Efficient Quasi-Maximum-Likelihood Multiuser Detection by Semi-Definite Relaxation

In multiuser detection, maximum-likelihood detection (MLD) is optimum in the sense of minimum error probability. Unfortunately, MLD involves a computationally difficult optimization problem for which there is no known polynomial-time solution (with respect to the number of users). In this paper, we develop an approximate maximum-likelihood (ML) detector using semi-definite (SD) relaxation for the case of anti-podal data transmission. SD relaxation is an accurate and efficient approximation algorithm for certain difficult optimization problems. In MLD, SD relaxation is efficient in that its complexity is $O(K^{3.5})$, where $K$ stands for the number of users. Simulation results indicate that the SD relaxation ML detector has its bit error performance close to the true ML detector, even when the cross-correlations between users are strong or the near-far effect is significant.