# LoRa Technology Propagation Models for IoT Network Planning in the Amazon Regions
## 4 Propagation Model
### Recommendation ITU P-833 and the Vegetation Loss Model  
Figures 5 and 6 depict significant vegetation between the gateway and LoRa end node. In this context, we present previous studies that examine the attenuation caused by vegetation loss [31; 46; 47; 48]. In [31], they consider two parameters related to trees--the leaf area index and the diameter of the tree trunk--for propagation loss studies in the LoRa channel, but they do not provide results for a link with dense vegetation. In [46], the LoRa operating frequency is 433 MHz and investigates the attenuation produced by the leaves. The study in [47] explores the transmission capacity of LoRa technology in environments covered by vegetation, characterized by attenuation due to foliage, branches, and tree trunks. The study involves multiple LoRa devices connected to the gateway, with a maximum distance of 200 m. Reference [48] highlights possible factors responsible for degrading the quality of the LoRa channel through the leaf medium, but it does not analyze dense vegetation. Therefore, studying the effect of Amazon vegetation on the LoRa uplink channel is crucial. ITU Recommendation P-833-10 provides several models for evaluating the impact of vegetation on radio wave signals, applicable to various path geometries and vegetation types [49]. The Recommendation also includes measured data on vegetation fading dynamics and propagation delay characteristics. The Recommendation presents the additional loss due to vegetation, and it can be characterized based on two parameters:  
1. The specific attenuation rate (dB/m) refers to the reduction in signal strength per unit distance due to energy dispersion occurring outside the direct path between the transmitter and the receiver;
2. The maximum additional attenuation due to vegetation in a radio path (limited by other mechanisms) is the sum of propagation of surface waves over the top of the vegetation medium and direct scattering within it (in dB). Figure 7 illustrates the radio path in a woodland area, with antennas positioned outside the woodland. Key factors influencing signal quality include the elevation angle (\(\theta\)) at which the radio signal travels, the length of vegetation (\(d\)) along the signal path, the average height of trees (\(h_{v}\)), the height of the receiving antenna above the ground (\(h_{u}\)), and the distance between the antenna and the roadside forest (\(d_{w}\)). In the modeling link shown in Figure 7, the transmitting equipment is higher than the receiving equipment. However, in our measurement methodology, the receiving equipment is higher than the transmitting equipment. This is because communication between LoRa devices is of the uplink type;  
the message is sent from the end node on the drone and received at the gateway fixed at Mirante do Rio. Consequently, our analysis considers an elevation angle value (\(\theta_{d}\)) dependent on the total vegetation depth distance (\(d_{vegetation}\)). Figure 8 illustrates the location of the LoRa gateway (blue icon), the LoRa end node (with an icon), and the vegetation depth (red rectangle) used to calculate the elevation angles (\(\theta_{d}\)). These elevation angles depend on the depth of vegetation along the entire route. The orange icons represent the locations where data were measured, as shown in Figure 6. It is important to note that we used total vegetation depth values throughout the route. This implies that for each SF value, we collected various distance values between the gateway and the LoRa end node, and then added each distance value with vegetation between the devices to calculate the elevation angles. The Recommendation presents modeling for vegetation in different seasons.