A unifying view of error nonlinearities in LMS adaptation

Tareq Y. Al-Naffouri; Azzedine Zerguine; Maamar Bettayeb

doi:10.1109/ICASSP.1998.681783

A unifying view of error nonlinearities in LMS adaptation

Tareq Y. Al-Naffouri, Azzedine Zerguine, Maamar Bettayeb

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Scopus citations

Abstract

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.

Original language	English (US)
Title of host publication	Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1697-1700
Number of pages	4
Volume	3
ISBN (Print)	0780344286, 9780780344280
DOIs	https://doi.org/10.1109/ICASSP.1998.681783
State	Published - 1998
Externally published	Yes
Event	1998 23rd IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998 - Seattle, WA, United States Duration: May 12 1998 → May 15 1998

Other

Other	1998 23rd IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998
Country	United States
City	Seattle, WA
Period	05/12/98 → 05/15/98

ASJC Scopus subject areas

Software
Signal Processing
Electrical and Electronic Engineering

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title = "A unifying view of error nonlinearities in LMS adaptation",

abstract = "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.",

author = "Al-Naffouri, {Tareq Y.} and Azzedine Zerguine and Maamar Bettayeb",

year = "1998",

doi = "10.1109/ICASSP.1998.681783",

language = "English (US)",

isbn = "0780344286",

volume = "3",

pages = "1697--1700",

booktitle = "Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

address = "United States",

note = "1998 23rd IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998 ; Conference date: 12-05-1998 Through 15-05-1998",

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Al-Naffouri, TY, Zerguine, A & Bettayeb, M 1998, A unifying view of error nonlinearities in LMS adaptation. in Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998. vol. 3, 681783, Institute of Electrical and Electronics Engineers Inc., pp. 1697-1700, 1998 23rd IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998, Seattle, WA, United States, 05/12/98. https://doi.org/10.1109/ICASSP.1998.681783

A unifying view of error nonlinearities in LMS adaptation. / Al-Naffouri, Tareq Y.; Zerguine, Azzedine; Bettayeb, Maamar.

Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998. Vol. 3 Institute of Electrical and Electronics Engineers Inc., 1998. p. 1697-1700 681783.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - A unifying view of error nonlinearities in LMS adaptation

AU - Al-Naffouri, Tareq Y.

AU - Zerguine, Azzedine

AU - Bettayeb, Maamar

PY - 1998

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N2 - 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.

AB - 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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DO - 10.1109/ICASSP.1998.681783

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BT - Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 1998

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ER -

A unifying view of error nonlinearities in LMS adaptation

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