A state-space approach to blind estimation of MIMO wireless channels

This dissertation focuses on blind channel estimation in wireless communications such that the estimated channel admits the minimum phase property. It assumes only the second order statistics of the transmitted signal at the receive side. Our proposed approach is based on the generalized spectral factorization because of the deficient normal rank for the power spectral density (PSD) function of the received signal. We will show the relationship between the generalized spectral factorization and inner-outer factorizations where the inner is square with smaller size. The inner-outer factorization is in turn related to the generalized Kalman filtering in which the dimension of the input noise processes is greater than the dimension of the output measurement and thus the covariance matrix is always singular. A dual problem is the generalized LQR control in which the dimension of the control input is smaller than the dimension of the controlled output and thus the weighting matrix on control signal is always singular. Iterative algorithms are proposed to obtain stabilizing solutions to algebraic Riccati equations (ARE) associated with the generalized Kalman filtering, LQR control, and spectral factorization. We will show the convergence of the proposed iterative algorithm that provides an effective algorithm for blind channel estimation. Examples are worked out to illustrate our proposed spectral factorization approach to blind channel estimation with comparisons to the existing method in the literature.