## 3 Path Loss Models
### RMa Path Loss Models  
The PL in a rural macro environment is measured using ITU-RM.2135/3 GPP TR 38.901 [43; 44]. The PL and its parameters are listed in Table 4.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Model** & **PL [dB]** &
\begin{tabular}{l} **Shadow** \\ **Fading [dB]** \\ \end{tabular} & **Parameters** \\ \hline
3 GPP LOS & \(PL-LOS=\begin{cases}PL_{1},&10\ m\leq R\leq d_{BP2}\\ PL_{2},&d_{BP2}\leq R\leq 10\ km\\ \end{cases}\) & \(0.5\) GHz \(<f<100\) GHz, \\  & \(PL_{1}=20 log_{10}(407\pi R_{3D}f/3)+min(0.03h^{1.72},10)log_{10}(R_{3D})-\\ min(0.044h^{1.72},14.77)+0.002 log_{10}(h)R_{3D}\) & \(\sigma=4.0\) & \(h_{1}=35\) m, h = 5 m \\  & \(PL_{2}=PL_{1}(d_{BP2})+40 log_{10}(R_{3D}/d_{BP2})\) & \(\sigma=8\) & \\  & where \(d_{BP2}\) is a break point distance, which is given by Equation (4). & \\ \hline
3 GPP NLOS & \(PL=max(PL-LOS,PL-NLOS)\) & \(\sigma=8\) & \(0.5\) GHz \(<f<100\) GHz \\  & \(PL-NLOS=161.94+(43.42-3.1 log_{10}(h_{1}))(log_{10}(R_{3D})-3)+20 log_{10}(f)- 3(2.3(log_{10}(11.75h_{2}))^{2}-4.97)-7.1 log_{10}(w)+\) & \(1\) m \(\leq h_{2}\leq 10\) m, \\  & \(7.5 log_{10}(h)-\left(24.37-3.7\left(\frac{h}{h_{1}}\right)^{2}\right)log_{10} (h_{1})\) & \(h_{1}=35\) m & \\ \hline \hline \end{tabular}
\end{table}
Table 4: RMa Path Loss Models.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Model** & **PL [dB]** &
\begin{tabular}{l} **Shadow** \\ **Fading [dB]** \\ \end{tabular} & **Parameters** \\ \hline
5 GCM LOS & \(PL=32.4+20 log_{10}(R_{3D})+20 log_{10}(f)\) & \(\sigma=4.1\) & \(6\) GHz \(<f<100\) GHz \\ \hline
5 GCM NLOS & \(\text{CI Model}:PL=32.4+30 log_{10}(R_{3D})+20 log_{10}(f)\) & \(\sigma=6.8\) & \(6\) GHz \(<f<100\) GHz \\  & \(\text{ABG Model}:PL=19.2+34 log_{10}(R_{3D})+23 log_{10}(f)\) & \(\sigma=6.5\) & \\ \hline
3 GPP LOS & \(PL-LOS=\begin{cases}PL_{1},&10\ m\leq R\leq d_{BP}\\ PL_{2},&d_{BP}\leq R\leq 5\ km\end{cases}\) & \(\sigma=6.0\) & \(0.5\) GHz \(<f<100\) GHz, \\  & \(PL_{1}=28+22 log_{10}(R_{3D}+20 log_{10}(f)-9 log_{10}((d_{BP})^{2}+(h_{1}-h_{2}) ^{2})\) \\  & where \(d_{BP}\) is a break point distance, which is given by Equation (1). & \\ \hline
3 GPP NLOS & \(PL=max(PL-LOS,PL-NLOS)\) & \(\sigma=6\) & \(0.5\) GHz \(<f<100\) GHz \\  & \(PL-NLOS=13.54+39.08 log_{10}(R_{3D})+20 log_{10}(f)-0.6(h_{2}-1.5)\) & \(1.5\) m \(\leq h_{2}\leq 22.5\) m, \\  & \(h_{1}=25\) m \\ \hline METIS LOS & \(PL-LOS=\begin{cases}PL_{1},&10\ m\leq R\leq d_{BP1}\\ PL_{2},&d_{BP1}\leq R\leq 5\ km\end{cases}\) & \(\sigma=4\) & \(0.45\) GHz \(<f<6\) GHz, \\  & \(PL_{1}=28+22 log_{10}(R_{3D})+20 log_{10}(f)\) & \(1.5\) m \(\leq h_{2}\leq 22.5\) m \\  & \(PL_{1}=28+22 log_{10}(R_{3D})+20 log_{10}(f)\) & \(h_{1}=25\) m \\  & \(PL_{2}=28+40 log_{10}(R_{3D}+20 log_{10}(f)-9 log_{10}((d_{BP})^{2}+(h_{1}-h_{2}) ^{2})\) \\  & where \(d_{BP1}\) is given by Equation (1) & \\ \hline METIS NLOS & \(PL=max(PL-LOS,PL-NLOS)\) & \(\sigma=6.0\) & \(0.45\) GHz \(\leq f\leq 6\) GHz \\  & \(PL-NLOS=161.94+(43.42-3.1 log_{10}(h_{1}))(log_{10}(R_{3D})-3)\) & \(10\) m \(<R<2000\) m, \\  & \(+20 log_{10}(f)-0.6(h_{2})-7.1 log_{10}(w)+7.5 log_{10}(h)\) & \(1.5\) m \(\leq h_{2}\leq 22.5\) m, \\  & \(-\left(24.37-3.7\left(\frac{h}{h_{1}}\right)^{2}\right)log_{10}(h_{1})\) & \(h_{1}=25\) m, w = 20 m, \\  & & h = 20 m \\ \hline \hline \end{tabular}
\end{table}
Table 3: UMa Path Loss Models.  
where \(G_{t}\), \(G_{r}\) are transmitter and receiver antenna gains, respectively, \(P_{t}\) is transmitter power, \(K\) is a Bolztman's constant, \(PL\) is the path loss due to various environments, \(T_{s}\) is noise temperature, \(\Gamma\) is the data rate and \(E_{b}/N_{0}\) is the ratio of energy per bit to noise spectral density.