Optimal beamformer designed for robustness against channel mismatch based on Monte Carlo Simulation

Abstract

Design of beamformers that withstand mismatch in channel characteristics of gain, phase, and position has been a key issue in array signal processing. These mismatch factors are random in nature and generally intractable by deterministic approaches. This paper examines the effects of channel mismatch on beamformer performance from a statistical perspective. The aim of this work is twofold: analysis and synthesis. In the analysis phase, the mismatch factors of microphone characteristics are assumed to be random variables following either uniform or Gaussian distribution. In the light of the Monte-Carlo Simulation (MCS), statistics including the mean, maximum, minimum, and the probability density function (pdf) of Directivity Factor (DF) can be efficiently obtained with random sampling. This provides useful information for choosing performance measures in the next synthesis phase. Optimal parameters of superdirective array designed using least squares (LS) and convex optimization (CVX) are determined based on the preceding performance measures. Simulation results have shown that the proposed statistical approach with different performance measures provided various performance-robustness tradeoffs in terms of parameter range for optimal beamformers.