Acoustic beamforming array design using an iterative microphone removal method

A well-designed acoustic beamforming array aims to simultaneously minimise the Maximum Sidelobe Level (MSL) and Main LobeWidth (MLW) within a desired acoustic frequency range, yet these properties tend to be mutually exclusive. This paper describes an iterative microphone removal method. By starting from a large initial array stencil, the microphone within the array that results in the smallest product of frequency-averaged MLW and MSL of the point spread function is identified and removed. This process is then repeated until a predetermined desired number of microphones is reached. Using the cross-spectral beamforming algorithm, several 841 and 961-channel equi-and-non-equispaced grid arrays are reduced to unique 48-channel arrays. The reduction method is implemented in two ways, i.e., one-by-one microphone removal and an accelerated procedure that removes several microphones per iteration, where the removed number of microphones decreases in an exponential manner with increasing iterations. The reduced arrays are compared against several logarithmic spiral and randomised 48-channel pattern arrays using a non-dimensional metric, evaluated as the product of the MSL normalised by main lobe magnitude, and the ratio of the MLW area to the total scanning grid area. The frequency range of investigation is 2000 Hz to 8000 Hz to replicate typical conditions in small scale anechoic facilities. The array reduction methods reveal improved array designs according to the aforementioned metric.