A robust algorithm for adaptive FIR filtering and its performance analysis with additive contaminated-Gaussian noise

Abstruct- We introduce a steepest descent linear adaptive algorithm, the proportion-sign algorithm (PSA), lo make the least mean square (LMS) algorithm robust to impulsive interference occurring in the desired response. Its performance analysis is presented when the signals are from zero-mean jlointly stationary Gaussian processes and the additive noise to the (desired response is from a zero-mean stationary contaminated-Gaussian (CG) process which is usually used to represent impulsive interference. Since a special case of the PSA becomes the LMS algorithm, the analysis of the LMS is also obtained as a by-product. By adding a minimal amount of computational complexity, thie PSA improves to some degree the convergence speed over the LMS algorithm without overly degrading the steady-state error performance for Gaussian noise. In addition, since the first derivative of its cost function with respect to estimation error is bounded, it has the properties of robustness to impulsive interference occurring in the desired response while the LMS algorithm is vulnerable to it. Computer simulations are used to demonstrate the validity of our analysis and the robustness of the PSA compared with the LMS algorithm.

[1]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[2]  Robert Price,et al.  A useful theorem for nonlinear devices having Gaussian inputs , 1958, IRE Trans. Inf. Theory.

[3]  B. Widrow,et al.  Stationary and nonstationary learning characteristics of the LMS adaptive filter , 1976, Proceedings of the IEEE.

[4]  K. Senne,et al.  Performance advantage of complex LMS for controlling narrow-band adaptive arrays , 1981 .

[5]  T. Claasen,et al.  Comparison of the convergence of two algorithms for adaptive FIR digital filters , 1981 .

[6]  D. Duttweiler.  Adaptive filter performance with nonlinearities in the correlation multiplier , 1982 .

[7]  N. Bershad,et al.  LMS adaptation with correlated data--A scalar example , 1984 .

[8]  Allen Gersho,et al.  Adaptive filtering with binary reinforcement , 1984, IEEE Trans. Inf. Theory.

[9]  Ehud Weinstein,et al.  Convergence analysis of LMS filters with uncorrelated Gaussian data , 1985, IEEE Trans. Acoust. Speech Signal Process..

[10]  C. P. Kwong,et al.  Dual Sign Algorithm for Adaptive Filtering , 1986, IEEE Trans. Commun..

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

[12]  V. J. Mathews,et al.  Improved convergence analysis of stochastic gradient adaptive filters using the sign algorithm , 1987, IEEE Trans. Acoust. Speech Signal Process..

[13]  R.-Y. Chen,et al.  On the optimum step size for the adaptive sign and LMS algorithms , 1990 .

[14]  Ioannis Pitas,et al.  Nonlinear Digital Filters - Principles and Applications , 1990, The Springer International Series in Engineering and Computer Science.

[15]  Sung Ho Cho,et al.  Tracking analysis of the sign algorithm in nonstationary environments , 1990, IEEE Trans. Acoust. Speech Signal Process..

[16]  V. John Mathews,et al.  Performance analysis of adaptive filters equipped with the dual sign algorithm , 1991, IEEE Trans. Signal Process..

[17]  Ioannis Pitas,et al.  Adaptive filters based on order statistics , 1991, IEEE Trans. Signal Process..

[18]  William A. Sethares,et al.  Adaptive algorithms with nonlinear data and error functions , 1992, IEEE Trans. Signal Process..

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

[20]  Philippe Salembier,et al.  Adaptive rank order based filters , 1992, Signal Process..

[21]  William A. Sethares,et al.  Performance characteristics of the median LMS adaptive filter , 1993, IEEE Trans. Signal Process..

[22]  I. Song,et al.  Performance analysis of the dual sign algorithm for additive contaminated-Gaussian noise , 1994, IEEE Signal Processing Letters.

[23]  Seung Chan Bang,et al.  Performance analysis of the dual sign algorithm with contaminated-Gaussian noise , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.