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In this paper, we analyze the bit-error-rate (BER) performance of the optimum multiuser detection (MUD) with channel mismatch in multicarrier code-division-multiple-access (MC-CDMA) systems. The BER performance of the optimum MUD without channel mismatch in MC-CDMA systems has been recently derived using the replica method. However, it is left unjustified, since the replica method is not a rigorous approach. In addition, it is NP-hard to implement an optimum MUD algorithm. To justify the BER performance and to make the optimum MUD feasible, based on Pearl's belief propagation (BP) scheme, we put together a low-complexity iterative MUD algorithm for MC-CDMA systems. Furthermore, channel mismatch is introduced into the BP-based MUD algorithm to make the scenario general. With channel mismatch, the analytical results of the BP-based MUD algorithm conform perfectly to, and the simulation results of the BP-based MUD algorithm conform very closely to the BER performance of the optimum MUD derived using the replica method, which is a nontrivial extension of the existing replica approach mentioned above. Without channel mismatch, the problem becomes a special case of our contribution.