Exact performance analysis of the ε-NLMS algorithm for colored circular Gaussian inputs

Tareq Al-Naffouri, Muhammad Moinuddin

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


This paper presents exact mean-square analysis of the 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 ∥ui2D 1(ε+∥ ui2D2 and using that to derive the first and second moments of such variables. These moments in turn completely characterize the mean square (MS) behavior of the ε -NLMS in explicit closed form expressions. Both transient and steady-state behavior are analyzed. Consequently, new explicit closed-form expressions for the mean-square-error (MSE) behavior are derived. Our simulations of the transient and steady-state behavior of the filter match the expressions obtained theoretically for various degrees of input correlation and for various values of ε.

Original languageEnglish (US)
Article number5483116
Pages (from-to)5080-5090
Number of pages11
JournalIEEE Transactions on Signal Processing
Issue number10
StatePublished - Oct 1 2010


  • Adaptive filters
  • Gaussian distributions
  • least mean square methods

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing


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