Fundamentals of Adaptive Filtering (Wiley - IEEE)

Fundamentals of Adaptive Filtering (Wiley - IEEE)

By: Ali H. Sayed (author)Hardback

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Description

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.

About Author

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.

Contents

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 Degrees Degrees Filters 1085 17.D Stationary Points 1089 BIBLIOGRAPHY 1090 AUTHOR INDEX 1113 SUBJECT INDEX 1118

Product Details

  • ISBN13: 9780471461265
  • Format: Hardback
  • Number Of Pages: 1168
  • ID: 9780471461265
  • weight: 1982
  • ISBN10: 0471461261

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