A New Rank-two Semidefinite Programming Relaxation Method for Multiuser Detection Problem

Based on the semidefinite programming relaxation model of the code division multiple access maximum likelihood multiuser detection problem, a detection strategy by the rank-two method is presented. The proposed method restricts the matrix variable in the semidefinite programming relaxation to be rank-two, and yields a quadratic objective function with simple quadratic constraints. A feasible direction method is used to solve the nonlinear programming. Coupled with randomized method, a suboptimal solution is obtained for the multiuser detection problem. Simulation results show that the bit error rate performances of a detection strategy based on the new rank-two method are almost similar to that of the detection strategy based on the semidefinite programming relaxation. Furthermore, average CPU time of the new rank-two method is at least 10 times lower than that of the semidefinite programming relaxation method, With the increasing of the users number, the average CPU time increasing rate of the new rank-two method is lower than that of the semidefinite programming relaxation method, especially for the large-scale detection problems. This approach provides good approximations to the optimal maximum likelihood performance.