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We investigate the performance of an uplink turbo-coded cooperative direct-sequence code-division multiple-access (DS-CDMA) system in slow frequency-selective relay channels. The effect of multi-user interference (MUI) is studied where we show that full diversity can only be achieved by using an interference suppression detector. In our cooperative system, perfect and imperfect inter-user channel scenarios are studied. At both the base station and relay, a decorrelator detector and a maximum-ratio combiner (MRC) are employed to decode the received data from different users. Simulation results show that full diversity order of 2P is achieved where P is the number of resolvable paths. Further, we examine the performance of a turbo coded cooperative system using detect-and-forward relaying scheme.