## 3 UABS Placement and ICIC Parameter Optimization in AG-HetNet
This table shows that the Brute force algorithm must consider a large search space to find all feasible solutions. However, to lessen the system complexity and simulation runtime, we apply the same \(\mathbf{S}_{\text{mbs}}^{\text{ICIC}}\) parameters across all MBSs and \(\mathbf{S}_{\text{uabs}}^{\text{ICIC}}\) across all UABSs. Finally, we define the dependency of the 5 pSE and coverage probability to the UABS locations, CRE, and ICIC parameters as  
\[C_{\text{5 pSE}}\left(\mathbf{L}_{\text{uabs}}^{\text{3D}},\mathbf{S}_{\text{ mbs}}^{\text{ICIC}},\mathbf{S}_{\text{uabs}}^{\text{ICIC}}\right), \tag{7}\]  
\[C_{\text{COV}}\left(\mathbf{L}_{\text{uabs}}^{\text{3D}},\mathbf{S}_{\text{ mbs}}^{\text{ICIC}},\mathbf{S}_{\text{uabs}}^{\text{ICIC}}\right),C_{\text{COV}}>T_{ \text{Cg}}^{\text{Shannon}}, \tag{8}\] \begin{table}
\begin{tabular}{c c} \hline
**SIR Ratio** & **Shannon Capacity of USF/CSF Radio Frames** \\ \hline \(\Gamma_{\text{usf}}^{\text{mbs}}=\frac{R_{\text{mbs}}(d_{\text{ss}})}{\pi_{ \text{abs}}(d_{\text{ss}})+\text{log}}\) & \(C_{\text{usf}}^{\text{mbs}}=\frac{\beta_{\text{mbs}}\log_{2}(1+\frac{\text{ true}}{\text{min}})}{N_{\text{uabs}}^{\text{mbs}}}\) \\ \(\Gamma_{\text{csf}}^{\text{mbs}}=\frac{aR_{\text{mbs}}(d_{\text{ss}})}{\pi_{ \text{abs}}(d_{\text{ss}})+\text{log}}\) & \(C_{\text{csf}}^{\text{mbs}}=\frac{(1-\beta_{\text{mbs}})\log_{2}(1+\frac{\text{ true}}{\text{min}})}{N_{\text{csf}}^{\text{mbs}}}\) \\ \hline \(\Gamma_{\text{usf}}^{\text{mbs}}=\frac{R_{\text{mbs}}(d_{\text{ss}})}{\pi_{ \text{abs}}(d_{\text{ss}})+\text{log}}\) & \(C_{\text{csf}}^{\text{mbs}}=\frac{(1-\beta_{\text{mbs}})\log_{2}(1+\frac{\text{ true}}{\text{min}})}{N_{\text{csf}}^{\text{mbs}}}\) \\ \hline \(\Gamma_{\text{csf}}^{\text{mbs}}=\frac{R_{\text{mbs}}(d_{\text{ss}})}{\pi_{ \text{abs}}(d_{\text{ss}})+\text{log}}\) & \(C_{\text{csf}}^{\text{mbs}}=\frac{(1-\beta_{\text{mbs}})\log_{2}(1+\frac{\text{ true}}{\text{min}})}{N_{\text{csf}}^{\text{mbs}}}\) \\ \hline \(\Gamma_{\text{csf}}^{\text{mbs}}=\frac{R_{\text{mbs}}(d_{\text{ss}})}{\pi_{ \text{abs}}(d_{\text{ss}})+\text{log}}\) & \(C_{\text{csf}}^{\text{mbs}}=\frac{(1-\beta_{\text{mbs}})\log_{2}(1+\frac{\text{ true}}{\text{min}})}{N_{\text{csf}}^{\text{mbs}}}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Shannon capacity definitions in terms of SIR and RSRP for USF/CSF radio frames. where \(C_{\text{5 PSE}}(. )\) denotes the objective function for 5 pSE, \(C_{\text{cov}}(. )\) denotes the objective function for coverage probability, and \(T_{\text{C}_{\text{SE}}}^{\text{Channon}}\) is the capacity threshold supporting broadband rates. Using this definition of objective functions, the best state (\(\text{{BS}^{\prime}}_{\text{KPI}}\)) of all the possible states (\(\mathbf{S}\)) is given as  
\[\mathbf{BS^{\prime}}_{\text{KPI}}=\text{arg}\;\underset{S}{\text{max}}\;\;C_{ \text{KPI}}(\mathbf{S}), \tag{9}\]  
where \(C_{\text{KPI}}(. )\) is a generic representation of the objective function defined in (7) and (8) and \(\mathbf{KPI}\in\left(5\text{pSE},\text{COV}\right)\). For the proposed AG-HetNet, UABSs are initially deployed on fixed hexagonal locations within the simulation area (ARsim) as shown in Figure 6. In Figure 5(a), we illustrate the UABSs' deployment on the fixed hexagonal location when 50% of the MBSs are destroyed, and in Figure 5(b), when 95% of the MBSs are destroyed. Each UABS sends its 2D location coordinates and the system-level resources allocation for a GUE to an edge server, and using the brute-force algorithm described in Algorithm 1, the two KPIs of the AG-HetNet will be determined at the edge server. The global maxima values of the best state (\(\mathbf{BS^{\prime}}_{\text{KPI}}\)) of all the possible states \(\mathbf{S}\) can be vectorized into \(\mathbf{BS^{\prime}}_{\text{KPI}}=\left[\hat{\mathbf{L}}_{\text{uabs}}^{( \text{hex})},\mathbf{BS^{\prime}}_{\text{rnbs}}^{\text{ICIC}},\mathbf{BS^{ \prime}}_{\text{uabs}}^{\text{ICIC}}\right]\).