## 4 Results
### O-FDTD for Spatially Resolved LoRa Signal Propagation Simulation
To compare the free-space decay scenario with the O-FDTD simulated, heterogeneity-rich cityscape scenario, we plotted in Figure 5a a 2D histogram of combined RSSI and distance occurrences together with the above-analyzed free-space model \(P_{\text{FS}}(\text{G}_{\text{TX}}=+20\) dBm). The plot allows a statistical observation of the fraction of covered versus non-covered map locations that show RSSI values above (shorter distances) and below (longer distances) the receiver sensitivity. The overall much lower RSSI values than the free-space \(P_{\text{FS}}(\text{G}_{\text{TX}}=+20\) dBm) indicate the rather drastic RSSI attenuation caused by the buildings. Figure 5b shows a plot of the average RSSI per distance. For distances up to 150 m, local minima and maxima can be assigned to the position of the first building layers, as both attenuate and concentrate the signal via wall absorption and reflections, respectively. It should be noted that the highly attenuated RSSI values inside the concrete walls themselves also contribute to the statistics, which leads to decreased average values in Figure 5b. The statistical representations of Figure 5 characterize the overall dynamics of the full O-FDTD simulated RSSI map. The 2D histogram from Figure 5a builds upon the sum of all spatial contributions from propagation pathways stemming over \(360^{\circ}\) from the central source. Still, the RSSI decay characteristics for specific directions can be identified and analyzed in further detail. As an example, we apply an angular gating \(\theta+\Delta\theta\) to analyze the RSSI over distance dynamics in four arbitrarily-defined directions. Figure 6a represents the selected gates of \(\Delta\theta\)= \(5^{\circ}\) and \(\theta=-135^{\circ}\), \(-45^{\circ}\), \(45^{\circ}\) and \(135^{\circ}\). The vivid and faded colors distinguish the considered from disregarded regions, respectively. Figure 6b shows the mean RSSI over distance in each direction of interest, where distinct direction-dependent dynamics with a strong dependence on the building density can be identified. In this case, the \(-135^{\circ}\) and \(-45^{\circ}\) directions show shorter coverage distances than the \(45^{\circ}\) and \(135^{\circ}\) directions. Interestingly, the RSSI drops in and out of the receiver sensitivity range, depending on the building arrangements. Figure 4: O-FDTD simulation of LoRa Received Signal Strength Indicator (RSSI) in Ourense for a signal source located indoors (center of the map). The building wall lines from Google Maps are overlaid onto the simulations for improved visualization. (**a**) Close-up \(200\times 200\) m\({}^{2}\) map. (**b**) Zoom-out (full) \(600\times 600\) m\({}^{2}\) map. The false color map turns to grayscale for RSSI values below the calculated receiver sensitivity of \(-124\) dBm. According to the simulation results, and assuming a receiver sensitivity of \(-124\) dBm, most of the simulated city area should lie within the LoRa network coverage. In Section 4.3, we present the experimental characterization of a LoRa network, and in Section 4.4, we compare the spatially resolved O-FDTD cityscape LoRa coverage simulations against the experimental results.