Beamfield analysis for statistically described planar microphone arrays

An analysis of Delay and Sum beamforming using microphone arrays with two-dimensional stochastic geometry in an office environment is carried out with two metrics proposed to rate the performance of these arrays: main lobe width (MLW) and peak-to-sidelobe ratio (PSR). Geometries with irregular microphone placements use a dispersion measure analogous to aperture and centroid to indicate array center relative to focal point. Sets of stochastic arrays are generated though Monte Carlo simulations and their performance is evaluated using the proposed metrics for varying number of microphones, sound source frequency, centroid location, and dispersion and compared to rectangular arrays. Performance results show increasing the number of microphones in a stochastic geometry increases the average PSR by 3 dB per doubling of microphones but remains one standard deviation below regular array performance while MLW remains relatively constant and close to that of the regular arrays. Increasing target frequency reduced MLW for both stochastic and regular geometries. Both types of arrays lost PSR while regular arrays were 5-10 dB superior. For increasing centroid displacement regular arrays display similar or inferior performance in PSR by as much as 5 dB versus the random arrays and mostly similar performance in MLW. Increasing the array dispersion reduces both the MLW and PSR, where the MLW for the stochastic geometries is on par with the corresponding regular geometries and the PSR is on the order of 5 to 10 dB below the regular arrays.