Regularization using Monte Carlo simulation to make optimal beamformers robust to system perturbations.

Design of optimal beamformers that withstand system perturbations such as channel mismatch, sensor position error, and pointing error has been a key issue in real-world applications of arrays. This paper aims to characterize the array performance in relation to the random perturbations from a statistical perspective. In the synthesis stage, directivity index and front-to-back ratio are employed as the performance measures for beamformer optimization. Filter coefficients of the arrays are determined using the least-squares and convex optimization approaches using the preceding performance measures. Next, Monte Carlo sampling are conducted to simulate the stochastic system perturbations following either uniform distribution or normal distribution. Statistics including the sample mean, maximum, minimum, and the maximum likelihood (ML) of the preceding performance measures are calculated. Three regularization criteria based on max-mean, max-min, and max-ML of performance measures are proposed for choosing regularization parameters used in beamformer optimization. The max-mean criterion was found most useful to determine either a simple constant or a frequency-dependent regularization parameter. To validate the proposed methods, experiments of beam patterns and automatic speech recognition test were conducted for directional and diffuse noise suppression problems, where optimal beamformers designed with the regularization parameter selected by the preceding procedures were utilized.