Analysis of a nonparametric blind equalizer for discrete-valued signals

An investigation is carried out to identify the variables that may affect the numerical properties of an inverse filtering method of blind equalization for linear channels with discrete input. The analysis is under a nonparametric framework in which all coefficients of the inverse filter (equalizer) can be freely chosen. It reveals, in particular, that the filter length plays two contradictory roles - increasing the length always helps improve the accuracy of inverse filtering, but when the filter is too long, the numerical properties of the method may deteriorate. Other influential variables include the constellation and (possibly time-varying) probability distribution of the input signals. The method is also shown to be highly efficient for nonparametric channel estimation, as was shown for estimating parametric channels. Simulations are carried out to verify the analytical findings concerning the numerical properties.