A theoretical note on the generalized ML optimality of constant modulus equalizers

In this work, we derive the optimum equalizer according to the General Maximum Likelihood (GML) principle and show the optimality of the constant-modulus algorithm (CMA) according to the GML principle. This reported discussion illustrates why CMA works well and hence is so popular. Moreover, we show that the minimization of normalized variance algorithm (MNVA) previously introduced by the authors, as much as the asymptotically equivalent Kurtosis maximization algorithm and “Rayleigh-ness” test criteria, are asymptotically optimum according to the GML criterion.