Beamforming techniques using microphone arrays

In this chapter, we provide the basic principles of beamforming and its application specifically for acoustic applications. As speech is a wideband signal, conventional narrowband beamformers are insufficient and hence we focus on wideband beamforming. For clarity, we begin by providing mathematical derivation of classical beamforming techniques for narrowband signals, leading to the delay-and-sum beamforming (DSB), after which we derive its wideband version-filter-and-sum beamforming. Taking into account practical applications, we further describe, in detail, the design, implementation, and limitations of the widely used nonadaptive and adaptive beamforming techniques including the super-directive (SD) beamformer, linearly constraint minimum variance (LCMV) beamformer, and minimum variance distortionless response (MVDR) beamformer in the frequency domain. Although the above methods can achieve significant improvement in speech quality, the beamformer output may still suffer from presence of residual noise and/or artifacts. These are mainly due to errors in the estimation of signal statistics, modeling, and environmental noise. To address this, postfiltering is generally employed and we describe a power spectrum density (PSD) estimation-based postfiltering technique to further reduce the residual noise.