Adaptive filters / Ali H. Sayed.

Format:

Book

Author/Creator:

Sayed, Ali H.

Language:

English

Subjects (All):

Adaptive filters.

Physical Description:

1 online resource (820 p.)

Edition:

1st ed.

Place of Publication:

Hoboken, N.J. : Wiley-Interscience : IEEE Press, c2008.

Language Note:

English

Summary:

Adaptive filtering is a topic of immense practical and theoretical value, having applications in areas ranging from digital and wireless communications to biomedical systems. This book enables readers to gain a gradual and solid introduction to the subject, its applications to a variety of topical problems, existing limitations, and extensions of current theories. The book consists of eleven parts?each part containing a series of focused lectures and ending with bibliographic comments, problems, and computer projects with MATLAB solutions.

Contents:

Preface and Acknowledgments

Notation and Symbols

BACKGROUND MATERIAL

A. Random Variables

A.1 Variance of a Random Variable

A.2 Dependent Random Variables

A.3 Complex-Valued Random Variables

A.4 Vector-Valued Random Variables

A.5 Gaussian Random Vectors

B. Linear Algebra

B.1 Hermitian and Positive-Definite 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 Cauchy-Riemann Conditions

C.2 Scalar Arguments

C.3 Vector Arguments

PART I: OPTIMAL ESTIMATION

1. Scalar-Valued Data

1.1 Estimation Without Observations

1.2 Estimation Given Dependent Observations

1.3 Orthogonality Principle

1.4 Gaussian Random Variables

2. Vector-Valued 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 Mean-Square Error Criterion

3.2 Minimization by Differentiation

3.3 Minimization by Completion-of-Squares

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 Nonzero-Mean 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: Multiple-Antenna Receivers

6. Constrained Estimation

6.1 Minimum-Variance 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 State-Space 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 Time-Update Form

PART III: STOCHASTIC GRADIENT ALGORITHMS

8. Steepest-Descent Technique

8.1 Linear Estimation Problem

8.2 Steepest-Descent Method

8.3 More General Cost Functions

9. Transient Behavior

9.1 Modes of Convergence

9.2 Optimal Step-Size

9.3 Weight-Error Vector Convergence

9.4 Time Constants

9.5 Learning Curve

9.6 Contour Curves of the Error Surface

9.7 Iteration-Dependent Step-Sizes

9.8 Newton?s Method

10. LMS Algorithm

10.1 Motivation

10.2 Instantaneous Approximation

10.3 Computational Cost

10.4 Least-Perturbation Property

10.5 Application: Adaptive Channel Estimation

10.6 Application: Adaptive Channel Equalization

10.7 Application: Decision-Feedback Equalization

10.8 Ensemble-Average Learning Curves

11. Normalized LMS Algorithm

11.1 Instantaneous Approximation

11.2 Computational Cost

11.3 Power Normalization

11.4 Least-Perturbation Property

12. Other LMS-Type Algorithms

12.1 Non-Blind Algorithms

12.2 Blind Algorithms

12.3 Some Properties

13. Affine Projection Algorithm

13.1 Instantaneous Approximation

13.2 Computational Cost

13.3 Least-Perturbation Property

13.4 Affine Projection Interpretation

14. RLS Algorithm

14.1 Instantaneous Approximation

14.2 Computational Cost

PART IV: MEAN-SQUARE 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 Step-Sizes

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 Sign-Error LMS

18.1 Real-Valued Data

18.2 Complex-Valued 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 Step-Sizes

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 Sign-Error 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 Step-Sizes

PART V: TRANSIENT PERFORMANCE

22. Weighted Energy Conservation

22.1 Data Model

22.2 Data-Normalized 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 Mean-Square Behavior

23.4 Mean-Square Stability

23.5 Steady-State Performance

23.6 Small Step-Size Approximations

23.A Convergence Time

24. LMS with non-Gaussian Regressors

24.1 Mean and Variance Relations

24.2 Mean-Square Stability and Performance

24.3 Small Step-Size Approximations

24.A Independence and Averaging Analysis

25. Data-Normalized Filters

25.1 NLMS Filter

25.2 Data-Normalized Filters

25.A Stability Bound

25.B Stability of NLMS

PART VI: BLOCK ADAPTIVE FILTERS

26. Transform Domain Adaptive Filters

26.1 Transform-Domain Filters

26.2 DFT-Domain LMS.

26.3 DCT-Domain LMS

26.A DCT-Transformed 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 Overlap-Add Block Adaptive Filters

PART VII: LEAST-SQUARES METHODS

29. Least-Squares Criterion

29.1 Least-Squares Problem

29.2 Geometric Argument

29.3 Algebraic Arguments

29.4 Properties of Least-Squares Solution

29.5 Projection Matrices

29.6 Weighted Least-Squares

29.7 Regularized Least-Squares

29.8 Weighted Regularized Least-Squares

30. Recursive Least-Squares

30.1 Motivation

30.2 RLS Algorithm

30.3 Regularization

30.4 Conversion Factor

30.5 Time-Update of the Minimum Cost

30.6 Exponentially-Weighted RLS Algorithm

31. Kalman Filtering and RLS

31.1 Equivalence in Linear Estimation

31.2 Kalman Filtering and Recursive Least-Squares

31.A Extended RLS Algorithms

32. Order and Time-Update Relations

32.1 Backward Order-Update Relations

32.2 Forward Order-Update Relations

32.3 Time-Update Relation

PART VIII: ARRAY ALGORITHMS

33. Norm and Angle Preservation

33.1 Some Difficulties

33.2 Square-Root 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

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 Time-Update of the Gain Vector

37.2 Time-Update 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 Low-Rank Factorization

39. Fast Fixed-Order Filters

39.1 Fast Transversal Filter

39.2 FAEST Filter

39.3 Fast Kalman Filter

39.4 Stability Issues

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 Order-Update Relations

41. Lattice Filter Algorithms

41.1 Significance of Data Structure

41.2 A Posteriori-Based Lattice Filter

41.3 A Priori-Based Lattice Filter

42. Error-Feedback Lattice Filters

42.1 A Priori Error-Feedback Lattice Filter

42.2 A Posteriori Error-Feedback Lattice Filter

42.3 Normalized Lattice Filter

43. Array Lattice Filters

43.1 Order-Update of Output Estimation Errors

43.2 Order-Update of Backward Estimation Errors

43.3 Order-Update of Forward Estimation Errors

43.4 Significance of Data Structure

PART XI: ROBUST FILTERS

44. Indefinite Least-Squares

44.1 Indefinite Least-Squares

44.2 Recursive Minimization Algorithm

44.3 Time-Update of the Minimum Cost

44.4 Singular Weighting Matrices

44.A Stationary Points

44.B Inertia Conditions

45. Robust Adaptive Filters

45.1 A Posteriori-Based Robust Filters

45.2 ε-NLMS Algorithm

45.3 A Priori-Based 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

REFERENCES AND INDICES

References

Author Index

Subject Index.

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 758-774) and indexes.

Description based on PDF viewed 12/21/2015.

ISBN:

1-118-21084-0

1-281-37431-8

9786611374310

0-470-37412-8

0-470-37411-X

OCLC:

352835054