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Successive interference cancellation (SIC) for code division multiple access (CDMA) systems, together with a suitable power control, is an attractive technique to reduce multiuser access interference in uplink transmissions. In this paper we propose a receiver design which minimizes the system transmit power while ensuring a constant signal to noise plus interference ratio (SNIR) at each user detection point by using a suitable order of user detection. Indeed, the problem is a joint optimization of power control and ordering of user detection and its optimum solution is NP-hard. Hence, we derive both a suboptimal greedy algorithm and a randomized search which explores many solutions. All these approaches are evaluated in an uplink multiuser scenario for the UMTS-TDD standard in terms of bit error rate and power consumption.