On Blind Equalization of Rank Deficient Nonlinear Channels

We consider the problem of blind equalization of nonlinear channels from the second-order statistics of the channel output. The channel model is linear in the parameters, with additive terms that are nonlinear functions of the transmitted symbols. All previous approaches assume that the corresponding channel matrix has full column rank, which ensures the existence of linear FIR zero forcing equalizers. We show that this assumption is not necessary, and that under certain circumstances linear FIR equalizers can be found despite the violation of this assumption. An important consequence of this fact is that equalization can be effected with a smaller level of diversity. In this paper necessary and sufficient conditions on the channel matrix are given. An algorithm for the computation of the equalizers is also given for those channels satisfying these conditions, assuming an i.i.d. symbol sequence and memory dominance of the linear part.