A perspective on multichannel noise reduction in the time domain

Conventional multichannel noise reduction techniques are formulated by splitting the processed microphone observations into two terms: filtered noise-free speech and residual additive noise. The first term is treated as desired signal while the second is a nuisance. Then, the objective has typically been to reduce the nuisance while keeping the filtered speech as similar as possible to the clean speech. It turns out that this treatment of the overall filtered speech as the desired signal is inappropriate as will become clear soon. In this paper, we present a new study of the multichannel time-domain noise reduction filters. We decompose the noise-free microphone array observations into two components where the first is correlated with the target signal and perfectly coherent across the sensors while the second consists of residual interference. Then, well-known time-domain filters including the minimum variance distortionless response (MVDR), the space-time (ST) prediction, the maximum signal-to-noise ratio (SNR), the linearly constrained minimum variance (LCMV), the multichannel tradeoff, and Wiener filters are derived. Besides, the analytical performance evaluation of these time-domain filters is provided and new insights into their functioning are presented. Numerical results are finally given to corroborate our study.