On mainlobe orientation of circular differential microphone array in the presence of sensor imperfections

The impact of sensor imperfections on the mainlobe orientation of the first-and second-order Circular Differential Microphone Array（CDMA） applicable to arbitrary number of array elements is theoretically investigated.It is revealed that the microphone phase mismatches can cause the mainlobe orientation reversal phenomenon of the first-order circular CDMA,which is the main factor affecting the mainlobe orientation.For the second-order CDMA,the microphone phase and gain mismatches can lead to the mainlobe orientation reversal and serious orientation deviation,which leads to the serious deterioration of the array directivity factor,and especially the effect is more remarkable in lower frequencies.Then,the conditions on the design parameters of the first-and second-order CDMA are derived to ensure correct mainlobe orientation,and on this basis,the microphone imperfections tolerance analysis is performed.The analysis results show that with the increase of the number of array elements,the tolerance increases,and the sensitivity of the CDMA to microphone imperfections is decreased accordingly.