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In this paper we want to maximize sum throughput of two interfering cells. ICI has been shown to be the predominant performance-limiting factor in wireless cellular networks and we propose a scheme that intercell interference in each subcarrier doesn't exceed a specific threshold. In this respect, a new problem entitled as "sum throughput maximization with intercell interference limitation" has been defined. Three subclasses of the problem are presented and solved analytically, which assist in developing three types of resource allocation algorithms: a) optimum resource allocation algorithm by exhaustive search based on the optimum power allocation problem solution, b) distributed resource allocation algorithm based on the single cell problem solution, and c) centralized resource allocation algorithm based on the joint multicell problem solution. Simulation results illustrate the performance improvements of the proposed schemes in comparison to the schemes with no intercell interference consideration.