Experimental investigations on coprime microphone arrays for direction-of-arrival estimation

Abstract

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. This work implements two coprime microphone arrays with different lengths and sub-array spacings. Experimental beam patterns are shown to correspond with simulated results even at frequencies above and below the array’s design frequency. Side lobes in the directional pattern are inversely correlated with bandwidth of analyzed signals.