Convergence Behavior of NLMS Algorithm for Gaussian Inputs: Solutions Using Generalized Abelian Integral Functions and Step Size Selection

Authors:
S. C. Chan;Y. Zhou
Affiliations:
Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hongkong;Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hongkong
Venue:
Journal of Signal Processing Systems
Year:
2010

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Abstract

This paper studies the mean and mean square convergence behaviors of the normalized least mean square (NLMS) algorithm with Gaussian inputs and additive white Gaussian noise. Using the Price's theorem and the framework proposed by Bershad in IEEE Transactions on Acoustics, Speech, and Signal Processing (1986, 1987), new expressions for the excess mean square error, stability bound and decoupled difference equations describing the mean and mean square convergence behaviors of the NLMS algorithm using the generalized Abelian integral functions are derived. These new expressions which closely resemble those of the LMS algorithm allow us to interpret the convergence performance of the NLMS algorithm in Gaussian environment. The theoretical analysis is in good agreement with the computer simulation results and it also gives new insight into step size selection.