## 3 Link Efficiency in Zenith Paths
### Probability Distributions \(P(R)\), \(P(A)\) and Channel Efficiency  
Figure 2 shows the average annual probability distribution \(P(R)\) of exceeding \(R\) (mm/h, averaged in 1 min) at the indicated sites. The different climatic conditions of these sites can be clearly observed by comparing the rain rate exceeded with the same probability.  
Figure 1: Flow–chart of the theoretical signal processing necessary for applying the method. The mathematical expressions of the symbols are given in Equations (8) and (9). The actual implementation of the processing depends on the technology of the time.  
Figure 2: Annual probability distribution (%) \(P(R)\) of exceeding the value indicated in abscissa at the indicated sites. 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.  
Figure 3 shows the average annual probability distribution \(P(A)\) of exceeding \(A\) (dB) in the zenith paths at the indicated sites, simulated with SST (see Equation (29) of [17]). These probability distributions are the data necessary to calculate the mean efficiency and its bounds (Equations (6) and (7)), the power margin (Equation (11)) and the bandwidth expansion factor (Equation (12)).  
Table 2 reports the mean and minimum (worst-case) efficiency. The mean efficiency ranges from 0.265 at Tampa (the \"worst\" site) to 0.502 at Fucino (the \"best\" site). Consequently, the power margins--reported in Table 3-and the bandwidth expansion factor--Table 4--are, respectively, 5.76 dB and 3.77 at Tampa and 2.99 dB and 1.99 at Fucino.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Site** & **Minimum** & **Mean** \\ \hline Spino d’Adda (Italy) & 0.378 & 0.403 \\ \hline Gera Lario (Italy) & 0.358 & 0.386 \\ \hline Fucino (Italy) & 0.483 & 0.502 \\ \hline Madrid (Spain) & 0.444 & 0.458 \\ \hline Prague (Czech Republic) & 0.473 & 0.492 \\ \hline Tampa (Florida) & 0.221 & 0.265 \\ \hline Norman (Oklahoma) & 0.282 & 0.318 \\ \hline White Sands (New Mexico) & 0.338 & 0.377 \\ \hline Vancouver (Canada) & 0.421 & 0.431 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Minimum (worst case) and mean values of channel efficiency \(\eta\), Equations (6) and (7), in zenith links working at 80 GHz at the indicated sites.  
Figure 3: Annual probability distribution (%) \(P(A)\) of exceeding the value indicated in abscissa—80 GHz, circular polarization, zenith paths–at the indicated sites. 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.  
The power margins are always small, well within the capabilities of current technology. The bandwidth expansion factors might be large if the bandwidth in clear--sky conditions is already large; therefore, this might be the most critical issue to consider in relation to practical applications of the method. The evolution of spread--spectrum technology could ease its application [24; 25; 26; 27; 28].  
Finally, notice that the different meteorological conditions of the sites (see Figures 2 and 3) lead to different efficiency.