adptive filtering,4th edition.pdf

【实例截图】

【核心代码】

Contents
1 Introduction to Adaptive Filtering........................................ 1
1.1 Introduction ......................................................... 1
1.2 Adaptive Signal Processing ........................................ 2
1.3 Introduction to Adaptive Algorithms .............................. 4
1.4 Applications......................................................... 7
References.................................................................... 11
2 Fundamentals of Adaptive Filtering...................................... 13
2.1 Introduction ......................................................... 13
2.2 Signal Representation............................................... 14
2.2.1 Deterministic Signals ..................................... 14
2.2.2 Random Signals ........................................... 15
2.2.3 Ergodicity.................................................. 22
2.3 The Correlation Matrix ............................................. 24
2.4 Wiener Filter ........................................................ 36
2.5 Linearly Constrained Wiener Filter ................................ 41
2.5.1 The Generalized Sidelobe Canceller ..................... 45
2.6 MSE Surface ........................................................ 47
2.7 Bias and Consistency ............................................... 50
2.8 Newton Algorithm .................................................. 51
2.9 Steepest-Descent Algorithm........................................ 51
2.10 Applications Revisited .............................................. 57
2.10.1 System Identification...................................... 57
2.10.2 Signal Enhancement ...................................... 58
2.10.3 Signal Prediction .......................................... 59
2.10.4 Channel Equalization ..................................... 60
2.10.5 Digital Communication System .......................... 69
2.11 Concluding Remarks................................................ 71
2.12 Problems ............................................................ 71
References.................................................................... 76
xv
xvi Contents
3 The Least-Mean-Square (LMS) Algorithm.............................. 79
3.1 Introduction ......................................................... 79
3.2 The LMS Algorithm ................................................ 79
3.3 Some Properties of the LMS Algorithm ........................... 82
3.3.1 Gradient Behavior ......................................... 82
3.3.2 Convergence Behavior of the Coefficient Vector ........ 83
3.3.3 Coefficient-Error-Vector Covariance Matrix ............. 85
3.3.4 Behavior of the Error Signal .............................. 88
3.3.5 Minimum Mean-Square Error ............................ 88
3.3.6 Excess Mean-Square Error and Misadjustment.......... 90
3.3.7 Transient Behavior ........................................ 92
3.4 LMS Algorithm Behavior in Nonstationary Environments ....... 94
3.5 Complex LMS Algorithm .......................................... 99
3.6 Examples ............................................................ 100
3.6.1 Analytical Examples ...................................... 100
3.6.2 System Identification Simulations........................ 111
3.6.3 Channel Equalization Simulations ....................... 118
3.6.4 Fast Adaptation Simulations.............................. 118
3.6.5 The Linearly Constrained LMS Algorithm .............. 123
3.7 Concluding Remarks................................................ 128
3.8 Problems ............................................................ 128
References.................................................................... 134
4 LMS-Based Algorithms .................................................... 137
4.1 Introduction ......................................................... 137
4.2 Quantized-Error Algorithms........................................ 138
4.2.1 Sign-Error Algorithm ..................................... 139
4.2.2 Dual-Sign Algorithm...................................... 146
4.2.3 Power-of-Two Error Algorithm........................... 147
4.2.4 Sign-Data Algorithm ...................................... 149
4.3 The LMS-Newton Algorithm ...................................... 149
4.4 The Normalized LMS Algorithm .................................. 152
4.5 The Transform-Domain LMS Algorithm .......................... 154
4.6 The Affine Projection Algorithm................................... 162
4.6.1 Misadjustment in the Affine Projection Algorithm ...... 168
4.6.2 Behavior in Nonstationary Environments................ 177
4.6.3 Transient Behavior ........................................ 180
4.6.4 Complex Affine Projection Algorithm ................... 183
4.7 Examples ............................................................ 184
4.7.1 Analytical Examples ...................................... 184
4.7.2 System Identification Simulations........................ 189
4.7.3 Signal Enhancement Simulations ........................ 192
4.7.4 Signal Prediction Simulations ............................ 196
