A multiuser detector based on Lagrangian multipliers estimating

In this paper, we propose a new multiuser detector that is based on the explicit estimation of Lagrange multipliers. The optimum multiuser detector, proposed by S. Verdu in 1986, is a binary quadratic problem. It belongs to NP hard problems and can not be used currently. In this paper, the binary quadratic problem is changed into a quadratic optimization problem with equation constraints, and then written in Lagrange form, the relationship between the Lagrange multipliers, user information codes and channel noise is derived. According to different methods of estimating Lagrange multipliers, two existing multiuser detectors are given: decorrelation and minimum mean-squared error (MMSE) detectors. According to the special features of the multiuser detection problem, a new method of estimating Lagrange multipliers is given in this paper and then a new multiuser detector is obtained. The numerical results showed that the bit-error-ratio (BER) of the new detector is close to that of the optimum multiuser detector and less than that of sub-optimum multiuser detection.