## 5 Coverage Analysis
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & & **LoRa** & **NB-IoT** \\ \hline \multirow{3}{*}{Vehicle} & \(P_{t}\) (dBm) & \(+14\) & \(+23\) \\  & \(L_{t}\) (dB) & \(0.5\) & \(0.5\) \\  & \(G_{t}\) (dBi) & \(2\) & \(2\) \\ \hline Channel & \(m\) (dB) & \(0\ldots 30\) & \(0\ldots 30\) \\ \hline \multirow{3}{*}{GW/BS} & \(G_{r}\) (dBi) & \(5\) & \(18\) \\  & \(L_{r}\) (dB) & \(0.5\) & \(3\) \\  & \(S\) (dBm) & \(-139.5\) (SF12) & \(-125\) \\ \hline \multirow{3}{*}{GW/BS} & \(PL_{max}\) (dB) & \(159.5\ldots 129.5\) & \(164.5\ldots 134.5\) \\ \cline{1-1}  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Link budget for uplink channel of LoRa and NB-IoT connectivity technologies. Path loss is a major characteristic of wireless channels that represents the attenuation of the radiated signal from a transmitter to a receiver due to the traveled distance. Therefore, the key factor for the link budget calculation is the path loss model [50]. Depending on the nature of the propagation environment, several path loss models have been introduced in the literature [51]. The Hata model (also known as the Okumura-Hata model) is widely used to predict propagation path loss in urban areas. The Hata model also has an extended formulation for path loss in suburban and rural areas. It should be emphasized that the Hata model is applicable in the range of frequency from 150 MHz to 1500 MHz, and it is suitable for a coverage range of up to 100 km [52]. In urban areas, the Hata model gives the path loss as follows [53]. \[ \begin{split} PL_{Urbm}&=69.55+26.16\times\log_{1 0}f-13.82\times\log_{10}h_{b}-\phi\\ &+\left(44.9-6.55\times\log_{10}h_{v}\right)\times\log_{10}d\end{split}  \tag{3}\]  
where \(d\) is the distance, \(\phi\) is the correction factor, \(h_{b}\) is the GW/BS antenna height, \(h_{v}\) is vehicle (or machinery) antenna height, and \(f\) is the frequency in MHz. The correction factor was given as follows:  
\[\phi=3.2\times[\log_{10}h_{v}]^{2}-4.92. \tag{4}\]  
The Hata model also specifies the path loss for suburban and rural areas as follows [53]:  
\[PL_{Suburban}=PL_{Urbm}-2\times\left(\log_{10}\left(\frac{f}{28}\right)\right) ^{2}-5.4, \tag{5}\]  
\[PL_{Rural}=PL_{Urbm}-4.78\times\left(\log_{10}f\right)^{2}+18.33\times\log_{10} f-40.98. \tag{6}\]  
Figure 5: LoRa uplink channel from vehicle to GW. Figure 6: NB-IoT uplink channel from vehicle to BS. It should be emphasized that the correction factor is different for rural/suburban areas, and it can be calculated as follows:  
\[\phi=0.8+(1.1\times\log_{10}f-0.7)\times h_{v}-1.56\times\log_{10}f. \tag{7}\]  
According to path loss expressions as a function of distance, the coverage of LoRa and NB-IoT links can be calculated from the \(10^{\psi}\) formula. Therefore, considering the different propagation environments, \(\psi\) parameter can be derived as follows:  
\[\psi_{Urban} =\frac{PL_{Urban}-74.47-26.16\times\log_{10}f-13.82\times\log_{10 }h_{b}}{44.9-6.55\times\log_{10}h_{v}} \tag{8}\] \[+\frac{3.2\times[\log_{10}h_{v}]^{2}}{44.9-6.55\times\log_{10}h_{v }},\]  
\[\psi_{Suburban} =\frac{PL_{Suburban}-63.35-27.72\times\log_{10}f-13.82\times\log _{10}h_{b}}{44.9-6.55\times\log_{10}h_{v}} \tag{9}\] \[+\frac{(1.1\times\log_{10}f-0.7)\times h_{v}+2\times\left(\log_{1 0}\left(\frac{f}{8}\right)\right)^{2}}{44.9-6.55\times\log_{10}h_{v}},\]  
\[PL_{Suburban}=PL_{Urbm}-2\times\left(\log_{10}\left(\frac{f}{28}\right)\right) ^{2}-5.4, \tag{5}\]0 \[PL_{Suburban}=PL_{Urbm}-2\times\left(\log_{10}\left(\frac{f}{28}\right)\right) ^{2}-5.4, \tag{5}\]1  
The obtained equations show that the transmission range can be determined depending on the path loss, antenna heights, and frequency. When these parameters are known, the maximum transmission distance can be estimated by using the link budget calculation on the uplink channel. In the presented framework, the coverage range of a single GW for LoRa connectivity and a single LTE BS for NB-IoT connectivity has been investigated through computer simulations using MATLAB software.