On optimal multi-channel mean-squared error estimators for speech enhancement

Abstract—In this letter we present discrete Fourier transform (DFT) domain minimum mean-squared error (MMSE) estimators for multichannel noise reduction. The estimators are derived assuming that the clean speech magnitude DFT coefficients are generalized-Gamma distributed. We show that for Gaussian distributed noise DFT coefficients, the optimal filtering approach consists of a concatenation of a minimum variance distortion-less response (MVDR) beamformer followed by well-known single-channel MMSE estimators. The multichannel Wiener filter follows as a special case of the presented MSE estimators and is in general suboptimal. For non-Gaussian distributed noise DFT coefficients the resulting spatial filter is in general nonlinear with respect to the noisy microphone signals and cannot be decomposed into an MVDR beamformer and a post-filter. Index Terms—MMSE, multichannel, noise reduction. I