The focus of this thesis is on blind identification techniques for multi-input, multi-output (MIMO) systems. In this respect we study three problems: (1) The joint diagonalization problem. Joint diagonalization is an efficient tool for blind identification techniques for MIMO systems. In this thesis we discuss new adaptive joint orthogonal diagonalization algorithms based on optimization methods over the Stiefel manifold. (2) Blind identification of MIMO systems. We demonstrate that by using the second-oder statistics of the system outputs, by exploiting the non-stationarity of sources, and some mild conditions on the sources and the system, the impulse response of the MIMO system can be identified up to an inherent scaling and permutation ambiguity. An efficient two-step frequency domain algorithm for identifying the MIMO system then has been proposed. Numerical simulations verify the theoretical results and the performance of the new algorithm. (3) Real room blind source separation problem. The final part of the thesis focuses on the practical problem of blind source separation of mixed audio signals in a real room. The new proposed algorithm exploits the non-stationarity of audio signals to separate them from their mixtures recorded in a reverberant environment. This method has successfully been applied to real data acquired during extensive recording experiments done in different office rooms on the McMaster campus.
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