It has recently been observed that with appropriate stepsize normaliza
tion, the convergence speed of the constant modulus (CM) algorithm can
be dramatically improved, In this correspondence, it is shown that if
a different normalization strategy is used, one that takes into accou
nt the finite alphabet structure of the signals, a standard normalized
version of the decision directed equalizer (DDE) is achieved. A simul
ation example is included to demonstrate the faster convergence of the
normalized DDE compared with its constant stepsize implementation and
the normalized CM.