# Green Small Cell Operation of Ultra-Dense Networks Using Device Assistance +
## 5 Numerical Results
### Expanding BP and DANCE Algorithms on UDN
#### 5.2.2 Ultra-Dense Network  
Next, we further densify both the UEs and APs; there are 1000 UE in the same area, and we vary the number of APs from 20 to 10,000, which is up to a 100-times densification. In Figure 8, the on/off state of 1000 APs is illustrated when proximity-ON is used in the case of 1000 UEs. Figure 8 shows the associations between UEs and APs. Each UE can be associated with an adequate AP, which is determined by the proposed algorithms. The APs that do not have the associated UE are turned off. Since we consider the ultra-dense deployment scenario, a UE can find the AP to be associated with, and thus, no coverage hole exists. It should be noted that this densification is extreme and  
Figure 7: Green small cell operation under dense networks. may not be practical because UE needs to send out feedback for each beacon signal from each AP. Nevertheless, we investigate this case to to better understand the proposed algorithms and see how much performance gain DANCE algorithms would achieve in the extreme case. In this case, it is computationally infeasible to run BP because each UE has too many neighboring APs, even if the approximated factor graph is used. Thus, we only consider the DANCE algorithms. Other parameters are the same as in Section 5.1. As can be seen in Figure 9, densification results in a higher data rate, but severe interference plays a role as densification goes on, specifically for the case of the baseline. We observe that the energy efficiency and data rate both grow rapidly in the low densification region, e.g., 100 APs or less. The benefit of densification in this region is well illustrated; a small increase of AP density brings the advantage of an increased data rate that outweighs the disadvantage of the increased power consumption. In addition to the baseline, one can compare the proposed algorithms with another type of baseline; since [28] corresponds to UE-1, one can see that UE-N can increase the energy efficiency up to 62.5% over that of [28] in Figure 9a. The energy efficiency gap between the baseline and proximity-ON implies that the AP on/off operation should be enforced to enhance energy efficiency. The gap gradually enlarges when the number of APs is more than 500, which implies that even the simplest DANCE algorithm, i.e., proximity-ON, can increase energy efficiency. Note that since all APs are turned on in the baseline, high interference among APs degenerates the data rate when the number of APs approaches 5000. This also yields very poor energy efficiency. However, even under extreme densification, the energy efficiency of DANCE is highly improved in all regions. For example, in the case of 10,000 APs, UE \(N\)-bit achieves 44-times higher energy efficiency than the baseline. Specifically, Figure 9c show that UE-N and AP-N keep power consumption lower by orders of magnitude compared to the baseline. Nevertheless, Figure 9a shows that AP/UE \(N\)-bit maintains high energy efficiency even when the number of APs is more than 2000, i.e., the density of APs is very high, such as 0.0308 APs/m\({}^{2}\). In this region, although energy efficiency remains constant, the data rate of AP/UE \(N\)-bit keeps growing, implying the fraction of turned-on APs is still very low. Thus, by turning off unnecessary APs, DANCE can reduce power consumption and also achieves a high data rate thanks to effectively mitigated interference. Figure 8: An example of the ON/OFF states of 1000 APs when the UE-N algorithm is used in the case of 1000 UEs. (**a**) Thirty nine APs turned on among 1000 APs; (**b**) user association between turned-ON APs and UEs. **Remark 2** (The impact of device assistance). : _Now, we discuss the impact of feedback on energy efficiency in UIDN. In Figure 8(a), the energy efficiency of both N-bit and one-bit feedback sharply increases for 20 APs to 100 APs (low densification region). Then, the energy efficiency of N-bit feedback is almost maintained, whereas the energy efficiency of one-bit feedback is decreased after 100 APs (high densification region).