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This paper proposes efficient rate and power allocation algorithms for OFDMA downlink systems where each tone is taken by at most one user. Weighted sum rate maximization (WSRmax) and weighted sum power minimization (WSPmin) problems are considered. Since these resource allocation problems are non-convex, complexity of finding the optimal solutions is prohibitively high. This paper employs the Lagrange dual decomposition method to efficiently solve both optimization problems. Because of their non-convex nature, there is no guarantee for the solution obtained by the dual decomposition method to be optimal. However, it is shown that with practical number of tones, the duality gap is virtually zero and the optimal solutions can be efficiently obtained
Seong et al. (Sat,) studied this question.