Spherically Steerable Vector Differential Microphone Arrays

Differential microphone arrays (DMAs) use multiple omnidirectional microphones for synthesising higher-order microphone directivity patterns. In their most basic form, they can be used to obtain fixed-directivity or horizontally steerable beamformers that can satisfy certain constraints. We propose a vector differential microphone array (VDMA) which is frequency- and direction-invariantly steerable in three dimensions. The proposed design comprises pressure and particle velocity sensors positioned on a circular constellation in a plane and allows extracting the third-order spherical harmonic decomposition of the sound field. This decomposition can then be used to obtain spherically direction-invariant steered beams. Synthesis of a maximum directivity factor (MaxDF) directivity pattern is demonstrated. A closed-form expression for the proposed array's white noise gain (WNG) is derived. The robustness of the proposed design to noise is analysed.