Contents xvii
4.8 Concluding Remarks................................................ 198
4.9 Problems ............................................................ 199
References.................................................................... 205
5 Conventional RLS Adaptive Filter ....................................... 209
5.1 Introduction ......................................................... 209
5.2 The Recursive Least-Squares Algorithm .......................... 209
5.3 Properties of the Least-Squares Solution .......................... 213
5.3.1 Orthogonality Principle ................................... 214
5.3.2 Relation Between Least-Squares and Wiener
Solutions................................................... 215
5.3.3 Influence of the Deterministic
Autocorrelation Initialization ............................. 217
5.3.4 Steady-State Behavior of the Coefficient Vector......... 218
5.3.5 Coefficient-Error-Vector Covariance Matrix ............. 220
5.3.6 Behavior of the Error Signal .............................. 221
5.3.7 Excess Mean-Square Error and Misadjustment.......... 225
5.4 Behavior in Nonstationary Environments.......................... 230
5.5 Complex RLS Algorithm ........................................... 234
5.6 Examples ............................................................ 236
5.6.1 Analytical Example ....................................... 236
5.6.2 System Identification Simulations........................ 238
5.6.3 Signal Enhancement Simulations ........................ 240
5.7 Concluding Remarks................................................ 240
5.8 Problems ............................................................ 243
References.................................................................... 246
6 Data-Selective Adaptive Filtering ......................................... 249
6.1 Introduction ......................................................... 249
6.2 Set-Membership Filtering .......................................... 250
6.3 Set-Membership Normalized LMS Algorithm .................... 253
6.4 Set-Membership Affine Projection Algorithm .................... 255
6.4.1 A Trivial Choice for Vector N.k/......................... 259
6.4.2 A Simple Vector N.k/..................................... 260
6.4.3 Reducing the Complexity in the Simplified
SM-AP Algorithm......................................... 262
6.5 Set-Membership Binormalized LMS Algorithms ................. 263
6.5.1 SM-BNLMS Algorithm 1 ................................ 265
6.5.2 SM-BNLMS Algorithm 2 ................................ 268
6.6 Computational Complexity ......................................... 269
6.7 Time-Varying N ..................................................... 270
6.8 Partial-Update Adaptive Filtering .................................. 272
6.8.1 Set-Membership Partial-Update NLMS Algorithm ..... 275
6.9 Examples ............................................................ 278
6.9.1 Analytical Example ....................................... 278
6.9.2 System Identification Simulations........................ 279
xviii Contents
6.9.3 Echo Cancellation Environment .......................... 283
6.9.4 Wireless Channel Environment ........................... 290
6.10 Concluding Remarks................................................ 298
6.11 Problems ............................................................ 299
References.................................................................... 303
7 Adaptive Lattice-Based RLS Algorithms ................................ 305
7.1 Introduction ......................................................... 305
7.2 Recursive Least-Squares Prediction................................ 306
7.2.1 Forward Prediction Problem .............................. 306
7.2.2 Backward Prediction Problem ............................ 309
7.3 Order-Updating Equations.......................................... 311
7.3.1 A New Parameter ı.k; i /.................................. 312
7.3.2 Order Updating of d
bmin .k; i / and wb.k; i /............... 314
7.3.3 Order Updating of d
fmin .k; i / and wf .k; i / .............. 314
7.3.4 Order Updating of Prediction Errors ..................... 315
7.4 Time-Updating Equations .......................................... 317
7.4.1 Time Updating for Prediction Coefficients............... 317
7.4.2 Time Updating for ı.k; i /................................. 319
7.4.3 Order Updating for .k; i /................................ 321
7.5 Joint-Process Estimation ........................................... 324
7.6 Time Recursions of the Least-Squares Error ...................... 329
7.7 Normalized Lattice RLS Algorithm................................ 330
7.7.1 Basic Order Recursions ................................... 331
7.7.2 Feedforward Filtering ..................................... 333
7.8 Error-Feedback Lattice RLS Algorithm ........................... 336
7.8.1 Recursive Formulas for the Reflection Coefficients ..... 336
7.9 Lattice RLS Algorithm Based on A Priori Errors ................. 337
7.10 Quantization Effects ................................................ 339
7.11 Concluding Remarks................................................ 344
