Fast Adaptive Blind MMSE Equalizer for Multichannel FIR Systems
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Fast Adaptive Blind MMSE Equalizer for Multichannel FIR Systems Ibrahim Kacha,1, 2 Karim Abed-Meraim,2 and Adel Belouchrani1 ´ ´ d’Electronique, Ecole Nationale Polytechnique (ENP), 10 avenue Hassen Badi El-Harrach, 16200 Algiers, Algeria ´ Traitement du Signal et de l’Image, Ecole Nationale Sup´erieure des T´el´ecommunications (ENST), 37-39 rue Dareau, 75014 Paris, France
1 D´ epartement 2 D´ epartement
Received 30 December 2005; Revised 14 June 2006; Accepted 22 June 2006 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 O(n3 ) to O(qnd), where q is the number of emitted signals, n the data vector length, and d 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. Copyright © 2006 Ibrahim Kacha et al. 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.
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INTRODUCTION
1.1. Blind equalization An elementary problem in the area of digital communications is that of intersymbol interference (ISI). ISI results from linear amplitude and phase dispersion in the transmission channel, mainly due to multipath propagation. To achieve reliable communications, channel equalization is necessary to deal with ISI. Conventional nonblind equalization algorithms require training sequence or a priori knowledge of the channel [1]. In the case of wireless communications these solutions are often inappropriate, since a training sequence is usually sent periodically, thus the effective channel throughput is considerably reduced. It follows that the blind and semiblind equalization of transmission channels represent a suitable alternative to traditional equalization, because they do not fully rely on training sequence or a priori channel knowledge. In the first contributions [2, 3], blind identification/equalization (BIE) schemes were based, implicitly or explicitly on higher-
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