Apolinario Jr QRD-RLS Adaptive Filtering

1. Auflage 2009
ISBN: 978-0-387-09734-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 356 Seiten

I feel very honoured to have been asked to write a brief foreword for this book on QRD-RLS Adaptive Filtering-asubjectwhichhas been close to my heart for many years. The book is well written and very timely - I look forward personally to seeing it in print. The editor is to be congratulated on assembling such a highly esteemed team of contributing authors able to span the broad range of topics and concepts which underpin this subject. In many respects, and for reasons well expounded by the authors, the LMS al- rithm has reigned supreme since its inception, as the algorithm of choice for prac- cal applications of adaptive ltering. However, as a result of the relentless advances in electronic technology, the demand for stable and ef cient RLS algorithms is growing rapidly - not just because the higher computational load is no longer such a serious barrier, but also because the technological pull has grown much stronger in the modern commercial world of 3G mobile communications, cognitive radio, high speed imagery, and so on.

Autoren/Hrsg.

Apolinario Jr, Jose

Inhaltsverzeichnis

1;Foreword;6
2;Preface;8
3;Contents;10
4;List of Contributors;16
5;1 QR Decomposition: An Annotated Bibliography;19
5.1;Marcello L. R. de Campos and Gilbert Strang;19
5.1.1;Preamble;19
5.1.2;Eigenvalues and Eigenvectors;20
5.1.3;Iterative Methods for the Solution of the Eigenproblem;21
5.1.3.1;The LR algorithm;21
5.1.3.2;The QR algorithm;22
5.1.4;QR Decomposition for Orthogonalization;23
5.1.4.1;The classical Gram--Schmidt orthogonalizationmethod;24
5.1.4.2;The modified Gram--Schmidt orthogonalizationmethod;26
5.1.4.3;Triangularization via Householder reflections;27
5.1.4.4;Triangularization via Givens plane rotations;28
5.1.5;QR Decomposition for Linear Least Squares Problems;30
5.1.5.1;QR Decomposition by systolic arrays;32
5.1.6;QR Decomposition for Recursive Least Squares AdaptiveFilters;32
5.1.6.1;Fast QR decomposition RLS adaptation algorithms;34
5.1.7;Conclusion;35
5.1.8;References;36
6;2 Introduction to Adaptive Filters;41
6.1;José A. Apolinário Jr. and Sergio L. Netto;41
6.1.1;Basic Concepts;41
6.1.2;Error Measurements;46
6.1.2.1;The mean-square error;46
6.1.2.2;The instantaneous square error;47
6.1.2.3;The weighted least-squares;47
6.1.3;Adaptation Algorithms;48
6.1.3.1;LMS and normalized-LMS algorithms;49
6.1.3.2;Data-reusing LMS algorithms;52
6.1.3.3;RLS-type algorithms;58
6.1.4;Computer Simulations;60
6.1.4.1;Example 1: Misadjustment of the LMS algorithm;60
6.1.4.2;Example 2: Convergence trajectories;61
6.1.4.3;Example 3: Tracking performance;61
6.1.4.4;Example 4: Algorithm stability;64
6.1.5;Conclusion;65
6.1.6;References;66
7;3 Conventional and Inverse QRD-RLS Algorithms;68
7.1;José A. Apolinário Jr. and Maria D. Miranda;68
7.1.1;The Least-Squares Problem and the QR Decomposition;68
7.1.2;The Givens Rotation Method;74
7.1.3;The Conventional QRD-RLS Algorithm;77
7.1.4;Initialization of the Triangularization Procedure;81
7.1.5;On the Q(k) Matrix;83
7.1.5.1;The backward prediction problem;86
