Blind equalization of nonlinear channels from second-order statistics

This paper addresses the blind equalization problem for single-input multip le-output nonlinear channels, based on the second-order statistics (SOS) of the received signal. We consider the class of "linear in the parameters" c hannels, which can be seen as multiple-input systems in which the additiona l inputs are nonlinear functions of the signal of interest. These models in clude (but are not limited to) polynomial approximations of nonlinear syste ms. Although any SOS-based method can only identify the channel to within a mixing matrix (at best), sufficient conditions are given to ensure that th e ambiguity is at a level that still allows for the computation of linear F IR equalizers from the received signal SOS, should such equalizers exist. T hese conditions involve only statistical characteristics of the input signa l and the channel nonlinearities and can therefore be checked a priori. Bas ed on these conditions, blind algorithms are developed for the computation of the linear equalizers. Simulation results show that these algorithms com pare favorably with previous deterministic methods.