Fast Adaptive Blind MMSE Equalizer for Multichannel FIR Systems

  • Ibrahim KachaEmail author
  • Karim Abed-Meraim
  • Adel Belouchrani
Open Access
Research Article
Part of the following topical collections:
  1. Multisensor Processing for Signal Extraction and Applications


We propose a new blind minimum mean square error (MMSE) equalization algorithm of noisy multichannel finite impulse response (FIR) systems, that relies only on second-order statistics. The proposed algorithm offers two important advantages: a low computational complexity and a relative robustness against channel order overestimation errors. Exploiting the fact that the columns of the equalizer matrix filter belong both to the signal subspace and to the kernel of truncated data covariance matrix, the proposed algorithm achieves blindly a direct estimation of the zero-delay MMSE equalizer parameters. We develop a two-step procedure to further improve the performance gain and control the equalization delay. An efficient fast adaptive implementation of our equalizer, based on the projection approximation and the shift invariance property of temporal data covariance matrix, is proposed for reducing the computational complexity from Open image in new window to Open image in new window , where Open image in new window is the number of emitted signals, Open image in new window the data vector length, and Open image in new window the dimension of the signal subspace. We then derive a statistical performance analysis to compare the equalization performance with that of the optimal MMSE equalizer. Finally, simulation results are provided to illustrate the effectiveness of the proposed blind equalization algorithm.


Minimum Mean Square Error Finite Impulse Response Signal Subspace Equalization Algorithm Shift Invariance 


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Copyright information

© Ibrahim Kacha et al. 2006

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.

Authors and Affiliations

  • Ibrahim Kacha
    • 1
    • 2
    Email author
  • Karim Abed-Meraim
    • 2
  • Adel Belouchrani
    • 1
  1. 1.Département d'ÉlectroniqueÉcole Nationale Polytechnique (ENP)AlgiersAlgeria
  2. 2.Département Traitement du Signal et de l'ImageÉcole Nationale Supérieure des Télécommunications (ENST)ParisFrance

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