Exact tracking analysis of the NLMS algorithm for correlated Gaussian inputs

Tareq Y. Al-Naffouri, Muhammad Moinuddin

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

Abstract

This work presents an exact tracking analysis of the Normalized Least Mean Square (NLMS) algorithm for circular complex correlated Gaussian inputs. Unlike the existing works, the analysis presented neither uses separation principle nor small step-size assumption. The approach is based on the derivation of a closed form expression for the cumulative distribution function (CDF) of random variables of the form (uD1 2)(uD2 2)-1 where u is a white Gaussian vector and D1 and D2 are diagonal matrices and using that to derive the first and second moments of such variables. These moments are then used to evaluate the tracking behavior of the NLMS algorithm in closed form. Thus, both the steady-state mean-square-error (MSE) and mean-square-deviation (MSD )tracking behaviors of the NLMS algorithm are evaluated. The analysis is also used to derive the optimum step-size that minimizes the excess MSE (EMSE). Simulations presented for the steady-state tracking behavior support the theoretical findings for a wide range of step-size and input correlation.

Original languageEnglish (US)
Title of host publication2013 Proceedings of the 21st European Signal Processing Conference, EUSIPCO 2013
PublisherEuropean Signal Processing Conference, EUSIPCO
ISBN (Print)9780992862602
StatePublished - 2013
Externally publishedYes
Event2013 21st European Signal Processing Conference, EUSIPCO 2013 - Marrakech, Morocco
Duration: Sep 9 2013Sep 13 2013

Other

Other2013 21st European Signal Processing Conference, EUSIPCO 2013
CountryMorocco
CityMarrakech
Period09/9/1309/13/13

Keywords

  • Adaptive filters
  • NLMS algorithm
  • Tracking analysis

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

Fingerprint

Dive into the research topics of 'Exact tracking analysis of the NLMS algorithm for correlated Gaussian inputs'. Together they form a unique fingerprint.

Cite this