# On Mathematical Modelling of Automated Coverage Optimization in Wireless 5G and beyond Deployments
## 4 Numerical Simulations and Results Discussion
### Simulation of Different Deployment Scenarios  
Based on the parameters set as presented in Table 5, for each scenario (urban, susburban, rural) we created five datasets. Within them, we considered various numbers of theoretical candidate locations given an identical number of users and total coverage area. The simulations carried out made it possible, in a reasonable time, to achieve the results presented in Table 6. For these simulations, the model presented by Equations (23)-(30) was used without extending the objective function, which might be an interesting problem for further research. Interferences were reduced by Equation (28). In that table, it is clearly shown that the area size is not the biggest problem for the gNodeB deployment, as opposed to the number of users and their required throughput which is the main aspect that needs to be considered for the 5G and beyond deployments. In addition, it is shown that even if the rural use-case contains the same number of users as the urban area, the number of the necessary gNodeB to cover the area is smaller. This is especially due to the larger number of theoretically available locations to deploy gNodeB on which the software can find better combinations of gNodeB nodes to cover the whole area to meet the given requirements. The theoretical candidate locations were generated randomly based on the assumption that larger areas should have better options to select locations to deploy gNodeB nodes. For the computational concept, we consider that, theoretically, the base station could be deployed on every possible place (see Figure 6) and then the software will produce the combination of the gNodeB nodes locations that is optimal for the considered deployment, based on the selected aspects. In this visualization, it is shown that, in the case of an urban area, users are spread throughout the area. It is further shown here that 81 possible locations for gNodeB node deployment were originally considered and, of these, an optimal combination of 19 gNodeB nodes was found. The calculated solution covers the whole area meeting the specified requirements (gNodeB capacities, expected throughput from the user and range of gNodeB). If the area changes significantly, e.g., some areas may be closed and users may move to another district, the only essential process to do is to provide updated input parameters for our models. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Scenarios**} & \begin{tabular}{c} **Theoretical Number of Candidate** \\ **Locations to Deploy gNodeB** \\ \end{tabular} & \begin{tabular}{c} **Number** \\ **of Users** \\ \end{tabular} & \
\begin{tabular}{c} **Total Coverage** \\ **Area [km\({}^{2}\)]** \\ \end{tabular} &
\begin{tabular}{c} **Resulting Number of gNodeB** \\ **Nodes to Be Deployed** \\ \end{tabular} \\ \hline urban & 81 & 7500 & 3 & 19 \\ suburban & 421 & 7500 & 18.75 & 22 \\ rural & 484 & 7500 & 75 & 18 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of different deployment scenarios. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Use-Case**} & \begin{tabular}{c} **Combined gNodeB** \\ **Capacity (DL + UL) [Gbit/s]** \\ \end{tabular} & \begin{tabular}{c} **Single Cell** \\ **Radius [km]** \\ \end{tabular} & \
\begin{tabular}{c} **Demanded User Throughput** \\ **(DL + UL) [Mbit/s]** \\ \end{tabular} &
\begin{tabular}{c} **Number of** \\ **Connections/km\({}^{2}\)[106]** \\ \end{tabular} \\ \hline urban & 30 & 0.5 & 43.9 & 2500 \\ \hline suburban & 30 & 1 & 43.9 & 400 \\ \hline rural & 30 & 8 & 43.9 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summarized list of parameters based on the deployment use-case. The optimal combination of gNodeB nodes is shown in Figure 7.  
Figure 6: Initial theoretical distribution of possible locations of gNodeB in an urban area (red cross symbol represents user; black plus symbol represents gNodeB; and blue circle represents the gNodeB coverage radius).