Mimo-ar Blind Source Separation for Gmm-distributed and Finite Alphabet Signals

In this work, two methods for blind separation of independent sources from the output of a convolutive multi-dimensional system are presented. The proposed methods assume a multiple-input multiple-output (MIMO) system, in which a multi-dimensional auto-regressive (AR) model relates the input and the output signals. The proposed algorithms exploit non-Gaussianity of the independent sources by modeling their distribution using the Gaussian mixture model (GMM). The first method considers a more general model for the input signals and it can be applied to problems with arbitrary input signals, such as speech, bio-medical and communication signals. In the second method, additional prior information regarding the input signals statistics is assumed. This method is useful for MIMO communication channel estimation where the input signal constellation is known. In these methods, the sensors distribution parameters and the separation matrix are estimated via the expectation-maximization (EM) and the generalized EM (GEM) algorithms for GMM parameter estimation. The resulted solution is an extension of an existing technique for single-input single-output (SISO) channel estimation. In addition, for Gaussian-distributed sources, the solution for state transition matrix estimation reduces to the well known Yule-Walker equations for MIMO-AR models. For the noiseless scenario, the second proposed method generalizes an existing blind method for flat-fading channel estimation with known finite alphabet (FA). The performances of the two convolutive blind source separation (BSS) problems are evaluated and compared to existing BSS techniques, via simulations of synthetic, audio and communication signals. The results show good performances of the proposed meth-iii ods in terms of signal-to-interference ratio (SIR), channel impulse response, and mean square error (MSE) of the multi-dimensional AR parameters estimate. It is demonstrated that the proposed algorithm outperforms the well-known multi-dimensional Yule-Walker equations for AR parameter estimation in terms of MSE. In the considered simulations for the second method, it is shown that the obtained symbol error rate (SER) is very close to the SER of the optimal algorithm which assumes perfect channel state information (CSI). iv Acknowledgment I am deeply indebted to my advisor, Dr. Joseph Tabrikian, for his guidance, instruction, assistance, and especially his patience and constant support. Without his help, this work would not be possible.