An analysis of vector CMA for multichannel receiver design

The vector-constant modulus (VCM) criterion is an extension of the constant modulus (CM) criterion introduced previously for equalization of channels involving Gaussian sources. We analyze the behavior of VCM for arbitrary source distributions and combined channel-receiver impulse responses of finite dimension for a multichannel receiver scenario. We provide a bound on the source kurtosis, for noise-free channels, under which VCM admits stable minima corresponding to zero-forcing (ZF) channel receivers. We show that for sub-Gaussian sources the VCM and CM criteria share the same global minima. For Gaussian and super-Gaussian sources, however, it appears that only ZF receivers corresponding to input/output transmission delays at the extremes of the range of possible delays are truly stable equilibria of VCM.