Affine-Projection-Like Adaptive-Filtering Algorithms Using Gradient-Based Step Size

A new class of affine-projection-like (APL) adaptive-filtering algorithms is proposed. The new algorithms are obtained by eliminating the constraint of forcing the a posteriori error vector to zero in the affine-projection algorithm proposed by Ozeki and Umeda. In this way, direct or indirect inversion of the input signal matrix is not required and, consequently, the amount of computation required per iteration can be reduced. In addition, as demonstrated by extensive simulation results, the proposed algorithms offer reduced steady-state misalignment in system-identification, channel-equalization, and acoustic-echo-cancelation applications. A mean-square-error analysis of the proposed APL algorithms is also carried out and its accuracy is verified by using simulation results in a system-identification application.

[1]  Andreas Antoniou,et al.  New Improved Recursive Least-Squares Adaptive-Filtering Algorithms , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Jacob Benesty,et al.  Regularization of the Affine Projection Algorithm , 2011, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  Bernard Widrow,et al.  Adaptive switching circuits , 1988 .

[4]  Dirk T. M. Slock,et al.  On the convergence behavior of the LMS and the normalized LMS algorithms , 1993, IEEE Trans. Signal Process..

[5]  Y. Nesterov.  Gradient methods for minimizing composite objective function , 2007 .

[6]  Kazuhiko Ozeki,et al.  An adaptive filtering algorithm using an orthogonal projection to an affine subspace and its properties , 1984 .

[7]  Ali H. Sayed,et al.  Mean-square performance of a family of affine projection algorithms , 2004, IEEE Transactions on Signal Processing.

[8]  Ali H. Sayed,et al.  Mean-square performance of data-reusing adaptive algorithms , 2005, IEEE Signal Processing Letters.

[9]  Tareq Y. Al-Naffouri,et al.  Transient analysis of data-normalized adaptive filters , 2003, IEEE Trans. Signal Process..

[10]  Jacob Benesty,et al.  Proportionate Adaptive Filters From a Basis Pursuit Perspective , 2010, IEEE Signal Processing Letters.

[11]  Paulo S. R. Diniz,et al.  Adaptive Filtering: Algorithms and Practical Implementation , 1997 .

[12]  Jacob Benesty,et al.  A Variable Step-Size Affine Projection Algorithm Designed for Acoustic Echo Cancellation , 2008, IEEE Transactions on Audio, Speech, and Language Processing.

[13]  Shirish Nagaraj,et al.  Set-membership filtering and a set-membership normalized LMS algorithm with an adaptive step size , 1998, IEEE Signal Processing Letters.

[14]  Paulo S. R. Diniz,et al.  Convergence Performance of the Simplified Set-Membership Affine Projection Algorithm , 2011, Circuits Syst. Signal Process..

[15]  Andreas Antoniou,et al.  A Family of Shrinkage Adaptive-Filtering Algorithms , 2013, IEEE Transactions on Signal Processing.

[16]  Jacob Benesty,et al.  A Nonparametric VSS NLMS Algorithm , 2006, IEEE Signal Processing Letters.

[17]  Weifeng Liu,et al.  Kernel Affine Projection Algorithms , 2008, EURASIP J. Adv. Signal Process..

[18]  Y. Nesterov.  A method for solving the convex programming problem with convergence rate O(1/k^2) , 1983 .

[19]  W. Kenneth Jenkins,et al.  Low-complexity data reusing methods in adaptive filtering , 2004, IEEE Transactions on Signal Processing.

[20]  Ali H. Sayed,et al.  Error-energy bounds for adaptive gradient algorithms , 1996, IEEE Trans. Signal Process..

[21]  Andreas Antoniou,et al.  A new quasi-Newton adaptive filtering algorithm , 1997 .

[22]  José Antonio Apolinário,et al.  Convergence analysis of the binormalized data-reusing LMS algorithm , 2000, IEEE Trans. Signal Process..

[23]  Ali H. Sayed,et al.  Fundamentals Of Adaptive Filtering , 2003 .

[24]  Ali H. Sayed,et al.  Variable step-size NLMS and affine projection algorithms , 2004, IEEE Signal Processing Letters.

[25]  P. Diniz,et al.  Set-membership affine projection algorithm , 2001, IEEE Signal Processing Letters.

[26]  Tokunbo Ogunfunmi,et al.  On the Convergence Behavior of the Affine Projection Algorithm for Adaptive Filters , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[27]  Andreas Antoniou,et al.  New constrained affine-projection adaptive-filtering algorithm , 2013, 2013 IEEE International Symposium on Circuits and Systems (ISCAS2013).

[28]  Steven G. Kratzer,et al.  The Partial-Rank Algorithm for Adaptive Beamforming , 1986, Optics & Photonics.

[29]  Chang Hee Lee,et al.  Scheduled-Step-Size Affine Projection Algorithm , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[30]  Ali H. Sayed,et al.  A unified approach to the steady-state and tracking analyses of adaptive filters , 2001, IEEE Trans. Signal Process..

[31]  Khaled A. Mayyas,et al.  A variable step-size affine projection algorithm , 2010, Digit. Signal Process..

[32]  Jacob Benesty,et al.  Variable Explicit Regularization in Affine Projection Algorithm: Robustness Issues and Optimal Choice , 2007, IEEE Transactions on Signal Processing.

[33]  Tareq Y. Al-Naffouri,et al.  Mean-square analysis of normalized leaky adaptive filters , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[34]  Stefan Werner,et al.  Set-membership binormalized data-reusing LMS algorithms , 2003, IEEE Trans. Signal Process..

[35]  A. A. Beex,et al.  Convergence behavior of affine projection algorithms , 2000, IEEE Trans. Signal Process..

[36]  T. Demeechai,et al.  OBA algorithm with a simplification and new optimal variable convergence factor , 1995 .

[37]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[38]  PooGyeon Park,et al.  An Affine Projection Algorithm Based on Reuse Time of Input Vectors , 2010, IEEE Signal Processing Letters.

[39]  Patrick Siarry,et al.  Optimization in signal and image processing , 2009 .

[40]  Michael Elad,et al.  L1-L2 Optimization in Signal and Image Processing , 2010, IEEE Signal Processing Magazine.

[41]  Tareq Y. Al-Naffouri,et al.  Transient analysis of adaptive filters with error nonlinearities , 2003, IEEE Trans. Signal Process..

[42]  Kwang-Hoon Kim,et al.  An Affine Projection Algorithm With Periodically Evolved Update Interval , 2011, IEEE Transactions on Circuits and Systems II: Express Briefs.

[43]  W. T. Federer,et al.  Stochastic Approximation and NonLinear Regression , 2003 .