Fast Adaptive Blind MMSE Equalizer for Multichannel FIR Systems

Abstract

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.