It is known that differential microphone arrays are sensitive to microphone mismatches. This paper studies the effects of microphone mismatches on the directivity factor (DF) of the first-order steerable differential array (FOSDA) whose response is constructed by a linear combination of monopole and two orthogonal dipoles via a small four-microphone array. In particular, the DF of the FOSDA is studied from two perspectives, i.e., a deterministic analysis for deterministic microphone gain/phase errors, and a worst-case analysis for uncertain microphone gain/phase errors. Based on the theoretical analysis, several interesting properties are revealed, which are helpful to better understand the robustness characteristics of the FOSDA. Moreover, by worst-case analysis, it provides a useful guidance for robust FOSDA design, i.e., how to determine array size and select microphones with required characteristics such that a desired DF value can be guaranteed. In addition, the effect of sensor self-noise on the DF of the FOSDA is also discussed.
['Xiaoguang Wu', 'Huawei Chen']
Directivity factors of the first-order steerable differential array with microphone mismatches: deterministic and worst-case analysis