Title: Theoretical Analysis of Quality of Conventional Beamforming for Phased Microphone Arrays

Abstract: A theoretical study is performed to analyze the directional response of different types of microphone array designs. 1-D (linear) and 2-D (planar) microphone array types are considered, and the delay and sum beamforming and conventional beamforming techniques are employed to localize the sound source. A non-dimensional parameter, G, is characterized to simplify and standardize the rejection performance of both 1-D and 2-D microphone arrays as a function of array geometry and sound source parameters. This parameter G is then used to determine an improved design of a 2-D microphone array for far-field sound localization. One such design, termed the Equi-area array is introduced and analyzed in detail. The design is shown to have an advantageous rejection performance compared to other conventionally used 2-D planar microphone arrays.