On the Performance of Two Constant Modulus Algorithms in Equalization with non-CM Signals

A global assessment of the performance of gradient descent algorithms based on the constant modulus criteria CM(2,2) and CM(1,2), and denoted CMA2-2 and CMA1-2 respectively, is provided. To begin with, it is shown that no theoretical excess error with respect to the MMSE solution is introduced by the CM(2,2) criterion if the source signal satisfies the usual conditions and its kurtosis is 4/3, and the excess error introduced by the criterion CM(1,2) is negligible. Then, existing gradient excess mean-squared error estimations are confirmed through a different approach and they are completed by time constant estimations. Finally, for the same minimum mean-squared error, CMA2-2 is shown to be twice as fast as CMA1-2, which confirms the superiority of the CM(2,2) criterion in equalization with non-CM signals.