Superdirective beamforming robust against microphone mismatch

Fixed superdirective beamformers using small-sized microphone arrays are known to be highly sensitive to errors in the assumed microphone array characteristics (gain, phase, position). This paper discusses the design of robust superdirective beamformers by taking into account the statistics of the microphone characteristics. Different design procedures are considered: applying a white noise gain constraint, trading off the mean noise and distortion energy, minimizing the mean deviation from the desired superdirective directivity pattern, and maximizing the mean or the worst case directivity factor. When computational complexity is not an issue, maximizing the mean or the worst case directivity factor is the preferred design procedure-In addition, it is shown how to determine a suitable parameter range for the other design procedures such that both a high directivity and a high level of robustness are obtained.