## 2 Connection Options and Topology Optimization after Site Densification
### Link Budget and Fading Margin Calculations  
The received signal level (RSL) behind the receiving antenna is calculated as follows [31; 43; 41]:  
\[P_{\rm RX}{}^{\rm[dBm]}=P_{\rm TX}{}^{\rm[dBm]}+G_{\rm TXa}{}^{\rm[dBi]}+G_{\rm RXa }{}^{\rm[dBi]}-PL{}^{\rm[dB]}, \tag{4}\]  
where \(PL\) is the propagation loss. With outdoor units integrated with or directly mounted onto the antenna (Figure 7a,b), the waveguide and additional branching loss terms are zero in Equation (4) [31; 40]. As the link is single-polarized, a polarization combiner between the ODU and the antenna (Figure 7c) is not discussed [34]. The propagation loss \(PL\) is calculated as follows:  
\[PL{}^{\rm[dB]}=FSL{}^{\rm[dB]}+A_{\rm r}{}^{\rm[dB]}+A_{\rm a}{}^{\rm[dB]}+A_{ \rm mp}{}^{\rm[dB]}+A_{\rm o}{}^{\rm[dB]}. \tag{5}\]  
In clear LoS conditions, the obstacle loss \(A_{\rm o}\) is zero. At high frequencies, the effect of multipath fading \(A_{\rm mp}\) is usually not relevant, thanks to the very short hops. Typically, in an urban environment, any alternative propagation path is blocked by buildings or other obstacles. Multipath fading is more relevant at lower frequencies (i.e., frequencies at 18 GHz or below) and where reflection from large water surfaces may happen, e.g., propagation over lake or sea. \(A_{\rm r}\) and \(A_{\rm a}\) are the terms of rain and atmospheric attenuation in Equation (5). The unfaded received signal level \(P_{\rm RXu}\) is determined by the free space loss (\(FSL\)), the transmitted power \(P_{\rm TX}\), and the gain of the antennas (Figure 8). \[P_{\rm RXu}{}^{\rm[dBm]}=P_{\rm TX}{}^{\rm[dBm]}+G_{\rm TXa}{}^{\rm[dBi]}+G_{ \rm RXa}{}^{\rm[dBi]}-FSL{}^{\rm[dB]}. \tag{6}\]  
The free space loss is calculated as follows [1; 40; 31]:  
\[FSL(f,d){}^{\rm[dB]}=92.44+20\cdot\log\Bigl{(}f{}^{\rm[GHz]}\Bigr{)}+20\cdot \log\Bigl{(}d{}^{\rm[km]}\Bigr{)}, \tag{7}\]  
where \(f\) is the frequency of the link, and \(d\) is the hop length. The constant of 92.44 dB allows the calculation in convenient GHz and km units for the frequency and distance, respectively. The fade margin (\(FM\)) is the difference between the unfaded RSL and the receiver sensitivity threshold. \[FM{}^{\rm[dB]}=P_{\rm RXu}{}^{\rm[dBm]}-P_{\rm RXth}(BER){}^{\rm[dBm]}. \tag{8}\]  
\(FM\) should compensate for all unwanted factors degrading the link availability: rain, fog, dust, snow, atmospheric attenuation, and interference. Interference degrades the sensitivity threshold \(P_{\rm RXth}\) of the receiver. In a sunny scenario, the link can switch to an elevated modulation mode to carry more data. Combining Equations (1), (6), and (8), we get  
\[FM{}(f,\,d,\,\varnothing){}^{\rm[dB]}=SG{}^{\rm[dB]}+G_{\rm TXa}{}^{\rm[dBi]} +G_{\rm RXa}{}^{\rm[dBi]}-FSL{}^{\rm[dB]}. \tag{9}\]  
Figure 7: (**a**) Integrated antenna assembled as part of the outdoor unit (ODU). (**b**) Slip-mount antenna fitted without feeder lines to the ODU. (**c**) Example of combining polarization; photo reproduced with permission from RACOM [34]. (**d**) Separated antenna with two ODUs and two feeder waveguides. Equation (9) simplifies to Equation (10) when the transmit and receive antennas have equal gain (i.e., same antenna type and dish size are used at both ends of the link). \[FM(f,\,d,\,\mathcal{O})\ ^{[\text{dB}]}=SG^{[\text{dB}]}+2G_{\text{ant}} ^{[\text{dBi}]}-FSL^{[\text{dB}]}. \tag{10}\]  
As seen, at a given frequency, a higher system gain results in a better fade margin of the link for a given \(d\) hop length and \(\mathcal{O}\) antenna diameter. In mobile front- and backhaul expansion projects (simply \"anyhaul\" or also called \"X-haul\" [13; 25]), the manufacturer and the type of the radio equipment are usually defined. Thus, parameters \(SG\), \(P_{\text{TX}}\), and \(P_{\text{RXth}}\) are given and cannot be selected freely. In several projects, for example, it is expected to re-use the equipment running in the field. Only few parameters remain free for the planners in practice, when the new links in the network are designed.