Adaptive beamforming and postfiltering

In this chapter, we explore many of the basic concepts of array processing with an emphasis on adaptive beamforming for speech enhancement applications. We begin in Sect. 47.1 by formulating the problem of microphone array in a noisy and reverberant environment. In Sect. 47.2, we derive the frequency-domain linearly constrained minimum-variance (LCMV) beamformer, and its generalized sidelobe canceller (GSC) variant. The GSC components are explored in Sect. 47.3, and several commonly used special cases of these blocks are presented. As the GSC structure necessitates an estimation of the speech related acoustical transfer functions (ATFs), several alternative system identification methods are addressed in Sect. 47.4. Beamformers often suffer from sensitivity to signal mismatch. We analyze this phenomenon in Sect. 47.5 and explore several cures to this problem. Although the GSC beamformer yields a significant improvement in speech quality, when the noise field is spatially incoherent or diffuse, the noise reduction is insufficient and additional postfiltering is normally required. In Sect. 47.6, we present multi-microphone postfilters, based on either minimum mean-squared error (MMSE) or log-spectral amplitude estimate criteria. An interesting relation between the GSC and the Wiener filter is derived in this Section as well. In Sect. 47.7, we analyze the performance of the transfer-function GSC (TF-GSC), and in Sect. 47.8 demonstrate the advantage of multichannel postfiltering over single-channel postfiltering in nonstationary noise conditions.