# Cooperative Game-Based Energy Efficiency Management over Ultra-Dense Wireless Cellular Networks
## 1 Introduction
In [11], the EE is investigated as a significant requirement of future HetNets, especially when SeNBs and MeNBs are densely deployed. The work in [35] addressed the fundamental tradeoff between the EE and SE in downlink OFDMA networks. The work in [32] explored the tradeoff between traffic offloading from the MeNB and the energy consumption of SeNBs in a cognitive small-cell network. According to the aforementioned literature, although ultradense wireless cellular networks have good SE performance, the serious interference must be reduced by potential cooperation schemes, especially in the comprehensive consideration of the network EE. Power coordination plays an important role in enhancing both the SE and EE, but few studies have focused on the DE and the inherent interaction between these three metrics (SE, EE and DE) under one unified cooperative game model in ultra-dense wireless cellular networks. Herein, we propose a cooperative bargaining game-based power-coordination scheme for ultra-dense wireless cellular networks to improve the comprehensive EE with consideration of the inter-tier and intra-tier interference limitations and maximum power constraints. The main contributions are summarized as follows:  
* We formulate the power-coordination problem in macro cells and small cells as a cooperative Nash bargaining game to improve the comprehensive EE, where the inter-tier and intra-tier interference limitations are imposed to provide reliable transmission for the network users, and the maximum power is considered to guarantee the fairness for the base stations in each cell. * We define a unified energy-efficient utility function for the optimization problem in ultradense wireless cellular networks, where the near optimal cooperative bargaining power-coordination strategy is derived by introducing time-sharing variables and the Lagrangian function. Accordingly, the closed-form power-coordination solutions with consideration of both interference mitigation and energy saving are derived, which show the convergence of a Pareto-optimal equilibrium for the cooperative game. * A simplified algorithm is proposed to combat the complicate signaling overhead, which is a challenge in the scenario of the ultradense deployment of small cells, and yields a suboptimal power-coordination solution. * The proposed algorithm is evaluated by numerical simulations, which illustrates the convergence property and the efficiency of our power-coordination scheme, allowing a good tradeoff between three different energy-efficiency metrics. The remainder of the paper is organized as follows: Section 2 introduces the system model and the energy-efficiency model. Section 3 provides the basics for the Nash cooperative bargaining game and a unified energy-efficient utility function. Section 4 provides the closed-form solution, the algorithm implementation, and a simplified algorithm in ultra-dense wireless cellular networks, and in Section 5, the performances of the proposed algorithms are evaluated by simulations. Finally, we conclude the work in Section 6.