An insight into the parametric multichannel wiener formulation

Parametric Wiener formulation in speech applications provides an engineering trade-off between noise suppression and target signal distortion levels. However, the tuning parameter is typically difficult to tune as there is a lack of insight into this parameter. Thus far, there is no direct and simple relationship between the tuning parameter and the target distortion constrained Wiener filter. This paper aims to fill this blank by providing a detailed derivation on the upper bound of the tuner to provide further insights on its selection. It is shown that the tuning parameter is bounded by a function of the signal to noise ratio (SNR) and the number of microphones under incoherent and diffuse noise. Further, a simple recursive estimation method is proposed for the estimation of the target signal and noise covariance information.