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In multi-carrier differential chaos shift keying (MC-DCSK) system, channel noises pollute both the reference and data signals, resulting in deteriorated performance. To reduce noises in received signals in MC-DCSK, a novel noise reduction MC-DCSK (NR-MC-DCSK) system is proposed in this paper. The proposed system utilizes duplicated chaotic samples, rather than different ones, as the reference. At the receiver side, identical samples can be averaged before correlation detection, which helps decrease the noise interferences and thus brings performance improvement. Theoretical bit error rate (BER) expressions are derived and verified by simulation results for additive white Gaussian noise and multipath Rayleigh fading channels. Finally, comparisons to MC-DCSK and other DCSK-based systems are given to confirm the superiority of the proposed system in BER performance.