Note: Supplemental materials are not guaranteed with Rental or Used book purchases.
- ISBN: 9780824704797 | 0824704797
- Cover: Hardcover
- Copyright: 1/9/2001
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.
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 |
Table of Contents provided by Syndetics. All Rights Reserved. |
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