The estimation of power spectral densities is a critical step in many speech enhancement algorithms. The demand for multi-channel speech enhancement systems is high with applications in teleconferencing, cellular phones, and hearing aids. The first objective of the thesis is to develop a general multi-channel framework to solve for the diffuse noise power spectral densities whenever the spatial correlation or coherence matrix is pre-estimated and the number of speakers is less than the number of microphones. The second objective is to develop closed-form analytical solutions. The performance of the developed algorithms is evaluated with pre-existing algorithms using prescribed performance measures.

The estimation of power spectral densities is a critical step in many speech enhancement algorithms. The demand for multi-channel speech enhancement systems is high with applications in teleconferencing, cellular phones, and hearing aids. The first objective of the thesis is to develop a general multi-channel framework to solve for the diffuse noise power spectral densities whenever the spatial correlation or coherence matrix is pre-estimated and the number of speakers is less than the number of microphones. The second objective is to develop closed-form analytical solutions. The performance of the developed algorithms is evaluated with pre-existing algorithms using prescribed performance measures.