On the convexity of the LCCM cost function for DS-CDMA blind multiuser detection

• Published in: IEEE communications letters Vol. 8; no. 6; pp. 351 - 353
• Main Authors: de Villiers, J.P., Linde, L.P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2004; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive white noise; Algorithms; Applied sciences; AWGN; Blinds; Constraints; Convergence; Convexity; Cost function; Criteria; Detection, estimation, filtering, equalization, prediction; Detectors; Exact sciences and technology; Gaussian noise; Information, signal and communications theory; Multiaccess communication; Multiuser detection; Signal and communications theory; Signal, noise; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Vectors; Multiuser detection; Blind multiuser detection; Continuous function; Blind identification; Algorithm; linearly constrained constant modulus algorithm (LCCMA); DS-CDMA; Code division multiple access; linearly constrained constant modulus (LCCM); Cost function; Convex function; Convexity; Direct sequence; Signal detection
• ISSN: 1089-7798; 1558-2558
• DOI: 10.1109/LCOMM.2004.831325

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.