# Monitoring System of Transmission Line in Mountainous Area Based on LPWAN
## 3 Model and Method  
### Path Loss Model Design  
The transmission line environment in a mountainous area has the characteristics of a deep valley, curved line, and rich surrounding vegetation. Therefore, the interference of radio signals in a mountainous area is stronger than that in a plain area, and the path loss is higher [36]. The transmission of a LoRa signal in a mountainous environment is easily affected by electromagnetic interference [37], mountain shelter, vegetation reflection and absorption, and other factors. It can be seen from [38] that in the mountain monitoring environment, mountain occlusion had the greatest interference on the LoRa signal. Therefore, the path loss model was established according to the influence of mountain shelter on the LoRa signal.  
Figure 1: Design of the system monitoring scheme in a mountainous area.  
Figure 2: Monitoring network structure of the transmission line in a mountainous area.  
The signal strength of the LoRa transceiver module at a certain point is the difference between the field strength excited by the base station at the antenna and the field strength loss when the signal propagates to the point:  
\[E_{R}=E_{T}-L_{ps} \tag{1}\]  
where \(E_{T}\) is the field strength excited by the LoRa transceiver module at the antenna and \(L_{ps}\) is the median path loss caused by signal propagation. When the signal has no direct propagation path, the diffraction effect will occur, as shown in Figure 3. The distance of the diffraction path is calculated as follows:  
\[d_{D}=\sqrt{d_{1}^{2}+\left(h_{m}-h_{T}\right)^{2}}+\sqrt{d_{2}^{2}+\left(h_{ m}-h_{R}\right)^{2}} \tag{2}\]  
where \(d_{D}\) is the diffraction distance; \(d_{1}\) is the distance between the LoRa transceiver module antenna and the mountain; \(d_{2}\) is the distance between the receiving antenna and the mountain; \(h_{m}\) is the altitude of the mountain; \(h_{T}\) is the altitude of the LoRa transceiver module antenna; and \(h_{r}\) is the altitude of the receiver antenna. In order to display the diffraction principle of a wireless signal in a mountainous area more intuitively, the schematic diagram, as shown in Figure 3, was constructed by simulating the topography of the southwest mountainous area.  
Figure 3 shows the LoRa signal transmission diffraction model established according to the western mountain environment. The LoRa signal passes through the diffraction path 1 from point \(a\) to point \(b\), and its diffraction law and signal field strength can be analyzed by the Egli model. The Egli propagation model is a simplified wireless propagation model on irregular terrain, which is a statistical model based on a large number of test data, which can reflect the attenuation law and signal trend in an irregular environment. Compared with other terrains, the Egli model can be used to evaluate hilly and mountainous areas as the field strength of the shape is more accurate. The empirical equation of the Egli wireless signal transmission loss is as follows:  
\[L_{ps}=88+20\lg f+40\lg d-20\lg(h_{t}h_{r})-K_{h} \tag{3}\]  
where \(f\) is the radio frequency; \(h_{t}\) is the height of transmitting antenna of LoRa transceiver module; \(h_{r}\) is the height of receiving antenna; \(d\) is the distance between receiving and transmitting antennas; and \(K_{h}\) is terrain correction factor. When the average relief height \(K_{h}\) of the terrain around the test point was equal to 15 m, \(K_{h}\) was taken as 0; when the terrain relief height \(H\) around the test point was greater than or less than 15 m, the terrain correction factor should be added. For the 150 MHz frequency band, the terrain correction factor \(K_{h}\) can be obtained by the following equation:  
\[K_{h}=-0.143H+2.143 \tag{4}\]  
where \(H\) is the average relief height of the terrain around the test point.  
Figure 3: Principle of wireless signal diffraction.