Abstract
Design of beamformers that withstand mismatch in channel characteristics (gain, phase and position) and pointing error (rotational) 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 these effects 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. Statistics including the mean, maximum, minimum and the maximum likelihood (ML) of performance measures (directivity index and white noise gain) are efficiently obtained via Monte-Carlo Simulation (MCS). 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 degrees of performance-robustness tradeoffs in the optimal beamformer design. © 2013 Acoustical Society of America.