We study the downlink of multicell orthogonal frequency-division multiple-access (OFDMA) networks and address the adaptive allocation of spectrum, power, and rate. We consider networks with adaptive frequency reuse and discrete-level rates. Initially, we formulate the joint allocation problem as a centralized nonlinear mixed integer program (MIP), which is computationally intractable to solve optimally for practical problem sizes. Then, we exploit the capability of the receivers to estimate the subcarrier channel gains and accordingly decompose the joint allocation into subproblems, each of which is solved by a different base station with linear complexity. In the proposed iterative algorithm, the base stations perform rate and receiver allocation per subcarrier, with concurrent iterations. We introduce a filtering method to further decrease the algorithm complexity. Furthermore, for benchmarking purposes, we transform the original nonlinear MIP to a linear MIP and find the optimal solution by means of standard branch-and-cut solvers. The merit of the proposed algorithm is demonstrated with numerical comparisons of its performance against the solutions of the linear MIP and the iterative waterfilling algorithm.
