Multichannel Eigenspace Beamforming in a Reverberant Noisy Environment With Multiple Interfering Speech Signals

In many practical environments we wish to extract several desired speech signals, which are contaminated by nonstationary and stationary interfering signals. The desired signals may also be subject to distortion imposed by the acoustic room impulse responses (RIRs). In this paper, a linearly constrained minimum variance (LCMV) beamformer is designed for extracting the desired signals from multimicrophone 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 nonstationary 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)]. The LCMV beamformer is then reformulated in a generalized sidelobe canceler (GSC) structure, consisting of a fixed beamformer (FBF), blocking matrix (BM), and adaptive noise canceler (ANC). It is shown that for spatially white noise field, the beamformer reduces to a FBF, satisfying the constraint sets, without power minimization. It is shown that the application of the adaptive ANC contributes to interference reduction, but only when the constraint sets are not completely satisfied. We show that relative transfer functions (RTFs), which relate the desired speech sources and the microphones, and a basis for the interference subspace suffice for constructing the beamformer. The RTFs are estimated by applying the generalized eigenvalue decomposition (GEVD) procedure to the power spectral density (PSD) matrices of the received signals and the stationary noise. A basis for the interference subspace is estimated by collecting eigenvectors, calculated in segments where nonstationary interfering sources are active and the desired sources are inactive. The rank of the basis is then reduced by the application of the orthogonal triangular decomposition (QRD). This procedure relaxes the common requirement for nonoverlapping activity periods of the interference sources. A comprehensive experimental study in both simulated and real environments demonstrates the performance of the proposed beamformer.