A unifying view of error nonlinearities in LMS adaptation

T.Y. Al-Naffouri; A. Zerguine; M. Bettayeb; IEEE

doi:10.1109/ICASSP.1998.681783

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A unifying view of error nonlinearities in LMS adaptation

T.Y. Al-Naffouri, A. Zerguine, M. Bettayeb and IEEE

Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181), Vol.3, pp.1697-1700 vol.3

1998

DOI: https://doi.org/10.1109/ICASSP.1998.681783

Abstract

Adaptive filters

Additive noise

Algorithm design and analysis

Approximation algorithms

Computer errors

Density functional theory

Least squares approximation

Numerical stability

Physics

Robust stability

This paper presents a unifying view of various error nonlinearities that are used in least mean square (LMS) adaptation such as the least mean fourth (LMF) algorithm and its family and the least-mean mixed-norm algorithm. Specifically, it is shown that the LMS algorithm and its error-modified variants are approximations of two previously developed optimum nonlinearities which are expressed in terms of the additive noise probability density function (PDF). This is demonstrated through an approximation of the optimum nonlinearities by expanding the noise PDF in a Gram-Charlier series. Thus a link is established between intuitively proposed and theoretically justified variants of the LMS algorithm. The approximation has also a practical advantage in that it provides a trade-off between simplicity and more accurate realization of the optimum nonlinearities.

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Title: A unifying view of error nonlinearities in LMS adaptation
Creators - without role: T.Y. Al-Naffouri - Georgia Institute of Technology
A. Zerguine
M. Bettayeb
IEEE
Publication Details: Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181), Vol.3, pp.1697-1700 vol.3
Publisher: IEEE
Identifiers: 9935498208331
Academic Unit: King Abdulaziz University
Language: English
Resource Type: Conference proceeding