Blind Equalization and Carrier Recovery - Adaptive Solutions and Analysis

Preface
Contents
List of Figures
List of Tables
1 Introduction
	1.1 Trained and Blind Adaptive Equalizers: Historical Perspectives
	1.2 System Model and ``Bussgang\'\' Blind Equalizer
	1.3 Blind Equalization Design Methodologies
		1.3.1 Minimum Entropy Deconvolution Criterion
		1.3.2 Constant Modulus Criterion
		1.3.3 Shtrom-Fan Criterion
		1.3.4 Shalvi-Weinstein Criterion
		1.3.5 Other Popular Variants
	1.4 Organization and Contributions
	Bibliography
2 Adaptive Minimum Dispersion Constant Modulus Algorithms
	2.1 Proposed Cost-Function
		2.1.1 A Composite Dispersion Measure
		2.1.2 The Cost-Function and its Relaxed Optimization
	2.2 Evaluation of Dispersion Constants
	2.3 Stochastic Stability of CMAp
		2.3.1 Derivation of the Bound
	2.4 Simulation Results
		2.4.1 Experiment 1: ISI Performances of CMAp-2 and CMAp
		2.4.2 Experiment 2: Validating the Stability Bound for CMAp
	2.5 Conclusions
	Bibliography
3 Adaptive Minimum Dispersion Multimodulus Algorithms
	3.1 Introduction
	3.2 A Family of Multimodulus Algorithms: MMAp-q
		3.2.1 MMAp-q: Phase Recovery Capability
	3.3 Second Family of MMA: MMAp
		3.3.1 MMAp: Phase Recovery Capability
	3.4 Evaluation of Dispersion Constants
		3.4.1 Derivation of R_L for MMAp-1
		3.4.2 Derivation of R_L for MMAp-2
		3.4.3 Derivation of R_L for MMAp
	3.5 Dynamic Convergence Analysis
	3.6 Simulation Results
		3.6.1 Experiment: MSE/ISI Analytical/Simulated Performances
	3.7 Conclusions
	Bibliography
4 Adaptive Minimum Entropy Constant Modulus Algorithm
	4.1 Introduction
	4.2 Minimum Entropy Deconvolution
		4.2.1 Derivation of the Cost J_AN(w)
		4.2.2 Admissibility of the Cost J_AN(w)
	4.3 Minimum Output Energy based Equalization
		4.3.1 Comparing the Cost (4.22) with that of Allen-Mazo
	4.4 Optimization of the Constrained Cost (4.22)
		4.4.1 Derivation of the Adaptive Realization: Beta-CMA
		4.4.2 Detailed Derivation of Parameter Beta
	4.5 Simulation Results
	4.6 Conclusions
	Bibliography
5 Adaptive Minimum Entropy Multimodulus Algorithm
	5.1 Meng-Tuqan-Ding l_2-Optimization Criterion
	5.2 Differentiable Cost and Adaptive Optimization
		5.2.1 Gradient Based Optimization
		5.2.2 Evaluation of Gain
		5.2.3 Cost-Function Interpretation and Phase Recovery Capability
		5.2.4 Dynamic Convergence Analysis
	5.3 Simulation Results
		5.3.1 Experiment 1: ISI Performances with TSE/FSE
		5.3.2 Experiment 2: SER Performances with TSE/FSE
		5.3.3 Experiment 3: Validating MSE/ISI Convergence Analysis
	5.4 Conclusions
	Bibliography
6 Equalizing Cross-QAM
	6.1 Introduction
	6.2 Proposed Algorithms
	6.3 Simulation Results
	6.4 Appendix A: Optimum values of R for CXA and SCXA
	6.5 Appendix B: Optimum values of k for CXA and SCXA
	Bibliography
7 Excess Mean-Square Analysis
	7.1 System Model
	7.2 Non-Stationary Environment and Energy Conservation Relation
	7.3 Steady-State EMSE Analysis
