A flexible high directivity beamformer with spherical microphone arrays.

The maximum directivity (MD) beamformer with spherical microphone arrays has many salient features in processing broadband acoustic and speech signals while suppressing noise and reverberation; but it is sensitive to sensors' self-noise and mismatch among these sensors. One effective way to deal with this sensitivity is by increasing the number of microphones, thereby improving the so-called white noise gain (WNG), but this increase may lead to many other design issues in terms of cost, array aperture, and possibly other performance degradation. This paper is tackling this sensitivity problem and presents a flexible high directivity (HD) beamforming algorithm. By approximating the ideal directivity pattern and the beamformer's beampattern with spherical harmonic series, the relationship between the two is obtained. This relationship is subsequently used to deduce a flexible HD beamformer, which can improve the WNG while achieving a directivity factor (DF) between the DF of an Nth-order MD beamformer and that of an (N-1)th-order MD one. Also derived is the analytical link between the DF and a tuning parameter and the link between the WNG and this parameter. Based on these links, one can easily determine the optimal value of the tuning parameter once the value of the DF or the WNG is specified.