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Adaptive Filter Theory, 5e, is ideal for courses in Adaptive Filters.
Haykin examines both the mathematical theory behind various linear adaptive filters and the elements of supervised multilayer perceptrons. In its fifth edition, this highly successful book has been updated and refined to stay current with the field and develop concepts in as unified and accessible a manner as possible.
Simon Haykin received his B.Sc. (First-class Honours), Ph.D., and D.Sc., all in Electrical Engineering from the University of Birmingham, England. He is a Fellow of the Royal Society of Canada, and a Fellow of the Institute of Electrical and Electronics Engineers. He is the recipient of the Henry Booker Gold Medal from URSI, 2002, the Honorary Degree of Doctor of Technical Sciences from ETH Zentrum, Zurich, Switzerland, 1999, and many other medals and prizes.
He is a pioneer in adaptive signal-processing with emphasis on applications in radar and communications, an area of research which has occupied much of his professional life.
Preface
Acknowledgments
Background and Preview
1. The Filtering Problem
2. Linear Optimum Filters
3. Adaptive Filters
4. Linear Filter Structures
5. Approaches to the Development of Linear Adaptive Filters
6. Adaptive Beamforming
7. Four Classes of Applications
8. Historical Notes
Bibliography
Chapter 1 Stochastic Processes and Models
1.1 Partial Characterization of a Discrete-Time Stochastic Process
1.2 Mean Ergodic Theorem
1.3 Correlation Matrix
1.4 Correlation Matrix of Sine Wave Plus Noise
1.5 Stochastic Models
1.6 Wold Decomposition
1.7 Asymptotic Stationarity of an Autoregressive Process
1.8 Yule—Walker Equations
1.9 Computer Experiment: Autoregressive Process of Order Two
1.10 Selecting the Model Order
1.11 Complex Gaussian Processes
1.12 Power Spectral Density
1.13 Properties of Spectral Density
1.14 Transmission of a Stationary Process Through a Linear Filter
1.15 Cramér Spectral Representation for a Stationary Process
1.16 Power Spectrum Estimation
1.17 Other Statistical Characteristics of a Stochastic Process
1.18 Polyspectra
1.19 Spectral-Correlation Density
1.20 Summary and Discussion
Problems
Bibliography
Chapter 2 Wiener Filters
2.1 Linear Optimum Filtering: Statement of the Problem
2.2 Principle of Orthogonality
2.3 Minimum Mean-Square Error
2.4 Wiener—Hopf Equations
2.5 Error-Performance Surface
2.6 Multiple Linear Regression Model
2.7 Example
2.8 Linearly Constrained Minimum-Variance Filter
2.9 Generalized Sidelobe Cancellers
2.10 Summary and Discussion
Problems
Bibliography
Chapter 3 Linear Prediction
3.1 Forward Linear Prediction
3.2 Backward Linear Prediction
3.3 Levinson—Durbin Algorithm
3.4 Properties of Prediction-Error Filters
3.5 Schur—Cohn Test
3.6 Autoregressive Modeling of a Stationary Stochastic Process
3.7 Cholesky Factorization
3.8 Lattice Predictors
3.9 All-Pole, All-Pass Lattice Filter
3.10 Joint-Process Estimation
3.11 Predictive Modeling of Speech
3.12 Summary and Discussion
Problems
Bibliography
Chapter 4 Method of Steepest Descent
4.1 Basic Idea of the Steepest-Descent Algorithm
4.2 The Steepest-Descent Algorithm Applied to the Wiener Filter
4.3 Stability of the Steepest-Descent Algorithm
4.4 Example
4.5 The Steepest-Descent Algorithm as a Deterministic Search Method
4.6 Virtue and Limitation of the Steepest-Descent Algorithm
4.7 Summary and Discussion
Problems
Bibliography
Chapter 5 Method of Stochastic Gradient Descent
5.1 Principles of Stochastic Gradient Descent
5.2 Application: Least-Mean-Square (LMS) Algorithm
5.3 Gradient-Adaptive Lattice Filtering Algorithm
5.4 Other Applications of Stochastic Gradient Descent
5.5 Summary and Discussion
Problems
Bibliography
Chapter 6 The Least-Mean-Square (LMS) Algorithm
6.1 Signal-Flow Graph
