# Optimal Base Station Density of Dense Network:
## 5 Numerical Results and Discussion
### The Areal Throughput of HetNets and the Optimal Deployment Scheme  
As aforementioned, it is not only the link rate but also the channel efficiency that has impact on the throughput of SmBS. Unlike existing literature, we analyze and simulate the impact of both of them, which gives many insights for densification deployment. With the parameter settings mentioned at the beginning of this section, we simulate a two-tier HetNet consisting of MaBSs and SmBSs. The term of total HetNets throughput (the sum of the throughput of all MaBSs and SmBSs) and the term of total HetNet areal throughput that is obtained by dividing the total HetNets throughput by the total HetNets area are selected to indicate the performance of the network.  
Figure 7a shows the total HetNets throughput. The network area in the simulation is 9 km\({}^{2}\), where 100 MaBSs are deployed in this area. We have simulated the performance of HetNets under different user densities and SmBS densities. The simulation results show the sum throughput of all MaBSs and SmBSs in this simulation area. With these results and dividing the total HetNets throughput by the total HetNets area, we can obtain the total HetNets areal throughput.  
Figure 7b illustrates the impact of SmBS density on the total HetNets areal throughput. As the figure shows, deploying more SmBSs can offer greater total areal throughput since it provides more access and reduces resource competition. However, always increasing SmBS density is not correct due to interstation interference. We can find that the optimal deployment density of SmBS always exists under different network load conditions that are described by the user density. In addition, as the user density varies, we can observe that higher user density needs higher SmBS density, which is consistent with the intuition.  
Figure 6: The effect of SmBS density on the channel efficiency under different user densities. \(P_{\text{m}}/P_{\text{M}}=0.001\).  
Figure 8 has compared the performance of the optimal deployment and other suboptimal ones. The optimal deployment is implemented by selecting the optimal SmBS density under different network conditions of user density. We take \(\lambda_{\text{m}}=550/\text{km}^{2}\), \(\lambda_{\text{m}}=4400/\text{km}^{2}\) and \(\lambda_{\text{m}}\)= 8800/\(\text{km}^{2}\) as examples of the suboptimal deployment, which indicate low density, medium density and relative high density. When the SmBSs are of low density, HetNets performance deteriorates rapidly as the user density increases because such few SmBSs cannot afford too many users. When the SmBSs are of higher density, they perform better than those of lower density do in the crowded network but act more poorly in the light-loaded network, since denser SmBSs have greater capability to offer service to massive users, and, meanwhile, they can also incur heavy interference. With the comparison, we find that the optimal deployment scheme outperforms other ones and achieves the best performance under any user density.  
Figure 8: Comparison between the optimal densification deployment and suboptimal ones. \(P_{\text{m}}=60\) mW.  
Figure 7: The impact of SmBS density on HetNets throughput. Network area = 9 km\({}^{2}\), \(P_{\text{m}}=60\) mW.