Blind Equalization And System Identification

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  • Format: Paperback
  • Copyright: 2006-04-01
  • Publisher: Springer Nature
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Discrete-time signal processing has had a momentous impact on advances in engineering and science over recent decades. The rapid progress of digital and mixed-signal integrated circuits in processing speed, functionality and cost-effectiveness has led to their ubiquitous employment in signal processing and transmission in diverse milieux.The absence of training or pilot signals from many kinds of transmission - in, for example, speech analysis, seismic exploration and texture image analysis - necessitates the widespread use of blind equalization and system identification. There have been a great many algorithms developed for these purposes, working with one- or two-dimensional (2-d) signals and with single-input single-output (SISO) or multiple-input multiple-output (MIMO), real or complex systems. It is now time for a unified treatment of this subject, pointing out the common characteristics and the sometimes close relations 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.Topics covered include:• SISO, MIMO and 2-d non-blind equalization (deconvolution) algorithms;• SISO, MIMO and 2-d blind equalization (deconvolution) algorithms;• SISO, MIMO and 2-d blind system identification algorithms;• algorithm analyses and improvements;• applications of SISO, MIMO and 2-d blind equalization/identification algorithms.Each chapter is completed by exercises and computer assignments designed to further understanding and to give practical experience with the algorithms discussed.This is a textbook for graduate-level courses in discrete-time random processes, statistical signal processing, and blind equalization and system identification. It contains material which will also interest researchers and practicing engineers working in digital communications, source separation, speech processing, image processing, seismic exploration, sonar, radar and other, similar applications.

Author Biography

Doctor Chong-Yung Chi is a Professor with the Department of Electrical Engineering, National Tsing Hua University, Taiwan. From July 1983 to September 1988, he was with the Jet Propulsion Laboratory, Pasadena, California, where he worked on the design of various spaceborne radar remote sensing systems including radar scatterometers, SAR's, altimeters, and rain mapping radars. From October 1988 to July 1989, he was a visiting specialist at the Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan, RoC. Since August 1989, Professor Chi has been a Professor with the Department of Electrical Engineering and since August 2002, the Chairman of Institute of Communications Engineering at the National Tsing Hua University, Hsinchu, Taiwan. He was a visiting researcher, at the Advanced Telecommunications Research Institute International, Kyoto, Japan, in May and June 2001. He has published more than 110 technical papers in radar remote sensing, system identification and estimation theory, deconvolution and channel equalization, digital filter design, spectral estimation, and higher-order statistics-based signal processing. His research interests include signal processing for wireless communications, statistical signal processing and digital signal processing and their applications.Dr. Chi is a member of the Society of Exploration Geophysicists, the European Association for Signal Processing, and an active member of the Chinese Institute of Electrical Engineering. He has served on numerous symposium and conference boards and is currently an Associate Editor for the IEEE Transactions on Signal Processing and an Editorial Board Member EURASIP Journal on Applied Signal Processing.Doctors Chih-Chun Feng and Ching-Yung Chen are engineers with the Transmission Technology Department, Digital Vedio and Optical Communiations Technologies Division, Computer and Communications Research Laboratories, Industrial Technology Research Institute, Taiwan. They are engaged in developing digital communication systems and algorithms which focus on baseband signal processing design. Doctor Chii-Horng Chen is an engineer with ADMtek Incorpolated, Taiwan. He is engaged in developing signal processing algorithms for IEEE 802.11b/a/g/h WLAN baseband systems.

