Blind Equalization and System Identification

Batch Processing Algorithms, Performance and Applications

By: Chih-Chun Feng, Chong-Yung Chi, Ching-Yung Chen, Chii-Horng Chen

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Paperback | 12 December 2005

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484 Pages

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The absence of training signals from many kinds of transmission necessitates the widespread use of blind equalization and system identification. There have been many algorithms developed for these purposes, working with one- or two-dimensional signals and with single-input single-output or multiple-input multiple-output, real or complex systems. It is now time for a unified treatment of this subject, pointing out the common characteristics of these algorithms as well as learning from their different perspectives. "Blind Equalization and System Identification" provides such a unified treatment presenting theory, performance analysis, simulation, implementation and applications.

This is a textbook for graduate courses in discrete-time random processes, statistical signal processing, and blind equalization and system identification. It contains material which will also interest researchers and engineers working in digital communications, source separation, speech processing, and other, similar applications.

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Introduction	p. 1
References	p. 8
Mathematical Background	p. 13
Linear Algebra	p. 13
Vectors and Vector Spaces	p. 13
Matrices	p. 17
Matrix Decomposition	p. 23
Mathematical Analysis	p. 26
Sequences	p. 27
Series	p. 30
Hilbert Spaces, Sequence Spaces and Function Spaces	p. 33
Fourier Series	p. 38
Optimization Theory	p. 41
Vector Derivatives	p. 42
Necessary and Sufficient Conditions for Solutions	p. 45
Gradient-Type Optimization Methods	p. 48
Least-Squares Method	p. 62
Full-Rank Overdetermined Least-Squares Problem	p. 64
Generic Least-Squares Problem	p. 65
Summary	p. 67
Proof of Theorem 2.15	p. 68
Some Terminologies of Functions	p. 72
Proof of Theorem 2.33	p. 74
Proof of Theorem 2.36	p. 75
Proof of Theorem 2.38	p. 76
Proof of Theorem 2.46	p. 77
Problems	p. 79
Computer Assignments	p. 81
References	p. 81
Fundamentals of Statistical Signal Processing	p. 83
Discrete-Time Signals and Systems	p. 83
Time-Domain Characterization	p. 83
Transformation Tools	p. 86
Transform-Domain Characterization	p. 91
Random Variables	p. 96
Statistical Characterization	p. 96
Moments	p. 99
Cumulants	p. 104
Some Useful Distributions	p. 109
Random Processes	p. 119
Statistical Characterization	p. 119
Stationary Processes	p. 123
Cyclostationary Processes	p. 139
Estimation Theory	p. 147
Estimation Problem	p. 147
Properties of Estimators	p. 150
Maximum-Likelihood Estimation	p. 158
Method of Moments	p. 160
Minimum Mean-Square-Error Estimation	p. 164
Wiener Filtering	p. 166
Least-Squares Estimation	p. 169
Summary	p. 172
Relationship between Cumulants and Moments	p. 172
Proof of Theorem 3.47	p. 173
Proof of Theorem 3.52	p. 174
Problems	p. 175
Computer Assignments	p. 178
References	p. 180
SISO Blind Equalization Algorithms	p. 183
Linear Equalization	p. 183
Blind Equalization Problem	p. 183
Peak Distortion and MMSE Equalization Criteria	p. 187
SOS Based Blind Equalization Approach: Linear Prediction	p. 190
Forward and Backward Linear Prediction	p. 191
Levinson-Durbin Recursion	p. 196
Lattice Linear Prediction Error Filters	p. 202
Linear Predictive Deconvolution	p. 205
HOS Based Blind Equalization Approaches	p. 209
Maximum Normalized Cumulant Equalization Algorithm	p. 211
Super-Exponential Equalization Algorithm	p. 214
Algorithm Analyses	p. 221
Algorithm Improvements	p. 226
Simulation Examples for Algorithm Tests	p. 231
