On the Design of Differential Kronecker Product Beamformers

In this paper, we present a generalized approach for differential microphone array (DMA) beamforming in the short-time Fourier transform (STFT) domain. We propose a multistage beamforming approach, which considers a Kronecker product (KP) decomposition of the global beamformer into two independent sub-beamformers. We derive differential KP beamformers according to different criteria and analyze their performances, which are tuned by three design parameters. These parameters allow a high beamforming design flexibility; in particular, non-differential or non-KP beamformers may be obtained as special cases. Depending on the selection of parameters, we demonstrate a preferable performance with the new approach with respect to the white noise gain and directivity factor measures. In addition, we consider the task of speech enhancement. We show that differential KP beamformers perform better than non-differential and non-KP beamformers in terms of the quality and intelligibility of their respective time-domain enhanced signals, particularly in moderately reverberant environments.