Exact tracking analysis of the ε-NLMS algorithm for circular complex correlated Gaussian input

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

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

This work presents exact tracking analysis of the E-normalized least mean square (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∥D12][ε+∥u i∥D22]-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 ε-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 ε.

Original languageEnglish (US)
Title of host publication2010 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010
Pages225-230
Number of pages6
DOIs
StatePublished - 2011
Externally publishedYes
Event10th IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010 - Luxor, Egypt
Duration: Dec 15 2010Dec 18 2010

Other

Other10th IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2010
CountryEgypt
CityLuxor
Period12/15/1012/18/10

Keywords

  • Adaptive algorithms
  • Indefinite quadratic forms
  • Tracking performance

ASJC Scopus subject areas

  • Information Systems
  • Signal Processing

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