A Time-domain Real-valued Generalized Wiener Filter for Multi-channel Neural Separation Systems

Frequency-domain beamformers have been successful in a wide range of multi-channel neural separation systems in the past years. However, the operations in conventional frequency-domain beamformers are typically independently-defined and complex-valued, which result in two drawbacks: the former does not fully utilize the advantage of end-to-end optimization, and the latter may introduce numerical instability during the training phase. Motivated by the recent success in end-to-end neural separation systems, in this paper we propose time-domain real-valued generalized Wiener filter (TD-GWF), a linear filter defined on a 2-D learnable real-valued signal transform. TD-GWF splits the transformed representation into groups and performs an minimum mean-square error (MMSE) estimation on all available channels on each of the groups. We show how TD-GWF can be connected to conventional filter-and-sum beamformers when certain signal transform and the number of groups are specified. Moreover, given the recent success in the sequential neural beamforming frameworks, we show how TD-GWF can be applied in such frameworks to perform iterative beamforming and separation to obtain an overall performance gain. Comprehensive experiment results show that TD-GWF performs consistently better than conventional frequency-domain beamformers in the sequential neural beamforming pipeline with various neural network architectures, microphone array scenarios, and task configurations.