# Cooperative Game-Based Energy Efficiency Management over Ultra-Dense Wireless Cellular Networks
## 4 Bargaining Problem Solutions for Ultradense Wireless Cellular Networks
### Simplified Algorithm for Sub-Optimal Solution
\begin{table}
\begin{tabular}{c c} \hline \hline
**Simulation Parameter** & **Value** \\ \hline Deployment scenario & 5 \(\times\) 5 grid model \\ \hline Carrier frequency & 2 GHz \\ \hline Bandwidth & 10 MHz \\ \hline Coverage radius of the MBS & 500 m \\ \hline Shadowing standard deviation*2 & 10 dB for link between SeNB and SUE \\  & 8 dB for other links \\ \hline Minimum distance between SeNB and eNB & 75 m \\ \hline Minimum distance between UE and eNB & 35 m \\ \hline Minimum distance between UE and SeNB & 3 m \\ \hline Minimum distance among SeNBs & 40-m cluster radius \\ \hline \hline \end{tabular}
\end{table} 
Table 2: This is a table. Network simulation parameters. Figure 2: Convergence of proposed Algorithm 1. To evaluate the performance of the proposed strategy with the increase of small cells, the area EE, area SE, and area DE of the proposed power-coordination scheme are simulated. Here, the area SE of the system, MeNB, and SeNB are calculated using the following equations, respectively, similarly to [31]:  
\[\text{System SE }=\frac{\sum\limits_{n=1}^{N}SE_{n}+\sum\limits_{m=1}^{M}SE_{m}}{3.14r^{2}} \tag{54}\]  
\[\text{MeNB SE }=\frac{\sum\limits_{n=1}^{M}SE_{m}}{M\cdot 3.14r^{2}} \tag{55}\]  
\[\text{SeNB SE }=\frac{\sum\limits_{n=1}^{N}SE_{n}}{N\cdot 3.14r^{2}} \tag{56}\]  
where \(r\) is the radius, which we set as 500 m.  
Then, the area EE and DE are calculated similarly. As shown in Figures 3-5, these area metrics are simulated when the number of small cells increases from 1 to 40. According to Figure 3, we conclude that the trend of the area EE of the SeNB, the MeNB and the whole system is to decrease with the increase of small cells, especially from two small cells. This is because when more small cells are overlaid in the coverage of the MeNB, the energy consumption is higher, and the interference between them increases. The same trend is observed for the area DE of the SeNB, the MeNB and the whole system, as shown in Figure 5, which is caused by the increase of the cost with the increase of small cells. However, as shown in Figure 4, the area SE of SeNB and MeNB decreases with respect to the number of small cells, but the system SE fluctuates widely. More small cells yield a larger system capacity, whereas more small cells may aggravate the interference of the whole system. Therefore, with the increase of small cells, the system performance is not always improved. That is, in network construction, there should be a good tradeoff considering the SE, EE, and DE. Figure 4: Area SE with the proposed power-coordination strategy. Figure 3: Area EE with the proposed power-coordination strategy. In Figures 6-11, the EE, SE, and DE cumulative distribution functions (CDFs) of the MeNB and the averaged EE, SE, and DE CDFs of the SeNB are simulated to reflect the performance advantages of our scheme. We also contrast them with the corresponding EE, SE, and DE CDFs of the joint scheme in [31]. According to Figures 6 and 7, the EE of the MeNB is improved in our strategy; however, the averaged EE of the SeNB can be further improved. The SE and DE are also improved, as shown in Figures 9-14. Owing to the consideration of the DE, the power of the MeNBs and SeNBs in our algorithm is coordinated slightly. Because more MeNBs are introduced, the power of the SeNBs is lower. Moreover, the CINRs of the MUEs and SUEs are smaller; therefore, the power adjustments of the MeNBs are not far better than those of the SeNBs. On the other hand, lower transmission power causes less SE but is beneficial for reducing the consumed energy and the cost, which leads to improvements in the EE and DE. Thus, we conclude that a slight sacrifice in the SE for MeNBs yields large savings in energy and cost. SeNBs obtain the biggest beneficiary of the power coordination between different base stations. Figures 12-14 illustrate the performance of our proposed simplified algorithm compared with that of Algorithm 1, which is measured via the EE, SE, and DE CDFs.