# Explainable Machine Learning for LoRaWAN Link Budget Analysis and Modeling
## 4 Discussion and Conclusions  
To summarize the benchmark, the Nash-Sutcliffe model coefficient (NSC) [38] and the RMSE values for all the models are compiled in Table 1. This comparison aims to assess the effectiveness of the various ML algorithms in developing a model for LoRa's signal propagation. The NSC is utilized primarily because it is not sensitive to the dynamic range of the dependent variable, in this case, the RSSI. This attribute of NSC is particularly advantageous, as the sensitivity of one wireless technology can vary, therefore providing a more consistent and technology-agnostic measure. NSC ranges from 1 to \(-\infty\), with \(\text{NSC}=1\) indicating a perfect prediction, and \(\text{NSC}\leq 0\) indicates that the model's predictive power is no better than a simple mean of the RSSI. Finally, RMSE is provided as the most commonly reported measure in the literature. Focus of this article is not on asserting a general superiority of one machine algorithm over others; instead, it emphasizes the importance of careful model selection based on factors such as dataset size, tunable parameters, computational power, and specific problem requirements, including explainability of decision-making. The article provided an overview of the cutting-edge developments in AI-driven LoRa propagation modeling. Different methods of extracting topographical features and embedding them in regression modeling algorithms were discussed and compared. Decoupling these two tasks via separate models alleviates the reliance on large simulation data, as even limited field measurement data proves to be adequate for effectively addressing the regression problem. Moreover, the utilization of deterministic terrain features in conjunction with tree-based models, particularly GR, marks a stride towards the realm of XAI. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Model**} & **RMSE** & **NSC** \\ \hline \multirow{3}{*}{Parametric regression} & Optimized FSPL & 9.01 & 0.25 \\  & LR & 8.01 & 0.37 \\  & PR & 6.65 & 0.67 \\ \hline \multirow{3}{*}{Advanced nonlinear} & MLP & 6.85 & 0.62 \\  & ANFIS & 7.16 & 0.57 \\ \hline \multirow{3}{*}{Kernel based} & SVM & 7.03 & 0.58 \\  & RVM & 7.19 & 0.57 \\ \hline Instance based & KNN & 6.7 & 0.63 \\ \hline Tree based & DT & 6.54 & 0.71 \\ \hline \multirow{3}{*}{Ensemble of trees} & RF & 5.7 & 0.77 \\  & GR & 5.53 & 0.78 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparing RMSE and NSC tuned models using the holdout set. GR emerged as a superior choice in terms of accuracy, efficiency in tuning, training, and prediction speed. SVM was highly sensitive to the kernel coefficient optimization, and ANNs were highly sensitive to the number of hidden layers. However, GR achieved much better results out of the box with minimal effort. Its interpretability was instrumental in both quantitative and qualitative analysis of the propagation variables and their impact. Decoupling the regression and feature extraction and use of GR facilitated a deeper comprehension of the underlying mechanisms governing LoRa's propagation. This unveiled a more nuanced understanding of these complex interactions, which is not possible through a black box feature extraction approach and is yet to be addressed with the further advanced techniques of the XAI. Employing parametric (LR, PR) or tree-based (DT, RF, and GR) models with pre-extracted features directly enhances the explainability of the propagation model. Their inherent transparency and simplicity make them ideal for generating insights into complex model behaviors. In fact, these models are exploited by advanced techniques such as local interpretable model-agnostic explanations (LIME) [39] to provide AI interpretability for more complex models. LIME, in particular, leverages these models to create local, understandable approximations of predictions made by more complex algorithms [40]. This is essential in domains where understanding the 'why' behind a prediction is as crucial as the prediction itself. Conceptualization, S.H.