Comparative Analysis of Generalized Sidelobe Cancellation and Multi-Channel Linear Prediction for Speech Dereverberation and Noise Reduction

For blind speech dereverberation, two frameworks are commonly used: on the one hand, the multi-channel linear prediction (MCLP) framework, and on the other hand, data-dependent beamforming, e.g., the generalized sidelobe canceler (GSC) framework. The MCLP framework is designed to perform deconvolution and hence has gained increased prominence in blind speech dereverberation. The GSC framework is commonly used for noise reduction, but may be applied for dereverberation as well. In previous work, we have shown that for the noiseless case, MCLP and the GSC yield in theory mathematically equivalent results in terms of dereverberation. In this paper, we assume additional coherent as well as incoherent-noise components and formally analyze and compare both frameworks in terms of dereverberation and noise reduction performance. Both the theoretical analysis and time domain simulation results demonstrate that unlike the GSC, MCLP expectably shows limited performance in terms of noise reduction, while both perform equally well in terms of dereverberation, provided that the GSC blocking matrix achieves complete blocking of the early reverberant-speech component and sufficiently many microphones are available. In case of incomplete blocking, however, the GSC performs inferior to MCLP in terms of dereverberation, as shown in short-time Fourier transform domain simulations.