7.1.5.2;The forward prediction problem;88
7.1.5.3;Interpreting the elements of Q(k) for a lower triangular Cholesky factor;91
7.1.5.4;Interpreting the elements of Q(k) for an upper triangular Cholesky factor;92
7.1.6;The Inverse QRD-RLS Algorithm;93
7.1.7;Conclusion;94
7.1.8;Appendix 1;96
7.1.9;Appendix 2;97
7.1.10;Appendix 3;98
7.1.11;References;101
8;4 Fast QRD-RLS Algorithms;103
8.1;José A. Apolinário Jr. and Paulo S. R. Diniz;103
8.1.1;Introduction;103
8.1.2;Upper Triangularization Algorithms (Updating Forward Prediction Errors);105
8.1.2.1;The FQR_POS_F algorithm;106
8.1.2.2;The FQR_PRI_F algorithm;108
8.1.3;Lower Triangularization Algorithms (Updating Backward Prediction Errors);109
8.1.3.1;The FQR_POS_B algorithm;111
8.1.3.2;The FQR_PRI_B algorithm;114
8.1.4;The Order Recursive Versions of the Fast QRD Algorithms;116
8.1.5;Conclusion;120
8.1.6;Appendix 1;121
8.1.7;Appendix 2;123
8.1.8;Appendix 3;127
8.1.9;References;129
9;5 QRD Least-Squares Lattice Algorithms;130
9.1;Jenq-Tay Yuan;130
9.1.1;Fundamentals of QRD-LSL Algorithms;131
9.1.2;LSL Interpolator and LSL Predictor;133
9.1.2.1;LSL interpolator;134
9.1.2.2;Orthogonal bases for LSL interpolator;136
9.1.2.3;LSL predictor;137
9.1.3;SRF Givens Rotation with Feedback Mechanism;138
9.1.4;SRF QRD-LSL Algorithms;140
9.1.4.1;QRD based on interpolation;141
9.1.4.2;SRF QRD-LSL interpolation algorithm;144
9.1.4.3;SRF QRD-LSL prediction algorithm and SRF joint process estimation;151
9.1.5;SRF (QRD-LSL)-Based RLS Algorithm;154
9.1.6;Simulations;155
9.1.7;Conclusion;157
9.1.8;References;158
10;6 Multichannel Fast QRD-RLS Algorithms;161
10.1;António L. L. Ramos and Stefan Werner;161
10.1.1;Introduction;161
10.1.2;Problem Formulation;163
10.1.2.1;Redefining the input vector;165
10.1.2.2;Input vector for sequential-type multichannelalgorithms;166
10.1.2.3;Input vector for block-type multichannel algorithms;167
10.1.3;Sequential-Type MC-FQRD-RLS Algorithms;167
10.1.3.1;Triangularization of the information matrix ;168
10.1.3.2;A priori and A posteriori versions;171
10.1.3.3;Alternative implementations;173
10.1.4;Block-Type MC-FQRD-RLS Algorithms;176
10.1.4.1;The backward and forward prediction problems;176
10.1.4.2;A priori and A posteriori versions;180
10.1.4.3;Alternative implementations;183
10.1.5;Order-Recursive MC-FQRD-RLS Algorithms;185
10.1.6;Application Example and Computational Complexity Issues;190
10.1.6.1;Application example;190
10.1.6.2;Computational complexity issues;192
10.1.7;Conclusion;193
10.1.8;References;193
11;7 Householder-Based RLS Algorithms;195
11.1;Athanasios A. Rontogiannis and Sergios Theodoridis;195
11.1.1;Householder Transforms;195
11.1.1.1;Hyperbolic Householder transforms;198
11.1.1.2;Row Householder transforms;198
11.1.2;The Householder RLS (HRLS) Algorithm;200
11.1.2.1;Applications;204
11.1.3;The Householder Block Exact QRD-RLS Algorithm;206
11.1.4;The Householder Block Exact Inverse QRD-RLS Algorithm;210
11.1.5;Sliding Window (SW) Householder Block Implementation;213
11.1.6;Conclusion;216
11.1.7;References;216
12;8 Numerical Stability Properties;218
12.1;Phillip Regalia and Richard Le Borne;218
12.1.1;Introduction;218
12.1.2;Preliminaries;219
12.1.2.1;Conditioning, forward stability, and backwardstability;221
