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A serious shortcoming of current downlink power control methods is that their performance may be severely degraded when the downlink channel information is known imprecisely at the transmitter. In this paper, a computationally and implementationally simple centralized downlink power control method is proposed for cellular wireless communication systems using code division multiple access (CDMA) or space division multiple access (SDMA). Our method provides a substantially improved robustness against imperfect knowledge of the wireless channel by means of maintaining the required quality of service for the worst-case channel uncertainty. In the SDMA case, the proposed technique can be straightforwardly combined with any of the existing transmit beamforming methods. Simulation results validate substantial robustness improvements achieved by our approach.