Optimum multi-user detection by nonsmooth optimization

The optimum multiuser detection (OMD) is a discrete (binary) optimization. The previously developed approaches often relax it by a semi-definite program (SDP) and then employ randomization for searching the optimal solution around the solution of this relaxed SDP. In this paper, we show the limited capacity of this SDP program, which at the end cannot give a better solution than the simple linear minimum mean square error detector (LMMSE). Our departure point is to express the problem as quadratic minimization over quadratic equality constraint (QMQE) or concave quadratic minimization over a box of continuous optimization (CQOB). The QMQE allows us to develop a nonsmooth optimization algorithm to locate the global optimal solution of OMD, while CQOB facilities effective confirmation of the solutions found by QMQE. Our intensive simulation clearly shows that the algorithm outperforms all previously developed algorithms while the computational burden is essentially reduced.