## 5 Coverage Analysis
Therefore, the end-to-end connection probability can be measured using the error function definition as follows:  
\[PL_{Suburban}=PL_{Urbm}-2\times\left(\log_{10}\left(\frac{f}{28}\right)\right) ^{2}-5.4, \tag{5}\]5 Coverage analysis of LoRa and NB-IoT technologies in rural areas. \[PL_{Suburban}=PL_{Urbm}-2\times\left(\log_{10}\left(\frac{f}{28}\right)\right) ^{2}-5.4, \tag{5}\]6  
where \(\text{erf}(t)=\frac{2}{\sqrt{\pi}}\int_{0}^{t}e^{-x^{2}}dx\) and \(\sigma\) is the standard deviation of the Gaussian distribution that describes the shadowing effect in dB. Based on the presented formulation, computer simulations were conducted for both the LoRa and NB-IoT connectivity to reveal the effect of the propagation environment on connection probability. In this simulation setup, the operating frequency was selected as 868 MHz for LoRa and 900 MHz for NB-IoT, respectively. In addition, the antenna heights were taken as \(h_{v}=2\) m, \(h_{b}=5\) m for LoRa and \(h_{v}=2\) m, \(h_{b}=20\) m for NB-IoT, respectively. Lastly, \(\sigma\) was set to 10 dB to identify the shadow-fading. The results acquired in the simulation study are shown in \[PL_{Suburban}=PL_{Urbm}-2\times\left(\log_{10}\left(\frac{f}{28}\right)\right) ^{2}-5.4, \tag{5}\]7 As seen from the plots, NB-IoT connectivity achieves better connection probability than LoRa for all environments. However, it was observed that shadowing-induced irregularities in the wireless channel significantly affect the covered area due to the presence of randomness in the radio propagation environment. Another simulation study was also performed to show the effectiveness of the theoretical analysis. In this way, the obtained simulation results were validated through the use of the XIRIO Online radio planning tool from Aptica [57]. XIRIO Online has worldwide high-resolution urban/rural mapping data that allows us to approximately predict the coverage of a typical LoRa GW or LTE BS. It has been empowered with a calculation engine, which is updated with the most widely used and internationally recognized propagation models (Rec. ITU-R P.526, Deygout, LOS, Rec. ITU-R P.1546, Rec. ITU-R P.530, Okumura-Hata, XIA-Bertoni, etc.). The simulation location was set to Konya Province, Turkey's agricultural capital city. Konya has large farmland areas, most of which can be easily and effectively used for agriculture due to the ground's fertility. It was assumed that the GW/BS is positioned in the rural area of C\(\upmu\)m District, which is located about 40 km away from the Konya city center. The coverage analysis was conducted considering the  
\[PL_{Suburban}=PL_{Urbm}-2\times\left(\log_{10}\left(\frac{f}{28}\right)\right) ^{2}-5.4, \tag{5}\]8 Coverage analysis of LoRa and NB-IoT technologies for different fade margins. 868 MHz and 900 MHz frequency bands for LoRa and NB-IoT, respectively. The antenna gain and height settings are given in \[PL_{Suburban}=PL_{Urbm}-2\times\left(\log_{10}\left(\frac{f}{28}\right)\right) ^{2}-5.4, \tag{5}\]9  
Figures 12 and 13 show the coverage maps for two different scenarios through LoRa and NB-IoT connectivity technologies, respectively. A coverage map shows the geographic area where a receiver will obtain a good reception when the received signal strength exceeds the sensitivity threshold. In the obtained maps, the covered areas were separated into four color groups (green, yellow, blue, and red) as the power level increased by 10 dBm. Apart from these, the locations outside the coverage area where the received signal is below the receiver sensitivity level were left uncolored. In the green-colored regions, it is possible to take a strong signal due to providing a better link budget availability. Towards the red-colored regions, the received signal strength decreases gradually. To easily compare the coverage maps, two reference distances (25 km and 40 km) are marked on the coverage maps. It is obvious that the NB-IoT connectivity has an extended coverage area compared with LoRa connectivity.