Exact Performance Analysis of the ε-NLMS Algorithm for Colored Circular Gaussian Inputs

被引：18

作者：

Al-Naffouri, Tareq Y. ^{[1
]}

Moinuddin, Muhammad ^{[2
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Elect Engn, Dhahran 31261, Saudi Arabia

[2] King Fahd Univ Petr & Minerals, Dept Elect & Elect Engn, Hafr Al Batin Community Coll, Dhahran 31261, Saudi Arabia

来源：

IEEE TRANSACTIONS ON SIGNAL PROCESSING | 2010年 / 58卷 / 10期

关键词：

Adaptive filters; Gaussian distributions; least mean square methods; LMS; CONVERGENCE; BEHAVIOR;

D O I：

10.1109/TSP.2010.2052359

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

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.

引用

页码：5080 / 5090

页数：11

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