Title :
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
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 [∥ui∥(D1)2][ϵ+∥ui∥(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;
Conference_Titel :
Signal Processing and Information Technology (ISSPIT), 2010 IEEE International Symposium on
Conference_Location :
Luxor
Print_ISBN :
978-1-4244-9992-2
DOI :
10.1109/ISSPIT.2010.5711782
