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The tremendous popularity of smart phones and electronic tablets has spurred the explosive growth of high-rate multimedia services and promptly boomed energy consumption in wireless networks. Therefore, energy-efficient design in wireless networks is very important and is attracting more and more attention, just like the conventional spectral-efficient design. In this paper, we study energy-efficient design in downlink orthogonal frequency division multiple access (OFDMA) networks with effective capacity-based delay provisioning for delay-sensitive traffic. By integrating information theory with the concept of effective capacity, we formulate an energy efficiency (EE) optimization problem with statistical delay provisioning, which is a complicated nonconvex combinatorial fractional programming problem. To solve the problem, we first relax it with an upper bound on the original one and then prove and exploit the …