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Energy-efficient orthogonal frequency division multiple access (OFDMA) aims to relieve the booming energy consumption in wireless communications networks and has recently received lots of attention. Meanwhile, two-way relay has been extensively studied and proves to be more spectral-efficient than direct transmission and one-way relay in many scenarios. In this paper, we study energy-efficient resource allocation for OFDMA-based two-way relay, maximizing the aggregated energy efficiency (EE) utility while provisioning proportional fairness in EE among different terminal pairs. The energy-efficient joint power and subchannel allocation and active subchannel selection problem is mixed-integer combinatorial and further demonstrates to be nonconvex. To approach the performance limit, we first find an upper-bound solution relying on continuous relaxation and the Lagrange dual method. To reduce the …