## 3 UABS Placement and ICIC Parameter Optimization in AG-HetNet  
The public safety scenario considered in Figure 2 with AG-HetNet can occur during a natural disaster such as a hurricane or earthquake. During such an event, the existing terrestrial infrastructure can receive severe damage and the remaining terrestrial infrastructure could see a surge in traffic. It would cause traffic congestion in the remaining commercial cellular networks and public safety networks. Thus, resulting in GUEs experiencing poor QoS and to address the lack of coverage in this scenario, the system design considers optimizing network parameters and maximizing the two KPIs. To this end, this simulative study is limited to investigating the gains using the _brute force algorithm_. For the AG-HetNet under consideration, the 5 pSE corresponds to the worst fifth-percentile GUE capacity amongst all the scheduled GUEs, whereas the coverage probability of the AG-HetNet is defined as the percentage of the geographical area with broadband rates and a capacity larger than a threshold of \(T_{\text{Cg}}^{\text{Shannon}}\). Through each UABS \(i\in\{1,2,...,N_{\text{uabs}}\}\) in the AG-HetNet, we capture individual locations in \((x_{i},y_{i})\), where \(\mathbf{L}_{\text{uabs}}^{\text{3D}}\) would be the matrix representing these locations in 3D. These UABSs are placed within the rectangular simulation area regardless of the existing MBS (\(\mathbf{L}_{\text{mbs}}^{\text{3D}}\)). Given the locations of the base station (\(\mathbf{L}_{\text{uabs}}^{\text{3D}}\) and \(\mathbf{L}_{\text{mbs}}^{\text{3D}}\)), the matrix representation of individual ICIC parameters for each UABS is given by \(\mathbf{S}_{\text{uabs}}^{\text{ICIC}}=[\boldsymbol{\tau_{\text{uabs}}}, \boldsymbol{\rho_{\text{uabs}}}]\in\mathbb{R}^{N_{\text{uabs}}\times 2}\). Similarly, the matrix representation of individual ICIC parameters for each MBS \(\mathbf{S}_{\text{mbs}}^{\text{ICIC}}=[\boldsymbol{\alpha_{\text{mbs}}}, \boldsymbol{\beta_{\text{mbs}}},\boldsymbol{\rho_{\text{mbs}}}]\in\mathbb{R}^{ N_{\text{uabs}}\times 3}\). We capture the resource management parameters in vectors, where \(\boldsymbol{\rho_{\text{mbs}}}=[\rho_{1},...,\rho_{N_{\text{uabs}}}]^{T}\) and \(\boldsymbol{\rho_{\text{uabs}}}=[\rho_{1},...,\rho_{N_{\text{uabs}}}]^{T}\) are the scheduling thresholds, respectively, for each MBS and UABS. The power reduction factor at each MBS is given by \(\boldsymbol{\alpha_{\text{mbs}}}=[\alpha_{1},...,\alpha_{N_{\text{uabs}}}]^{T}\), and \(\boldsymbol{\beta_{\text{mbs}}}=[\beta_{1},...,\beta_{N_{\text{uabs}}}]^{T}\) is the USF/CSF duty cycle for each MBS. Finally, the positive range expansion bias at each UABS is captured in \(\boldsymbol{\tau_{\text{uabs}}}=[\tau_{1},...,\tau_{N_{\text{uabs}}}]^{T}\). Using these vectors, the initial state of the public safety AG-HetNet under consideration can be given as \(\mathbf{S}=\left[\mathbf{L}_{\text{uabs}}^{\text{3D}},\mathbf{S}_{\text{ mbs}}^{\text{ICIC}},\mathbf{S}_{\text{uabs}}^{\text{ICIC}}\right].\)  
In this simulative study, the upper bound, lower bound, and step size of these variables are defined in Table 4, where \(\mathbb{D}\alpha_{\text{mbs}}\), \(\mathbb{D}\beta_{\text{mbs}}\), \(\mathbb{D}\rho_{\text{mbs}}\), \(\mathbb{D}\rho_{\text{uabs}}\), \(\mathbb{D}\tau_{\text{uabs}}\), \(\mathbb{D}\chi\), and \(\mathbb{D}\psi\) denote the step sizes for the \(\alpha_{\text{mbs}}\), \(\beta_{\text{mbs}}\), \(\rho_{\text{mbs}}\), \(\rho_{\text{uabs}}\), \(\tau_{\text{uabs}}\), and \(x\) coordinate of a UABS's location and the \(y\) coordinate of a UABS's location, respectively. Whereas \(\rho_{\text{mbs}}^{\text{low}}\) and \(\rho_{\text{uabs}}^{\text{low}}\) denote the lower bounds for \(\rho_{\text{mbs}}\) and \(\rho_{\text{uabs}}\), respectively. Similarly, \(\rho_{\text{mbs}}^{\text{high}}\) and \(\rho_{\text{uabs}}^{\text{high}}\) denote the upper bounds for \(\rho_{\text{mbs}}\) and \(\rho_{\text{uabs}}\), respectively.