Behavior of fractionally-spaced constant modulus algorithm: mean square error, robustness and local minima

The fractionally-spaced constant modulus algorithm (FSCMA) is an effective technique for blind receiver design in practice. Its global convergence has been proved for a nonsingular channel and in the absence of noise. In this paper, we study the effects of noise and singular channel. The performance gap between the FSCMA receiver and the optimal linear receiver is investigated. In particular, a mean square error (MSE) upper bound of the FSCMA is derived. Using the MSE bound, we show that the FSCMA is robust to the effects of noise, model mismatch, equalizer length, channel common zeros, etc. Our analysis shows that, despite of the local minimum problem, the FSCMA can achieve almost the same performance as the (nonblind) MMSE receiver.