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A cooperative frequency-modulated differential chaos shift keying (FM-DCSK) ultra-wideband (UWB) systems, named cooperative FM-DCSK UWB system, is investigated under indoor environments of IEEE 802.15.4a in this article. The performance of the cooperative FM-DCSK UWB system is evaluated in such channel models (CMs), that is, CM1-CM4, by means of the moment generating function. Monte Carlo simulation results show that the bit-error-rate performance of the proposed system is much better than the conventional multi-access FM-DCSK UWB system, which is showed to be highly consistent with the theoretical results. The integration interval of the proposed cooperative UWB system is optimised to further improve the system performance through the binary search algorithm. Meanwhile, aiming to provide a good compromise between the system performance and implementation complexity, the number of received antenna at the destination (single-input multiple-output architecture) is also investigated and discussed. For the aforementioned advantages, the proposed system can be seen as a viable alternative to other multi-access FM-DCSK UWB schemes for the low-rate and low-power wireless personal area network and wireless sensor network applications.