Room acoustics investigations of beamforming performance using coprime linear microphone arrays

Abstract

In this work beam patterns are simulated for a range of single frequencies, as well as for arbitrary bands of frequencies. Three coprime microphone arrays are built with different lengths and sub-array spacings. Two different techniques are explored for sub-array data processing and combination. Experimental beam patterns are shown to correspond with simulated results even at frequencies other than the array's design frequency. Beam width and side lobe locations are shown to correspond to the derived values. Side lobes in the directional pattern are mitigated by increasing bandwidth of analyzed signals. Accurate single-source direction of arrival (DOA) estimation is shown to be possible in free field and reverberant conditions. DOA estimation is also implemented for two simultaneous noise sources in the free field condition. Room reflections can be resolved in the reverberant condition, provided adequate reduction of side lobes.

Linear microphone arrays are powerful tools for determining the direction of a sound source. Traditionally, uniform linear arrays (ULA) have inter-element spacing of half of the wavelength in question. This produces the narrowest possible beam without introducing grating lobes -- a form of aliasing governed by the spatial Nyquist theorem. Grating lobes are often undesirable because they make direction of arrival indistinguishable among their passband angles. Exploiting coprime number theory however, an array can be arranged sparsely with fewer total elements, exceeding the aforementioned spatial sampling limit separation. Two sparse ULA sub-arrays with coprime number of elements, when nested properly, each produce narrow grating lobes that overlap with one another exactly in just one direction. By combining the sub-array outputs it is possible to retain the shared beam while mostly canceling the other superfluous grating lobes.