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This paper proposes a joint energy efficiency (EE) and spectrum efficiency (SE) tradeoff analysis as a multi-objective optimization problem (MOP) in the uplink of multi-user multi-carrier two-tier orthogonal frequency division multiplexing access heterogeneous networks subject to users' maximum transmission power and minimum rate constraints. The proposed MOP is modeled such that the network providers can dynamically tune the tradeoff parameters to switch between different communication scenarios with diverse design requirements. In order to find its Pareto optimal solution, the MOP is transformed, using a weighted sum method, into a single-objective optimization problem (SOP), which itself can further be transformed from a fractional form, by exploiting fractional programming, into a subtractive form. Since the formulated SOP is hard to solve due to the combinatorial channel allocation indicators, we reformulate the SOP into a better tractable problem by relaxing the combinatorial indicators using the idea of time-sharing. We then prove that this reformulated SOP is strictly quasi-concave with respect to the transmission power and the subcarrier allocation indicator. We then propose an iterative two-layer distributed framework to achieve an upper bound Pareto optimal solution of the original proposed MOP. The numerical simulations demonstrate the effectiveness of our proposed two-layer framework achieving an upper bound Pareto optimal solution, which is very close to an optimal solution, with fast convergence, lower and acceptable polynomial complexity, and balanced EE-SE tradeoff.

Energy and Spectrum Efficient Transmission Techniques Under QoS Constraints Toward Green Heterogeneous Networks