Abstract
This paper presents exact mean-square analysis of the epsilon-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 parallel to u(i)parallel to(2)(D1)/(epsilon + parallel to u(i)parallel to(2)(D2)) 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 epsilon-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 epsilon.