Tight Semidefinite Relaxation for Combinatorial Optimization in UWB Multiuser Detection Systems

In this paper, two near-optimal detectors based on the convex optimization algorithm are proposed for multiuser detection (MUD) in the ultra-wide bandwidth (UWB) systems. The first detector performs semidefinite relaxation (SDR) to approximate the optimum multiuser detection (OMD) which is a nondeterministic polynomial time hard (NP-hard) problem. When the cutting planes generation algorithm is employed to strengthen the relaxation of the SDR, a tight MUD detector for combinatorial optimization is obtained by adding triangle inequalities to the well-known SDR in strict feasible region. Simulations demonstrate that the semidefinite programming (SDP) approaches can provide bit error rate (BER) performance close to the OMD efficiently using the interior point method, and the tight detector provides a better BER performance than the previous detector with a slightly higher complexity.