Error surfaces of the constant modulus algorithm

Abstract

The authors derive closed-form expressions for the performance function of the constant modulus algorithm (CMA) that are based on two different Gaussian assumptions, and they present examples of the corresponding error surfaces for a binary transmitted signal. In one case, they assume that the received signal of the equalizer is unconditionally Gaussian with zero mean. This approach leads to an infinity of stationary points, each of which corresponds to a minimum of the error surface and which depend only on the correlation properties of the received signal. In the second case, the authors assume that the received signal conditioned on one of the transmitted symbols is Gaussian with nonzero mean. The resulting stationary points are not so easily characterized, and they depend on the channel impulse response as well as the correlation of the received signal.