Extraction of desired speech signals in multiple-speaker reverberant noisy environments

In many practical environments we wish to extract several desired speech signals, which are contaminated by non-stationary and stationary interfering signals. The desired signals may also be subject to distortion imposed by the acoustic room impulse response (RIR). In this chapter, a linearly constrained minimum variance (LCMV) beamformer is designed for extracting the desired signals from multi-microphone measurements. The beamformer satisfies two sets of linear constraints. One set is dedicated to maintaining the desired signals, while the other set is chosen to mitigate both the stationary and non-stationary interferences. Unlike classical beamformers, which approximate the RIRs as delay-only filters, we take into account the entire RIR [or its respective acoustic transfer function (ATF)]. We show that the relative transfer functions (RTFs), which relate the speech sources and the microphones, and a basis for the interference subspace suffice for constructing the beamformer. Additionally, in the case of one desired speech signal, we compare the proposed LCMV beamformer and the minimum variance distortionless response (MVDR) beamformer. These algorithms differ in their treatment of the interference sources. A comprehensive experimental study in both simulated and real environments demonstrates the performance of the proposed beamformer. Particularly, it is shown that the LCMV beamformer outperforms the MVDR beamformer provided that the acoustic environment is time-invariant.