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In this paper, we propose a low rate bandwidth efficient channel coding scheme for MC-CDMA system so that by using it, the coded system without any extra bandwidth, significantly improves the performance of an un-coded system over fading channels. Moreover, we investigate the performance of multiple antennas array aided coded MC-CDMA system by employing different smart antennas techniques at the receiver and in order to reduce the search space and computational complexity of Maximum Likelihood (ML) post-FFT Multiuser Detection (MUD) technique, we propose a ML algorithm based on Sensitive Bits Algorithm (SBA) and Less Complex Norm Approximation (LCNA) based Euclidean distance. The performance and complexity of the proposed MUD algorithms are compared with nonlinear MMSE-SIC and ML MUD algorithms. It is shown that with a minimal penalty in performance compared to ML algorithm, the SBA-LCNA-based proposed two-step schemes for multiple antennas array aided coded MC-CDMA system have significant reduction in the complexity.