Fast least mean M-estimate algorithms for robust adaptive filtering in impulse noise

Adaptive filters with suitable nonlinear devices are very effective in suppressing the adverse effect due to impulse noise. In a previous work, the authors have proposed a new class of nonlinear adaptive filters using the concept of robust statistics [1,2]. The robust M-estimator is used as the objective function, instead of the mean square errors, to suppress the impulse noise. The optimal coefficient vector for such nonlinear filter is governed by a normal equation which can be solved by a recursive least squares like algorithm with O(N2) arithmetic complexity, where N is the length of the adaptive filter. In this paper, we generalize the robust statistic concept to least mean square (LMS) and transform domain LMS algorithms. The new fast nonlinear adaptive filtering algorithms called the least mean M-estimate (LMM) and transform domain LMM (TLMM) algorithms are derived. Simulation results show that they are robust to impulsive noise in the desired and input signals with an arithmetic complexity of order O(N).

[1]  Seong Rag Kim,et al.  Adaptive robust impulse noise filtering , 1995, IEEE Trans. Signal Process..

[2]  Yuexian Zou,et al.  Robust statistics based adaptive filtering algorithms for impulsive noise suppression , 2000 .

[3]  Peter M. Clarkson,et al.  A class of order statistic LMS algorithms , 1992, IEEE Trans. Signal Process..

[4]  Tung-Sang Ng,et al.  A robust M-estimate adaptive filter for impulse noise suppression , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

[5]  Saeed Gazor,et al.  Selection of orthonormal transforms for improving the performance of the transform domain normalised LMS algorithm , 1992 .

[6]  Jae Chon Lee,et al.  Performance of transform-domain LMS adaptive digital filters , 1986, IEEE Trans. Acoust. Speech Signal Process..

[7]  John Law,et al.  Robust Statistics—The Approach Based on Influence Functions , 1986 .

[8]  Paul Petrus,et al.  Robust Huber adaptive filter , 1999, IEEE Trans. Signal Process..

[9]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[10]  Shin'ichi Koike.  Adaptive threshold nonlinear algorithm for adaptive filters with robustness against impulse noise , 1997, IEEE Trans. Signal Process..

[11]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[12]  Zou Yuexian,et al.  A robust M-estimate adaptive equaliser for impulse noise suppression , 1999 .

[13]  Simon Haykin,et al.  Adaptive filter theory (2nd ed.) , 1991 .

[14]  Werner A. Stahel,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[15]  E. Vittoz,et al.  An analytical MOS transistor model valid in all regions of operation and dedicated to low-voltage and low-current applications , 1995 .

[16]  M. Najim,et al.  Order statistic fast Kalman filter , 1996, 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96.

[17]  T. Ng,et al.  A recursive least M-estimate (RLM) adaptive filter for robust filtering in impulse noise , 2000, IEEE Signal Processing Letters.

[18]  Bernabé Linares-Barranco,et al.  A General Translinear Principle for Subthreshold MOS Transistors , 1999 .

[19]  Salvatore Pennisi,et al.  Dynamic biasing for true low-voltage CMOS class AB current-mode circuits , 2000 .

[20]  A. Peterson,et al.  Transform domain LMS algorithm , 1983 .

[21]  J. Weng,et al.  Adaptive nonlinear RLS algorithm for robust filtering in impulse noise , 1997, Proceedings of 1997 IEEE International Symposium on Circuits and Systems. Circuits and Systems in the Information Age ISCAS '97.

[22]  Kwabena Boahen,et al.  Translinear circuits in subthreshold MOS , 1996 .

[23]  W. K. Jenkins,et al.  The use of orthogonal transforms for improving performance of adaptive filters , 1989 .

[24]  J. Chambers,et al.  A robust mixed-norm adaptive filter algorithm , 1997, IEEE Signal Processing Letters.