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A new technique for the uplink transmission of a cooperative system consisting of single-antenna source and relay nodes and a multi-antenna destination node is presented. The proposed technique is based on the singular value decomposition of the channel matrix and, for the same rate, it exhibits higher diversity gain as compared to the existing ones. Theoretical analysis of the technique is carried out when the Decode-and-Forward protocol is employed. The analysis reveals the way the decoding errors occurring at the relays degrade the performance of the system. Furthermore, the proposed technique is extended to a multi-user environment so as to exploit multi-user diversity. A novel criterion is suggested for selecting the best transmitting user at each time slot. The performance of the system in the multi-user case is theoretically studied and the number of users needed so as the system to achieve its maximum performance is computed. The derived theoretical results are verified via typical simulations.