## 6 Comparison to Theoretical Results  
To strengthen the experimental results presented in this paper, we compared the results obtained in our experiments with those produced by the theoretical model described in Section 3. To compare the empirical and theoretical results, we began by estimating the path-loss exponent (\(\alpha\)) and the shadowing standard deviation (\(\sigma\)) from the empirical data [30]. The idea was to find the values of \(\alpha\) and \(\sigma\) that minimized the MSE (Mean Square Error) between the simplified model and the empirical power measurements. Using the methodology described in [30], we obtained the values shown in Table 5 in the case of the flat and hill deployments. We used these values of \(\alpha\) and \(\sigma\) as an input for the theoretical model described in Section 3, and then we generated theoretical values for the PRR and RSSI metrics. To check whether the empirical and theoretical distributions are comparable, we used the Mann-Whitney-Wilcoxon (MWW) test [44], a non-parametric test which does not make any assumption on the shape of the distributions. This test allows checking if two distinct sets of data come from the same distribution. The MWW test allowed us to verify the null-hypothesis \(H_{0}\): values from the two independent sample sets (i.e., empirical and theoretical data in this case) come from the same distribution. In the case of the PRR metric, the MWW test validatef \(H_{0}\) in the case of the flat area deployment, but rejected it for the hill deployment. Thus, if we considered a flat environment, the theoretical model was close to the experimentation, while, in the hill environment, there was no correlation between \begin{table}
\begin{tabular}{l c c} \hline \hline  & **Flat** & **Hill** \\ \hline \(AVG_{[PRR,\textsc{a}-PRR_{\textsc{a}}]}\) & 0.0505 & **0.1** \\ \hline \(MAX_{[PRR,\textsc{a}-PRR_{\textsc{a}}]}\) & **0.55** & 0.4 \\ \hline \(AVG_{[\overline{RSSI}_{\textsc{a}-\overline{RSSI}_{\textsc{a}}]}}\) & 1.67 & **4.3** \\ \hline \(MAX_{[\overline{RSSI}_{\textsc{a}-\overline{RSSI}_{\textsc{a}}]}}\) & 4.7 & **14.75** \\ \hline \%_{Unidirectional_} & 8 & **45.83** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Link asymmetry for flat and hill environments. Figure 14: Link quality classification for different deployment environments. \begin{table}
\begin{tabular}{l c c} \hline \hline  & \(\alpha\) & \(\sigma\) \\ \hline
**Flat deployment** & 3.56 & 6.08 \\ \hline
**Hill deployment** & 5.05 & 9.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Path-loss exponent and shadowing standard deviation for flat and hill deployment. theory and practise. This can also be observed visually in Figure 15, which shows the empirical and theoretical CDF for the flat and the hill deployments. This indicates that the poor radio link quality on the hill deployment was the consequence of a phenomenon that is not taken into account in the theoretical model. We also tested \(H_{0}\) for the PRR distribution on every individual link in our deployment: the null-hypothesis was rejected for 15% of links in the flat area deployment and for 37% of the links in the hill deployment. Regarding the RSSI metric, the MWW test rejected the null-hypothesis \(H_{0}\) for both deployment topographies (flat and hill) (see Figure 16). Thus, there was no correlation between theory and practise results, regardless of the considered environment. This result is in line with the one presented in [45], where the authors conducted multiple statistical tests to check whether the empirical RSSI measured on a link can be approximated by a known probability distribution function. For all the probability distribution functions verified in their study, the null-hypothesis was rejected. This can be explained by the fact that the theoretical model for RSSI considers the received power strength decreases with distance, a property we already showed not to be true in the experiments presented in Section 5.4.