## 3 Link Level Parameters and Channel Coefficient Generation
### Propagation Conditions and Pathloss Calculation  
In this step, we need to evaluate the propagation condition for each BS-UT link by calculating the \(LOS\) probability. If UT \(k\) is an outdoor user, the parameter \(d_{3D}^{k}\) denotes the pure distance between the BS and the \(k\)-th UT in a 3-D coordinate system, while the parameter \(d_{2D}^{k}\) denotes the projection of \(d_{3D}^{k}\) on the \(x\)-\(y\) plane. The relation between the 2-D distance \(d_{2D}^{k}\) and the 3-D distance \(d_{3D}^{k}\) is given by  
\[d_{3D}^{k}=\sqrt{(d_{2D}^{k})^{2}+(h_{BS}-h_{UT}^{k})^{2}} \tag{29}\]  
where \(h_{BS}\) is the height of the BS and \(h_{UT}^{k}\) represents the height of \(k\)-th user. Instead, if UT \(k\) is an indoor user located inside a building, the parameter \(d_{3D}^{k}\) can be considered as the sum of the two components \(d_{3D-out}^{k}\) and \(d_{3D-in}^{k}\), the former denotes the distance from the BS to the building external wall while the latter denotes the distance from building external wall to the user. The same consideration can be made for \(d_{2D}^{k}\), the projection of \(d_{3D}^{k}\) on the \(x\)-\(y\) plane, therefore \(d_{2D}^{k}=d_{2D-out}^{k}+d_{2D-in}^{k}\) and so the new relation between the 2-D and 3-D distances becomes \[d^{k}_{3D-out}+d^{k}_{3D-in}=\sqrt{\left(d^{k}_{2D-out}+d^{k}_{2D-in}\right)^{2}+ \left(h_{BS}-h^{k}_{UT}\right)^{2}}. \tag{30}\]  
Table 7.4.2-1 of [21] provides all details to evaluate the \(LOS\) probability \(P_{LOS}\) for each scenario. Mainly, the proposed \(P_{LOS}\) depends on the 2-D distance between BS and UT, \(d^{k}_{2D}\) for outdoor-to-outdoor (O2O) users and \(d^{k}_{2D-out}\) for outdoor-to-indoor (O2I) ones. As an example, we show how to evaluate the \(LOS\) probability for the UMi-Street canyon scenario for the \(k\)-th user:  
\[P^{k}_{LOS}=\left\{ \begin{array}{ll}1&d^{k}_{2D-out}\leq 18\,\mathrm{m}\\ \frac{18}{d^{k}_{2D-out}}+\exp\left(-\frac{d^{k}_{2D-out}}{36}\right)\left(1- \frac{18}{d^{k}_{2D-out}}\right)&d^{k}_{2D-out}>18\,\mathrm{m}\end{array} \right. \tag{31}\]  
for UMi and UMa scenarios, the \(LOS\) probability is 1 for distances smaller than 18 m, and decreases with the distance above this threshold. According to the propagation conditions described in the previous step, here we calculate the path loss (PL) for each BS-UT link. Table 7.4.1-1 of [21] depicts the formulae for PL evaluation, for UMi and UMa in both cases, \(LOS\) and \(NLOS\). Unlike the \(LOS\) probability, the path loss is mainly dependent on the 3-D distance between BS and UT, and the carrier frequency \(f_{c}\). In (32) it is shown, as an example, how to evaluate the path loss for the UMi-Street canyon scenario for the \(k\)-th user in the case of \(LOS\) presence:  
\[PL^{k}_{LOS}=\left\{ \begin{array}{ll}PL_{1}&10\,\mathrm{m}\leq d^{k}_{2D} \leq d^{k}_{BP}\\ PL_{2}&d^{k}_{BP}<d^{k}_{2D}\leq 5\,\mathrm{km}\end{array} \right. \tag{32}\]  
with  
\[PL_{1}=32.4+21\log_{10}(d^{k}_{3D})+20\log_{10}(f_{c}) \tag{33}\] \[PL_{2}=32.4+40\log_{10}(d^{k}_{3D})+20\log_{10}(f_{c})-9.5\log_{ 10}\left[(d^{k}_{BP})^{2}+(h_{BS}-h^{k}_{UT})^{2}\right]\]  
Moreover, \(d^{k}_{BP}\) is the breakpoint distance for the \(k\)-th user (Table 7.4.1-1 of [21]), \(h_{BS}\) is the height of the base station, while \(h^{k}_{UT}\) represents the height of the \(k\)-th user, both expressed in meters, and \(f_{c}\) is the carrier frequency in \(Hz\). For indoor users, additional losses are added by taking into account the walls of the building and the losses inside the building as follows  
\[PL^{ind}=PL_{b}+PL_{tw}+PL_{in}+\mathcal{N}(0,\sigma^{2}_{P}) \tag{34}\]  
where \(PL_{b}\) is the basic outdoor path loss, \(PL_{tw}\) is the building penetration loss through the external wall, \(PL_{in}\) describes the inside loss dependent on the depth into the building, and \(\sigma_{P}\) represents the standard deviation for the penetration loss.