Blind Deconvolution of Linear Systems with Multilevel Nonstationary Inputs

Abstract

A method is proposed to deal with the problem of blind deconvolution of a special non-Gaussian linear process, in which the input to the linear system is a real- or complex-valued multilevel random sequence that satisfies certain regularity conditions. The gist of the method is to apply a linear filter to the observed process and adjust the filter until a multilevel output is obtained. It is shown that the deconvolution problem can be solved (with only scale/rotation and shift ambiguities) if the output sequence of the filter contains a subsequence that converges weakly to a multilevel random variable. A cost function is proposed so that any minimizer of the cost function provides a solution to the deconvolution problem. Moreover, when the process is parametric, it is shown that a consistent estimator of the parameter can be obtained by minimizing an empirical criterion. The estimation accuracy is shown to depend on the tail behavior of the inverse system, which in many cases decays exponentially as the sample size grows. Special consideration is given to applications in the equalization of digital communications systems.