Mean weight behavior of the NLMS algorithm for correlated Gaussian inputs

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

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


This letter presents a novel approach for evaluating the mean behavior of the well known normalized least mean squares (NLMS) adaptive algorithm for a circularly correlated Gaussian input. The mean analysis of the NLMS algorithm requires the calculation of some normalized moments of the input. This is done by first expressing these moments in terms of ratios of quadratic forms of spherically symmetric random variables and finding the cumulative density function (CDF) of these variables. The CDF is then used to calculate the required moments. As a result, we obtain explicit expressions for the mean behavior of the NLMS algorithm.

Original languageEnglish (US)
Article number5613147
Pages (from-to)7-10
Number of pages4
JournalIEEE Signal Processing Letters
Issue number1
StatePublished - Jan 1 2011


  • Adaptive algorithms
  • indefinite quadratic forms
  • mean behavior
  • spherically symmetric random variables

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing
  • Applied Mathematics


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