# Feasibility Analysis of a LoRa-Based WSN Using Public Transport
## 3 Theoretical Analysis of Propagation Performance
\[\mathrm{L_{P}}\big{|}_{\mathrm{dB}} = 69.55+26.16\log_{10}\mathrm{f}-13.82\log_{10}\mathrm{h_{T}}- \mathrm{a(h_{R})}+\ \left(44.9-6.55\log_{10}\mathrm{h_{T}}\right)\log_{10}\mathrm{d} \tag{2}\] \[\text{where for large cities a(h_{R}) }=\ 3.2\big{[}\log_{10}(11.75\cdot\mathrm{h_{R}})\big{]}^{2}-4.97. \tag{3}\]  
Even if a LoRa receiver can have a sensitivity up to \(-157\) dBm [39], a lower reasonable limit for received power \(\mathrm{P_{R}}\) has been set to \(-120\) dBm. It is a receiver hypothetical sensitivity value that ensures correct reception with a good margin, including all the possible sources of additive path losses. A 0-dB gain antenna for both transmitter and receiver antennae is assumed, in order to simulate them as omnidirectional sources because we do not know their orientation, and by varying the transmitted power it is possible to obtain different distances covered by the signal. According to LoRa specifications and European regulations, the transmitter power can vary from a minimum value of 0 dBm up to maximum value of 14 dBm. The LoRa operating frequency is 868 MHz. At first, the heights of transmitter and receiver are supposed to both equal 3 m and then the receiver height was assumed at 20 m in order to simulate a different possible scenario of installations in an urban environment. By means of Equations (1)-(3), we can evaluate the maximum communication ranges reported in Table 1, assuming a real antenna with gains = 3.16 dB. The results are reasonable for the deployment of a DMS based on the LoRa technology in an urban area. The LoRa end-node installed on a public transport vehicle can communicate with the nearest gateway at less than 500 m apart if operating in the lower possible power consumption mode (transmitting only 0 dBm). Of course, this range can be increased using proper antenna with a gain greater than 0 dB. In that case, the maximum distance between nodes and gateways can be around half a kilometer: An example of tentative installation of gateways in Turin is reported in Figure 1. It appears that the maximum distance between two bus stops, where the first level gateways will be installed, does not exceed some hundreds of meters. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Transmitted Power [dBm]**} & \multicolumn{2}{c}{**Maximum Range [m]**} \\ \cline{2-3}  & \(\mathrm{h_{r}}\) = 3 m & \(\mathrm{h_{r}}\) = 20 m \\ \hline
0 & 552 & 923 \\
5 & 727 & 121 \\
14 & 1194 & 1998 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Transmitted power and maximum range using the Okumura–Hata model for urban environments and two receiver heights \(\mathrm{h_{r}}\) = 3 m and \(\mathrm{h_{r}}\) = 20 m.  
A comparison between the theoretical results obtained with the Okumura-Hata model and some experimental measurements is given in [40], where some preliminary propagation tests using both a point-to-point and a star topology network are introduced. The tests demonstrate the capability of the system to correctly receive data, in terms of both received power and packet error rate, over a range of about 800 m. They demonstrate that LoRa can be used in a noisy urban environment.