Stationary points of the constant modulus algorithm for real Gaussian signals

An analysis of the stationary points for four versions of the constant modulus algorithm (CMA) when the received signal is a zero-mean, real Gaussian process is presented. With this type of signal, it is well known that CMA generally cannot equalize a communication channel; the analysis of the CMA performance function demonstrates how this occurs. It is shown that in each case the stationary points are determined by a condition on the variance of the equalizer output, and they depend only on the modulus factor r and the received signal correlation matrix R. As a result, there can be an infinity of weight vector solutions, each corresponding to a stationary point of the CMA performance function