Does Fractionally-Spaced CMA converge faster than LMS?

This paper addresses the convergence rate study of the Fractionally-Spaced Equalizer updated by Constant Modulus Algorithm (FSE-CMA). By analyzing the average algorithm behavior we compare the FSE-CMA to the FSE-LMS. Although the FSE-CMA is based on a fourth order statistics criterion, we will show for constant modulus input that the algorithm has the amazing property to converge locally twice as fast as FSE-LMS (which requires a training sequence). Furthermore, we will show that the global FSE-CMA transient behavior convergence is accomplished in two steps.