Textbook
Adaptive FiltersISBN: 9780470253885
824 pages
April 2008, ©2008, WileyIEEE Press

Notation and Symbols.
BACKGROUND MATERIAL.
A. Random Variables.
A.1 Variance of a Random Variable.
A.2 Dependent Random Variables.
A.3 ComplexValued Random Variables.
A.4 VectorValued Random Variables.
A.5 Gaussian Random Vectors.
B. Linear Algebra.
B.1 Hermitian and PositiveDefinite Matrices.
B.2 Range Spaces and Nullspaces of Matrices.
B.3 Schur Complements.
B.4 Cholesky Factorization.
B.5 QR Decomposition.
B.6 Singular Value Decomposition.
B.7 Kronecker Products.
C. Complex Gradients.
C.1 CauchyRiemann Conditions.
C.2 Scalar Arguments.
C.3 Vector Arguments.
PART I: OPTIMAL ESTIMATION.
1. ScalarValued Data.
1.1 Estimation Without Observations.
1.2 Estimation Given Dependent Observations.
1.3 Orthogonality Principle.
1.4 Gaussian Random Variables.
2. VectorValued Data.
2.1 Optimal Estimator in the Vector Case.
2.2 Spherically Invariant Gaussian Variables.
2.3 Equivalent Optimization Criterion.
Summary and Notes.
Problems and Computer Projects.
PART II: LINEAR ESTIMATION.
3. Normal Equations.
3.1 MeanSquare Error Criterion.
3.2 Minimization by Differentiation.
3.3 Minimization by CompletionofSquares.
3.4 Minimization of the Error Covariance Matrix.
3.5 Optimal Linear Estimator.
4. Orthogonality Principle.
4.1 Design Examples.
4.2 Orthogonality Condition.
4.3 Existence of Solutions.
4.4 NonzeroMean Variables.
5. Linear Models.
5.1 Estimation using Linear Relations.
5.2 Application: Channel Estimation.
5.3 Application: Block Data Estimation.
5.4 Application: Linear Channel Equalization.
5.5 Application: MultipleAntenna Receivers.
6. Constrained Estimation.
6.1 MinimumVariance Unbiased Estimation.
6.2 Example: Mean Estimation.
6.3 Application: Channel and Noise Estimation.
6.4 Application: Decision Feedback Equalization.
6.5 Application: Antenna Beamforming.
7. Kalman Filter.
7.1 Innovations Process.
7.2 StateSpace Model.
7.3 Recursion for the State Estimator.
7.4 Computing the Gain Matrix.
7.5 Riccati Recursion.
7.6 Covariance Form.
7.7 Measurement and TimeUpdate Form.
Summary and Notes.
Problems and Computer Projects.
PART III: STOCHASTIC GRADIENT ALGORITHMS.
8. SteepestDescent Technique.
8.1 Linear Estimation Problem.
8.2 SteepestDescent Method.
8.3 More General Cost Functions.
9. Transient Behavior.
9.1 Modes of Convergence.
9.2 Optimal StepSize.
9.3 WeightError Vector Convergence.
9.4 Time Constants.
9.5 Learning Curve.
9.6 Contour Curves of the Error Surface.
9.7 IterationDependent StepSizes.
9.8 Newton?s Method.
10. LMS Algorithm.
10.1 Motivation.
10.2 Instantaneous Approximation.
10.3 Computational Cost.
10.4 LeastPerturbation Property.
10.5 Application: Adaptive Channel Estimation.
10.6 Application: Adaptive Channel Equalization.
10.7 Application: DecisionFeedback Equalization.
10.8 EnsembleAverage Learning Curves.
11. Normalized LMS Algorithm.
11.1 Instantaneous Approximation.
11.2 Computational Cost.
11.3 Power Normalization.
11.4 LeastPerturbation Property.
12. Other LMSType Algorithms.
12.1 NonBlind Algorithms.
12.2 Blind Algorithms.
12.3 Some Properties.
13. Affine Projection Algorithm.
13.1 Instantaneous Approximation.
13.2 Computational Cost.
13.3 LeastPerturbation Property.
13.4 Affine Projection Interpretation.
14. RLS Algorithm.
14.1 Instantaneous Approximation.
14.2 Computational Cost.
Summary and Notes.
