Beampattern null characterization in planar differential microphone arrays: Analytical modeling and experiment results

Planar differential microphone arrays (PDMAs) offer flexible beam steering with frequency-invariant beampatterns within compact array geometries. Formation of deep and well-defined beampattern nulls are crucial for effective suppression of interfering sources in applications, such as hearing-aids, rotor-noise mitigation in drones and unmanned aerial vehicles, and hand-free voice communication. While performance measures, such as white-noise gain and directivity factor, assess noise robustness and global spatial selectivity, they do not explicitly quantify the depth and angular extent of these nulls. To address this, we first investigated null-related measures, namely, null-depth (ND) and null-width for different beampatterns of a first-order PDMA configuration. Second, the paper presents a study on signal quantization effects across different PDMA beampatterns by deriving an analytical expression for the quantized beampattern and ND. ND invariance with respect to steering angle is demonstrated, and its dependence on temporal frequency and inter-sensor spacing is characterized. Third, this work reports the achievement of a measured ND of –61.93 dB for a first-order planar cardioid. The experiment results provide proof-of-concept evidence for the analytical framework and demonstrate practical effectiveness of PDMA in suppressing interference. Key experimental considerations required to achieve such sharp and well-defined null are also discussed.