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A necessary and sufficient condition for blind deconvolution (without observing the input) of nonminimum-phase linear time-invariant systems (channels) is derived. Based on this condition, several optimization criteria are proposed, and their solution is shown to correspond to the desired response. These criteria involve the computation only of second- and fourth-order moments, implying a simple tap update procedure. The proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the (unobserved) input sequence. It is shown that in several important cases (e.g. when the additive noise is Gaussian), the proposed criteria are essentially unaffected.>
Shalvi et al. (Thu,) studied this question.