Open Access

Analysis of the Sign Regressor Least Mean Fourth Adaptive Algorithm

  • Mohammed Mujahid Ulla Faiz1,
  • Azzedine Zerguine1Email author and
  • Abdelmalek Zidouri1
EURASIP Journal on Advances in Signal Processing20112011:373205

Received: 25 June 2010

Accepted: 5 January 2011

Published: 16 January 2011


A novel algorithm, called the signed regressor least mean fourth (SRLMF) adaptive algorithm, that reduces the computational cost and complexity while maintaining good performance is presented. Expressions are derived for the steady-state excess-mean-square error (EMSE) of the SRLMF algorithm in a stationary environment. A sufficient condition for the convergence in the mean of the SRLMF algorithm is derived. Also, expressions are obtained for the tracking EMSE of the SRLMF algorithm in a nonstationary environment, and consequently an optimum value of the step-size is obtained. Moreover, the weighted variance relation has been extended in order to derive expressions for the mean-square error (MSE) and the mean-square deviation (MSD) of the proposed algorithm during the transient phase. Computer simulations are carried out to corroborate the theoretical findings. It is shown that there is a good match between the theoretical and simulated results. It is also shown that the SRLMF algorithm has no performance degradation when compared with the least mean fourth (LMF) algorithm. The results in this study emphasize the usefulness of this algorithm in applications requiring reduced implementation costs for which the LMF algorithm is too complex.


Computational CostQuantum InformationVariance RelationGood MatchPerformance Degradation

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Authors’ Affiliations

Electrical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia


© Mohammed Mujahid Ulla Faiz et al. 2011

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.