## 2 Connection Options and Topology Optimization after Site Densification
### Rain and Atmospheric Attenuation  
The rain attenuation calculation follows the methodology discussed in ITU-R P.530 [36; 37; 38]. The rain attenuation term \(A_{0.01\%}\) refers to the attenuation that is exceeded for 0.01% of the time and caused by intensive rainfall. This rain attenuation--exceeded in 0.01% of the time--is given as  
\[A_{0.01\%}{}^{[\text{dB}]}=\gamma_{\text{R}}d_{\text{eff}}=\gamma_{\text{R}} \frac{d}{1+d/d_{0}}. \tag{12}\]  
In Equation (12), \(\gamma_{\text{R}}\) is the specific attenuation (in dB/km) due to rain, and \(d_{\text{eff}}\) is the effective hop length. \[d_{\text{eff}}=\frac{d}{1+d/d_{0}}. \tag{13}\]  
When the rain rate is \(R_{0.01\%}\leq 100\) mm/h, then  
\[d_{0}=35e^{-0.015R_{0.01\%}}. \tag{14}\]  
When \(R_{0.01\%}>100\) mm/h, then \(d_{0}=35\times e^{-1.5}\) (i.e., \(R=100\) mm/h is used for all rain rates above 100 mm/h). However, such intensive rain is not relevant in the Central and Eastern Europe region [37]. According to ITU-R P.838, the specific attenuation for vertical polarization is calculated as follows:  
\[\gamma_{\text{R,V}}=k_{\text{V}}R^{\alpha_{\text{V}}}, \tag{15}\]  
and that for horizontal polarization is calculated as follows:  
\[\gamma_{\text{R,H}}=k_{\text{H}}R^{\alpha_{\text{H}}}, \tag{16}\]  
where the constants \(k_{\text{V}}\), \(\alpha_{\text{V}}\), \(k_{\text{H}}\), and \(\alpha_{\text{H}}\) depend on the frequency \(f\) and the polarization of the link [38]. V and H stand for vertical and horizontal polarization, respectively. The atmospheric attenuation, \(A_{\text{a}}\), is caused by the absorption of gaseous particles in the air. Compared to rain attenuation (\(A_{\text{r},0.01\%}\) in Equation (11)), for few-km short hops, \(A_{\text{a}}\) is negligibly small in most of the frequency bands used by \(\upmu\)mmW links. As seen in Figure 10, up to 300 GHz, there are four remarkable attenuation peaks [39]. Water vapor causes extra attenuation in the 23 GHz band (where \(A_{\text{sp}}=0.2\) dB/km) and around 180 GHz. Figure 9: Adaptive link modulation when ensuring guaranteed bit rate during intensive rain. Other high attenuation peaks are caused by oxygen absorption in the 56-64 GHz and in the 120  GHz range [39; 44; 45]. As seen in Figure 11, the attenuation due to oxygen absorption is very high: about \(A_{\rm sp}\) = 13-15 dB/km in the 58-62-GHz band. Therefore, the 57-63 GHz links are limited to a few hundred meters, and the use of vertical polarization is recommended [44; 45]. On the other hand, at 56-64 GHz, due to the very high atmospheric attenuation, the chance for interference from other links is rather small, enabling severe frequency re-use. The 30 or 50 MHz bands are allocated by CEPT in this range, as listed in Table 1.  
Figure 11: Atmospheric attenuation at 50–70 GHz (in dB/km, red line: sea level), according to ITU-R P.676-12. Reproduced with permission from ITU [39]. Figure 10: Specific attenuation due to oxygen (blue line), water vapor (orange line), and total attenuation (red line) according to International Telecommunication Union, ITU-R P.676-12. Reproduced with permission from ITU [39]. For the frequently used bands, Table 2 summarizes the typical atmospheric attenuation values per km (at sea level). These values are used in the calculations. For the entire link distance \(d\), the total gaseous attenuation caused by water vapor and oxygen is calculated as follows:  
\[A_{\mathrm{a}}{}^{\mathrm{[dB]}}=A_{\mathrm{sp}}{}^{\mathrm{[dB/km]}}.d{}^{ \mathrm{[km]}}. \tag{17}\]  
The atmospheric attenuation per km, \(A_{\mathrm{sp}}\), is shown together with rain attenuation in Figure 12 up to 200 GHz [12; 30; 32]. As seen, between 64 GHz and 120 GHz, there is a useful frequency \"window\" where new mmW links can benefit from a wide spectrum with atmospheric attenuation below 1 dB/km. Also, as seen in Figure 12, rain attenuation is dominant at all frequencies, except for 60, 120, and 180 GHz, where the atmospheric attenuation peaks are visible even when the rainfall rate is above 20 mm/h.