On the Design of Square Differential Microphone Arrays with a Multistage Structure

This paper studies the problem of designing square differential microphone arrays (SDMAs). It presents a multistage approach, which first divides an SDMA composed of M ² microphones into (M − 1) ² subarrays with each subarray being a 2 × 2 square array formed by four adjacent microphones. Then, differential beamforming is performed with each subarray in the first-stage. The first-stage differential beamformers’ outputs are subsequently used as the inputs of the second stage to form (M − 2) ² subarrays and a second-stage differential beamforming is then performed. Continuing this process till the (M −1)th stage, we obtain the final output of the SDMA. The SDMA designed in such a multistage structure has two important properties. First, the global weighting matrix is equal to the two dimensional convolution of weighting matrices from the first stage to the last one. Second, the global beampattern is equal to the product of beampatterns from all stages. Consequently, we can combine different kinds of beamformers in different stages and have better control of the performance metrics.