Sensor Imperfection Tolerance Analysis of Robust Linear Differential Microphone Arrays

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An $M$ th-order linear differential microphone array (LDMA) is conventionally designed by using a linear array of $M+1$ closely-spaced microphones. It is known that the conventional LDMAs suffer from the white noise amplification problem which may cause significant performance degradation in the presence of sensor imperfections. In order to resolve this, a more advanced solution has been proposed to employ more than $M+1$ microphones in the design of the LDMAs, which is shown to be effective against the white noise amplification and, hence, the resultant LDMAs are known as the robust LDMAs. Previous studies have shown that sensor imperfections can lead to dramatic performance degradation or even failure of the LDMAs due to the presence of the mainlobe orientation reversal (MOR) phenomenon. Therefore, avoiding the occurrence of the detrimental MOR phenomenon can serve as a minimum condition for the design of robust LDMAs in the presence of sensor imperfections. However, it is not yet quite clear how the sensor imperfections, such as microphone gain and phase mismatches, affect the robust LDMAs. Particularly in practical design, it will be of interest to know what the requirement is on the microphone imperfection tolerance for a given number of microphones, or alternatively, how many microphones should be used with a given microphone imperfection tolerance to guarantee no occurrence of the MOR phenomenon, which remains to be addressed. Motivated by the above, in this paper we first give an in-depth analysis of the impact of microphone imperfections on the mainlobe orientation of the robust LDMAs, and reveal how the MOR phenomenon occurs with the robust LDMAs. Then based on our theoretical foundation, the microphone imperfection tolerance analysis is performed, which provides a useful guidance when incorporating the influence of sensor imperfections into the practical design of robust LDMAs. Extensive numerical results are also presented to validate the effectiveness of our analysis.