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

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 (US)
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
Externally published	Yes

Keywords

Adaptive algorithms
indefinite quadratic forms
mean behavior
spherically symmetric random variables

ASJC Scopus subject areas

Signal Processing
Applied Mathematics
Electrical and Electronic Engineering

Access to Document

10.1109/LSP.2010.2090142

Cite this

@article{4bfb671e64f748858a53860e187f325d,

title = "Mean weight behavior of the NLMS algorithm for correlated Gaussian inputs",

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.",

keywords = "Adaptive algorithms, indefinite quadratic forms, mean behavior, spherically symmetric random variables",

author = "Al-Naffouri, {Tareq Y.} and Muhammad Moinuddin and Sohail, {Muhammad S.}",

year = "2011",

doi = "10.1109/LSP.2010.2090142",

language = "English (US)",

volume = "18",

pages = "7--10",

journal = "IEEE Signal Processing Letters",

issn = "1070-9908",

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

number = "1",

}

TY - JOUR

T1 - Mean weight behavior of the NLMS algorithm for correlated Gaussian inputs

AU - Al-Naffouri, Tareq Y.

AU - Moinuddin, Muhammad

AU - Sohail, Muhammad S.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Adaptive algorithms

KW - indefinite quadratic forms

KW - mean behavior

KW - spherically symmetric random variables

UR - http://www.scopus.com/inward/record.url?scp=78649400203&partnerID=8YFLogxK

U2 - 10.1109/LSP.2010.2090142

DO - 10.1109/LSP.2010.2090142

M3 - Article

AN - SCOPUS:78649400203

SN - 1070-9908

VL - 18

SP - 7

EP - 10

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

IS - 1

M1 - 5613147

ER -

Mean weight behavior of the NLMS algorithm for correlated Gaussian inputs

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this