# Green Small Cell Operation of Ultra-Dense Networks Using Device Assistance +
## 5 Numerical Results
### BP and DANCE Algorithms for a Small-Sized Network  
We assume that nine APs and 20 UEs are randomly distributed in a hexagonal cell area with a 100-m radius. The AP and UE locations are determined by following a uniform distribution [2]. From the Alcatel-Lucent device (Model 9361 home cell v2), the transmission power of the AP is 13 dBm, and the operational power of the AP is 9 W. According to the IEEE 802.16 m Evaluation Methodology Document (EMD), we use the winner model assuming the non-line-of-sight (NLOS) case and propagation through light walls with a 2.1-GHz carrier frequency. The total bandwidth is 20 MHz, and the power spectral density of thermal noise is \(-174\) dBm/Hz. Our numerical simulations are performed by taking snap shots about possible AP/UE dense deployment scenarios. This approach is also popular; see [12; 29; 30]. One may want to perform network-level simulations to observe packet-level behaviors, such as packet loss, related with network protocols. In this paper, however, we focus on physical-layer performance metrics, such as data rate and power consumption, to compute energy efficiency, which are in our objective function in (3). Figure 4 shows the average energy efficiency obtained through 200 iterations, and the results are summarized in Table 2. For every iteration of the proposed BP algorithm, UE update and AP update are repeated five times where \(\frac{1}{\tau}=1\) and \(\eta=5.5\). The baseline is the case when all APs are turned on. In addition, proximity-ON is a simple heuristic algorithm, and thus, it can provide performance guidelines for other DANCE algorithms, such as AP-first and UE-first. Furthermore, we find the optimal solution by using exhaustive search. Therefore, it can be possible to compare our algorithms' results to the case that maximizes energy efficiency. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**BP** & **AP-N** & **AP-1** & **UE-N** & **UE-1** & **Prox-ON** \\ \hline
129\% & 101\% & 100\% & 102\% & 98\% & 14\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The average energy efficiency improvement percentages of the proposed algorithms to the baseline. Prox-ON, proximity-ON. Figure 3: Green small cell operation and procedure using the DANCE algorithm. First, we compare the average energy efficiency among BP, DANCE and the baseline in Figure 4. Table 2 represents the improvement of the average energy efficiency. Results show that BP and DANCE increase energy efficiency significantly, e.g., by 129% compared to the baseline. As expected, BP exhibits better energy efficiency than DANCE. However, the gap is not substantial, and considering that DANCE is a low complexity algorithm, the performance of DANCE is noticeable. Overall, all four cases of DANCE (AP-N, AP-1, UE-N, UE-1) achieve more or less 100% improved energy efficiency and outperform proximity-ON and the baseline substantially. In Figure 5, we compare the average power consumption and the average data rate, which are averaged over all iterations. Considering that the nature of the problem is indeed a combinatorial optimization, we compare our algorithms with an optimal solution by performing an exhaustive search. The result shows that the proposed algorithms are near optimal, e.g., achieving 83% of the optimal performance. We observe that BP and DANCE consume substantially less power than the average power consumption of the baseline. However, as the trade-off of BP's significant power reduction, it achieves a lower average data rate. By contrast, DANCE achieves similar or even higher average data rate, which isclose to the optimal energy efficiency case because the interference is mitigated by the AP off operation, and the set of turned-on APs is well chosen to provide a high data rate. Energy efficiency, power consumption and data rate can vary with respect to \(\eta\). As shown in Figure 6a, energy efficiency is maximized when \(\eta=5.5\). In Figure 6b, average power consumption decreases as \(\eta\) increases.