Fractionally-spaced constant modulus algorithm blind equalizer error surface characterization: effects of source distributions

The constant modulus algorithm (CMA) is a popular blind equalization algorithm. A common device used in demonstrating the convergence properties of CMA is the assumption that the source sequence is i.i.d. (independent, identically distributed). Previous results in the literature show that a finite length fractionally-spaced equalizer allows for perfect equalization of moving average channels (under certain channel conditions known as zero-forcing criteria). CMA has previously been shown to converge to such perfectly equalizing settings under an independent, platykurtic source. This paper investigates the effect of the distribution from which an independent source sequence is drawn on the CMA error surface and stationary points in the perfectly-equalizable fractionally-sampled equalizer case. Results include symbolic identification of all stationary points, as well as the eigenvalues and eigenvectors associated with their Hessian matrix. Results show quantitatively the loss of error surface curvature (in both direction and magnitude) at all stationary points. Simulations included demonstrate the affect this has on convergence speed