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An optimum downlink power control that maximizes the user-capacity of a Direct Sequence-Code Division Multiple Access (DS-CDMA) cellular system is proposed based on a convex programming method. First, the downlink beamforming weights for the base-station antenna-array are designed based on the maximum Signal-Interference-Ratio (SIR) criterion. Then by optimizing the downlink power subject to a fixed total transmit power constraint, we further increase the Signal-Interference-Noise-Ratio (SINR) at the mobile terminal, thus increasing the capacity of the system. With the same methodology, we can also minimize the required transmit power while satisfying the SINR threshold constraints. Additionally, a robust downlink power control approach for mitigating the performance degradation due to channel estimates error is also proposed. Computer simulations are given to demonstrate the improvement of downlink capacity, received SINR, robustness, and the minimization of the required transmit power for a DS-CDMA system with antenna-array at the base-station.