12.1.3;The Conditioning of the Least-Squares Problem;223
12.1.3.1;The conditioning of the least-squares problem;224
12.1.3.2;Consistency, stability, and convergence;225
12.1.4;The Recursive QR Least-Squares Methods;227
12.1.4.1;Full QR decomposition adaptive algorithm;227
12.1.5;Fast QR Algorithms;233
12.1.5.1;Past input reconstruction;236
12.1.5.2;Reachable states in fast least-squares algorithms;240
12.1.5.3;QR decomposition lattice algorithm;242
12.1.6;Conclusion;244
12.1.7;References;245
13;9 Finite and Infinite-Precision Properties of QRD-RLS Algorithms;247
13.1;Paulo S. R. Diniz and Marcio G. Siqueira;247
13.1.1;Introduction;247
13.1.2;Precision Analysis of the QR-Decomposition RLS Algorithm;248
13.1.2.1;Infinite-precision analysis;249
13.1.2.2;Stability analysis;254
13.1.2.3;Error propagation analysis in steady-state;256
13.1.2.4;Simulation results;267
13.1.3;Precision Analysis of the Fast QRD-Lattice Algorithm;268
13.1.3.1;Infinite-precision analysis;270
13.1.3.2;Finite-precision analysis;273
13.1.3.3;Simulation results;277
13.1.4;Conclusion;278
13.1.5;References;278
14;10 On Pipelined Implementations of QRD-RLS Adaptive Filters;280
14.1;Jun Ma and Keshab K. Parhi;280
14.1.1;QRD-RLS Systolic Architecture;281
14.1.2;The Annihilation-Reording Look-Ahead Technique;284
14.1.2.1;Look-ahead through block processing;285
14.1.2.2;Look-ahead through iteration;287
14.1.2.3;Relationship with multiply--add look-ahead;288
14.1.2.4;Parallelism in annihilation-reording look-ahead;290
14.1.2.5;Pipelined and block processing implementations;291
14.1.2.6;Invariance of bounded input and bounded output;294
14.1.3;Pipelined CORDIC-Based RLS Adaptive Filters;294
14.1.3.1;Pipelined QRD-RLS with implicit weight extraction;295
14.1.3.2;Stability analysis;297
14.1.3.3;Pipelined QRD-RLS with explicit weight extraction;299
14.1.4;Conclusion;302
14.1.5;Appendix;305
14.1.6;References;307
15;11 Weight Extraction of Fast QRD-RLS Algorithms;309
15.1;Stefan Werner and Mohammed Mobien;309
15.1.1;FQRD-RLS Preliminaries;310
15.1.1.1;QR decomposition algorithms;310
15.1.1.2;FQR_POS_B algorithm;311
15.1.2;System Identification with FQRD-RLS;313
15.1.2.1;Weight extraction in the FQRD-RLS algorithm;314
15.1.2.2;Example;316
15.1.3;Burst-trained Equalizer with FQRD-RLS;318
15.1.3.1;Problem description;319
15.1.3.2;Equivalent-output filtering;319
15.1.3.3;Equivalent-output filtering with explicit weightextraction;321
15.1.3.4;Example;323
15.1.4;Active Noise Control and FQRD-RLS;324
15.1.4.1;Filtered-x RLS;325
15.1.4.2;Modified filtered-x FQRD-RLS;326
15.1.4.3;Example;329
15.1.5;Multichannel and Lattice Implementations;330
15.1.6;Conclusion;330
15.1.7;References;331
16;12 On Linearly Constrained QRD-Based Algorithms;333
16.1;Shiunn-Jang Chern;333
16.1.1;Introduction;333
16.1.2;Optimal Linearly Constrained QRD-LS Filter;335
16.1.3;The Adaptive LC-IQRD-RLS Filtering Algorithm;337
16.1.4;The Adaptive GSC-IQRD-RLS Algorithm;341
16.1.5;Applications;345
16.1.5.1;Application 1: Adaptive LCMV filtering for spectrum estimation;345
16.1.5.2;Application 2: Adaptive LCMV antenna array beamformer;348
16.1.6;Conclusion;353
16.1.7;References;353
17;Index;356