On the Design of Flexible Kronecker Product Beamformers with Linear Microphone Arrays

This paper proposes a method for the design of flexible Kronecker product beamformers based on the decomposition of the steering vector of a physical array as a Kronecker product of steering vectors of two smaller virtual arrays. With this decomposition, the global beamforming filter is designed by optimizing the two sub-beamformers in a cascaded manner, which can offer much flexibility to control the performance of beamforming or control the compromise between different, conflicted performance measures. In comparison with a recently developed method that restricts the number of microphones of the given physical array to a multiplication of two integers, each corresponding to the number of sensors of one virtual array, the approach in this work decomposes the physical array in such a way that the sensors in the two virtual arrays may share positions and the number of microphones of the physical array can be any positive integer. Simulations demonstrate the properties of the proposed approach.