL Photonic Signal Processing Using Higher-Order Spectra
      1. 8.2.1 Introductory Remarks
      2. 8.2.2 FWM and Photonic Processing
        1. 8.2.2.1 Bispectral Optical Structures
        2. 8.2.2.2 The Phenomena of FWM
      3. 8.2.3 Third-Order Nonlinearity and Parametric FWM Process
        1. 8.2.3.1 NL Wave Equation
        2. 8.2.3.2 FWM Coupled-Wave Equations
        3. 8.2.3.3 Phase Matching
        4. 8.2.3.4 Coupled Equations and Conversion Efficiency
      4. 8.2.4 Optical Domain Implementation
        1. 8.2.4.1 NL Wave Guide
        2. 8.2.4.2 Third-Harmonic Conversion
        3. 8.2.4.3 Conservation of Momentum
        4. 8.2.4.4 Estimate of Optical Power Required for FWM
      5. 8.2.5 Transmission Models and NL Guided Wave Devices
      6. 8.2.6 System Applications of Third-Order Parametric Nonlinearity in Optical Signal Processing
        1. 8.2.6.1 Parametric Amplifiers
        2. 8.2.6.2 Wavelength Conversion and NL Phase Conjugation
        3. 8.2.6.3 High-Speed Optical Switching
        4. 8.2.6.4 Triple Correlation
        5. 8.2.6.5 Remarks
      7. 8.2.7 NL Photonic Pre-Processing in Coherent Reception Systems
      8. 8.2.8 Remarks
    3. References
  17. Index