7.12 Problems ............................................................ 344
References.................................................................... 347
8 Fast Transversal RLS Algorithms ........................................ 349
8.1 Introduction ......................................................... 349
8.2 Recursive Least-Squares Prediction................................ 350
8.2.1 Forward Prediction Relations............................. 350
8.2.2 Backward Prediction Relations........................... 352
8.3 Joint-Process Estimation ........................................... 353
8.4 Stabilized Fast Transversal RLS Algorithm ....................... 355
8.5 Concluding Remarks................................................ 361
8.6 Problems ............................................................ 362
References.................................................................... 365
9 QR-Decomposition-Based RLS Filters ................................... 367
9.1 Introduction ......................................................... 367
Contents xix
9.2 Triangularization Using QR-Decomposition ...................... 367
9.2.1 Initialization Process ...................................... 369
9.2.2 Input Data Matrix Triangularization ..................... 370
9.2.3 QR-Decomposition RLS Algorithm...................... 377
9.3 Systolic Array Implementation ..................................... 380
9.4 Some Implementation Issues ....................................... 388
9.5 Fast QR-RLS Algorithm............................................ 390
9.5.1 Backward Prediction Problem ............................ 392
9.5.2 Forward Prediction Problem .............................. 394
9.6 Conclusions and Further Reading .................................. 402
9.7 Problems ............................................................ 403
References.................................................................... 408
10 Adaptive IIR Filters ........................................................ 411
10.1 Introduction ......................................................... 411
10.2 Output-Error IIR Filters ............................................ 412
10.3 General Derivative Implementation ................................ 416
10.4 Adaptive Algorithms................................................ 419
10.4.1 Recursive Least-Squares Algorithm...................... 419
10.4.2 The Gauss–Newton Algorithm ........................... 420
10.4.3 Gradient-Based Algorithm................................ 422
10.5 Alternative Adaptive Filter Structures ............................. 423
10.5.1 Cascade Form ............................................. 423
10.5.2 Lattice Structure ........................................... 425
10.5.3 Parallel Form .............................................. 432
10.5.4 Frequency-Domain Parallel Structure .................... 433
10.6 Mean-Square Error Surface ........................................ 442
10.7 Influence of the Filter Structure on the MSE Surface ............. 449
10.8 Alternative Error Formulations..................................... 451
10.8.1 Equation Error Formulation .............................. 451
10.8.2 The Steiglitz–McBride Method........................... 455
10.9 Conclusion .......................................................... 461
10.10 Problems ............................................................ 461
References.................................................................... 464
11 Nonlinear Adaptive Filtering .............................................. 467
11.1 Introduction ......................................................... 467
11.2 The Volterra Series Algorithm ..................................... 468
11.2.1 LMS Volterra Filter ....................................... 470
11.2.2 RLS Volterra Filter ........................................ 474
11.3 Adaptive Bilinear Filters............................................ 480
11.4 MLP Algorithm ..................................................... 484
11.5 RBF Algorithm ..................................................... 489
11.6 Conclusion .......................................................... 495
11.7 Problems ............................................................ 497
References.................................................................... 498
xx Contents
12 Subband Adaptive Filters.................................................. 501
12.1 Introduction ......................................................... 501
12.2 Multirate Systems................................................... 502
12.2.1 Decimation and Interpolation............................. 502
12.3 Filter Banks ......................................................... 505
12.3.1 Two-Band Perfect Reconstruction Filter Banks ......... 509
12.3.2 Analysis of Two-Band Filter Banks ...................... 510
12.3.3 Analysis of M-Band Filter Banks........................ 511
12.3.4 Hierarchical M-Band Filter Banks....................... 511
12.3.5 Cosine-Modulated Filter Banks .......................... 512
12.3.6 Block Representation ..................................... 513
