Window beamformer for sparse concentric circular array

This work proposes a practical fixed beamformer for a sparse concentric circular array (CCA) of microphones. Firstly, a method is proposed which enables the reduction of the number of microphones in a CCA based on the optimal placement of the microphones to maximize the directivity-factor (DF). Thereafter, a beamformer is derived which strives to obtain a beamwidth that is not smaller than a desired target beamwidth (in both the elevation and azimuth) without neglecting the DF and white-noise-gain (WNG) across the speech spectrum. The proposed beamformer weights the microphones based on their corresponding ring number or radius, and further uses a Gaussian-window function to emphasize the microphones which are aligned with the direction-of-arrival of the signal. The results showcase the superiority of the proposed Gaussian-window (GW) beamformer over known solutions.