In this paper, we concentrate on the robust multiobjective optimization (MOO) for the tradeoff between energy efficiency (EE) and spectral efficiency (SE) in device-to-device (D2D) communications underlaying heterogeneous networks (HetNets). Different from traditional resource optimization, we focus on finding robust Pareto optimal solutions for spectrum allocation and power coordination in D2D communications underlaying HetNets with the consideration of interference channel uncertainties. The problem is formulated as an uncertain MOO problem to maximize EE and SE of cellular users (CUs) simultaneously while guaranteeing the minimum rate requirements of both CUs and D2D pairs. With the aid of ε-constraint method and strict robustness, we propose a general framework to transform the uncertain MOO problem into a deterministic single-objective optimization problem. As exponential computational complexity is required to solve this highly non-convex problem, the power coordination and the spectrum allocation problems are solved separately, and an effective two-stage iterative algorithm is developed. Finally, simulation results validate that our proposed robust scheme converges fast and significantly outperforms the non-robust scheme in terms of the effective EE-SE tradeoff and the quality of service satisfying probability of D2D pairs.

In this paper, we propose a general framework to study the tradeoff between energy efficiency (EE) and spectral efficiency (SE) in massive MIMO enabled HetNets while ensuring proportional rate fairness among users and taking into account the backhaul capacity constraint. We aim at jointly optimizing user association, spectrum allocation, power coordination, and the number of activated antennas, which is formulated as a multi-objective optimization problem maximizing EE and SE simultaneously. With the help of weighted Tchebycheff method, it is then transformed into a single-objective optimization problem, which is a mixed-integer non-convex problem and requires unaffordable computational complexity to find the optimum. Hence, a low-complexity effective algorithm is developed based on primal decomposition, where we solve the power coordination and number of antenna optimization problem and the user association and spectrum allocation problem separately. Both theoretical analysis and numerical results demonstrate that our proposed algorithm can fast converge within several iterations and significantly improve both the EE-SE tradeoff performance and rate fairness among users compared to other algorithms.

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In resource constraint wireless systems, achieving higher spectral efficiency (SE) and energy efficiency (EE), and greater rate fairness are conflicting objectives. Here a general framework is presented to analyze the tradeoff among these three performance metrics in cooperative OFDMA systems with decode-and-forward (DF) relaying, where subcarrier pairing and allocation, relay selection, choice of transmission strategy, and power allocation are jointly considered. In our analytical framework, rate fairness is represented utilizing α-fairness model and the resource allocation problem is formulated as a multiobjective optimization (MOO) problem. We then propose a cross-layer resource allocation algorithm across application and physical layers, and further devise a heuristic algorithm to tackle the computational complexity issue. The SE-EE tradeoff is characterized as a Pareto optimal set, and the efficiency and fairness tradeoff is investigated through the price of fairness (PoF). Simulations indicate that higher fairness results in a worse SE-EE tradeoff. It is also shown imposing fairness helps to reduce the outage probability. For a fixed number of relays, by increasing circuit power, the performance of SE-EE tradeoff is degraded. Interestingly, by increasing the number of relays, although the total circuit power is increased, the SE-EE tradeoff is not necessarily degraded. This is thanks to the extra degree of freedom provided in relay selection.