# PS-CARA: Context-Aware Resource Allocation Scheme for Mobile Public Safety Networks
## 3 System Model
Thus, user received SINR (\(\gamma\)) can be evaluated as  
\[\gamma_{u\to k}^{\text{rx}}(j,r)=\frac{P_{u\to k}^{\text{tx}}(j,r)|h_{u\to k}(j,r)| ^{2}}{\sum_{u=2,u\
eq 1}^{U}|h_{u}(j,r)|^{2}P_{u}^{\text{rx}}(j,r)+\sigma^{2}}. \tag{4}\]  
The channel gain \(h_{u}\) in (4) can be expressed as \(h_{u}=FSL\), where \(L\), \(F\), and \(S\) are the pathloss, fading, and shadowing models, respectively. In this paper, \(L\) for user \(u\) connected to MBS and mPC can be evaluated by using Urban area path loss model and WINNER + B1 model [34], respectively. The urban area path loss model is considered to model the path loss between the outdoor MBS and outdoor user connected with MBS based on 3 rd generation partner ship project (3 GPP) recommendation [35]. To model the path loss between the user connected to the mPC and user, we consider WINNER + B1 model with line-of-sight (LOS) scenario as suggested in [34] for moving networks. Moreover, different values used in these path loss models are calculated based on different parameters such as base station and user antenna height, and carrier frequency [36]. The path loss models considered are \[L(dB)=\left\{ \begin{array}{ll}15.3+37.6\log 10(d)&\text{Urban area model}\\ 35.4+22.7\log 10(d)&\text{WINNER + B1},\end{array} \right. \tag{5}\]  
where \(d\) is the distance from user \(u\) to BS. The fading \(F\) is calculated by using Ped-B model defined by International Telecommunication Union (ITU) [37]. The shadowing \(S\) follows the log-normal distribution, that is if any positive random variable \(X\in S\) is log-normally distributed, then their logarithm is normally distributed \(\mathcal{N}(\mu,\sigma)\). To efficiently allocate the access link (AL) resources among users, mPC spectrum access ratio \(\eta\in\{0,1\}\) is introduced. This can dynamically adjust the allocated BW based on mPC load conditions [14]. That is, if the number of mPUEs are less in a system, then remaining BW is distributed among the non-PS users. By simulations, we found that \(\eta=0.4\) and \(\eta=0.7\) suits for non public safety and public safety scenarios, respectively. Moreover, two indicators are introduced in this paper: (1) the user association indicator \(\beta_{u,\text{m/k}}\in\{0,1\}\) which indicates whether user \(u\) is associated with m/k-th BS and (2) the public safety priority indicator variable \(\delta_{u}\in\{0,1\}\), where \(\delta_{u}=0\) indicates that user \(u\) is non-public safety user and \(\delta_{u}=1\) indicates it is a public safety user. Since our target is to associate users based on the loading conditions of BSs. The total load on k-th MBS and m-th mPC is calculated as  
\[\rho_{\text{k}}^{\text{PS/NPS}} =\sum_{u\in U}\beta_{u,\text{k}}r_{u}, \tag{6}\] \[\rho_{\text{m}}^{\text{PS}} =\sum_{u\in U}\delta_{u}\beta_{u,\text{m}}r_{u},\] (7) \[\rho_{\text{m}}^{\text{NPS}} =\sum_{u\in U}\beta_{u,\text{m}}r_{u}, \tag{8}\]  
where \(r_{u}\) is the allocated RB to user \(u\). Moreover, in (7) there is an additional \(\delta_{u}\) parameter that allows only PS users with high priority to access the mPC spectrum. Based on these loads, the total achievable data rate for the users connected with MBS and mPC are evaluated as  
\[C_{\text{k}}^{\text{NPS}}= \rho_{\text{k}}^{\text{PS/NPS}}[R+(1-\eta)R]\sum_{u\in U}(1+\gamma _{u\to k}^{\text{rx}}(j,r)), \tag{9}\] \[C_{\text{m}}^{\text{PS}}= \rho_{\text{m}}^{\text{PS}}R\eta\sum_{u\in U}(1+\gamma_{u\to k }^{\text{rx}}(j,r)),\] (10) \[C_{\text{m}}^{\text{NPS}}= \rho_{\text{m}}^{\text{NPS}}R\eta\sum_{u\in U}(1+\gamma_{u\to k }^{\text{rx}}(j,r)), \tag{11}\]  
where in (9), the term \((R+(1-\eta)R)\) represents that the MBS users (MUE) can access some RBs of mPC based on \(\eta\). If enough free spectrum of mPC is available then \(\eta\) reduces, and non-PS users can also access the freely available mPC spectrum.