 | Adaptive signal processing: next generation solutions / ed. by T.Adali, S.Haykin. - New York: IEEE, Institute of Electrical and Electronics Engineers; Hoboken: Wiley, 2010. - xv, 407 p.: ill. - (Adaptive and learning systems for signal processing, communications, and control). - Incl. bibl. ref. - Ind.: p.393-407. - ISBN 978-0470-19517-8
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Preface ........................................................ xi
Contributors ................................................... xv
Chapter 1 Complex-Valued Adaptive Signal Processing ............ 1
1.1 Introduction ............................................... 1
1.1.1 Why Complex-Valued Signal Processing ................ 3
1.1.2 Outline of the Chapter .............................. 5
1.2 Preliminaries .............................................. 6
1.2.1 Notation ............................................ 6
1.2.2 Efficient Computation of Derivatives in the
Complex Domain ...................................... 9
1.2.3 Complex-to-Real and Complex-to-Complex Mappings .... 17
1.2.4 Series Expansions .................................. 20
1.2.5 Statistics of Complex-Valued Random Variables and
Random Processes ................................... 24
1.3 Optimization in the Complex Domain ........................ 31
1.3.1 Basic Optimization Approaches in  N ................ 31
1.3.2 Vector Optimization in  N .......................... 34
1.3.3 Matrix Optimization in N .......................... 37
1.3.4 Newton-Variant Updates ............................. 38
1.4 Widely Linear Adaptive Filtering .......................... 40
1.4.1 Linear and Widely Linear Mean-Square Error
Filter ............................................. 41
1.5 Nonlinear Adaptive Filtering with Multilayer
Perceptrons ............................................... 47
1.5.1 Choice of Activation Function for the MLP Filter ... 48
1.5.2 Derivation of Back-Propagation Updates ............. 55
1.6 Complex Independent Component Analysis .................... 58
1.6.1 Complex Maximum Likelihood ......................... 59
1.6.2 Complex Maximization of Non-Gaussianity ............ 64
1.6.3 Mutual Information Minimization: Connections to
ML and MN .......................................... 66
1.6.4 Density Matching ................................... 67
1.6.5 Numerical Examples ................................. 71
1.7 Summary ................................................... 74
1.8 Acknowledgment ............................................ 76
1.9 Problems .................................................. 76
References ..................................................... 79
Chapter 2 Robust Estimation Techniques for Complex-Valued
Random Vectors
2.1 Introduction .............................................. 87
2.1.1 Signal Model ....................................... 88
2.1.2 Outline of the Chapter ............................. 90
2.2 Statistical Characterization of Complex Random Vectors .... 91
2.2.1 Complex Random Variables ........................... 91
2.2.2 Complex Random Vectors ............................. 93
2.3 Complex Elliptically Symmetric (CES) Distributions ........ 95
2.3.1 Definition ......................................... 96
2.3.2 Circular Case ...................................... 98
2.3.3 Testing the Circularity Assumption ................. 99
2.4 Tools to Compare Estimators .............................. 102
2.4.1 Robustness and Influence Function ................. 102
2.4.2 Asymptotic Performance of an Estimator ............ 106
2.5 Scatter and Pseudo-Scatter Matrices ................. 107
2.5.1 Background and Motivation ......................... 107
2.5.2 Definition ........................................ 108
2.5.3 M-Estimators of Scatter ........................... 110
2.6 Array Processing Examples ................................ 114
2.6.1 Beamformers ....................................... 114
2.6.2 Subspace Methods .................................. 115
2.6.3 Estimating the Number of Sources .................. 118
2.6.4 Subspace DOA Estimation for Noncircular Sources ... 120
2.7 MVDR Beamformers Based on M-Estimators ................... 121
2.7.1 The Influence Function Study ...................... 123
2.8 Robust ICA ............................................... 128
2.8.1 The Class of DOGMA Estimators ..................... 129
2.8.2 The Class of GUT Estimators ....................... 132
2.8.3 Communications Example ............................ 134
2.9 Conclusion ............................................... 137
2.10 Problems ................................................. 137
References .................................................... 138
Chapter 3 Turbo Equalization ................................. 143
3.1 Introduction ............................................. 143
3.2 Context .................................................. 144
3.3 Communication Chain ...................................... 145
3.4 Turbo Decoder: Overview .................................. 147
3.4.1 Basic Properties of Iterative Decoding ............ 151
3.5 Forward-Backward Algorithm ............................... 152
3.5.1 With Intersymbol Interference ................... 160
3.6 Simplified Algorithm: Interference Canceler .............. 163
3.7 Capacity Analysis ........................................ 168
3.8 Blind Turbo Equalization ................................. 173
3.8.1 Differential Encoding ............................. 179
3.9 Convergence .............................................. 182
3.9.1 Bit Error Probability ............................. 187
3.9.2 Other Encoder Variants ............................ 190
3.9.3 EXIT Chart for Interference Canceler .............. 192
3.9.4 Related Analyses .................................. 194
3.10 Multichannel and Multiuser Settings ...................... 195
3.10.1 Forward-Backward Equalizer ........................ 196
3.10.2 Interference Canceler ............................. l97
3.10.3 Multiuser Case .................................... 198
3.11 Concluding Remarks ....................................... 199
3.12 Problems ................................................. 200
References .................................................... 206
