Mean weight behavior of the NLMS algorithm for correlated Gaussian inputs

Tareq Y. Al-Naffouri; Muhammad Moinuddin; Muhammad S. Sohail

doi:10.1109/LSP.2010.2090142

Mean weight behavior of the NLMS algorithm for correlated Gaussian inputs

Tareq Y. Al-Naffouri, Muhammad Moinuddin, Muhammad S. Sohail

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

This letter presents a novel approach for evaluating the mean behavior of the well known normalized least mean squares (NLMS) adaptive algorithm for a circularly correlated Gaussian input. The mean analysis of the NLMS algorithm requires the calculation of some normalized moments of the input. This is done by first expressing these moments in terms of ratios of quadratic forms of spherically symmetric random variables and finding the cumulative density function (CDF) of these variables. The CDF is then used to calculate the required moments. As a result, we obtain explicit expressions for the mean behavior of the NLMS algorithm.

Original language	English
Article number	5613147
Pages (from-to)	7-10
Number of pages	4
Journal	IEEE Signal Processing Letters
Volume	18
Issue number	1
DOIs	https://doi.org/10.1109/LSP.2010.2090142
State	Published - 2011

Bibliographical note

Funding Information:
Manuscript received August 23, 2010; revised October 19, 2010; accepted October 19, 2010. Date of publication October 28, 2010; date of current version November 22, 2010. This work was supported by King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Ricardo Merched.

Keywords

Adaptive algorithms
indefinite quadratic forms
mean behavior
spherically symmetric random variables

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering
Applied Mathematics

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10.1109/LSP.2010.2090142

Cite this

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abstract = "This letter presents a novel approach for evaluating the mean behavior of the well known normalized least mean squares (NLMS) adaptive algorithm for a circularly correlated Gaussian input. The mean analysis of the NLMS algorithm requires the calculation of some normalized moments of the input. This is done by first expressing these moments in terms of ratios of quadratic forms of spherically symmetric random variables and finding the cumulative density function (CDF) of these variables. The CDF is then used to calculate the required moments. As a result, we obtain explicit expressions for the mean behavior of the NLMS algorithm.",

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Mean weight behavior of the NLMS algorithm for correlated Gaussian inputs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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