Analysis of Null Related Beampattern Measures and Signal Quantization Effects for Linear Differential Microphone Arrays

A differential microphone array (DMA) offers enhanced capabilities to obtain sharp nulls at the cost of relatively broad peaks in the beam power pattern. This can be used for applications that require nullification or attenuation of interfering sources. To the best of our knowledge, the existing literature lacks measures that directly assess the efficacy of nulls, and null-related measures have not been investigated in the context of differential microphone arrays (DMAs). This paper offers new insights about the utility of DMAs by proposing measures that characterize the nulls in their beam power patterns. We investigate the performance of differential beamformers by presenting and evaluating null-related measures namely null depth (ND) and Null Width (NW) as a function of depth level relative to the beam power pattern maxima. A study of signal quantization effects due to data acquisition for 1st, 2nd and 3rd order linear DMAs and for different beampatterns i.e. dipole, cardioid, hypercardioid and supercardioid is presented. An analytical expression for the quantized beamformed output for any general $ N^{th} $ order DMA is formulated. Simulation results of the variation of ND with number of quantization bits and the variation of NW as a function of depth are also presented and inferences are drawn. Lab experiments are conducted in a fully anechoic room to support the simulation results. The measured beampattern exhibits a pronounced null depth, confirming the effectiveness of the experimental setup.