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We address the problem of the blind identification of a non-minimum phase FIR communication channel by exploiting the cyclostationarity of the received signal sampled at rate greater of the symbol rate. By explicitely taking into account the (known) color of the additive noise, we extend the approach presented by Giannakis (see Proc. 28th Asilomar Conf. Sig., Sys. and Comp., California, USA, 1994), based on second-order cyclic correlations. Moreover, we propose the use of higher-order cyclic correlations to overcome the lack of channel identifiability when second-order only cyclic correlations are considered. The resulting nonlinear equations are solved using the same numerical techniques commonly adopted in the classical minimum eigenvalue/eigenvector problem.