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Fundamentals of Adaptive Filtering
ISBN-13: 9780471461265 / Angielski / Twarda / 2003 / 1168 str.
Fundamentals of Adaptive Filtering
ISBN-13: 9780471461265 / Angielski / Twarda / 2003 / 1168 str.
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This book is based on a graduate level course offered by the author at UCLA and has been classed tested there and at other universities over a number of years. This will be the most comprehensive book on the market today providing instructors a wide choice in designing their courses.
* Offers computer problems to illustrate real life applications for students and professionals alike
* An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.
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"...a remarkably clear, accessible, and up–to–date text. It is highly recommended for students at the graduate level is an invaluable and comprehensive reference for researchers at all levels." ( IEEE Control Systems Magazine, August 2005)
PREFACE xix
ACKNOWLEDGMENTS xxix
NOTATION xxxi
SYMBOLS xxxv
1 OPTIMAL ESTIMATION 1
1.1 Variance of a Random Variable 1
1.2 Estimation Given No Observations 5
1.3 Estimation Given Dependent Observations 6
1.4 Estimation in the Complex and Vector Cases 18
1.5 Summary of Main Results 30
1.6 Bibliographic Notes 31
1.7 Problems 33
1.8 Computer Project 37
l.A Hermitian and Positive–Definite Matrices 39
l.B Gaussian Random Vectors 42
2 LINEAR ESTIMATION 47
2.1 Normal Equations 48
2.2 Design Examples 54
2.3 Existence of Solutions 60
2.4 Orthogonality Principle 63
2.5 Nonzero–Mean Variables 65
2.6 Linear Models 66
2.7 Applications 68
2.8 Summary of Main Results 76
2.9 Bibliographic Notes 77
2.10 Problems 79
2.11 Computer Project 95
2.A Range Spaces and Nullspaces of Matrices 103
2.B Complex Gradients 105
2.C Kalman Filter 108
3 CONSTRAINED LINEAR ESTIMATION 114
3.1 Minimum–Variance Unbiased Estimation 115
3.2 Application: Channel and Noise Estimation 119
3.3 Application: Decision Feedback Equalization 120
3.4 Application: Antenna Beamforming 128
3.5 Summary of Main Results 131
3.6 Bibliographic Notes 131
3.7 Problems 133
3.8 Two Computer Projects 143
3.A Schur Complements 155
3.B Primer on Channel Equalization 159
3.C Causal Wiener–Hopf Filtering 167
4 STEEPEST–DESCENT ALGORITHMS 170
4.1 Linear Estimation Problem 171
4.2 Steepest–Descent Method 174
4.3 Transient Behavior 179
4.4 Iteration–Dependent Step–Sizes 187
4.5 Newton′s Method 191
4.6 Summary of Main Results 193
4.7 Bibliographic Notes 194
4.8 Problems 196
4.9 Two Computer Projects 204
5 STOCHASTIC–GRADIENT ALGORITHMS 212
5.1 Motivation 213
5.2 LMS Algorithm 214
5.3 Application: Adaptive Channel Estimation 218
5.4 Application: Adaptive Channel Equalization 220
5.5 Application: Decision–Feedback Equalization 223
5.6 Normalized LMS Algorithm 225
5.7 Other LMS–type Algorithms 233
5.8 Affine Projection Algorithms 238
5.9 RLS Algorithm 245
5.10 Ensemble–Average Learning Curves 248
5.11 Summary of Main Results 251
5.12 Bibliographic Notes 252
5.13 Problems 256
5.14 Three Computer Projects 267
6 STEADY–STATE PERFORMANCE OF ADAPTIVE FILTERS 281
6.1 Performance Measure 282
6.2 Stationary Data Model 284
6.3 Fundamental Energy–Conservation Relation 287
6.4 Fundamental Variance Relation 290
6.5 Mean–Square Performance of LMS 292
6.6 Mean–Square Performance of –NLMS 300
6.7 Mean–Square Performance of Sign–Error LMS 305
6.S Mean–Square Performance of LMF and LMMN 308
6.9 Mean–Square Performance of RLS 317
6.10 Mean–Square Performance of e–APA 322
6.11 Mean–Square Performance of Other Filters 325
6.12 Performance Table for Small Step–Sizes 327
6.13 Summary of Main Results 327
6.14 Bibliographic Notes 329
6.15 Problems 332
6.16 Computer Project 343
6.A Interpretations of the Energy Relation 348
6.B Relating e–NLMS to LMS 353
6.C Affine Projection Performance Condition 355
7 TRACKING PERFORMANCE OF ADAPTIVE FILTERS 357
7.1 Motivation 357
7.2 Nonstationary Data Model 358
7.3 Fundamental Energy–Conservation Relation 364
7.4 Fundamental Variance Relation 364
