Directivity Factors of the First-Order Steerable Differential Array With Microphone Mismatches: Deterministic and Worst-Case Analysis

Abstract

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.