In this paper, we provide joint subcarrier assignment and power allocation schemes for quality-of-service (QoS)- constrained energy-efficiency (EE) optimization in the downlink of an orthogonal frequency division multiple access (OFDMA)- based two-tier heterogeneous cellular network (HCN). Considering underlay transmission, where spectrum-efficiency (SE) is fully exploited, the EE solution involves tackling a complex mixed-combinatorial and non-convex optimization problem.With appropriate decomposition of the original problem and leveraging on the quasi-concavity of the EE function, the problem can be efficiently solved. On the other hand, the inherent intertier interference from spectrum underlay access may degrade EE particularly under dense small-cell deployment and large bandwidth utilization. We therefore develop a novel resource allocation approach based on the concepts of spectrum overlay access and resource efficiency (RE) (normalized EE-SE tradeoff). Specifically, the optimization procedure is separated where the macro-cell optimal RE and the corresponding bandwidth is first determined, then the EE of small-cells utilizing the remaining spectrum is maximized. Simulation results confirm the theoretical
findings and demonstrate that the proposed resource allocation schemes can approach the optimal EE with each strategy being superior under certain system settings.