12.4 Subband Adaptive Filters........................................... 514
12.4.1 Subband Identification .................................... 517
12.4.2 Two-Band Identification .................................. 518
12.4.3 Closed-Loop Structure .................................... 519
12.5 Cross-Filters Elimination ........................................... 523
12.5.1 Fractional Delays.......................................... 526
12.6 Delayless Subband Adaptive Filtering ............................. 529
12.6.1 Computational Complexity ............................... 536
12.7 Frequency-Domain Adaptive Filtering............................. 537
12.8 Conclusion .......................................................... 545
12.9 Problems ............................................................ 546
References.................................................................... 548
13 Blind Adaptive Filtering ................................................... 551
13.1 Introduction ......................................................... 551
13.2 Constant-Modulus Related Algorithms............................ 553
13.2.1 Godard Algorithm......................................... 553
13.2.2 Constant-Modulus Algorithm ............................ 554
13.2.3 Sato Algorithm ............................................ 555
13.2.4 Error Surface of CMA .................................... 556
13.3 Affine Projection CM Algorithm................................... 562
13.4 Blind SIMO Equalizers............................................. 568
13.4.1 Identification Conditions.................................. 572
13.5 SIMO-CMA Equalizer.............................................. 573
13.6 Concluding Remarks................................................ 579
13.7 Problems ............................................................ 579
References.................................................................... 582
14 Complex Differentiation ................................................... 585
14.1 Introduction ......................................................... 585
14.2 The Complex Wiener Solution ..................................... 585
14.3 Derivation of the Complex LMS Algorithm ....................... 589
14.4 Useful Results....................................................... 589
References.................................................................... 590
Contents xxi
15 Quantization Effects in the LMS Algorithm............................. 591
15.1 Introduction ......................................................... 591
15.2 Error Description.................................................... 591
15.3 Error Models for Fixed-Point Arithmetic .......................... 593
15.4 Coefficient-Error-Vector Covariance Matrix ...................... 594
15.5 Algorithm Stop ...................................................... 596
15.6 Mean-Square Error.................................................. 597
15.7 Floating-Point Arithmetic Implementation ........................ 598
15.8 Floating-Point Quantization Errors in LMS Algorithm ........... 600
References.................................................................... 603
16 Quantization Effects in the RLS Algorithm ............................. 605
16.1 Introduction ......................................................... 605
16.2 Error Description.................................................... 605
16.3 Error Models for Fixed-Point Arithmetic .......................... 607
16.4 Coefficient-Error-Vector Covariance Matrix ...................... 609
16.5 Algorithm Stop ...................................................... 612
16.6 Mean-Square Error.................................................. 613
16.7 Fixed-Point Implementation Issues ................................ 614
16.8 Floating-Point Arithmetic Implementation ........................ 615
16.9 Floating-Point Quantization Errors in RLS Algorithm ........... 617
References.................................................................... 621
17 Kalman Filters 623
17.1 Introduction ......................................................... 623
17.2 State–Space Model.................................................. 623
17.2.1 Simple Example ........................................... 624
17.3 Kalman Filtering .................................................... 626
17.4 Kalman Filter and RLS ............................................. 632
References.................................................................... 633
18 Analysis of Set-Membership Affine Projection Algorithm............. 635
18.1 Introduction ......................................................... 635
18.2 Probability of Update ............................................... 635
18.3 Misadjustment in the Simplified SM-AP Algorithm .............. 637
18.4 Transient Behavior .................................................. 638
18.5 Concluding Remarks................................................ 639
References.................................................................... 641
Index ............................................................................... 643