Frequency-domain criterion for the speech distortion weighted multichannel Wiener filter for robust noise reduction

Recently, a generalized multi-microphone noise reduction scheme, referred to as the spatially pre-processed speech distortion weighted multichannel Wiener filter (SP-SDW-MWF), has been presented. This scheme consists of a fixed spatial pre-processor and a multichannel adaptive noise canceler (ANC) optimizing the SDW-MWF cost function. By taking speech distortion explicitly into account in the design criterion of the multichannel ANC, the SP-SDW-MWF adds robustness to the standard generalized sidelobe canceler (GSC). In this paper, we present a multichannel frequency-domain criterion for the SDW-MWF, from which several – existing and novel – adaptive frequency-domain algorithms can be derived. The main difference between these adaptive algorithms consists in the calculation of the step size matrix (constrained vs. unconstrained, block-structured vs. diagonal) used in the update formula for the multichannel adaptive filter. We investigate the noise reduction performance, the robustness and the tracking performance of these adaptive algorithms, using a perfect voice activity detection (VAD) mechanism and using an energy-based VAD. Using experimental results with a small-sized microphone array in a hearing aid, it is shown that the SP-SDW-MWF is more robust against signal model errors than the GSC, and that the block-structured step size matrix gives rise to a faster convergence and a better tracking performance than the diagonal step size matrix, only at a slightly higher computational cost.