In this paper, we investigate an energy-efficient joint subcarrier and power allocation algorithm for improving the worst energy efficiency (worst-EE) in multiuser two-way amplify-and-forward (AF) relay networks, that not only balances the EE of the two-way links, but also ensures the desired quality-of-service (QoS) of each user. In order to maximize the worst-EE, an EE-balancing optimization problem is formulated as the ratio of the spectral efficiency (SE) over the total network power consumption subject to a total transmit power and users' QoS constraints. Since the formulated primal problem is a non-convex fractional mixed binary-integer program, i.e., NP-hard to solve, thus a concave lower bound on the objective function and a series of convex transformations are applied to transform the problem into a tractable convex form. An iterative algorithm is proposed to achieve the optimal solution of the dual problem. We further propose an efficient, low-complexity suboptimal resource allocation algorithm. Simulation results demonstrate the effectiveness of the proposed iterative and suboptimal algorithms.
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