## 2 Related Work  
Previous works have experimentally analyzed the performance of LoRa systems for multiple parameters, with coverage areas ranging from typical indoors [14; 15; 16] to campus [17; 18; 19; 20] and city scales [21; 22; 23; 24]. Standard analytic prediction models are based on path-loss formulations optimized for specific power damping conditions, e.g., cityscapes [20; 22] and others [25]. For the spatially-resolved RSSI, different numerical approaches may be considered, depending on the distance regime [22; 26]: for shorter distances (line-of-sight), ray-based models are used [27; 28]. For longer distances, diffraction effects become dominant, and either the uniform geometrical theory of diffraction (UTD) [29], often combined with ray-launching methods [30; 31; 32; 33] (indoors), or knife-edge models [34; 35] can be applied. Different knife-edge methods include the forward [36] and two-way [37; 38] parabolic equation (PE)-based approaches, which are implemented either in the frequency [35] or time-domain [39; 40]. For longer distances, scattering becomes the dominant effect, and the Okumura-Hata model [41] and the Longley-Rice irregular terrain model (ITM) [42; 43] are most popular. The latter is prevalent because it uses real-world data, such as topography and weather parameters, to generate simulated RSSI maps. More recently, the updated ITM with obstructions model (ITWOM) [24; 44] provides improved signal descriptions around obstacles. In the cityscape regime, diffraction effects are dominant. This rules out the usage of simpler ray-based algorithms that do not take diffraction into account. Knife-edge methods such as the two-way PE [45] consider diffraction, but its application to complex real-world building geometries is challenging. The ITM is likely the most thorough method. However, it is highly demanding on computational requirements and simulation time. Recent efforts to improve the simulation times include a parallel graphical processing unit (GPU) [46] enhanced ITM implementations. Still, ITM is better suited for high power, very long-range scenarios, as ITM-generated maps usually lack the diffraction resolution required for city-scale low-power IoT and smart-city applications. This work aims to overcome the lack of physical accuracy associated with standard ray-based signal-coverage models and single and two-way PE methods, which do not consider multiple reflections between building walls. We present a new approach to achieving high-resolution city-scale RSSI maps while minimizing the computational resources required. We propose using a versatile electromagnetic wave-propagation algorithm that considers crucial effects such as absorption and reflection. Such radiation-matter interaction algorithms are conventional in light-propagation applications, for which the Finite Element Method (FEM) [47] and the Finite-Difference Time-Domain (FDTD) [48; 49] methods are the most popular. Both methods exist in commercially available software solutions. However, they focus on micro- and nano-scale light-matter interactions, resulting in computational requirements that are prohibitively large for city-scale spatial signal-propagation simulations. Alternatively, the recently developed O-FDTD [13] uses a much simpler approach than conventional FDTD. Instead of solving [PERSON]'s equations for four field components, O-FDTD uses an approximation derived from the Lorentz Oscillator Model solution. The resulting formulation enables the field propagation using a single global electric field updating equation, which excludes the need for alternating orthogonal electromagnetic field components found in conventional FDTD. As a result, O-FDTD yields a single electric field component orthogonal to the 2D simulation space. The approach closely approximates the more complex electromagnetic FDTD predictions for dielectric materials and effectively reduces the memory and simulation time requirements, which enables its application to city-wide simulations.