6.2 Optimality Considerations
6.3 Applications
6.4 Statistical Learning Theory
6.5 Transient Behavior and Convergence Considerations
6.6 Efficiency
6.7 Computer Experiment on Adaptive Prediction
6.8 Computer Experiment on Adaptive Equalization
6.9 Computer Experiment on Minimum-Variance Distortionless-Response Beamformer
6.10 Summary and Discussion
Problems
Bibliography
Chapter 7 Normalized Least-Mean-Square (LMS) Algorithm and Its Generalization
7.1 Normalized LMS Algorithm: The Solution to a Constrained Optimization Problem
7.2 Stability of the Normalized LMS Algorithm
7.3 Step-Size Control for Acoustic Echo Cancellation
7.4 Geometric Considerations Pertaining to the Convergence Process for Real-Valued Data
7.5 Affine Projection Adaptive Filters
7.6 Summary and Discussion
Problems
Bibliography
Chapter 8 Block-Adaptive Filters
8.1 Block-Adaptive Filters: Basic Ideas
8.2 Fast Block LMS Algorithm
8.3 Unconstrained Frequency-Domain Adaptive Filters
8.4 Self-Orthogonalizing Adaptive Filters
8.5 Computer Experiment on Adaptive Equalization
8.6 Subband Adaptive Filters
8.7 Summary and Discussion
Problems
Bibliography
Chapter 9 Method of Least Squares
9.1 Statement of the Linear Least-Squares Estimation Problem
9.2 Data Windowing
9.3 Principle of Orthogonality<ALT1> Revisited</ALT>
9.4 Minimum Sum of Error Squares
9.5 Normal Equations and Linear Least-Squares Filters
9.6 Time-Average Correlation Matrix Φ
9.7 Reformulation of the Normal Equations in Terms of Data Matrices
9.8 Properties of Least-Squares Estimates
9.9 Minimum-Variance Distortionless Response (MVDR) Spectrum Estimation
9.10 Regularized MVDR Beamforming
9.11 Singular-Value Decomposition
9.12 Pseudoinverse
9.13 Interpretation of Singular Values and Singular Vectors
9.14 Minimum-Norm Solution to the Linear Least-Squares Problem
9.15 Normalized Least-Mean-Square (LMS) Algorithm Viewed as the Minimum-Norm Solution to an Underdetermined Least-Squares Estimation Problem
9.16 Summary and Discussion
Problems
Bibliography
Chapter 10 The Recursive Least-Squares (RLS) Algorithm
10.1 Some Preliminaries
10.2 The Matrix Inversion Lemma
10.3 The Exponentially Weighted RLS Algorithm
10.4 Selection of the Regularization Parameter
10.5 Update Recursion for the Sum of Weighted Error Squares
10.6 Example: Single-Weight Adaptive Noise Canceller
10.7 Statistical Learning Theory
10.8 Efficiency
10.9 Computer Experiment on Adaptive Equalization
10.10 Summary and Discussion
Problems
Bibliography
Chapter 11 Robustness
11.1 Robustness, Adaptation, and Disturbances
11.2 Robustness: Preliminary Considerations Rooted in H ∞ Optimization
11.3 Robustness of the LMS Algorithm
11.4 Robustness of the RLS Algorithm
11.5 Comparative Evaluations of the LMS and RLS Algorithms from the Perspective of Robustness
11.6 Risk-Sensitive Optimality
11.7 Trade-Offs Between Robustness and Efficiency
11.8 Summary and Discussion
Problems
Bibliography
Chapter 12 Finite-Precision Effects
12.1 Quantization Errors
12.2 Least-Mean-Square (LMS) Algorithm
12.3 Recursive Least-Squares (RLS) Algorithm
12.4 Summary and Discussion
Problems
Bibliography
Chapter 13 Adaptation in Nonstationary Environments
13.1 Causes and Consequences of Nonstationarity
13.2 The System Identification Problem
13.3 Degree of Nonstationarity
13.4 Criteria for Tracking Assessment
13.5 Tracking Performance of the LMS Algorithm
13.6 Tracking Performance of the RLS Algorithm
13.7 Comparison of the Tracking Performance of the LMS and RLS Algorithms
13.8 Tuning of Adaptation Parameters
13.9 Incremental Delta-Bar-Delta (IDBD) Algorithm
13.10 Autostep Method
13.11 Computer Experiment: Mixture of Stationary and Nonstationary Environmental Data
13.12 Summary and Discussion
Problems
Bibliography
Chapter 14 Kalman Filters
14.1 Recursive Minimum Mean-Square Estimation for Scalar Random Variables