Problems and Computer Projects.
PART IV: MEANSQUARE PERFORMANCE.
15. Energy Conservation.
15.1 Performance Measure.
15.2 Stationary Data Model.
15.3 Energy Conservation Relation.
15.4 Variance Relation.
15.A Interpretations of the Energy Relation.
16. Performance of LMS.
16.1 Variance Relation.
16.2 Small StepSizes.
16.3 Separation Principle.
16.4 White Gaussian Input.
16.5 Statement of Results.
16.6 Simulation Results.
17. Performance of NLMS.
17.1 Separation Principle.
17.2 Simulation Results.
17.A Relating NLMS to LMS.
18. Performance of SignError LMS.
18.1 RealValued Data.
18.2 ComplexValued Data.
18.3 Simulation Results.
19. Performance of RLS and Other Filters.
19.1 Performance of RLS.
19.2 Performance of Other Filters.
19.3 Performance Table for Small StepSizes.
20. Nonstationary Environments.
20.1 Motivation.
20.2 Nonstationary Data Model.
20.3 Energy Conservation Relation.
20.4 Variance Relation.
21. Tracking Performance.
21.1 Performance of LMS.
21.2 Performance of NLMS.
21.3 Performance of SignError LMS.
21.4 Performance of RLS.
21.5 Comparison of Tracking Performance.
21.6 Comparing RLS and LMS.
21.7 Performance of Other Filters.
21.8 Performance Table for Small StepSizes.
Summary and Notes.
Problems and Computer Projects.
PART V: TRANSIENT PERFORMANCE.
22. Weighted Energy Conservation.
22.1 Data Model.
22.2 DataNormalized Adaptive Filters.
22.3 Weighted Energy Conservation Relation.
22.4 Weighted Variance Relation.
23. LMS with Gaussian Regressors.
23.1 Mean and Variance Relations.
23.2 Mean Behavior.
23.3 MeanSquare Behavior.
23.4 MeanSquare Stability.
23.5 SteadyState Performance.
23.6 Small StepSize Approximations.
23.A Convergence Time.
24. LMS with nonGaussian Regressors.
24.1 Mean and Variance Relations.
24.2 MeanSquare Stability and Performance.
24.3 Small StepSize Approximations.
24.A Independence and Averaging Analysis.
25. DataNormalized Filters.
25.1 NLMS Filter.
25.2 DataNormalized Filters.
25.A Stability Bound.
25.B Stability of NLMS.
Summary and Notes.
Problems and Computer Projects.
PART VI: BLOCK ADAPTIVE FILTERS.
26. Transform Domain Adaptive Filters.
26.1 TransformDomain Filters.
26.2 DFTDomain LMS.
26.3 DCTDomain LMS.
26.A DCTTransformed Regressors.
27. Efficient Block Convolution.
27.1 Motivation.
27.2 Block Data Formulation.
27.3 Block Convolution.
28. Block and Subband Adaptive Filters.
28.1 DFT Block Adaptive Filters.
28.2 Subband Adaptive Filters.
28.A Another Constrained DFT Block Filter.
28.B OverlapAdd Block Adaptive Filters.
Summary and Notes.
Problems and Computer Projects.
PART VII: LEASTSQUARES METHODS.
29. LeastSquares Criterion.
29.1 LeastSquares Problem.
29.2 Geometric Argument.
29.3 Algebraic Arguments.
29.4 Properties of LeastSquares Solution.
29.5 Projection Matrices.
29.6 Weighted LeastSquares.
29.7 Regularized LeastSquares.
29.8 Weighted Regularized LeastSquares.
30. Recursive LeastSquares.
30.1 Motivation.
30.2 RLS Algorithm.
30.3 Regularization.
30.4 Conversion Factor.
30.5 TimeUpdate of the Minimum Cost.
30.6 ExponentiallyWeighted RLS Algorithm.
31. Kalman Filtering and RLS.
31.1 Equivalence in Linear Estimation.
31.2 Kalman Filtering and Recursive LeastSquares.
31.A Extended RLS Algorithms.
