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.

Solutions for frequency-invariant or constant-beamwidth beamforming with concentric circular arrays (CCAs) generally control only the azimuth-beampattern. This work introduces a beamforming methodology, which instead of designing a fixed beamwidth across the spectrum, maximizes the directivity-factor under the constraint that the beamwidth is greater than or equal to a pre-defined target-beamwidth, in both the elevation and the azimuth. The principal idea lies in dynamically weighting the microphones of the CCA based on two factors - (i) their corresponding ring number or radius, and (ii) their alignment with the signal-path. The parameters controlling the weights are determined using a modified gradient-descent algorithm. Experimental results show the flexibility and advantage of the proposed methodology over state-of-the-art methods.