Multivariate LP based MMSE-ZF equalizer design considerations, and application to multimicrophone dereverberation

The linear prediction algorithm estimates a zero-forcing (ZF) equalizer from the SIMO channel output's second order statistics. Linear prediction can be easily extended in the presence of an additive white noise, since the white noise variance can be easily identified and compensated for in the reverberant signal covariance matrix. However, the presence of the additive noise has so far not been considered for the design of the ZF equalizer, and the resulting equalizer is not optimal. In this paper, we consider two issues in the design of the LP-based equalizer in the presence of additive white noise. First, we investigate the effect of relative subchannel delay compensation on the output SNR. We show that such relative delay can reduce considerably the output SNR. Then, we optimize the transformation of the multivariate prediction filter to a longer equalizer filter using the SNR criterion. The optimization corresponds to MMSE-ZF design, and the filter length increase allows for the introduction of some equalization delay, that can also be optimized