Multichannel Wiener filter performance analysis in presence of mis-modeling

A randomly positioned microphone array is considered in this work. In many applications, the locations of the array elements are known up to a certain degree of random mismatch. We derive a novel statistical model for performance analysis of the multi-channel Wiener filter (MWF) beamformer under random mismatch in sensors location. We consider the scenario of one desired source and one interfering source arriving from the far-field and impinging on a linear array. A theoretical model for predicting the MWF mean squared error (MSE) for a given variation in sensors location is developed and verified by simulations. It is postulated that the probability density function (p.d.f) of the MSE of the MWF obeys Γ distribution. This claim is verified empirically by simulations.