Blind Equalization and Identification

by Ding; Zhi

ISBN13: 9780824704797

ISBN10: 0824704797

Format: Hardcover

Pub. Date: 2001-01-09

Publisher(s): CRC Press

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Summary

This text seeks to clarify various contradictory claims regarding capabilities and limitations of blind equalization. It highlights basic operating conditions and potential for malfunction. The authors also address concepts and principles of blind algorithms for single input multiple output (SIMO) systems and multi-user extensions of SIMO equalization and identification.

Author Biography

Zhi Ding is a Professor at the University of California, Davis. Ye (Geoffrey) Li is an Associate Professor at the Georgia Institute of Technology, Atlanta.

Series Introduction	p. iii
Preface	p. v
Introduction	p. 1
Blind Equalization: A Popular Research Topic	p. 1
Motivation For This Book	p. 1
Blind Equalization and Identification of Communication Channels	p. 3
Network Collision Resolution of Transmitted Packets	p. 5
Blind Deconvolution: A Related Application	p. 6
A Brief History	p. 7
1975 to Present: Blind Single Channel Equalization	p. 7
1981 to Present: Blind Statistical Channel Identification	p. 8
1991 to Present: Multichannel Identification and Equalization	p. 8
Organization and Contents	p. 9
Basic Concepts and Approaches	p. 15
Channel Equalization in QAM Data Communication Systems	p. 15
SISO and SIMO Discrete Channel Model	p. 16
Channel Equalization	p. 17
T-Spaced Equalizers	p. 18
Fractionally-Spaced Equalizers	p. 19
Nonlinear Equalization	p. 21
The Need for Blind Channel Equalization and Identification	p. 24
Basic Approaches to Blind Equalization and Identification	p. 25
Blind SISO Equalization	p. 25
Blind SISO Channel Identification	p. 27
Blind SIMO Channel Identification	p. 28
Blind Multichannel Equalization	p. 29
Single Input Single Output Blind Equalization Algorithms	p. 36
Introduction	p. 36
SISO Channel Equalization	p. 37
Channel Equalization in QAM Communication Systems	p. 37
Blind Adaptive Channel Equalizer	p. 39
Basic Facts on Blind Adaptive Equalization	p. 40
Adaptive Blind SISO Equalizers	p. 42
FIR Linear Equalizers	p. 42
Cost Functions and Associated Adaptive Algorithms	p. 44
The Sato Algorithm and Its Generalizations	p. 45
The Sato Algorithm	p. 45
BGR Algorithms (an Extension of the Sato Algorithm)	p. 46
Stop-and-Go Algorithms	p. 47
Bussgang Algorithms	p. 47
Constant Modulus Algorithms and Related Schemes	p. 51
Constant Modulus (Godard) Algorithm	p. 51
Shalvi and Weinstein Algorithms	p. 52
Stochastic Gradient Descent Adaptation	p. 52
A Blind Equalization Example	p. 53
Convergence of Blind SISO Adaptive Algorithms	p. 57
Convergence Requirement of Open Eye Equalizers	p. 57
Some Known Convergence Results	p. 59
Local Convergence of Blind Equalizers	p. 60
Convergence Requirement of Bussgang Algorithms	p. 61
Initialization Issues	p. 63
QAM Algorithms Based on Convex Cost Functions	p. 64
Background	p. 64
Linearly Constrained Equalizer with Convex Cost	p. 65
Convex Cost Function and Parameter Constraint	p. 67
Global Convergence	p. 68
Remarks and Comments	p. 72
Implementation and Simulation	p. 74
A Fast Linear Programming Algorithm for Convex Cost	p. 79
Weakness of Batch and Adaptive Implementations	p. 79
Linear Programming Formulations	p. 79
Implementation and Simulation	p. 81
Summary	p. 85
Local Convergence Analysis of SISO Blind Equalizers	p. 92
Convergence Equilibria of Blind Equalizers	p. 93
The Constant Modulus Algorithm and Godard Algorithm	p. 97
Undesirable Equilibria of Godard Algorithms	p. 97
Stability Condition for the Undesirable Equilibria	p. 99
Consequences of Ill-Convergence	p. 103
Examples of Stable Undesirable Equilibria	p. 103
Effect of Channel Noise and Mismodeling	p. 105
Shalvi-Weinstein and Standard Cumulant Algorithms	p. 109
Geometric Relationship between SWA and CMA	p. 112
Initial Kurtosis Effect on SWA Finite Equalizer convergence	p. 116
SWA Minimum Location and An Initialization Strategy	p. 118
Extension of Results to QAM Communication Systems	p. 123
Convergence Analysis of Equalizers Driven by SCA	p. 125
The Sato Algorithm	p. 126
Decision-Direct and Stop-and-Go Algorithms	p. 129
Stop-and-Go Algorithms	p. 130
Decision-Directed Equalizer	p. 131
Computer Simulation Example	p. 131
Non-Equivalence of Two Parameter Spaces	p. 132
Nullspace Analysis for Causal Parameterizations	p. 134
Nullspace Analysis for Doubly Infinite Parameterizations	p. 135
Comments	p. 137
Example	p. 137
Length-Dependent and Cost-Dependent Local Minima	p. 140
