Evaluation of dispersion constants for signed-error blind equalization algorithms

Blind equalization is a technique for adaptive equalization of a communication channel without the aid of the usual training sequence. Stochastic gradient based blind equalization algorithms equalize the dispersive signals by exploiting the high-order statistics of the transmitted signal which are embedded in some pre-calculated constants. These constants, usually termed as dispersion constants, contain the information about the size, shape and energy of the transmitted signal. Dispersion constants also provide proper gain of the equalizer such that the mean fluctuation in adaptation process is zero (or minimum). Constant modulus algorithm (CMA) is a widely-studied and probably the most famous blind equalization method in literature and practice. In this work, we contribute a little by providing simple formulas for the dispersion constants used in CMA and signed-error CMA for PAM and QAM signals.