CMA convergence for constant envelope, non-zero bandwidth signals

Abstract

The gradient-descent-based constant modulus algorithm (CMA) is commonly thought to converge much more slowly than its least mean square (LMS) counterpart, particularly for quadrature-amplitude-modulated (QAM) signals. Experiments shown in this paper indicate that in fact there is no substantial difference in the convergence rates of the two methods in the important special case of constant envelope signals (e.g., FM and FSK). For both CMA and LMS algorithms the convergence for nontrivially frequency-modulated signals depends on the same eigenvalue disparity problem that affects all gradient-descent techniques.