Length-Dependent Local Minima	p. 140
Cost-Dependent Local Minima of Some Blind Algorithms	p. 143
Static and Dynamic Convergence Behavior of FIR Equalizers	p. 143
Basic Relationships	p. 144
Properties of Prediction Error Function	p. 145
Static Convergence Analysis	p. 147
Dynamic Convergence Analysis	p. 149
Computer Simulations	p. 158
Summary and Further Reading	p. 161
Linear Multichannel Identification Methods Based On Second Order Statistics	p. 167
Introduction	p. 167
Multiple Discrete Channel Model for Identification	p. 168
Linear Baseband Model	p. 168
Channel Diversity from Integer Oversampling	p. 169
Fractional Oversampling	p. 170
Second Order Statistics of Multichannel Outputs	p. 173
The TXK Time Domain SIMO Algorithm	p. 175
Two SIMO Methods for Blind Identification	p. 179
A Subspace Based Algorithm	p. 179
A Subchannel Matching Algorithm	p. 182
Exploiting Partial System Information	p. 186
Motivations	p. 186
Partial Knowledge of the Composite Channel	p. 187
Simulation Results	p. 189
Least Square Estimation Approaches to SIMO Identification	p. 194
Multichannel Identification from Second Order Statistics	p. 195
Linear Prediction Algorithm for Multichannel Identification	p. 197
Outer-Product Decomposition Algorithm	p. 199
Multi-Step Linear Prediction	p. 202
Channel Estimation by Linear Smoothing	p. 204
Channel Estimation by Constrained Output Energy Minimization	p. 207
Discussion	p. 209
Simulation Results	p. 211
Chapter Summary	p. 213
Frequency Domain Approaches to Single User Channel Identification	p. 226
Overview	p. 226
Second Order Cyclostationarity	p. 227
Channel Identification via Frequency Response Sampling	p. 229
Channel Phase Information in Output SCD	p. 229
Rational Transfer Function Identification	p. 232
Discussions	p. 234
SCD Estimation and Simulation	p. 235
Estimating SCD from Data	p. 235
Simulation Example	p. 235
Discrete ARMA System Identification	p. 237
Cyclostationary Channel Information	p. 238
The Need for a Parametric Channel Model	p. 239
A Parametric Identification Method for ARMA Channels	p. 240
Basic Conditions	p. 241
Identifying Poles and Zeros	p. 241
Remarks	p. 244
Non-Parametric Identification of ARMA Channels	p. 245
Magnitude Identification	p. 245
Phase Identification	p. 246
Phase Distortion Analysis	p. 247
Phase Unwrapping and a Combined Method	p. 250
Simulation Results of Frequency Domain Methods	p. 250
Phase Response Recovery Based on Partial Knowledge	p. 259
Exploiting Known Phase Information	p. 259
Simulation Results	p. 260
Summary	p. 261
Adaptive Multichannel Equalization	p. 265
Multichannel Equalization	p. 265
SIMO Equalizers	p. 266
MIMO Equalizers	p. 270
SIMO Constant Modulus Algorithm	p. 272
Basic Properties	p. 272
Uniqueness of Hyper-cone	p. 274
Global Convergence of CMA-FSE	p. 274
Initialization of CMA-FSE	p. 275
Discussions	p. 276
Simulation Results	p. 276
SIMO Super-Exponential Algorithm	p. 283
An Unwilling Approximation in TSE Implementation	p. 283
Exact Implementation in FSE	p. 284
Convergence Issues	p. 285
Higher Order Statistical Realization of SEA	p. 285
Simulation Results	p. 286
General Convergence Properties of SIMO Equalizers (FSE)	p. 289
Two Classes of Minima	p. 290
Disappearance of LDM in FSE	p. 292
Cost-Dependent Minima	p. 294
MIMO CMA Equalizer	p. 294
Linear Equalizability	p. 295
CMA Signal Capturing	p. 296
Global Convergence	p. 298
MIMO Signal Recovery Example	p. 300
Multiple Signal Equalization and Recovery	p. 302
CMA Cost Modification	p. 302
Global Convergence of Modified CMA MIMO Equalizers	p. 304
Local Convergence	p. 310
Simulation Example	p. 311
Summary and Further Reading	p. 313
Selected Topics in Multichannel Equalization	p. 320
Deterministic Approaches to Blind Equalization	p. 321
Direct Multichannel Blind Equalization	p. 321
Direct Symbol Estimation	p. 322
Deterministic Channel Equalization	p. 324
Column Anchored Equalization	p. 327
Input Statistical Information	p. 327
Column Shifting	p. 330
Fixed Delay Column Anchoring	p. 331
Variable Delay Column Anchoring	p. 332
Channel Noise Considerations	p. 335
MMSE Equalization	p. 335
Basic Assumptions and Matrix Properties	p. 336
MMSE Blind Equalizers	p. 337
Estimation of Cross-Correlation Vector	p. 338
MMSE Blind Equalization for SIMO Systems	p. 341
Simulation Examples	p. 344
Summary and Further Reading	p. 348
Scanning the Literature	p. 354
Blind Channel Equalization and Symbol Estimation	p. 354
Blind and Semi-blind Channel Identification	p. 377
Applications in CDMA, OFDM, and Other Systems	p. 393
Index	p. 404
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