Chapter 4 Subspace Tracking for Signal Processing ............ 211
4.1 Introduction ............................................. 211
4.2 Linear Algebra Review .................................... 213
4.2.1 Eigenvalue Value Decomposition .................... 213
4.2.2 QR Factorization .................................. 214
4.2.3 Variational Characterization of Eigenvalues/
Eigenvectors of Real Symmetric Matrices ........... 215
4.2.4 Standard Subspace Iterative Computational
Techniques ........................................ 216
4.2.5 Characterization of the Principal Subspace of
a Covariance Matrix from the Minimization of
a Mean Square Error ............................... 218
4.3 Observation Model and Problem Statement .................. 219
4.3.1 Observation Model ................................. 219
4.3.2 Statement of the Problem .......................... 220
4.4 Preliminary Example: Oja's Neuron ........................ 221
4.5 Subspace Tracking ........................................ 223
4.5.1 Subspace Power-Based Methods ...................... 224
4.5.2 Projection Approximation-Based Methods ............ 230
4.5.3 Additional Methodologies .......................... 232
4.6 Eigenvectors Tracking .................................... 233
4.6.1 Rayleigh Quotient-Based Methods ................... 234
4.6.2 Eigenvector Power-Based Methods ................... 235
4.6.3 Projection Approximation-Based Methods ............ 240
4.6.4 Additional Methodologies .......................... 240
4.6.5 Particular Case of Second-Order Stationary Data ... 242
4.7 Convergence and Performance Analysis Issues .............. 243
4.7.1 A Short Review of the ODE Method .................. 244
4.7.2 A Short Review of a General Gaussian
Approximation Result .............................. 246
4.7.3 Examples of Convergence and Performance
Analysis .......................................... 248
4.8 Illustrative Examples .................................... 256
4.8.1 Direction of Arrival Tracking ..................... 257
4.8.2 Blind Channel Estimation and Equalization ......... 258
4.9 Concluding Remarks ....................................... 260
4.10 Problems ................................................. 260
References .................................................... 266
Chapter 5 Particle Filtering ................................. 271
5.1 Introduction ............................................. 272
5.2 Motivation for Use of Particle Filtering ................. 274
5.3 The Basic Idea ........................................... 278
5.4 The Choice of Proposal Distribution and Resampling ....... 289
5.4.1 Choice of Proposal Distribution ................... 290
5.4.2 Resampling ........................................ 291
5.5 Some Particle Filtering Methods .......................... 295
5.5.1 SIR Particle Filtering ............................ 295
5.5.2 Auxiliary Particle Filtering ...................... 297
5.5.3 Gaussian Particle Filtering ....................... 301
5.5.4 Comparison of the Methods ......................... 302
5.6 Handling Constant Parameters ............................. 305
5.6.1 Kernel-Based Auxiliary Particle Filter ............ 306
5.6.2 Density-Assisted Particle Filter .................. 308
5.7 Rao-Blackwellization ..................................... 310
5.8 Prediction ............................................... 314
5.9 Smoothing ................................................ 316
5.10 Convergence Issues ....................................... 320
5.11 Computational Issues and Hardware Implementation ......... 323
5.12 Acknowledgments .......................................... 324
5.13 Exercises ................................................ 325
References .................................................... 327
Chapter 6 Nonlinear Sequential State Estimation for
Solving Pattern-Classification Problems ............ 333
6.1 Introduction ............................................. 333
6.2 Back-Propagation and Support Vector Machine-Learning
Algorithms: Review ....................................... 334
6.2.1 Back-Propagation Learning ......................... 334
6.2.2 Support Vector Machine ............................ 337
6.3 Supervised Training Framework of MLPs Using Nonlinear
Sequential State Estimation .............................. 340
6.4 The Extended Kalman Filter ............................... 341
6.4.1 The EKF Algorithm ................................. 344
6.5 Experimental Comparison of the Extended Kalman
Filtering Algorithm with the Back-Propagation and
Support Vector Machine Learning Algorithms ............... 344
6.6 Concluding Remarks ....................................... 347
6.7 Problems ................................................. 348
References .................................................... 348
Chapter 7 Bandwidth Extension of Telephony Speech ............ 349
7.1 Introduction ............................................. 349
7.2 Organization of the Chapter .............................. 352
7.3 Nonmodel-Based Algorithms for Bandwidth Extension ........ 352
7.3.1 Oversampling with Imaging ......................... 353
7.3.2 Application of Nonlinear Characteristics .......... 353
7.4 Basics ................................................... 354
7.4.1 Source-Filter Model ............................... 355
7.4.2 Parametric Representations of the Spectral
Envelope .......................................... 358
7.4.3 Distance Measures ................................. 362
7.5 Model-Based Algorithms for Bandwidth Extension ........... 364
7.5.1 Generation of the Excitation Signal ............... 365
7.5.2 Vocal Tract Transfer Function Estimation .......... 369
7.6 Evaluation of Bandwidth Extension Algorithms ............. 383
7.6.1 Objective Distance Measures ....................... 383
7.6.2 Subjective Distance Measures ...................... 385
7.7 Conclusion ............................................... 388
7.8 Problems ................................................. 388
References .................................................... 390
7.7 Index .................................................... 393
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