Title :
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
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;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2010.2090142
