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

TL;DR

This paper introduces null-related measures for evaluating differential microphone arrays, analyzes the effects of signal quantization on their beampatterns, and validates findings through simulations and lab experiments.

Contribution

It proposes new null-related measures for DMAs, provides an analytical expression for quantized outputs, and studies quantization effects across different array orders and beampatterns.

Findings

Null depth and width effectively characterize null performance.

Quantization reduces null depth and broadens null width.

Lab experiments confirm simulation results.

Abstract

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.