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This letter investigates a power allocation problem in a downlink single-input single-output non-orthogonal multiple access (NOMA) system. Our goal is to maximize the sum rate of users subject to minimum user rate requirements. We rigorously prove the optimal user decoding order, and show that the sum rate maximization problem is convex, which guarantees the globally optimal solution. Numerical results validate the performance gain by the proposed NOMA compared with conventional schemes.