# Cooperative Game-Based Energy Efficiency Management over Ultra-Dense Wireless Cellular Networks
## 2 System Model and Network Energy-Efficiency Model
### Network Energy-Efficiency Model  
In this paper, we aim to maximize the total EE of the whole network. An appropriate energy-efficiency metric is most important, which is directly related to the optimized strategies across all the layers. Here, a network energy-efficiency model is defined with regard to three aspects--spectrum, energy, and deployment--to realize comprehensive energy-efficient management. The SE is defined as the network throughput for unit bandwidth, and is a widely accepted metric for wireless-network optimization. The downlink throughput is related to the transmission power of the base station in the network, which includes MeNBs and SeNBs. Therefore, we analyze the SE of SeNBs and MeNBs separately. According to Equations (6) and (7), the spectral efficiencies of MeNB\({}_{\rm m}\) and SeNB\({}_{\rm n}\) can be expressed as:  
\[SE_{m}=\sum\limits_{i=1}^{I}\log_{2}(1+p_{m}h_{m,i}) \tag{8}\]  
\[SE_{n}=\sum\limits_{j=1}^{I}\log_{2}(1+p_{n}h_{n,j}) \tag{9}\]where \(SE_{m}\) and \(SE_{n}\) are calculated as the sum capacity of all the MUEs and SUEs associated with the \(m\)th MeNB\({}_{\text{m}}\) and the \(n\)th SeNB\({}_{\text{n}}\). The EE is defined as the network throughput per unit energy consumption and is mostly considered during network operation. According to [10], a large electricity bill results from the large energy consumption of a wireless base station. Thus, we analyze the EE of each base station, which reflects the EE of the whole network. According to [15], power consumption includes two parts: transmission power consumption and circuit power consumption. Therefore, the EE of MeNB\({}_{\text{m}}\) and SeNB\({}_{\text{n}}\) can be expressed as:  
\[EE_{m}=\frac{\sum\limits_{i=1}^{I}{\log_{2}(1+p_{m}h_{m,i})}}{a_{sitem}*P_{m}+ b_{sitem}} \tag{10}\]  
\[EE_{n}=\frac{\sum\limits_{i=1}^{J}{\log_{2}(1+p_{n}h_{n,j})}}{a_{sitem}*P_{n}+ b_{sitem}} \tag{11}\]  
where \(a_{sitem}*P_{m}\) represents the \(m\)th MeNB\({}_{\text{m}}\) transmission power consumption; \(b_{sitem}\) is the circuit power consumption; \(a_{sitem}\) is the \(m\)th MeNB\({}_{\text{m}}\) power-conversion efficiency, accounting for the power amplifier efficiency, feeder loss, extra loss in transmission-related cooling, etc. Similarly, \(a_{sitem}*P_{n}\) is the \(n\)th SeNB\({}_{\text{n}}\) transmission power consumption, \(b_{sitem}\) is the circuit power consumption, and \(a_{sitem}\) is the \(n\)th SeNB\({}_{\text{n}}\) power-conversion efficiency. The DE is defined as the network throughput for unit deployment cost and is an important network-performance metric for users. According to [15], the deployment cost includes the CapEx and OpEx. Key cost drivers with respect to the CapEx and OpEx are summarized in Table 1.  
With the increase of base stations, the base station-related expenditure accounts for a large proportion. Thus, discussing the cost efficiency of each base station is important for the DE of the whole network. According to [15], the annual average cell deployment cost can be expressed as:  
\[\overset{-}{C}(R)=C^{Ca}(R)/10+C^{Op}(R) \tag{12}\] \[=\left\{ \begin{array}{c}0.86c_{0}+c_{1}\overset{-}{E}_{site}(R ),R\geq 0.5\\ 0.57c_{0}+c_{1}\overset{-}{E}_{site}(R),0.1\leq R\leq 0.5\end{array} \right.\]  
where \(R\) is the cell radius, whose unit is km; \(c_{0}\) denotes the equipment cost of a base station (unit: \(\mathbf{\xi}\)); and \(c_{1}\) denotes the electricity charge in units of K\(\mathbf{\xi}\)/J. Therefore, the DE of SeNB\({}_{\text{n}}\) and MeNB\({}_{\text{m}}\) can be expressed as:  
\[DE_{m}=\frac{\sum\limits_{i=1}^{I}{\log_{2}(1+p_{m}h_{m,i})}}{c_{1m}*(a_{sitem}* P_{m}+b_{sitem})+c_{om}} \tag{13}\]