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

Tareq Y. Al-Naffouri; Muhammad Moinuddin

doi:10.1109/TSP.2010.2052359

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

Tareq Y. Al-Naffouri, Muhammad Moinuddin

Physical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

This paper presents exact mean-square analysis of the ε-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 ∥u_i∥²D ₁(ε+∥ u_i∥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.

Original language	English (US)
Article number	5483116
Pages (from-to)	5080-5090
Number of pages	11
Journal	IEEE Transactions on Signal Processing
Volume	58
Issue number	10
DOIs	https://doi.org/10.1109/TSP.2010.2052359
State	Published - Oct 2010

Keywords

Adaptive filters
Gaussian distributions
least mean square methods

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering

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10.1109/TSP.2010.2052359

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title = "Exact performance analysis of the ε-NLMS algorithm for colored circular Gaussian inputs",

abstract = "This paper presents exact mean-square analysis of the ε-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∥2D 1(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.",

keywords = "Adaptive filters, Gaussian distributions, least mean square methods",

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AU - Moinuddin, Muhammad

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N2 - This paper presents exact mean-square analysis of the ε-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∥2D 1(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.

AB - This paper presents exact mean-square analysis of the ε-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∥2D 1(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.

KW - Adaptive filters

KW - Gaussian distributions

KW - least mean square methods

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JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

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

Abstract

Keywords

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