## 3 UABS Placement and ICIC Parameter Optimization in AG-HetNet
```
1:procedure\(C_{\text{KPI}}(\hat{\mathbf{L}}_{\text{uabs}}^{(\text{hex})},\mathbf{S}_{\text{ prbs}}^{\text{ICIC}},\mathbf{S}_{\text{uabs}}^{\text{ICIC}})\)
2:KPI : 5 pSECOV
3:COV,5 pSE, Best state \(\mathbf{BS^{\prime}}\leftarrow\mathbf{NULL}\)
4:forallValuesofStateSdo
5: Current 5 pSE \(\leftarrow\) C\({}_{\text{5 pSE}}(\mathbf{S})\)
6:ifCurrent 5 pSE \(>\) 5 pSEthen
7: 5 pSE \(\leftarrow\) Current 5 pSE
8: BS \(\leftarrow\) S
9:endif
10: Current COV \(\leftarrow\)\(C_{\text{COV}}(\mathbf{S})\)
11:ifCurrent COV \(>\) COVthen
12: COV \(\leftarrow\) Current COV
13: BS \(\leftarrow\) S
14:endif
15:endfor
16: Return 5 pSE,COV, Best state BS^
17:endprocedure
```  
**Algorithm 1** Pseudocode for brute-force algorithm \begin{table}
\begin{tabular}{c c c} \hline \hline
**Search Parameter** & **Parameter Range** & **Search Space Size** \\ \hline \(a_{\text{mabs}}\) & \(0\), \(\mathbb{D}a_{\text{mabs}}\), \(2\mathbb{D}a_{\text{mabs}}\)... \(1\) & \(1/\mathbb{D}a_{\text{mabs}}+1\) \\ \(\beta_{\text{mabs}}\) & \(0\), \(\mathbb{D}\beta_{\text{mabs}}\), \(2\mathbb{D}\beta_{\text{mabs}}\)... \(1\) & \(1/\mathbb{D}\beta_{\text{mabs}}+1\) \\ \(\rho_{\text{mabs}}\) & \(\rho_{\text{mabs}}^{\text{low}}\), \(\rho_{\text{mabs}}^{\text{low}}+\mathbb{D}\rho_{\text{mabs}}\), \(\rho_{\text{mabs}}^{\text{low}}+2\mathbb{D}\rho_{\text{mabs}}\)...\(\rho_{\text{mabs}}^{\text{high}}\) & \(\frac{(\rho_{\text{mabs}}^{\text{low}}-\rho_{\text{mabs}}^{\text{low}})}{( \mathbb{D}\rho_{\text{mabs}})}\) \\ \hline \(\rho_{\text{uabs}}\) & \(\rho_{\text{mabs}}^{\text{low}}\), \(\rho_{\text{uabs}}^{\text{low}}+\mathbb{D}\rho_{\text{uabs}}\), \(\rho_{\text{uabs}}^{\text{low}}\) + \(2\mathbb{D}\rho_{\text{uabs}}\)...\(\rho_{\text{mabs}}^{\text{high}}\) & \(\frac{(\rho_{\text{mabs}}^{\text{high}}-\rho_{\text{mabs}}^{\text{low}})}{( \mathbb{D}\rho_{\text{mabs}})}\) \\ \(\tau_{\text{uabs}}\) & \(0\), \(\mathbb{D}_{\text{Tabs}}\), \(2\mathbb{D}_{\text{Tabs}}\),...\(\mathbb{D}_{\text{uabs}}^{\text{high}}\) & \(\frac{1}{\mathbb{D}\tau_{\text{mabs}}}\) \\ \hline \(\mathsf{X}\) coordinate of UABS & \(-1/2\), \(-1/2+\mathbb{D}x\), \(-1/2+2\mathbb{D}x\), \(.../2\) & \(\frac{1}{\mathbb{D}\tau}\) \\ \(\mathsf{Y}\) coordinate of UABS & \(-1/2\), \(-1/2+\mathbb{D}y\), \(-1/2+2\mathbb{D}y\), \(.../2\) & \(\frac{1}{\mathbb{D}y}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Boundary values and the step size of each parameter to be optimized within the search space. As a function of the step size and parameter range defined in Table 4, the time complexity for the brute-force algorithm and with UABS deployed on a fixed hexagonal grid is defined as  
\[\mathcal{O}\Bigg{(}\Big{(}1/\mathbb{D}\alpha_{\text{mbs}}+1\Big{)} \times\Big{(}1/\mathbb{D}\beta_{\text{mbs}}+1\Big{)}\times\Big{(}\frac{(\rho_{ \text{mbs}}^{\text{high}}-\rho_{\text{mbs}}^{\text{low}})}{(\mathbb{D}\rho_{ \text{mbs}})}\Big{)}\times\] \[\Big{(}\frac{\tau_{\text{pbs}}^{\text{high}}}{\mathbb{D}\tau_{ \text{pbs}}}\Big{)}\times\Big{(}\frac{(\rho_{\text{uabs}}^{\text{high}}-\rho_{ \text{uabs}}^{\text{low}})}{(\mathbb{D}\rho_{\text{uabs}})}\Big{)}\times\Big{(} \frac{\tau_{\text{uabs}}^{\text{high}}}{\mathbb{D}\tau_{\text{uabs}}}\Big{)} \Bigg{)}.\]  
Lastly, a step-by-step articulation of the system design to system flow is given in Figure 7 using the system-level details discussed in Section 2, objective functions in Section 3, and brute force algorithms proposed in Algorithm 1. Furthermore, each step in the flow diagram refers to relevant figures, tables, and equations in the system design. Figure 6: Illustration of PSC network after a disaster and UABSs deployed to restore mission-critical communications. (**a**) Illustration of PSC network after a disaster, with 50% of the infrastructure destroyed and UABSs deployed on a fixed hexagonal grid and at the height of 120 m. (**b**) Illustration of PSC network after a disaster, with 95% of the infrastructure destroyed and UABSs deployed on a fixed hexagonal grid and at the height of 120 m.