Table of Contents

Introductionp. 1
Referencesp. 8
Mathematical Backgroundp. 13
Linear Algebrap. 13
Vectors and Vector Spacesp. 13
Matricesp. 17
Matrix Decompositionp. 23
Mathematical Analysisp. 26
Sequencesp. 27
Seriesp. 30
Hilbert Spaces, Sequence Spaces and Function Spacesp. 33
Fourier Seriesp. 38
Optimization Theoryp. 41
Vector Derivativesp. 42
Necessary and Sufficient Conditions for Solutionsp. 45
Gradient-Type Optimization Methodsp. 48
Least-Squares Methodp. 62
Full-Rank Overdetermined Least-Squares Problemp. 64
Generic Least-Squares Problemp. 65
Summaryp. 67
Proof of Theorem 2.15p. 68
Some Terminologies of Functionsp. 72
Proof of Theorem 2.33p. 74
Proof of Theorem 2.36p. 75
Proof of Theorem 2.38p. 76
Proof of Theorem 2.46p. 77
Problemsp. 79
Computer Assignmentsp. 81
Referencesp. 81
Fundamentals of Statistical Signal Processingp. 83
Discrete-Time Signals and Systemsp. 83
Time-Domain Characterizationp. 83
Transformation Toolsp. 86
Transform-Domain Characterizationp. 91
Random Variablesp. 96
Statistical Characterizationp. 96
Momentsp. 99
Cumulantsp. 104
Some Useful Distributionsp. 109
Random Processesp. 119
Statistical Characterizationp. 119
Stationary Processesp. 123
Cyclostationary Processesp. 139
Estimation Theoryp. 147
Estimation Problemp. 147
Properties of Estimatorsp. 150
Maximum-Likelihood Estimationp. 158
Method of Momentsp. 160
Minimum Mean-Square-Error Estimationp. 164
Wiener Filteringp. 166
Least-Squares Estimationp. 169
Summaryp. 172
Relationship between Cumulants and Momentsp. 172
Proof of Theorem 3.47p. 173
Proof of Theorem 3.52p. 174
Problemsp. 175
Computer Assignmentsp. 178
Referencesp. 180
SISO Blind Equalization Algorithmsp. 183
Linear Equalizationp. 183
Blind Equalization Problemp. 183
Peak Distortion and MMSE Equalization Criteriap. 187
SOS Based Blind Equalization Approach: Linear Predictionp. 190
Forward and Backward Linear Predictionp. 191
Levinson-Durbin Recursionp. 196
Lattice Linear Prediction Error Filtersp. 202
Linear Predictive Deconvolutionp. 205
HOS Based Blind Equalization Approachesp. 209
Maximum Normalized Cumulant Equalization Algorithmp. 211
Super-Exponential Equalization Algorithmp. 214
Algorithm Analysesp. 221
Algorithm Improvementsp. 226
Simulation Examples for Algorithm Testsp. 231
Some Applicationsp. 235
Seismic Explorationp. 236
Speech Signal Processingp. 245
Baud-Spaced Equalization in Digital Communicationsp. 252
Summary and Discussionp. 265
Proof of Property 4.17p. 267
Problemsp. 268
Computer Assignmentsp. 269
Referencesp. 270
MIMO Blind Equalization Algorithmsp. 275
MIMO Linear Time-Invariant Systemsp. 275
Definitions and Propertiesp. 275
Smith-McMillan Formp. 281
Linear Equalizationp. 286
Blind Equalization Problemp. 287
Peak Distortion and MMSE Equalization Criteriap. 290
SOS Based Blind Equalization Approachesp. 292
Blind SIMO Equalizationp. 292
Blind MIMO Equalizationp. 300
HOS Based Blind Equalization Approachesp. 304
Temporally IID Inputsp. 305
Temporally Colored Inputsp. 314
Algorithm Testsp. 318
Summary and Discussionp. 325
Proof of Property 5.34p. 326
Proof of Property 5.35p. 328
A GCD Computation Algorithmp. 329
Problemsp. 330
Computer Assignmentsp. 330
Referencesp. 331
Applications of MIMO Blind Equalization Algorithmsp. 335
Fractionally Spaced Equalization in Digital Communicationsp. 335
Blind Maximum Ratio Combiningp. 340
SIMO Blind System Identificationp. 342
MIMO-MNC Equalizer-System Relationp. 344
Analysis on System Identification Based on MIMO-MNC Equalizer-System Relationp. 345
SIMO Blind System Identification Algorithmp. 346
Multiple Time Delay Estimationp. 351
Model Assumptionsp. 351
MTDE with Space Diversity Gainp. 352
Blind Beamforming for Source Separationp. 357
Model Assumptionsp. 357
Blind Beamformingp. 358
Multistage Source Separationp. 359
Multiuser Detection in Wireless Communicationsp. 362
Model Assumptions and Problem Statementp. 363
Signature Waveform Matched Filtering Based Multiuser Detectionp. 364
Chip Waveform Matched Filtering Based Multiuser Detectionp. 369
Multiple Antennas Based Multiuser Detectionp. 375
Summary and Discussionp. 378
Proof of Theorem 6.3p. 379
Proof of Fact 6.4p. 380
Proof of Property 6.10p. 381
Multichannel Levinson Recursion Algorithmp. 383
Integrated Bispectrum Based Time Delay Estimationp. 385
Problemsp. 387
Computer Assignmentsp. 387
Referencesp. 388
Two-Dimensional Blind Deconvolution Algorithmsp. 391
Two-Dimensional Discrete-Space Signals, Systems and Random Processesp. 391
2-D Deterministic Signalsp. 391
2-D Transformsp. 393
2-D Linear Shift-Invariant Systemsp. 395
2-D Stationary Random Processesp. 400
2-D Deconvolutionp. 402
Blind Deconvolution Problemp. 402
Peak Distortion and Minimum Mean-Square-Error Deconvolution Criteriap. 404
SOS Based Blind Deconvolution Approach: Linear Predictionp. 406
HOS Based Blind Deconvolution Approachesp. 409
2-D Maximum Normalized Cumulant Deconvolution Algorithmp. 409
2-D Super-Exponential Deconvolution Algorithmp. 413
Improvements on 2-D MNC Deconvolution Algorithmp. 416
Simulationp. 418
Summary and Discussionp. 423
Problemsp. 424
Computer Assignmentsp. 424
Referencesp. 425
Applications of Two-Dimensional Blind Deconvolution Algorithmsp. 427
Nonparametric Blind System Identification and Texture Synthesisp. 427
Nonparametric 2-D BSIp. 428
Texture Synthesisp. 434
Parametric Blind System Identification and Texture Image Classificationp. 438
Parametric 2-D BSIp. 439
Texture Image Classificationp. 449
Summary and Discussionp. 454
Proof of Property 8.2p. 455
Proof of Property 8.3p. 456
Proof of Theorem 8.6p. 458
Proof of Fact 8.9p. 459
Problemsp. 460
Computer Assignmentsp. 460
Referencesp. 461
Indexp. 463
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