		7.3.1 The EMSE of MMA2-2 Equalizer
		7.3.2 The EMSE of MMA2-1 Equalizer
		7.3.3 The EMSE of MMA1-2 Equalizer
		7.3.4 The EMSE of MMA1-1 Equalizer
		7.3.5 The EMSE of Beta-MMA Equalizer
		7.3.6 The EMSE of CMA2-2 Equalizer
		7.3.7 EMSE of Beta-CMA Equalizer
			7.3.7.1 Approximate Expressions for Q_(1,0)(a,b) and Q_(3,0)(a,b)
	7.4 Comparison with Existing Methods
	7.5 Simulation Results
		7.5.1 Performance Evaluation for MMAp-q
			7.5.1.1 Considering Zero-forcing Equalization
			7.5.1.2 Equalizing Time-Varying Channel
			7.5.1.3 Effect of Filter-Length on EMSE
			7.5.1.4 Adaptive Polarization Demultiplexing
		7.5.2 Performance Evaluation for CMA2-2 and Beta-CMA
		7.5.3 Performance Evaluation for Beta-MMA
	7.6 Conclusions
	Bibliography
8 Deterministic Stability Analysis
	8.1 Deterministic Stability of Beta-CMA
	8.2 Deterministic Stability Analysis of CMAp
	8.3 Simulation Results and Conclusions
	Bibliography
9 Equalization with Recursive Structure
	9.1 Introduction
	9.2 System Model
	9.3 Newton-Like Realization of Beta-CMA
	9.4 Steady-State Performance of NL-Beta-CMA
	9.5 Simulation Results
		9.5.1 Experiment 1: Equalizing Low Eigen-Spread Channel
		9.5.2 Experiment 2: Equalizing High Eigen-Spread Channel
		9.5.3 Experiment 3: Validating Analytical EMSE
	9.6 Conclusions
	Bibliography
10 Hardware Efficient Sign Equalizer
	10.1 Introduction
	10.2 Proposed Algorithm
	10.3 Simulation Results
	10.4 Conclusions
	Bibliography
11 Sparse Channel Equalization
	11.1 Introduction
	11.2 Proposed Algorithm
	11.3 Steady-state Stability
	11.4 Explicit Regularization
		11.4.1 Closed-form solution for l_(1/2) regularization
		11.4.2 Closed-form solution for l_(2/3) regularization
	11.5 Simulation Results
	11.6 Conclusions
	Bibliography
12 Carrier Phase Recovery
	12.1 Introduction
	12.2 Problem Formulation
	12.3 Existing Adaptive Phase Recovery Algorithm
	12.4 Modified Phase Recovery Algorithms
		12.4.1 QPSK-Like Partitioning of QAM
			12.4.1.1 Proposed Modifications
			12.4.1.2 Remarks
		12.4.2 QAM-to-QPSK Transformation
			12.4.2.1 Square-QAM
			12.4.2.2 Cross-QAM
			12.4.2.3 Obtaining Centroid
	12.5 Performance Analysis
		12.5.1 Performance in the Presence of Frequency-Offset
		12.5.2 Performance in the Presence of Phase Noise
		12.5.3 Performance Under Both Frequency-Offset and Phase Noise
		12.5.4 Performance With Imperfect Equalization
	12.6 Adaptive Estimation of the Optimal Step-Size
	12.7 Batch Processing Complex-Valued Updates
	12.8 Hardware-Efficient Complex-Valued Updates
	12.9 Simulation Results
		12.9.1 Admissibility of Transformation Based Phase Recovery
		12.9.2 Transient Performance in AWGN Environment
		12.9.3 Steady-State Performance in AWGN Environment
		12.9.4 Performance Evaluation With FO and/or PN
		12.9.5 Performance Evaluation under the Influence of ISI
		12.9.6 Adaptive Estimation of Optimal Step-size
		12.9.7 Performance of Batch FP-PRA
	12.10 Conclusions
	Bibliography