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Most of the resource allocation literature on the energy-efficient orthogonal frequency division multiple access (OFDMA)-based wireless communication systems assume continuous power allocation/control, while, in practice, the power levels are discrete (such as in 3GPP LTE). This convenient continuous power assumption has mainly been due to either the limitations of the used optimization tools and/or the high computational complexity involved in addressing the more realistic discrete power allocation/control. In this paper, we introduce a new optimization framework to maximize the energy efficiency of the downlink transmission of cellular OFDMA networks subject to power budget and quality-of-service constraints, while considering discrete power and resource blocks (RBs) allocations. The proposed framework consists of two parts: 1) we model the predefined discrete power levels and RBs allocations by a single binary variable and 2) we propose a close-to-optimal semidefinite relaxation algorithm with Gaussian randomization to efficiently solve this non-convex combinatorial optimization problem with polynomial time complexity. We notice that a small number of power levels suffice to approach the energy efficiency performance of the continuous power allocation. Based on this observation, we propose an iterative suboptimal heuristic to further reduce the computational complexity. Simulation results show the effectiveness of the proposed schemes in maximizing the energy efficiency, while considering the practical discrete power levels.

Optimization of Discrete Power and Resource Block Allocation for Achieving Maximum Energy Efficiency in OFDMA Networks