14.2 Statement of the Kalman Filtering Problem
14.3 The Innovations Process
14.4 Estimation of the State Using the Innovations Process
14.5 Filtering
14.6 Initial Conditions
14.7 Summary of the Kalman Filter
14.8 Kalman Filter as the Unifying Basis for RLS Algorithms
14.9 Variants of the Kalman Filter
14.10 Summary and Discussion
Problems
Bibliography
Chapter 15 Square-Root Adaptive Filters
15.1 Square-Root Kalman Filters
15.2 Building Square-Root Adaptive Filters on Their Kalman Filter Counterparts
15.3 QRD-RLS Algorithm
15.4 Adaptive Beamforming
15.5 Inverse QRD-RLS Algorithm
15.6 Finite-Precision Effects
15.7 Summary
Problems
Bibliography
Chapter 16 Order-Recursive Adaptive Filters
16.1 Order-Recursive Adaptive Filters Using Least-Squares Estimation: An Overview
16.2 Adaptive Forward Linear Prediction
16.3 Adaptive Backward Linear Prediction
16.4 Conversion Factor
16.5 Least-Squares Lattice (LSL) Predictor
16.6 Angle-Normalized Estimation Errors
16.7 First-Order State-Space Models for Lattice Filtering
16.8 QR-Decomposition—Based Least-Squares Lattice (QRD-LSL) Filters
16.9 Fundamental Properties of the QRD-LSL Filter
16.10 Computer Experiment on Adaptive Equalization
16.11 Recursive LSL Filters Using a Posteriori Estimation Errors
16.12 Recursive LSL Filters Using a Priori Estimation Errors with Error Feedback
16.13 Relation Between Recursive LSL and RLS Algorithms
16.14 Finite-Precision Effects
16.15 Summary and Discussion
Problems
Bibliography
Chapter 17 Blind Deconvolution
17.1 Overview of the Blind Deconvolution
17.2 Channel Identifiability Using Cyclostationary Statistics
17.3 Subspace Decomposition for Fractionally Spaced Blind Identification
17.4 Bussgang Algorithm for Blind Equalization
17.5 Extension of the Bussgang Algorithm to Complex Baseband Channels
17.6 Special Cases of the Bussgang Algorithm
17.7 Fractionally Spaced Bussgang Equalizers
17.8 Estimation of Unknown Probability Distribution Factor of Signal Source
17.9 Summary and Discussion
Problems
Bibliography
Epilogue
1. Robusness, Efficiency, and Complexity
2. Kernel-Based Nonlinear Adaptive Filtering
Bibliography
Appendix A Theory of Complex Variables
A.1 Cauchy—Reimann Equations
A.2 Cauchy’s Integral Formula
A.3 Laurent’s Series
A.4 Singularities and Residues
A.5 Cauchy’s Residue Theorem
A.6 Principle of the Argument
A.7 Inversion Integral for the z-Transform
A.8 Parseval’s Theorem
Bibliography
Appendix B Computation of Derivatives in the Complex Domain
B.1 Differentiability and Analyticity
B.2 Wirtinger Derivatives
B.3 Matrix and Vector Derivatives
B.4 Newton Updates
Bibliography
Appendix C Method of Lagrange Multipliers
C.1 Optimization Involving a Single Equality Constraint
C.2 Optimization Involving Multiple Equality Constraints
C.3 Optimization Beamformer
Bibliography
Appendix D Estimation Theory
D.1 Likelihood Function
D.2 Cramér—Rao Inequality
D.3 Properties of Maximum-Likelihood Estimators
D.4 Conditional Mean Estimator
Bibliography
Appendix E Eigenanalysis
E.1 The Eigenvalue Problem
E.2 Properties of Eigenvalues and Eigenvectors
E.3 Low-Rank Modeling
E.4 Eigenfilters
E.5 Eigenvalue Computations
Bibliography
Appendix F Langevin Equation of Nonequilibrium Thermodynamics
F.1 Brownian Motion
F.2 Langevin Equation
Bibliography
Appendix G Rotations and Reflections
G.1 Plane Rotations
G.2 Two-Sided Jacobi Algorithm
G.3 Cyclic Jacobi Algorithm
G.4 Householder Transformation
G.5 The QR Algorithm
Bibliography
Appendix H Complex Wishart Distribution
H.1 Definition
H.2 The Chi-Square Distribution as a Special Case
H.3 Properties of the Complex Wishart Distribution
H.4 Expectation of the Inverse Correlation Matrix Φ −1(n)
Bibliography
Glossary
Bibliography
Suggested Readings
Index
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