Effect of Steering Vector Estimation on MVDR Beamformer for Noisy Speech Recognition

The minimum variance distortionless response (MV-DR) beamformer is a widely used beamforming technique that extracts sound components coming from a direction specified by a steering vector. In this paper, we present four different steering vector estimation methods and analyze their influence on the MVDR beamformer in speech recognition. The first one is based on the direction of arrival under the plane wave propagation assumption with the prior knowledge of microphone array geometry. The other three methods are based on the decomposition of the observed speech covariance matrix, including the covariance subtraction based method, the eigenvalue decomposition based method, and the generalized eigenvalue decomposition (GEVD) based method. We theoretically prove that the three decomposition based methods are equivalent under the narrowband approximation or after the rank -1 speech covariance matrix approximation. The speech recognition experiments conducted on the CHiME-3 dataset shows that the MVDR beamformer using GEVD-based steering vector estimation achieves the best performance, and word error rates can be further reduced with the rank -1 approximation.