On the relationship between least squares and constant modulus criteria for adaptive filtering

Another contribution is the proposal of an upper bound for the CM cost function based on the mean fourth error (MFE) criterion, whose tightness is verified with the aid of simulations. When used for channel equalization, constant modulus (CM) algorithms have a higher mean square error (MSE) than the data aided algorithms. The purpose of this paper is to clarify this observation and give, through simple derivations, approximate expressions for the relationships between the corresponding coefficient vectors. It is shown that the CM(2,2) criterion can lead to coefficient vectors that are approximately proportional to the Wiener vectors for some values of the delay of the reference data sequences. The proportionality factors obtained are related to the output mean square errors and, computing the extra MSE from the proportionality relations leads to the bound previously obtained through a different approach. The validity of the estimations is verified through simulations.