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.

This thesis investigates the semi-blind channel estimation in uplink (UL) of Orthogonal Frequency Division Multiple Access (OFDMA) systems based on subspace decomposition. We exploit the orthogonality between signal subspace and noise subspace induced by virtual carriers (VCs) and cyclic prefix (CP) and the property of that the exclusive sub-carriers set is assigned to each user to estimate and identify the channels for each user individually. In OFDMA systems, when some users don¡¦t communicate with base station, the sub-carriers of non-active user provide extra redundancy for channel estimate to enhance the accuracy of channel estimation. Furthermore, the sufficient channel identifiability condition is developed. Furthermore, a novel scheme, called as virtual carriers recovery (VCR) scheme, is proposed to improve the performance of the subspace-based channel estimation method. It suppresses the noise interference by recovering the VCs to zeros at receiver. The simulation results illustrate that the enhancement of VCR scheme is particularly apparent for the partially loaded OFDMA system at low signal to noise ratio (SNR). In addition, the VCR scheme increases the convergence rate of the subspace-base semi-blind channel estimation.