## 5 Long-Term Results  
By applying the theory of Section 2 to all rain events collected at the sites of Table 1, in this section, we show the average and standard deviations of passband and equivalent baseband transfer functions for several rain attenuation ranges for Spino d'Adda. The results concerning the other sites are reported in Appendix A.  
Figures 9-12 show the equivalent baseband transfer functions for rain attenuation centered at 3, 10, 20, and 30 dB to show the differences as attenuation increases. Notice that in these Figures we have always adopted the same scales to allow comparisons.  
Figure 10: Spino d’Adda. Average value (continuous line) and \(\pm\)1 standard deviation (dashed lines) baseband equivalent transfer functions in the range 2.5 \(\leq\) A < 3.5 dB. **Left column**: Real (**upper panel**) and imaginary (**lower panel**) transfer functions of the direct channel; **Right column**: Real (**upper panel**) and imaginary (**lower panel**) transfer functions of the cross-channel. 9 \(\leq\) A < 11 dB.  
Figure 9: Spino d’Adda. Average value (continuous line) and \(\pm\)1 standard deviation (dashed lines) baseband equivalent transfer functions in the range 2.5 \(\leq\) A < 3.5 dB. **Left column**: Real (**upper panel**) and imaginary (**lower panel**) transfer functions of the direct channel; **Right column**: Real (**upper panel**) and imaginary (**lower panel**) transfer functions of the cross-channel.  
We can observe the following general features.  
\(H_{edt}(f)\): it is not constant; it increases with attenuation range; the standard deviation is small. It will produce different amplitude distortions in different attenuation ranges.  
\(H_{edt}(f)\): it is practically a straight line, but its slope increases (more negatives) with attenuation range; the standard deviation is small. It will produce different phase distortions and, therefore, different time delays as the attenuation range increases.  
\(H_{eqt}(f)\): it is of the order of \(10^{-3}\) of \(H_{edt}(f)\); it is not constant; it increases with attenuation range; the standard deviation is small. It will produce different amplitude distortions in different attenuation ranges.  
\(H_{eqi}(f)\): it is practically a straight line, but its slope increases (more negative) with attenuation range; the standard deviation is small. Its magnitude is larger than \(H_{edi}(f)\). It will produce different phase distortions and different time delays as the attenuation range increases.  
Figure 11: Spino d’Adda. Average value (continuous line) and \(\pm 1\) standard deviation (dashed lines) baseband equivalent transfer functions in the range \(2.5\leq\) A < 3.5 dB. **Left column**: Real (**upper panel**) and imaginary (**lower panel**) transfer functions of the direct channel; **Right column**: Real (**upper panel**) and imaginary (**lower panel**) transfer functions of the cross-channel. \(18\leq\) A < 22 dB.  
Figure 12: Spino d’Adda. Average value (continuous line) and \(\pm 1\) standard deviation (dashed lines) baseband equivalent transfer functions in the range \(2.5\leq\) A < 3.5 dB. **Left column**: Real (**upper panel**) and imaginary (**lower panel**) transfer functions of the direct channel; **Right column**: Real (**upper panel**) and imaginary (**lower panel**) transfer functions of the cross-channel. \(27\leq\) A < 33 dB.  
In conclusion, both the direct channel and the cross channel will introduce amplitude and phase distortions, which depend on attenuation range, in a 10-GHz bandwidth centered ta 80 GHz. Only the channels defined here as narrow band (\(100\,\sim 200\) MHz) will not be affected. In the next Section, we will present and discuss the likely effects on the probability of bit error.