Mean Weight Behavior of the NLMS Algorithm for Correlated Gaussian Inputs

Author

Al-Naffouri, Tareq Y. ; Moinuddin, Muhammad ; Sohai, Muhammad S.

Author_Institution

Electr. Eng. Dept., King Fahd Univ. of Pet. & Miner., Dhahran, Saudi Arabia

Volume

18

Issue

1

fYear

2011

Firstpage

7

Lastpage

10

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

correlation methods; least mean squares methods; NLMS algorithm; circularly correlated Gaussian input; cumulative density function; mean weight behavior; normalized least mean squares adaptive algorithm; normalized moments; quadratic forms; spherically symmetric random variables; Algorithm design and analysis; Convergence; Correlation; Estimation error; Mathematical model; Random variables; Symmetric matrices; Adaptive algorithms; indefinite quadratic forms; mean behavior; spherically symmetric random variables;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2010.2090142

Filename

5613147