# Explainable Machine Learning for LoRaWAN Link Budget Analysis and Modeling
## 2 AI for Propagation Modeling
### Deep Learning for Propagation Modeling  
To improve feature extraction in the AI-based propagation models, researchers have incorporated topographical characteristics of the outdoor environments (terrain features) into the propagation models. Authors in [29] recognize that empirical models only coarsely characterize the environment, and they can be inaccurate. Ray tracing solutions [30], although more accurate, have a higher computational complexity and are inflexible when utilizing global information system (GIS) maps. Hence, authors in [29; 31; 32; 33; 34] proposed deep learning (DL) through the use of the convolutional neural network (CNN) that can take GIS images of the propagation environment as input and automate the extraction of the topographical features to improve path loss estimation. The images can be collected from GIS, QGIS, Open-StreetMap, GoogleMaps, or similar platforms and could include terrain elevation, land cover, and clutter, or they could be custom-made images [32]. During the training process, DL-based models extract the features from these images in a \"black-box\" approach. Since there are no deterministic rules as to what constitutes helpful features, there is no transparency and traceability in their decision-making.  
The regression part of the problem has been addressed by using U-Net architecture [29; 31], whereas others have used MLPs. The feature maps from the last layer of the CNN are used as the inputs of the MLP to predict propagation or path loss. Each pixel within the feature map would become the input of the MLP, and the measured RSS serves as the ground truth output. Following several training iterations, updating the feature maps and MLP parameters (weights and biases), the model would be able to predict the propagation, given sets of 2D images as input. This approach essentially trains two sub-models, one of which is the CNN, trained to extract relevant features from 2D images, and a second sub-model, the MLP, to estimate the propagation. These two sub-models are inseparable as they are trained together.  
In this approach, preparing the training data requires matching the RSS with the geographical location map, which is presented as 2D images. The map is divided into grids; for instance, in [34], the propagation area was divided into blocks of 10 \(\times\) 10 square meters, where each block corresponds to a single pixel on the input image, and each pixel has a measured RSS value. In the majority of these approaches, the models are then trained using data that is simulated using various ray tracing software rather than real measurements. For instance, [PERSON] et al [32] used ray tracing to create 35,395 pairs of images and RSS predictions, Similar strategy was also used to generate 56,000 radio simulation maps in [31; 33], [PERSON] et al. [4] used a combination of 800,000 ray tracing simulations and 400,000 empirical field data, and [PERSON] et al. [34] used ray tracing, however, do not provide any information about the number of simulation samples.  
The DL-based models were able to mimic the performance of the ray tracing simulations that served as the ground truth; however, the important achievement is the run-time of using DL-based models, which is two to three orders of magnitude faster [30].  
DeepLoRa [35] uses a similar approach with a grid size of 10 \(\times\) 10 square meters. However, to solve the path-loss regression problem, a bidirectional-long short-term memory (bi-LSTM) is used instead of an MLP. The authors conducted a measurement campaign and collected a total of 30,000 RSS indicators (RSSI); however, after preprocessing and griding, it was reduced to 4000 records.