Universal criteria for blind deconvolution

Abstract

We present necessary and sufficient conditions for blind equalization/deconvolution (without observing the input) of an unknown, possible non-minimum phase linear time invariant system (channel). Based on that, we propose a family of optimization criteria and prove that their solution correspond to the desired response. These criteria, and the associated gradient-search algorithms, involve the computation of high order cumulants. The proposed criteria are universal in the sense that they do not impose any restrictions on the probability distrbution of the input symbols. We also address the problem of additive noise in the system and show that in several important cases, e.g. when the additive noise is Gaussian, the proposed criteria are unaffected.