Replica Analysis of Multiuser Detection for Code Division Multiple Access with M-Ary Phase-Shift Keying

We analyze the performance of the maximizer of the posterior marginals (MPM) detector for code division multiple access (CDMA) multiuser detection with M-ary phase shift keying (M-ary PSK) in the large system limit by the replica method. The obtained theory agrees with computer simulation reasonably well. We also derive the theory in the case of the large M limit and discuss the dependence of the properties of M-ary PSK CDMA communication on M. We show that the waterfall phenomenon occurs for both the finite and infinite values of M. We also show that a value of M for which the decoded phase information on the original user symbol becomes minimum exists. Furthermore, we discuss the relationship between the theory based on the replica method and that based on self-consistent signal-to-noise analysis (SCSNA).