In this paper, a pair of analytic expressions describing the correlation functions due to spherically symmetric radial Gaussian and uniform volume near-field source position distributions are presented. An approximate spatial correlation function solution for a radial Gaussian source location distribution is derived and compared with the existing numerical methods. An exact solution for a uniform volume source location distribution is also derived and compared with existing numerical methods. The approximate radial Gaussian solution produces a result consistent with numerical methods for compact source location distributions. The uniform volume solution matches the expected behavior. Finally, the spatial correlation functions were used to design spatially robust beamformers for compact microphone arrays. Both of the spatial correlation function solutions lead to improved spatial robustness for the applications of signal enhancement and suppression.

In this paper, a method of adaptive noise suppression combining spatially robust fixed beamforming and the TRINICON blind source separation algorithm is presented. A multichannel sensor array is first processed using complementary fixed beamformers into maximum and minimum SINR channels. The channels form the inputs to a single 2×2 second-order statistics TRINICON-BSS system which adaptively compensates for imperfections of the fixed beamformer design relative to the acoustic scenario. It is demonstrated that integrating the TRINICON-BSS algorithm leads to improved SINR performance over the initial imperfect beamformer design, and achieves a performance comparable to a perfect MVDR beamformer.

This paper presents spatially robust far-field microphone beamformers and nullformers derived using the von Mises and von Mises-Fisher distributions to model the expected direction of arrival. Simple analytic expressions are presented for 2D and 3D far-field correlation functions and used to design spatially robust beamformers and nullformers. It is demonstrated that the spatially robust beamformers show a modest improvement in tolerating uncertainty in the target direction of arrival without incurring a significant penalty in terms of SINR performance compared with the MVDR beamformer. In addition, the spatially robust formulation shows significantly improved numerical robustness, indicating improved ability in tolerating intrinsic array errors.