## 5 Data Transmission Tests
### Measurements
For the same reason, an overestimation of the link margin \(L_{m}\) may be computed by exploiting Equation (2) bearing in mind that the Gateways shown in Section 5.3 have a sensitivity which varies along with the SF and the bandwidth. Indeed, according to the LoRaWAN concentrators datasheet [35] and considering that a bandwidth of 125 kHz was exploited throughout the tests, the Gateways sensitivity \(S_{RX}\) spans from \(-137\,\mathrm{dBm}\) at \(SF=12\) to \(-126\,\mathrm{dBm}\) at \(SF=7\). Another consequence stemming from the presence of miscellaneous losses is that a lower value of \(P_{RX}\), with respect to the one that would have been obtained from Equation (3), was truly experienced on average during the measurements thus entailing a narrower \(L_{m}\). Notice that all of these quantities are independent of the set of tests since they only depend on the length of the link \(D\). All the results stemmed out from the aforementioned Equations are reported in Table 3.  
The last condition to be assessed is the percentage of clearance the first Fresnel zone \(F_{1_{C}}\). Indeed, despite the LoS status between the link endpoints, \(F_{1}\) is partially occupied by the sea because of the Earth bulge. Figure 8 shows a qualitative report of the wireless link respectively when \(h_{TX_{1}}\) is exploited (**a**) and \(h_{TX_{2}}\) is used (**b**). Such images are obtained by making use of BotRf [36] which is a Telegram Bot that aids in the planning phase of wireless links. The cyan line represents the direct LoS path between the link endpoints while the magenta one represents the 60% of \(F_{1}\). Finally, the brown area indicates the Earth curvature while the green one indicates the terrain profile. The reason for which the green area is for the most part flat is that it is actually occupied by the sea. Either the brown and green areas take into account the factor \(k\) (see Equation (4)) for the bending effect on radio waves due \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Group** & \(h_{TX}\) **[m]** & \(h_{RX}\) **[m]** & **SFs** & **Transmitted Packets** & \(D_{h}\) **[km]** \\ \hline \#1 & 3.5 & 13.2 & \(7\div 12\) & 300 & 12.969 \\ \#2 & 2.1 & 13.2 & \(7\div 12\) & 300 & 12.969 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Antennas heights, exploited SFs, number of transmitted packets and distance of the horizon from the receiver antennas for each trial group. to the declining of atmospheric pressure. As it can be noticed, LoS is effectively achieved and the first Fresnel zone is densely occupied. At this stage one can evaluate the percentage of clearance of the first Fresnel zone. Due to the fact that the transmitting and receiving antennas were installed at different heights, let us suppose that they shared the same altitude so as to ease the computation. In so doing, an overestimate of the clearance will be obtained. However, this is not an issue at all since such assessment has the mere scope of giving a flavour of the toughness of this specie of transmission over the sea. The maximum extent of the occupation of the first Fresnel zone by the sea due to the Earth bulge is experienced at the midpoint of the link since in the same location occur both of the maxima of \(F_{1}\) radius as well as of the Earth lump. Such a percentage could be evaluated by firstly computing the distance between the sea level and the line connecting the link endpoints (i.e., \(D\) in Figure 2) at half of the link length \(D\) relying on the flat Earth model. This term can be computed as the sum of two factors: one is length of the minor cathetus belonging to the right triangle having half of the link length \(D\) as major cathetus and the transmitting antenna as the corner of its acute angle, and the other one is the height of the transmitting antenna \(h_{TX}\). Secondly, the Earth curvature have to be taken into account by subtracting the maximum height \(H\) of the Earth bulge. Finally, this difference is the portion of \(F_{1}\) free from obstacles.