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This study addresses resource allocation for weighted sum throughput maximisation (WSTM) in a sectorised two-cell downlink orthogonal frequency-division multiple access systems impaired by multicell interference. It is well known that the optimisation problem for this scenario is NP-hard and combinational, which is here converted to a novel WSTM problem based on the intercell interference limitation. In the new problem, we use a lower bound of throughout as a cost function which is convex, and so it simplifies the power allocation algorithm and offers a better convergence. Then, two subclasses of this new problem are solved based on the dual Lagrange framework. By the first subclass, on the assumption that subcarrier allocation parameters are fixed, an algorithm for optimal power allocation (OPA) is obtained. However, the optimal resource allocation requires an exhaustive search, including the OPA which cannot be implemented in practice because of its high complexity. By the second subclass, the joint subcarrier allocation and power distribution for two adjacent cells as a general problem is solved. Here, the algorithm allocates simultaneously the subcarriers and the power of the considered two cells while the resource allocation parameters of both cells are coupled mutually. After that, we propose a new centralised algorithm which combines the proposed power allocation with the non-convex subcarrier allocation without increase in the complexity. Simulation results show that the proposed algorithms achieve efficient performance in many practical situations.