A note on the design of frequency-invariant beamforming with uniform concentric circular microphone array

Compared to the frequency-invariant beamformer (FIB) with uniform circular microphone arrays, the FIB with uniform concentric circular microphone arrays (UCCAs) can mitigate the deep nulls problem in the white noise gain (WNG) and the directivity factor (DF). The WNG of the FIB-UCCAs can be improved by increasing the number of microphones. However, certain Jacobi-Anger expansion based methods for FIB-UCCAs utilize a linearly transformed version of the beamformer coefficients to optimize the WNG, which may result in severe beampattern distortion at high frequencies. In this paper, we present a beamformer design method that is based on the Jacobi-Anger expansion but optimizes the WNG directly. We analyze the effect of the truncation error of Jacobi-Anger expansion and demonstrate that the proposed method can effectively reduce the beampattern distortion. Computer simulations illustrate the performance advantages of the developed method in terms of the DF and WNG.