7.5 Tracking Performance of LMS 367
7.6 Tracking Performance of e–NLMS 370
7.7 Tracking Performance of Sign–Error LMS 372
7.8 Tracking Performance of LMF and LMMN 374
7.9 Comparison of Tracking Performance 378
7.10 Tracking Performance of RLS 380
7.11 Tracking Performance of e–APA 384
7.12 Tracking Performance of Other Filters 386
7.13 Performance Table for Small Step–Sizes 387
7.14 Summary of Main Results 387
7.15 Bibliographic Notes 389
7.16 Problems 391
7.17 Computer Project 401
8 FINITE PRECISION EFFECTS 408
8.1 Quantization Model 409
8.2 Data Model and Quantization Error Sources 410
8.3 Fundamental Energy–Conservation Relation 413
8.4 Fundamental Variance Relation 416
8.5 Performance Degradation of LMS 419
8.6 Performance Degradation of e–NLMS 421
8.7 Performance Degradation of Sign–Error LMS 423
8.8 Performance Degradation of LMF and LMMN 424
8.9 Performance Degradation of Other Filters 425
8.10 Summary of Main Results 426
8.11 Bibliographic Notes 428
8.12 Problems 430
8.13 Computer Project 437
9 TRANSIENT PERFORMANCE OF ADAPTIVE FILTERS 441
9.1 Data Model 442
9.2 Data–Normalized Adaptive Filters 442
9.3 Weighted Energy–Conservation Relation 443
9.4 Weighted Variance Relation 445
9.5 Transient Performance of LMS 452
9.6 Transient Performance of e–NLMS 471
9.7 Performance of Data–Normalized Filters 474
9.8 Summary of Main Results 477
9.9 Bibliographic Notes 481
9.10 Problems 487
9.11 Computer Project 516
9.A Stability Bound 522
9.B Stability of e–NLMS 524
9.C Adaptive Filters with Error Nonlinearities 526
9.D Convergence Time of Adaptive Filters 538
9.E Learning Behavior of Adaptive Filters 545
9.F Independence and Averaging Analysis 559
9.G Interpretation of Weighted Energy Relation 568
9.H Kronecker Products 570
10 BLOCK ADAPTIVE FILTERS 572
10.1 Transform–Domain Adaptive Filters 573
10.2 Motivation for Block Adaptive Filters 584
10.3 Efficient Block Convolution 586
10.4 DFT–Based Block Adaptive Filters 597
10.5 Subband Adaptive Filters 605
10.6 Summary of Main Results 612
10.7 Bibliographic Notes 614
10.8 Problems 616
10.9 Computer Project 620
10.A DCT–Transformed Regressors 626
10.B More Constrained DFT Block Filters 628
10.C Overlap–Add DFT–Based Block Adaptive Filter 632
10.D DCT–Based Block Adaptive Filters 640
10.E DHT–Based Block Adaptive Filters 648
11 THE LEAST–SQUARES CRITERION 657
11.1 Least–Squares Problem 658
11.2 Weighted Least–Squares 666
11.3 Regularized Least–Squares 669
11.4 Weighted Regularized Least–Squares 671
11.5 Order–Update Relations 672
11.6 Summary of Main Results 688
11.7 Bibliographic Notes 689
11.8 Problems 693
11.9 Three Computer Projects 703
11.A Equivalence Results in Linear Estimation 724
ll.B QR Decomposition 726
ll.C Singular Value Decomposition 728
12 RECURSIVE LEAST–SQUARES 732
12.1 Motivation 732
12.2 RLS Algorithm 733
12.3 Exponentially–Weighted RLS Algorithm 739
12.4 General Time–Update Result 741
12.5 Summary of Main Results 745
12.6 Bibliographic Notes 745
12.7 Problems 748
12.8 Two Computer Projects 755
12.A Kalman Filtering and Recursive Least–Squares 763
12.B Extended RLS Algorithms 768
13 RLS ARRAY ALGORITHMS 775
13.1 Some Difficulties 775
13.2 Square–Root Factors 776
13.3 Norm and Angle Preservation 778
13.4 Motivation for Array Methods 780
13.5 RLS Algorithm 784
13.6 Inverse QR Algorithm 785
13.7 QR Algorithm 788
13.8 Extended QR Algorithm 793
13.9 Summary of Main Results 794
13.10 Bibliographic Notes 795
13.11 Problems 797
13.12 Computer Project 802
13.A Unitary Transformations 804
13.A.I Givens Rotations 804
13.A.2 Householder Transformations 808
13.B Array Algorithms for Kalman Filtering 812
14 FAST FIXED–ORDER FILTERS 816
14.1 Fast Array Algorithm 817
14.2 Regularized Prediction Problems 825
14.3 Fast Transversal Filter 832
14.4 FAEST Filter 836
14.5 Fast Kalman Filter 838
14.6 Stability Issues 839
14.7 Summary of Main Results 845
14.8 Bibliographic Notes 846
14.9 Problems 848
14.10 Computer Project 857
14.A Hyperbolic Rotations 860
14.B Hyperbolic Basis Rotations 867
14.C Backward Consistency and Minimality 869
14.D Chandrasekhar Filter 871
15 LATTICE FILTERS 874
