Exact performance analysis of the ε-NLMS algorithm for colored circular Gaussian inputs

Authors:
Tareq Y. Al-Naffouri;Muhammad Moinuddin
Affiliations:
Electrical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia;Electrical and Electronics Engineering Department, Hafr Al-Batin Community College, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
Venue:
IEEE Transactions on Signal Processing
Year:
2010

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Abstract

This paper presents exact mean-square analysis of the -NLMS algorithm for circular complex correlated Gaussian input. The analysis is based on the derivation of a closed form expression for the cumulative distribution function (CDF) of random variables of the form ∥ui∥2D1/(ε + ∥ui∥2D2) and using that to derive the first and second moments of such variables. These moments in turn completely characterize the mean square (MS) behavior of the ε-NLMS in explicit closed form expressions. Both transient and steady-state behavior are analyzed. Consequently, new explicit closed-form expressions for the mean-square-error (MSE) behavior are derived. Our simulations of the transient and steady-state behavior of the filter match the expressions obtained theoretically for various degrees of input correlation and for various values of ε.