Simplified Maximum SNR Beamformers with Spatial Coherence Matrix Modeling

The maximum signal-to-noise ratio (SNR) beamformer is useful in a wide range of applications to enhance speech signals of interest and attenuate as much as possible the noise. But robust implementation of this beamformer is challenging in practical applications as it requires to know the signal and noise covariance matrices. This paper investigates how to simplify the beamformer for use in small-spacing microphone arrays. Indeed, with small-spacing arrays, a practical parametric model can be used to model the covariance matrix of the observations, which is closely related to the front-to-back ratio (FBR) in differential beamforming. With this parametric model, we derive two simplified maximum SNR beamformers, which depend on the signal power spectral density (PSD) only. We then propose an estimator based on Frobenius-norm minimization to estimate the PSD. Since PSDs are usually easier to estimate than covariance matrices, the developed beamformers have great advantage over its traditional counterparts in terms of implementation in practical systems. The performance of the developed beamformers are validated in a simulated classroom environment.