## 5 Conclusions  
We have recalled that the traditional approach of considering the average probability distribution of rain attenuation is too pessimistic, in terms of power margin, when designing data transfer channels. In fact, if the data volume downloadable during rainfall is more valuable than the instantaneous symbol rate--such as in remote sensing and the internet of things (IoT) using satellites--the method discussed in [6], and summarized in Section 2 of the present paper, can avoid overdesign. However, this method is useful only if (a) data must also be downloaded when it is raining; (b) real--time communication is not strictly required. Figure 11: Left panel: Extra power factor versus the threshold \(S\); Right panel: Maximum bandwidth factor versus the threshold \(S\) at the indicated sites, details of Figures 8 and 9. Spino d’Adda: continuous blue line; Gera Lario: continuous black line; Fucino: continuous red line; Madrid: continuous green line; Prague: continuous magenta line; Tampa: dashed red line; Norman: dashed magenta line; White Sands: dashed green line; Vancouver: dashed blue line. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Site** & **Total Power Margin** & **Bandwidth Expansion Factor** \\ \hline Spino d’Adda (Italy) & \(1.0+3.9=4.9\) & 1.95 \\ \hline Gera Lario (Italy) & \(1.0+4.2=5.2\) & 2.10 \\ \hline Fucino (Italy) & \(0.3+3.0=3.5\) & 1.75 \\ \hline Madrid (Spain) & \(1.0+3.5=4.5\) & 1.80 \\ \hline Prague (Czech Republic) & \(1.5+3.8=5.3\) & 1.70 \\ \hline Tampa (Florida) & \(1.5+5.9=7.4\) & 2.80 \\ \hline Norman (Oklahoma) & \(1.5+5.0=2.0\) & 2.25 \\ \hline White Sands (New Mexico) & \(1.0+4.4=5.4\) & 2.20 \\ \hline Vancouver (Canada) & \(1.0+3.7=4.7\) & 1.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Minimum total power margin (dB) and minimum bandwidth expansion factor at the indicated sites, from Figure 11. For example, in the Tampa geographical area, the final total power margin is \(1.5+5.9=7.4\) dB, with a bandwidth expansion factor \(\approx 2.8\), being \(S=1.5\) dB the threshold of minimum bandwidth expansion factor (Figure 11, right panel) and \(\sim 5.9\) dB the extra power factor (Figure 11, left panel). The method is characterized only by a single parameter, namely the mean efficiency \(0\leq\eta\leq 1\) of the link, and it can transfer the same data volume as if the link were in clear--sky conditions. In theory, a small power margin and a relatively small bandwidth expansion--regardless of instantaneous rain attenuation--allow us to deliver a mean symbol rate equal to the symbol rate obtainable with no rainfall. We have applied the method to the links of GeoSurf satellite constellations [16], which have vertical (zenith) paths at any latitude. Since no measurements or predictions are available for zenith paths, we have considered as experimental results the rain attenuation time series \(A(t)\) simulated at 80 GHz (mm--wave), circular polarization, with the Synthetic Storm Technique [17] from rain--rate time series \(R(t)\), recorded on--site for several years. We have found that the power margins are always small, well within the capabilities of current technology. The maximum bandwidth necessary might be large if the bandwidth in clear--sky conditions is already large; therefore, this might be the most critical issue in practical applications. The evolution of spread--spectrum technology could ease its application. We have generalized the method by supposing that a small power margin \(S\) (dB) is already available so that the method is applied only in the intervals in which the attenuation threshold \(S\) is exceeded, i.e., when \(A(t)\geq S>0\). In this case, the total power margin ranges from 2.0 dB to 7.4 dB and the bandwidth expansion factor ranges from 1.70 to 2.80. The power margin required is very small for all sites, well within the capabilities of current technology; the bandwidth expansion factor _per se_ is not very large, but it can pose a problem if the clear--sky bandwidth is already large.