## 5 Discussion
We demonstrate here that combining the O-FDTD method with a simplistic cityscape to building walls information from Google Maps, and using a single permittivity value, excellently predicts the LoRa signal distribution and coverage regions with high spatial accuracy. Compared to previous approaches that do not take real-world building maps into account, the proposed O-FDTD approach provides a significant improvement. Conceivable benefactors include end-users aiming to implement a continuous LoRa network in a dedicated area or network users to access the local LoRa network distribution information. Many previous works have used much more general approximations, ignoring real-world data-based cityscape heterogeneities [14; 16; 20; 22; 33; 63; 64]. Neural networks have been used to increase the computational efficiency of UTD ray-launching [65] methods to integrated spatial information but are still mostly limited to indoor scenarios. Knife-edge and PE approaches are the closest related to O-FDTD. However, such methods are limited in the number of wave reflections [36; 37] and thus usually limited to a few knife edges or simplified models [45; 66]. Multiple knife-edge diffraction [35] solves this issue but is still limited to simple geometries, which renders it unsuited for complex real-world building arrangements. ITM succeeds in real-world terrain and weather-dependent solutions but is highly demanding on computational resources. The simulation spatial resolution obtained is usually low compared to the achieved in this study. Therefore, it is typically applied to high-power telecommunications extending over extensive areas [22; 24; 44], far too large for the O-FDTD method. The spatial resolution required by O-FDTD for the wave propagation may become unsustainable for LoRa maps much larger than the 600 \(\times\) 600 m\({}^{2}\) maps shown in this paper, depending on the RAM resources available. In O-FDTD, the spatial resolution (simulation step size) must be at least four times smaller than the signal wavelength, limiting the maximum simulation step size. As a result, the field-of-view of an NxN pixel simulation map depends on the signal wavelength. A possible strategy to increase the spatial step size, and thus the simulation's field-of-view, is to use the following approximation: According to the FSPL model, a wave propagating with wavelength \(2\lambda\) will see its signal strength attenuated by a factor of four, compared to a signal with wavelength \(\lambda\), i.e., (\(FSPL\))(\(2\lambda\)) = (\(FSPL\))(\(\lambda\))/4. This relation can be generalized as  
\[\mathrm{FSPL(n\lambda)}=(\mathrm{FSPL})(\lambda)/n^{2}, \tag{17}\]  
and thus,  
\[\mathrm{P_{FSPL}(n\lambda)}\;[\mathrm{dBm}]=\mathrm{P_{FSPL}(\lambda)}+20 \log_{10}(n), \tag{18}\]  
which states the relationship between the RSSI of signals with wavelengths \(\lambda\) and \(n\lambda\). Hence, an approximated result can be obtained by performing the simulation with a longer wavelength \(n\lambda\) and using Equation (13) to convert the RSSI map back to the \(\lambda\) scenario, thereby increasing the field-of-view by a factor of \(n\), using the same number of pixels. It should also be noted that, according to the Beer-Lambert law, Equation (9), a change in the wavelength requires an updated wall dielectric constant. However, this approximation may introduce errors associated with (a) poor building resolution or (b) incorrect wavelength-dependent diffraction properties. The LoRa signal coverage region was experimentally determined by thresholding the time-between packet arrivals, which is not as rich as an experimental RSSI mapping. However, the developed method provides a simple approximation of the binary signal coverage area, which can be achieved directly by any LoRa communication system, regardless of its simplicity, or the accurate knowledge of the receiver sensitivity or transmission power. This is particularly important for system implementations where the RSSI measurements are not possible.