The MSE performance of constant modulus receivers

The constant modulus algorithm (CMA) is an effective technique for blind receiver design in practice. Treating CMA as a linear estimation problem, effects of noise and channel conditions are investigated. For the class of channels with arbitrary finite impulse responses, an analytical description of locations of constant modulus receivers and an upper bound of their mean squared errors (MSE) are derived. We show that, with proper initializations, CMA can achieve almost the same performance as the (nonblind) minimum mean square error (MMSE) receiver. Our analysis reveals a strong relationship between the (blind) constant modulus and the (nonblind) MMSE receivers. It also highlights the significance of initialization/reinitialization schemes. The approach developed in this paper also applies to CMA blind beamforming in array signal processing