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Multi-carrier code division multiple access (MC-CDMA) demonstrates good probability of error performances in frequency selective fading channels, a direct result of its ability to resolve the available frequency diversity. However, MC-CDMA performances may be limited by degradation due to large multiple-access interference (MAI). Frequency division multi-carrier code division multiple access (FD-MC-CDMA), a novel multiple access architecture proposed in this paper, exploits the available frequency diversity benefits while reducing MAI. Specifically, instead of transmitting all users' information bits over all carriers, FD-MC-CDMA employs a subset of carriers to support a subset of users (while maintaining the same overall system capacity and throughput as in MC-CDMA). By careful selection of each subset of carriers, the available frequency diversity benefits are fully exploited, while the MAI experienced by each user is reduced. Furthermore, since the number of carriers employed by each user is significantly reduced, the complexity of the truly optimal multiuser detection (MUD) receiver for FD-MC-CDMA is low. An optimal MUD based on the maximum likelihood (ML) criteria is employed to optimize the system performance of FD-MC-CDMA. The proposed FD-MC-CDMA (with MUD) provides significantly better bit error rate (BER) performances than traditional MC-CDMA systems with little increase in system complexity.