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The maximum-likelihood (ML) multiuser detector is a powerful method of suppressing the performance degrading effects of multiuser interference, however it is computationally too complex to implement in most practical cases. For the-binary and quadratic PSK cases, it has been recently illustrated that multiuser ML detection (MLD) can be accurately and efficiently approximated by the so-called semidefinite relaxation (SDR) algorithm. In this sequel, we show how the SDR technique is applied to the more difficult problem of MLD with M-ary PSK (MPSK) constellations, to which the previous SDR algorithm is not applicable. We propose an extended SDR algorithm which approximates the MPSK MLD problem with an attractive computational cost of O(K3.5), where K is the number of users. The promising approximation accuracy of the SDR-ML detector is demonstrated by simulation results, where the SDR-ML detector exhibits substantially improved symbol error performance compared with several commonly used suboptimal multiuser detectors.