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User cooperation, whereby multiple users share their antennas and transmit to a common destination in a collaborative manner, has been shown to be an effective way to achieve spatial diversity. We propose in this paper, a strategy to minimize the total transmit power in a decode-and-forward (DF) multi-user, multi-relay cooperative uplink, such that each user satisfies its quality-of-service (QoS) data rate. Each user in the proposed system transmits its own data towards the base station and also serves as a relay for other users. The base station assigns one or more relays to each user in order to minimize total power in the uplink. The relay selection is based upon the instantaneous user to base station channels, inter-user channels and also the target rates of the users. The simulation results indicate significant power savings over a non-cooperative uplink, under proposed joint relay selection and power minimization algorithm in a DF cooperative uplink when using a space-time coded cooperative diversity.