This thesis addresses the blind signal separation (BSS) problem. The essence of the BSS problem is to recover a set of source signals from a group of sensor observations. These observations can be modeled as instantaneous or convolutive mixtures of the sources. Accordingly, the BSS problem is known as blind separation of instantaneously mixed signals or blind separation of convolutively mixed signals. In this thesis, we tackle both problems. For blind separation of instantaneously mixed signals, we first cast the separation problem as an optimization problem using mutual information based criterion, and solve it with an extended Newton's method on the Stiefel manifold. Then, for a special case in which the sources are constant modulus (CM) signals, we formulate the separation problem a constrained minimization problem utilizing the constant modulus property of the signal. Again, we solve it using the Newton's method on the Stiefel manifold. For the problem of blind separation of convolutively mixed signals, which is also known as blind deconvolution problem, we first propose a time domain method. We cast the separation problem as an optimization problem using a mutual information based criterion and solve it using a sequential quadratic programming (SQP) method. Then, we propose a set of higher-order statistics (HOS) based criteria for blind deconvolution. We also discuss the relationship of our proposed criteria and other HOS based criteria. We then propose a frequency domain HOS based blind channel identification approach. In this approach, we identify the channel frequency response by jointly diagonalizing a set of so called polyspectrnm matrices. Finally, we propose a second-order statistics (SOS) based method for blind channel identification. Assuming the channel inputs are cyclostationary signals, we identify the channel frequency response through the singular value decomposition (SVD) of a cyclic cross-spectrum based matrix. Numerical simulations are used throughout this thesis to compare our proposed methods with other methods from the literature and to demonstrate the validity and competitiveness of our proposed methods.

Doctor of Philosophy (PhD)