Adaptive and hybrid Kronecker product beamforming for far-field speech signals

Abstract

This work presents a Kronecker product based methodology of frequency-domain beamforming of large sensor arrays for far-field broadband speech signals. The principal idea involves splitting up a given uniform linear array (ULA) into two smaller virtual ULAs (VULAs), using the Kronecker product. The linear system of the original ULA is bifurcated into two smaller linear systems of the VULAs. Henceforth, traditional adaptive beamformers such as the minimum-variance-distortionless-response (MVDR) beamformer may be obtained for each of the VULAs, using lesser data to estimate the statistics. The short-length beamformers, obtained from the VULAs, are finally combined by the Kronecker product to derive the full-length Kronecker product beamformer. Additionally, the VULAs allow fixed and adaptive beamforming to be implemented separately on each of them. As fixed beamformers do not employ statistical information, the Kronecker product hybrid beamformers reduce the original linear system to just a small linear system involving one VULA. Accordingly, hybrid beamformers may be implemented using traditional fixed beamformers, such as the delay-and-sum (DS) beamformer, on one VULA, and traditional adaptive beamformers, such as the MVDR, on the other. The proposed Kronecker product beamformers are observed to provide faster convergence and superior robustness with respect to the traditional beamformers.