Analysis of the power spectral deviation of the general transfer function GSC

In recent work, we considered a microphone array located in a reverberated room, where general transfer functions (TFs) relate the source signal and the microphones, for enhancing a speech signal contaminated by interference. It was shown that it is sufficient to use the ratio between the different TFs rather than the TFs themselves in order to implement the suggested algorithm. An unbiased estimate of the TFs ratios was obtained by exploiting the nonstationarity of the speech signal. In this correspondence, we present an analysis of a distortion indicator, namely power spectral density (PSD) deviation, imposed on the desired signal by our newly suggested transfer function generalized sidelobe canceller (TF-GSC) algorithm. It is well known that for speech signals, PSD deviation between the reconstructed signal and the original one is the main contribution for speech quality degradation. As we are mainly dealing with speech signals, we analyze the PSD deviation rather than the regular waveform distortion. The resulting expression depends on the TFs involved, the noise field, and the quality of estimation of the TF´s ratios. For the latter dependency, we provide an approximated analysis of estimation procedure that is based on the signal´s nanstationarity and explore its dependency on the actual speech signal and on the signal-to-noise ratio (SNR) level. The theoretical expression is then used to establish empirical evaluation of the PSD deviation for several TFs of interest, various noise fields, and a wide range of SNR levels. It is shown that only a minor amount of PSD deviation is imposed on the beamformer output. The analysis presented in this correspondence is in good agreement with the actual performance presented in the former TF-GSC paper.