32. Order and TimeUpdate Relations.
32.1 Backward OrderUpdate Relations.
32.2 Forward OrderUpdate Relations.
32.3 TimeUpdate Relation.
Summary and Notes.
Problems and Computer Projects.
PART VIII: ARRAY ALGORITHMS.
33. Norm and Angle Preservation.
33.1 Some Difficulties.
33.2 SquareRoot Factors.
33.3 Norm and Angle Preservation.
33.4 Motivation for Array Methods.
34. Unitary Transformations.
34.1 Givens Rotations.
34.2 Householder Transformations.
35. QR and Inverse QR Algorithms.
35.1 Inverse QR Algorithm.
35.2 QR Algorithm.
35.3 Extended QR Algorithm.
35.A Array Algorithms for Kalman Filtering.
Summary and Notes.
Problems and Computer Projects.
PART IX: FAST RLS ALGORITHMS.
36. Hyperbolic Rotations.
36.1 Hyperbolic Givens Rotations.
36.2 Hyperbolic Householder Transformations.
36.3 Hyperbolic Basis Rotations.
37. Fast Array Algorithm.
37.1 TimeUpdate of the Gain Vector.
37.2 TimeUpdate of the Conversion Factor.
37.3 Initial Conditions.
37.4 Array Algorithm.
37.A Chandrasekhar Filter.
38. Regularized Prediction Problems.
38.1 Regularized Backward Prediction.
38.2 Regularized Forward Prediction.
38.3 LowRank Factorization.
39. Fast FixedOrder Filters.
39.1 Fast Transversal Filter.
39.2 FAEST Filter.
39.3 Fast Kalman Filter.
39.4 Stability Issues.
Summary and Notes.
Problems and Computer Projects.
PART X: LATTICE FILTERS.
40. Three Basic Estimation Problems.
40.1 Motivation for Lattice Filters.
40.2 Joint Process Estimation.
40.3 Backward Estimation Problem.
40.4 Forward Estimation Problem.
40.5 Time and OrderUpdate Relations.
41. Lattice Filter Algorithms.
41.1 Significance of Data Structure.
41.2 A PosterioriBased Lattice Filter.
41.3 A PrioriBased Lattice Filter.
42. ErrorFeedback Lattice Filters.
42.1 A Priori ErrorFeedback Lattice Filter.
42.2 A Posteriori ErrorFeedback Lattice Filter.
42.3 Normalized Lattice Filter.
43. Array Lattice Filters.
43.1 OrderUpdate of Output Estimation Errors.
43.2 OrderUpdate of Backward Estimation Errors.
43.3 OrderUpdate of Forward Estimation Errors.
43.4 Significance of Data Structure.
Summary and Notes.
Problems and Computer Projects.
PART XI: ROBUST FILTERS.
44. Indefinite LeastSquares.
44.1 Indefinite LeastSquares.
44.2 Recursive Minimization Algorithm.
44.3 TimeUpdate of the Minimum Cost.
44.4 Singular Weighting Matrices.
44.A Stationary Points.
44.B Inertia Conditions.
45. Robust Adaptive Filters.
45.1 A PosterioriBased Robust Filters.
45.2 εNLMS Algorithm.
45.3 A PrioriBased Robust Filters.
45.4 LMS Algorithm.
45.A H1 Filters.
46. Robustness Properties.
46.1 Robustness of LMS.
46.2 Robustness of εNLMS.
46.3 Robustness of RLS.
Summary and Notes.
Problems and Computer Projects.
REFERENCES AND INDICES.
References.
Author Index.
Subject Index.
 Includes solved practical computer projects that illustrate how the material developed in the textbook can be used to solve problems of practical relevance. Examples of topics addressed in the computer projects include: channel estimation, linear and decisionfeedback equalization, beamforming, tracking of fading channels, line and acoustic echo cancellation, active noise control, and OFDM receivers
 Contains numerous tables, figures, problems, computer simulations, bibliography, and appendices on both basic and advanced concepts.
 Contains several detailed computer projects with MATLAB solutions available to all readers (instructors and students and practitioners)
 A complete solutions manual for the problems is also available for instructors.
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