The impact of sensor mismatch errors on the robustness of circular directional differential microphone arrays

Circular directional differential microphone arrays (CDDMAs) are composed of directional microphones, and the mismatch error of the microphones may lead to a significant degradation in array performance. The effects of the gain and phase mismatch errors of microphones on the mainlobe directivity of first-order and second-order CDDMAs are analyzed theoretically in this paper. The theoretical results are verified by simulation. The results indicate that, for the first-order CDDMAs, similar to the first-order circular differential microphone arrays (CDMAs) which are composed of omnidirectional microphones, the gain errors of directional microphones do not alter the mainlobe direction of the beampattern. However, unlike the CDMAs with omnidirectional microphones, the phase errors of the CDDMAs with directional microphones also do not change the mainlobe direction of the beampattern. For the second-order CDDMAs, both gain and phase errors can cause deviations in the mainlobe direction or even mainlobe orientation reversal. Nevertheless, the CDDMAs exhibit better robustness than that of the CDMAs in terms of beampattern, directivity factor, white noise gain and front-to-back ratio, especially in the low and middle frequency ranges.