Tracking analysis of the NLMS algorithm in the presence of both random and cyclic nonstationarities

Muhammad Moinuddin*, Azzedine Zerguine

*Corresponding author for this work

Research output: Contribution to journalLetterpeer-review

19 Scopus citations


In this letter, tracking analysis of the normalized least mean square (NLMS) algorithm is carried out in the presence of two sources of nonstationarites: 1) carrier frequency offset between transmitter and receiver and 2) random variations in the environment. A novel approach to this analysis is carried out here using the concept of energy conservation. Close agreement between analytical analysis and simulation results is obtained. The results show that, unlike in the stationary case, the steady-state excess mse is not a monotonically increasing function of the step size. Moreover, the ability of the adaptive algorithm to track the variations in the environment is shown to degrade with increasing frequency offset.

Original languageEnglish
Pages (from-to)256-258
Number of pages3
JournalIEEE Signal Processing Letters
Issue number9
StatePublished - Sep 2003

Bibliographical note

Funding Information:
Manuscript received April 3, 2002; revised October 9, 2002. This work was supported by the King Fahd University of Petroleum and Minerals. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Yu-Hen Hu.


  • Normalized least mean square (NLMS) algorithm
  • Random and cyclic nonstationarities
  • Tracking analysis

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics


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