## 5 Discussion
Future study could be envisioned to investigate how a modified O-FDTD approach, e.g., via dielectric permittivity gradients, could model terrain features. However, the topography should not significantly impact the area considered in this work since this is usually only considered for far more extended regions [44]. Previous works describe the influence of weather parameters in LoRa propagation [61]. Again due to the area contemplated, relevant air temperature gradients across the considered cityscape can be disregarded. A more refined approach could take into account shades cast by tall buildings in sunny countries. However, additional information on the building height would be required, and the shade regions vary with the hour of the day. Thus, a linear correction to the RSSI maps could be considered to account for the average temperature, following previously identified dependences of the signal-coverage on weather parameters. 3. Effect of RF noise: Previous works demonstrate that high-levels of RF noise can be found in urban environments [62]. However, LoRa's modulation characteristics make it particularly invulnerable to noise interference [54], and thus, we neglected such effects in our approximation. 4. Indoor LoRa signal distribution: the concrete walls can be considered the dominant source of damping and reflection, not only because concrete is a very absorbent material in itself but also because walls represent full floor-to-ceiling barriers, while furniture items, aside from impossible to determine, are only partial barriers, thus allowing most of the signal to diffract around them. On the one hand, we consider all building walls as made of concrete and therefore ignore far less absorbent glass windows. This is a reasonable approximation since concrete is the predominant building material. On the other hand, one could argue that the exaggerated wall absorption may somehow compensate for the absence of furniture, even though the scattering features would be slightly different. 5. Use of a single permittivity value: At a glance, this could be a significant error source since considering a single permittivity may overlook highly scattering materials such as metals. However, we are interested in modeling radiation-matter interactions, mainly in terms of reflection and absorption by building walls. In the RF regime, the dielectric properties of metals are dominated by their electrical conductivity, leading to a virtually infinite permittivity, making them almost perfect mirrors. In this work, we used a dielectric permittivity value estimated to reproduce the absorption of about 50 dB/m. Hence, the associated contrast in the dielectric permittivity, or equivalent refractive index, leads to a reflectance \(r=(n-1)^{2}/(n+1)^{2}\) of about 20% for normal incidence, which is not a very good approximation for metallic surfaces. The O-FDTD method can reproduce the metallic mirror behavior via the use of arbitrarily large refractive index values e.g., r(\(n\) = 100) = 96%, r(\(n\) = 200) = 98%, which is similar to previously reported approaches using knife-edge methods [35]. However, to accurately incorporate the cityscape contributions of metals would require a much more complete representation of the cityscape, containing the mapping of metals within the building walls. Considering this level of detail might be feasible for small-scale indoor applications, but it is not practical in the cityscape scope. Instead, we assumed that walls are dominantly composed of concrete, with a common permittivity. Alternatively, one could incorporate the effects of metals within the wall structures by increasing the real part of the refractive index to induce a higher reflectance, which could approximate the average metal composition in building materials, provided that information is available.