# An Advanced Path Planning and UAV Relay System: Enhancing Connectivity in Rural Environments
## 1 Introduction
### Previous Studies  
Several studies have investigated risk prioritization to determine areas of higher risk to people. In [5], fuzzy logic was used to create a risk/occupancy map and determine emergency zones in terms of visiting frequencies, wildlife, and environmental conditions. Such an approach, however, requires expert knowledge of the area and other data that are often not available. Deterministic propagation models [6] have been further used to identify areas that require assistance due to a lack of signal connectivity [7]. Here, factors such as rain, vegetation, and interference caused by nearby channels or solar radiation attenuate and distort the signal [8]. The Longley-Rice propagation model was combined with digital elevation terrain data to calculate the pathloss along the trajectory of mobile network nodes in mountains [9]. The study concluded that optimally positioned relays are required to ensure communication between nodes. Similarly, ref. [10] proposed terrain-based channel modeling for a fixed height static UAV relay to generate propagation pathloss and blockage maps for LTE using terrain and LIDAR data of rural areas. Terrain elevations and obstacles, however, were not considered in this study, reducing its applicability to mountainous areas.  
Relay path planning has been studied to overcome the challenges of a static relay. Biologically inspired search-based algorithms have shown better performance when faced with high uncertainty in unknown dynamic environments, but are too slow for real-time applications and can converge at local minima [11; 12]. Other approaches adopt statistical learning methods to optimize the charging [13] and energy consumption [14] of UAVs. These studies, however, do not consider the effect of wind, which becomes a significant factor in mountainous regions. Probabilistic channel models have also been extensively used for UAV relay paths [15; 16; 17], using either iterative convex optimization [18] or non-convex optimization techniques [19; 20]. Moreover, channel models have been combined with reinforcement learning for path optimization and relay deployment between UAVs and cell-towers in a post-disaster scenario [21]. This method, however, lacks robustness in the face of obstacles and adverse weather conditions [22]. Channel models, in fact, have been criticized for not adequately considering environmental factors and conditions [23].  
An autonomous dynamic UAV relay algorithm was proposed in [24] to adjust UAV movement in parallel to that of the mobile ground nodes. A similar approach was proposed using the \(A^{*}\) algorithm for communication and energy-aware path planning in [25; 26]. These approaches, however, use simplistic terrain models that cannot adequately cover the complex topology of mountains in the UAV-environment interaction. This is a common challenge in current air-to-ground channel modeling [27; 28; 29]. Furthermore, ref. [30] concludes that an open issue in path optimization is to design a trajectory that prevents the UAV from crossing areas with no cellular coverage. This is particularly relevant in mountain scenarios with many areas of limited or no coverage. To address this concern, ref. [31] proposed a colony optimization algorithm to plan the shortest safe path in a dense mountainous area. Nonetheless, mountains were still modeled as simple regular objects. Similarly, ref. [32] optimized the shortest flight path by considering the distances between the UAV and relevant obstacles using unrealistic terrain models that do not match the complexity of real-world data. Conversely, ref. [33] employed a viewshed algorithm to generate UAV paths that maximize the visual coverage of hidden areas in a target territory.