## 5 Results and Discussion
The values of \(\tau\), \(\eta_{W}\), \(\alpha\) and \(\beta\) are computed respectively from Equations (7), (8), (4) and (5) once the complex permittivity is estimated using Equations (9)-(26) (assuming operating temperature \(T=20\)\({}^{\circ}\)C and the salinity values reported in Table 1). A comparison between model-estimated (round markers) and actually measured (star markers) RSSI is reported in Figure 9 versus the salinity level, distinguishing between configurations #1-#3 at \(d_{UW}=12\,\mathrm{cm}\) and configurations #4-#11 at \(d_{UW}=6\,\mathrm{cm}\). Vertical error bars are added to highlight the uncertainty contributions in the RSSI measurements, while the positioning errors in \(d_{UW}\) of \(\pm 0.5\,\mathrm{cm}\) are accounted for by plotting a range of values where the estimated RSSI can fall (triangular markers). The test-measured RSSI is obtained as the average of the SF-mean RSSI for each configuration. These outcomes prove a good match between modeled and measured values even assuming a small positioning error, thus validating the proposed link budget model. Evidently, these results are strongly linked to the considered scenario and substantial difference can be observed moving from a controlled laboratory environment to a real scenario, where additional miscellaneous losses can contribute to the degradation of the received signal strength. This can be seen by comparing the results shown till now, gathered in laboratory conditions, with those obtained in the field in the experimental conditions described in Section 4.2. The results are reported in Table 3 for each SF, in terms of RSSI and SNR mean and standard deviation and PL percentage. Figure 8: PL percentages for SF from 7 to 12 (as per the legend) for the laboratory test configurations reported in Table 1.  
Figure 9: Comparison between modeled RSSI according to Equation (27) (round markers) and measured RSSI during the tests (star markers) as a function of the salinity for (**a**) configurations #1-#3 and (**b**) configurations #4-#11 of Table 1, together with vertical error bars and modeled RSSI assuming a positioning error in \(d_{\text{UW}}\) of \(\pm 0.5\) cm (triangular markers). In the inset of (**a**) a magnification of the results for configuration #1 is shown. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & **SF 7** & **SF 8** & **SF 9** & **SF 10** & **SF 11** & **SF 12** \\ \hline \multirow{2}{*}{RSSI} & \(\mu_{RSSI}\) (dBm) & \(-97\) & \(-90\) & \(-93\) & \(-97\) & \(-99\) & \(-115\) \\  & \(\sigma_{RSSI}\) (dB) & \(14\) & \(17\) & \(16\) & \(15\) & \(17\) & \(7\) \\ \hline \multirow{2}{*}{SNR (dB)} & \(\mu_{SNR}\) & \(2.6\) & \(5.5\) & \(5.2\) & \(2.4\) & \(-1.7\) & \(-7.2\) \\  & \(\sigma_{SNR}\) & \(5.6\) & \(7.0\) & \(7.3\) & \(7.5\) & \(7.7\) & \(6.2\) \\ \hline \multirow{2}{*}{PL (\%)} & & \(67\) & \(67.25\) & \(59.5\) & \(61.5\) & \(82.75\) & \(96.5\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Numerical results for the field tests in the Venice lagoon: means and standard deviations for RSSI and SNR values and PLs percentages. A larger variability in the measured data with respect to the laboratory outcomes despite similar depth and salinity conditions can be noticed both in the RSSI and in the SNR, leading also to a higher packet loss. This fact can be justified with the higher disturbances of the field deployment that add up to a higher positioning error of the transmitter, due for example to the presence of waves, that introduces subsequent increases and decreases of the \(d_{UW}\) by few centimeters, and the tide, that causes a trend in the data due to the variation of the water level above the node. The waves variability can be better observed from Figure 10, where portions of the RSSI and SNR trends for SF 9 are reported in red, together with the analogous trends measured during the laboratory tests for SF 9 (in blue).