15.1 Motivation and Notation 875
15.2 Joint Process Estimation 878
15.3 Backward Estimation Problem 880
15.4 Forward Estimation Problem 883
15.5 Time and Order–Update Relations 885
15.6 Significance of Data Structure 891
15.7 A Posteriori–Based Lattice Filter 894
15.8 A Priori–Based Lattice Filter 895
15.9 A Priori Error–Feedback Lattice Filter 897
15.10 A Posteriori Error–Feedback Lattice Filter 902
15.11 Normalized Lattice Filter 904
15.12 Array–Based Lattice Filter 910
15.13 Relation Between RLS and Lattice Filters 915
15.14 Summary of Main Results 917
15.15 Bibliographic Notes 918
15.16 Problems 920
15.17 Computer Project 925
16 LAGUERRE ADAPTIVE FILTERS 931
16.1 Orthonormal Filter Structures 932
16.2 Data Structure 934
16.3 Fast Array Algorithm 936
16.4 Regularized Projection Problems 942
16.5 Extended Fast Transversal Filter 954
16.6 Extended FAEST Filter 957
16.7 Extended Fast Kalman Filter 958
16.8 Stability Issues 959
16.9 Order–Recursive Filters 960
16.10 A Posteriori–Based Lattice Filter 968
16.11 A Priori–Based Lattice Filter 970
16.12 A Priori Error–Feedback Lattice Filter 972
16.13 A Posteriori Error–Feedback Lattice Filter 976
16.14 Normalized Lattice Filter 978
16.15 Array Lattice Filter 982
16.16 Summary of Main Results 985
16.17 Bibliographic Notes 986
16.18 Problems 989
16.19 Computer Project 994
16.A Modeling with Orthonormal Basis Functions 999
16.B Efficient Matrix–Vector Multiplication 1007
16.C Lyapunov Equations 1009
17 ROBUST ADAPTIVE FILTERS 1012
17.1 Indefinite Least–Squares 1013
17.2 Recursive Minimization Algorithm 1018
17.3 A Posteriori–Based Robust Filters 1027
17.4 A Priori–Based Robust Filters 1036
17.5 Energy Conservation Arguments 1043
17.6 Summary of Main Results 1052
17.7 Bibliographic Notes 1052
17.8 Problems 1056
17.9 Computer Project 1072
17.A Arbitrary Coefficient Matrices 1078
17.B Total–Least–Squares 1081
17.C H°° Filters 1085
17.D Stationary Points 1089
BIBLIOGRAPHY 1090
AUTHOR INDEX 1113
SUBJECT INDEX 1118
ALI H. SAYED, PhD, is a professor of electrical engineering at UCLA, where he established and directs the Adaptive Systems Laboratory. He is a Fellow of the IEEE for his contributions to adaptive filtering and estimation algorithms.
The most comprehensive treatment of adaptive filtering available
Here is a fresh, broad, and systematic treatment of adaptive filtering, a subject of immense practical and theoretical value. The author illustrates extensive commonalities that exist among different classes of adaptive algorithms and even among different filtering theories. He also provides a uniform treatment of the subject matter, addressing some existing limitations, providing additional insights, and detailing extensions of current theory.
The book is designed to be self–contained, with careful attention given to appendices, problems, examples, and a variety of practical computer projects. The bibliography is up–to–date with extensive commentaries on how the contributions relate to each other in time and in context.
Each chapter includes concepts that reinforce the principles covered, bibliographic notes for further study, numerous problems that vary in difficulty and applications, computer projects that illustrate real–life applications, and helpful appendices.
MATLAB® programs that solve all projects are available for download by all readers from the publisher’s Web site at ftp://ftp.wiley.com/public/sci—tech—med/filtering. The computer projects feature topics such as linear and decision–feedback equalization, channel estimation, beamforming, tracking of fading channels, line and acoustic echo cancellation, active noise control, OFDM receivers, CDMA receivers, and even finite–precision effects.
A complete solutions manual for all problems in the book is available to instructors upon request.
To gain insight into this vast and fast–moving field, you need a resource that is logically organized, specific in its presentation of each topic, and far–reaching in scope. Fundamentals of Adaptive Filtering is just that kind of resource.
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