An Improved Solution to the Frequency-Invariant Beamforming with Concentric Circular Microphone Arrays

Frequency-invariant beamforming with circular microphone arrays (CMAs) has drawn a significant amount of attention for its steering flexibility and high directivity. However, frequency-invariant beam-forming with CMAs often suffers from the so-called null problem, which is caused by the zeros of the Bessel functions; then, concentric CMAs (CCMAs) are used to deal with this problem. While frequency-invariant beamforming with CCMAs can mitigate the null problem, the beampattern is still suffering from distortion due to s-patial aliasing at high frequencies. In this paper, we find that the spatial aliasing problem is caused by higher-order circular harmonics. To deal with this problem, we take the aliasing harmonics into account and approximate the beampattern with a higher truncation order of the Jacobi-Anger expansion than required. Then, the beam-forming filter is determined by minimizing the errors between the desired directivity pattern and the approximated one. Simulation results show that the developed method can mitigate the distortion of the beampattern caused by spatial aliasing.