On equivariant adaptation in blind deconvolution

In blind source separation, equivariance has been shown to be a useful property for designing simple and efficient iterative algorithms for the task. In this paper, we explore iterative equivariant algorithms for block-based blind deconvolution, in which the deconvolved symbol sequence is found by successively filtering the estimated symbol sequence. A procedure based on maximum likelihood estimation of the source symbol sequence is given, and its performance is studied through simulations. In addition, we show that in the absence of truncation effects, the well-known Shalvi-Weinstein blind deconvolution algorithm is an iterative equivariant blind deconvolution procedure.