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The authors consider the joint sub-channel allocation and power control problem for OFDMA femtocell networks in this paper. Specifically, they are interested in the fair resource sharing solution for users in each femtocell that maximizes the sum min rate of all femtocells subject to protection constraints for the prioritized macro users. Toward this end, they describe the mathematical formulation for the problem and present an optimal exhaustive search algorithm. Given the exponential complexity of the optimal exhaustive search algorithm, they then develop a distributed and low-complexity algorithm to solve the resource allocation problem. They prove that the proposed algorithm converges.
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