An iterative microphone removal method for acoustic beamforming array design

This paper presents a beamforming array design method that uses a large array of microphones and systematically reduces it to a predetermined number of microphones. The microphone, while included in the array, that results in the smallest (defined as Phi in this paper) product of frequency-averaged Main Lobe Width (MLW) and Maximum Sidelobe Level (MSL) of the point spread function using the cross-spectral beamforming algorithm is identified and removed. The reduction method is implemented in two ways: 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. Multi-frequency array reductions, using 841 and 961-channel equi-and-non-equispaced grid initial arrays, are conducted over the frequency range of 2000 Hz-8000 Hz to replicate typical conditions in a small scale anechoic facility. These reduced arrays are compared against several logarithmic spiral and randomised pattern arrays and in most cases, reveal superior values of MSL, MLW and Phi. Single-frequency array reductions, using both 961 and 169-channel initial arrays, at the best-case frequencies for the logarithmic spirals, also display superior performance. Both the multi-and-single-frequency arrays can be used practically: the multi-frequency arrays possess an even performance across the simulated frequency range, whereas the single-frequency arrays possess excellent performance over narrowband frequency ranges and can be modified within an array stencil for each acoustic experiment. (C) 2018 Elsevier Ltd. All rights reserved.