Clock skew invariant beamforming

Abstract

This thesis is focused on Wireless Acoustic Sensor Networks (WASNs) used for beamforming in a speech enhancement task. Since each node in a WASN has its own clock, clock offsets and clock skews between the nodes are inevitable. Clock offsets and clock skew can be detrimental to the beamformer performance. In this thesis we focus on the effect of clock skew on the beamformer performance. Existing methods for clock skew compensation for the speech enhancement application do this explicitly. In this thesis we investigate the possibility to formulate the beamformer such that explicit clock skew compensation is not necessary. Instead, we propose an algorithm for implicit clock skew compensation, which takes advantage of the Generalized Eigenvalue Decomposition (GEVD) to construct beamformers (e.g. Minimum Variance Distortionless Response (MVDR)), recently proposed in the literature. Using the GEVD, no explicit compensation has to be applied to the received data. Compared to the state-of-the-art, where clock skew estimation/compensation algorithms are used, this reduces the computational complexity for beamformer processing. The algorithm depends on exact knowledge of the noisy correlation matrix across the microphones. In practice, this matrix is unknown and estimation will reduce the performance of the proposed algorithm. We therefore quantify the error made in the estimation of the correlation matrix using the standard Welch method and also look at a recursive smoothing based method for correlation matrix estimation. Compared to a selected state-of-the-art algorithm, the proposed algorithm shows similar or better performance using this recursive smoothing method. For future work on this subject, more study can be done on correlation matrix estimation methods, as these play a key role in clock skew invariant beamforming.