Kronecker product beamforming with multiple differential microphone arrays

Differential microphone arrays (DMAs) are very attractive because of their high directional gains and frequency-invariant beampatterns. However, it is generally required that the array aperture is small, such that the DMA can respond to acoustic pressure differentials. In this paper, we propose a method to design differential beamformers with larger arrays consisting of multiple DMAs. In our study, conventional DMAs are considered as elementary units. The beamforming process consists of elementary differential beamformers and an additional beamformer that combines the multiple DMAs' outputs. The steering vector of the global array is written as a Kronecker product of the steering vectors of an elementary DMA unit and the virtual array constructed from all the DMA units. This enables to design the global beamformer as a Kronecker product of the differential beamformer and the beamformer that corresponds to the virtual array. With the proposed method, one can take advantage of the good properties of DMAs for the design of beamformers with any size of microphone array.