Exact Tracking Analysis of the ∈-NLMS algorithm for circular complex correlated Gaussian input

Author

Moinuddin, Muhammad ; Al-Naffouri, Tareq Y. ; Sohail, Muhammad S.

Author_Institution

Hafr Al-Batin Community Coll., King Fahd Univ. of Pet. & Miner., Dhahran, Saudi Arabia

fYear

2010

fDate

15-18 Dec. 2010

Firstpage

225

Lastpage

230

Abstract

This work presents exact tracking analysis of the ∈-normalized least mean square (∈-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∥_(D1)²][ϵ+∥u_i∥_(D2)²]^-1. The CDF is then used to derive the first and second moments of these variables. These moments in turn completely characterize the tracking performance of the ∈-NLMS algorithm in explicit closed form expressions. Consequently, new explicit closed-form expressions for the steady state tracking excess mean square error and optimum step size are derived. The simulation results of the tracking behavior of the filter match the expressions obtained theoretically for various degrees of input correlation and for various values of ∈.

Keywords

Gaussian processes; correlation methods; higher order statistics; least mean squares methods; random processes; target tracking; ∈-NLMS algorithm; ∈-normalized least mean square algorithm; CDF; circular complex correlated gaussian input; cumulative distribution function; exact tracking analysis; random variable; steady state tracking; Gold; Variable speed drives; Adaptive algorithms; indefinite quadratic forms; tracking performance;

fLanguage

English

Publisher

ieee

Conference_Titel

Signal Processing and Information Technology (ISSPIT), 2010 IEEE International Symposium on

Conference_Location

Luxor

Print_ISBN

978-1-4244-9992-2

Type

conf

DOI

10.1109/ISSPIT.2010.5711782

Filename

5711782