# Explainable Machine Learning for LoRaWAN Link Budget Analysis and Modeling
## 1 Introduction  
The Internet of Things (IoT) and Artificial Intelligence (AI) are at the forefront of the fast-growing technology. The growth in IoT devices has been extraordinary, with a significant surge in recent years, where projections suggest over 75 billion interconnected devices by 2025 [1]. The deployment of Artificial Intelligence (AI) has led to its more profound integration into daily life, intertwining closely with technologies like the Internet of Things (IoT) [2]. The widespread adoption and deployment of IoT devices pose many challenges, and it necessitates thorough and meticulous planning to ensure the smooth and uninterrupted operation of these extensive networks [3]. It is established in [4] that a dense deployment of IoT devices may have high levels of interference and result in packet loss. This planning overlooks several aspects of the IoT networks, such as seamless functionality by minimizing dead zones, interference mitigation and quality of service, cost optimization, scalability, and energy efficiency. [PERSON] et al. [5] state that enhancing the transmission performance is a key issue that should be resolved by effectively optimizing the resource allocation in the LoRa network [6], and that can be achieved by adjusting the transmission parameters. [PERSON] et al. [7] characterize long-range communication, low data rate transmission, low energy consumption, and cost-effectiveness as the main requirements of IoT applications, all of which are present in Low-Power Wide Area Networks (LPWAN) technologies. LoRaWAN, Sigfox, NB-IoT, LTE-M, and EC-GSM are some of the well-established technologies in this category, with LoRaWAN being the most cost-efficient, especially where device density is low. A comprehensive comparison of LPWAN technologies is provided in [8]. One of the main advantages of LoRa, which has contributed to its popularity and extensive utilization, is its open-source technology, which enables autonomous and cost-effective setup [9]. Additionally, the spreading factor (SF) of the proprietary chirp spread spectrum (CSS) modulation further improves the overall sensitivity of the device and increases interference immunity [10]. The impact of SF on the data rate and time-on-air can be precisely calculated [11], whereas its impact on propagation range and the link budget requires empirical experimentation. For instance, [PERSON] et al. [10] observed an equivalent range extension of about 500 m when switching from SF 7 to SF 12 in an urban area. Additionally, adjusting the transmission power and SF can directly impact the per-bit energy consumption of the LoRa network [12]. To fully understand the behavior of CSS and SF in various environments, researchers have conducted several empirical measurement campaigns in indoor environments [13; 14; 15; 16], outdoor urban and rural areas [7; 17], and even on the sea with line of sight (LoS) [18]. These empirical measurements are then compared and analyzed against propagation models to establish a model for LoRa and estimate the coverage using the received signal strength (RSS). Therefore, it is crucial to use accurate models to estimate and plan the network. Traditional empirical models, often used in this context, were initially developed for technologies and frequencies different from those used in LoRa. For instance, models like the Log-distance and Okumura-Hata are employed in simulation tools such as LoRaSim, SimLoRaSF, LoRWAN-Sim, and the NS3-Module for their simplicity [11]. These models take a simplistic approach to characterize the propagation in the environment [19]. However, in recent years, many have taken advantage of AI to develop innovative complex models to enhance their performance. [PERSON] et al. [20] highlight that even the AI-based models show limited ability to generalize to new hardware effects and channel conditions across different transmitter and receiver pairs. The main contributions of this article are:  
1. Critical analysis of the latest AI advancements in the area of propagation modeling. 2.