On the performance of widely linear quaternion based MVDR beamformer for an acoustic vector sensor

Widely linear model has recently been used for signal processing applications due to its ability to achieve better performance than conventional linear filtering for non-circular complex random variables (CRVs) and improper quaternion random variables (QRVs). In this paper, we study the time-domain widely linear quaternion model based minimum variance distortionless response beamformer (WL-QMVDR) for a single acoustic vector sensor (AVS) and analyze its performance in general through the use of beampatterns. We verify by simulation results that the estimated output of the WL-QMVDR is identical to the conventional linear model based MVDR beamformer when applied to an AVS in the non-reverberant and ideal sensor response scenario.