Abstract
Blind deconvolution (equalization) is a signal processing procedure to restore a source signal, distorted by an unknown linear time-invariant (LTI) channel, from channel's output measurements. A class of inverse filter criteria using two cumulants has been proposed by Wiggins, Donoho, Shalvi and Weinstein, Tugnait, and Chi and Wu for blind deconvolution of nonminimum-phase LTI channels when source signal is non-Gaussian and measurement noise is Gaussian. The equalization capability of the class of inverse filter criteria was proved, based on the assumptions of infinite signal-to-noise ratio (SNR) and channels without zeros on the unit circle, but closed-form solutions for the optimum deconvolution filter (inverse filter) have not been found so far.This thesis analyzes the performance of the class of inverse filter criteria for finite SNR with channels allowed to have zeros on the unit circle. The analytic results include several noticeable characteristics of the associated deconvolution filter, a connection of the deconvolution filter with the well-known nonblind minimum mean square error (MMSE) equalizer, and a computationally efficient iterative algorithm for obtaining the theoretical deconvolution filter. Moreover, the analytic results further lead to a novel noise-insensitive approach to blind channel estimation.On the other hand, highly related to the class of inverse filter criteria, the Shalvi and Weinstein's iterative super-exponential algorithm is improved in performance as well as convergence rate.