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A semidefinite programming (SDP) relaxation approach is proposed to solve multiuser detection problems in systems with M-ary quadrature amplitude modulation (M-QAM). In the proposed approach, the optimal M-ary maximum likelihood (ML) detection is carried out by converting the associated M-ary integer programming problem into a binary integer programming problem. Then a relaxation approach is adopted to convert the binary integer programming problem into an SDP problem. This relaxation process leads to a detector of much reduced complexity. A multistage approach is then proposed to improve the performance of the SDP relaxation based detectors. Computer simulations demonstrate that the symbol-error rate (SER) performance offered by the proposed multistage SDP relaxation based detectors outperforms that of several existing suboptimal detectors.