Some Applications	p. 235
Seismic Exploration	p. 236
Speech Signal Processing	p. 245
Baud-Spaced Equalization in Digital Communications	p. 252
Summary and Discussion	p. 265
Proof of Property 4.17	p. 267
Problems	p. 268
Computer Assignments	p. 269
References	p. 270
MIMO Blind Equalization Algorithms	p. 275
MIMO Linear Time-Invariant Systems	p. 275
Definitions and Properties	p. 275
Smith-McMillan Form	p. 281
Linear Equalization	p. 286
Blind Equalization Problem	p. 287
Peak Distortion and MMSE Equalization Criteria	p. 290
SOS Based Blind Equalization Approaches	p. 292
Blind SIMO Equalization	p. 292
Blind MIMO Equalization	p. 300
HOS Based Blind Equalization Approaches	p. 304
Temporally IID Inputs	p. 305
Temporally Colored Inputs	p. 314
Algorithm Tests	p. 318
Summary and Discussion	p. 325
Proof of Property 5.34	p. 326
Proof of Property 5.35	p. 328
A GCD Computation Algorithm	p. 329
Problems	p. 330
Computer Assignments	p. 330
References	p. 331
Applications of MIMO Blind Equalization Algorithms	p. 335
Fractionally Spaced Equalization in Digital Communications	p. 335
Blind Maximum Ratio Combining	p. 340
SIMO Blind System Identification	p. 342
MIMO-MNC Equalizer-System Relation	p. 344
Analysis on System Identification Based on MIMO-MNC Equalizer-System Relation	p. 345
SIMO Blind System Identification Algorithm	p. 346
Multiple Time Delay Estimation	p. 351
Model Assumptions	p. 351
MTDE with Space Diversity Gain	p. 352
Blind Beamforming for Source Separation	p. 357
Model Assumptions	p. 357
Blind Beamforming	p. 358
Multistage Source Separation	p. 359
Multiuser Detection in Wireless Communications	p. 362
Model Assumptions and Problem Statement	p. 363
Signature Waveform Matched Filtering Based Multiuser Detection	p. 364
Chip Waveform Matched Filtering Based Multiuser Detection	p. 369
Multiple Antennas Based Multiuser Detection	p. 375
Summary and Discussion	p. 378
Proof of Theorem 6.3	p. 379
Proof of Fact 6.4	p. 380
Proof of Property 6.10	p. 381
Multichannel Levinson Recursion Algorithm	p. 383
Integrated Bispectrum Based Time Delay Estimation	p. 385
Problems	p. 387
Computer Assignments	p. 387
References	p. 388
Two-Dimensional Blind Deconvolution Algorithms	p. 391
Two-Dimensional Discrete-Space Signals, Systems and Random Processes	p. 391
2-D Deterministic Signals	p. 391
2-D Transforms	p. 393
2-D Linear Shift-Invariant Systems	p. 395
2-D Stationary Random Processes	p. 400
2-D Deconvolution	p. 402
Blind Deconvolution Problem	p. 402
Peak Distortion and Minimum Mean-Square-Error Deconvolution Criteria	p. 404
SOS Based Blind Deconvolution Approach: Linear Prediction	p. 406
HOS Based Blind Deconvolution Approaches	p. 409
2-D Maximum Normalized Cumulant Deconvolution Algorithm	p. 409
2-D Super-Exponential Deconvolution Algorithm	p. 413
Improvements on 2-D MNC Deconvolution Algorithm	p. 416
Simulation	p. 418
Summary and Discussion	p. 423
Problems	p. 424
Computer Assignments	p. 424
References	p. 425
Applications of Two-Dimensional Blind Deconvolution Algorithms	p. 427
Nonparametric Blind System Identification and Texture Synthesis	p. 427
Nonparametric 2-D BSI	p. 428
Texture Synthesis	p. 434
Parametric Blind System Identification and Texture Image Classification	p. 438
Parametric 2-D BSI	p. 439
Texture Image Classification	p. 449
Summary and Discussion	p. 454
Proof of Property 8.2	p. 455
Proof of Property 8.3	p. 456
Proof of Theorem 8.6	p. 458
Proof of Fact 8.9	p. 459
Problems	p. 460
Computer Assignments	p. 460
References	p. 461
Index	p. 463
Table of Contents provided by Ingram. All Rights Reserved.

Blind Equalization and System Identification

Batch Processing Algorithms, Performance and Applications

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Paperback

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