Differential Kronecker Product Beamforming

Differential beamformers have attracted much interest over the past few decades. In this paper, we introduce differential Kronecker product beamformers that exploit the structure of the steering vector to perform beamforming differently from the well-known and studied conventional approach. We consider a class of microphone arrays that enable to decompose the steering vector as a Kronecker product of two steering vectors of smaller virtual arrays. In the proposed approach, instead of directly designing the differential beamformer, we break it down following the decomposition of the steering vector, and show how to derive differential beamformers using the Kronecker product formulation. As demonstrated, the Kronecker product decomposition facilitates further flexibility in the design of differential beamformers and in the tradeoff control between the directivity factor and the white noise gain.