GEVD Based Speech and Noise Correlation Matrix Estimation for Multichannel Wiener Filter Based Noise Reduction

In a single speech source noise reduction scenario, the frequency domain correlation matrix of the speech signal is often assumed to be a rank-l matrix. In multichannel Wiener filter (MWF) based noise reduction, this assumption may be used to define an optimization criterion to estimate the positive definite speech correlation matrix together with the noise correlation matrix, from sample `speech+noise' and `noise-only' correlation matrices. The estimated correlation matrices then define the MWF. In generalized eigenvalue decomposition (GEVD) based MWF, this optimization criterion involves a prewhitening with the sample `noise-only' correlation matrix, which in particular leads to a compact expression for the MWF. However, a more accurate form would include a prewhitening with the estimated noise correlation matrix instead of with the sample `noise-only' correlation matrix. Unfortunately this leads to a more difficult optimization problem, where the prewhitening indeed involves one of the optimization variables. In this paper, it is demonstrated that the modified optimization criterion, remarkably, leads to only minor modifications in the estimated correlation matrices and eventually the same MWF, which justifies the use of the original optimization criterion as a simpler substitute.