Theoretical noise reduction limits of the generalized sidelobe canceller (GSC) for speech enhancement

We present an analysis of the generalized sidelobe canceller (GSC). It can be shown that the theoretical limits of the noise reduction performance depend only on the auto- and cross-spectral densities of the input signals. Furthermore, we compute the limits of the noise reduction performance for the theoretically determined diffuse noise field, which is an approximation for reverberant rooms. Our results show that the GSC cannot reduce noise further than 1 dB. These results were verified by simulation of reverberant environments. Only in sound-proof rooms with a reverberation time less than 100 ms the GSC performs well.