On the Convexity of the LCCM Cost Function for DS-CDMA Blind Multiuser Detection

The linearly constrained constant modulus algorithm (LCCMA) applied to blind DS-CDMA multiuser detection was widely considered in the last few years. In some papers, global convergence of the linearly constrained constant modulus (LCCM) algorithm was incorrectly claimed, after which corrections were published by other authors (see the Introduction section for references). In this letter, analysis of the LCCM criterion is extended to prove convexity of the LCCM cost function between any point and the global minimum, subject to certain conditions, by using the definition of a continuous convex function.