## 2 System Methodology for Coexisting Public Safety Networks
### Details of the Network Layout  
Low-power smalls cells are used in the existing macro-cell infrastructure to achieve a 1000-times data rate for 5G systems [23]. Furthermore, benefits like suitability for less consumption of power and reliability for PS scenarios are driving 5G systems to focus on a user-centric strategy, thus providing an even user experience everywhere and anytime. These objectives can be accomplished by setting up a centrally managed software-defined networking (SDN) architecture-based 5G mobile personal cell that can meet users' needs by giving extensive connectivity, depending on the situation [19].  
In this paper, we consider an uplink LTE-A system. We assume a K-tier system (K = 1) in which M macro-cells (eNBs), N mPCs, and L hexagonal sectors (L = 3) are deployed. The N mPCs are randomly deployed. We denote all base stations (BSs) with B (eNBs M + mPCs N), and all users (i.e., LTE-R users, PS-LTE users, and mPC users) with U. We consider base stations and users to be transmitting with power \(P_{K}^{R}\) and \(P_{K}^{U}\), resepectively. The user \(u\) association is done with only one base station at a time. According to the eICIC, the all resource blocks (RBs), R, are allocated to users in such mechanism, i.e., the user can either get blank (b) or non-blank (n) RBs. As we consider the PS priority mechanism, both high-priority and low-priority users exist in the system. In order to facilitate a high-priority user, we reserve the blank RBs, and after that, low-priority users will be served. Moreover, we consider the following two variables: (1) \(\beta_{j,u}^{(n)},\;\;\beta_{j,u}^{(b)}\in\{0,1\}\) means the user is connected to BS \(j\) using a non-ABS (n) or a blank (b) RB; and (2) \(\delta_{u}\in\{0,1\}\) shows the PS priority indicator, i.e., \(\delta_{u}\) = 0 for non-LTE-R user \(u\), and \(\delta_{u}\) = 1 for LTE-R user \(u\). Furthermore, users can shift to connect with another BS in order to balance the system load, while the LTE-R user sticks to the attached serving BS. Two factors are involved in the user association with BS \(j\)[13]:  
\[\rho_{eN\beta_{j}/m\mathrm{PC}_{j}}^{(n)}=\;\frac{1}{(1-v)R}\sum\
olimits_{u \in U}\beta_{j,u}^{(n)}r_{j,u}^{(n)} \tag{1}\]  
\[\rho_{eN\beta_{j}}^{(b)}=\;\frac{1}{vR}\sum\
olimits_{u\in U}\beta_{j,u}^{(b) }r_{j,u}^{(b)} \tag{2}\]  
where \(r_{j,u}^{(n)}\) and \(r_{j,u}^{(b)}\) present the required RBs for user \(u\) associated with BS \(j\) by using (\(n\)) or (\(b\)) RBs, respectively. LTE-R users have priority to access the blank RBs of mPC \(j\) during the ABS period. However, when high-priority users are fewer in number, and enough RBs are available, then the low-priority users can connect with mPC \(j\). The normalized load on mPC \(j\) during RBs is written as follows [13]:  
\[\begin{array}{c}\rho_{eN\beta_{j}/m\mathrm{PC}_{j}}^{(n)}=\;\frac{1}{(1-v)R} \sum\
olimits_{u\in U}\delta_{j,u}^{(n)}\beta_{j,u}^{(n)}r_{j,u}^{(n)}\\ \rho_{m\mathrm{PC}_{j}}^{(b)}=\;\frac{1}{vR}\sum\
olimits_{u\in U}\delta_{j,u} ^{(b)}\beta_{j,u}^{(b)}r_{j,u}^{(b)}\\ \text{with }\delta_{u}=\left\{\begin{array}{ll}1,&LTE-R\;user\\ 0,&non-LTE-R\;user\end{array}\right.\end{array} \tag{3}\]where \(r_{j,u}^{(n)}\) and \(r_{j,u}^{(b)}\) present the required RBs for user \(u\) associated with BS \(j\) by using \((n)\) or \((b)\) RBs, respectively. \(\delta_{u}\in\{0,1\}\) shows the PS priority indicator, i.e., \(\delta_{u}=0\) for non-LTE-R user \(u\), and \(\delta_{u}=1\) for LTE-R user u. Hence, the total of the required RBs for BS \(j\) is calculated as follows [13]:  
\[\rho_{eNB_{j}/mPC_{j}}=(1-v)R\rho_{eNB_{j}/mPC_{j}}^{(n)}+vR\rho_{eNB_{j}/mPC_{ j}}^{(b)} \tag{4}\]  
where \(\rho_{j}\) represents the load of BS \(j\) as calculated in Equations (1)-(3).  
QoS for users can be potentially improved by deploying the mPC in the targeted deployment area, like PS scenarios. The mPC can try for offloading gain by facilitating more users.