On the Design of Low-Rank Differential Beamformers with Nonuniform Linear Microphone Arrays

Kronecker product beamforming is an effective technique for designing beamformers with nonuniform linear arrays (NULAs). However, current techniques are restricted to NULAs with specific configurations, where the steering vector of the array is represented as a Kronecker product of steering vectors from smaller virtual arrays. This paper overcomes these constraints by proposing a novel approach to designing Kronecker product beamformers for NULAs from a low-rank perspective. Our approach involves decomposing the NULA into overlapping subarrays and organizing the sensor signals from these subarrays into a matrix. We then apply filters to both sides of this matrix to produce an output, which is then converted into a low-rank beamforming process. This method is highly adaptable and can be utilized for NULAs with any number of microphones.