## 2 Connection Options and Topology Optimization after Site Densification
### System Gain Calculation  
The International Telecommunication Union (ITU) defines system gain as follows [1; 40; 41]:  
\[SG(BER)^{\rm(dB)}=P_{\rm TX}{}^{\rm(dBm)}-P_{\rm RXth}(BER)^{\rm(dBm)}. \tag{1}\]  
The system gain appropriately characterizes the transmitter and the receiver modules of the digital \(\mu\)W or mmW radio link. Thus, SG helps to determine the maximum distance that the equipment can connect with a given, pre-defined availability. \(P_{\rm TX}\) is the \"nominal\" transmit power at the output of the transceiver module (point C/C' in Figure 5). The reference points are according to the definition of ETSI (as provided in Reference [24]). For simplicity, neither feeder lines nor additional branching are indicated in the figure (for multi-channel or dual-polar links). When there is no feeder or additional branching network, then the transceiver can be directly connected to the transmitting antenna, as plotted in Figure 5. In this case (C' = D'), the output power \(P_{\rm TX}\) can be measured at the connection point of the antenna (D/D' in Figure 5). \"Nominal\" refers to the fact that, in a wide frequency band and at changing ambient temperatures, variation of a few dB of the output power may occur and is tolerated [24; 42]. The calculations focus on the output power level that is guaranteed at any frequency and temperature within the operational  
Figure 5: Block diagram of the microwave and millimeter-wave (\(\mu\)/mmW) transceiver (without feeder lines), according to European Telecommunication Standards Institute, ETSI EN 302 217. The reference points follow Reference [24]. range of the outdoor unit (ODU). \(P_{\text{RXth}}\) is the receiver sensitivity threshold, i.e., the input power at the receiver that is required for demodulation. Again, if there is no feeder and branching network, then this input power level can be measured directly at the antenna connection point (point D in Figure 5). In a digital link, the sensitivity threshold of the receiver is defined for a given modulation mode and bit error rate (BER) [41; 43]. In the case of transceivers capable of adaptive modulation, each modulation mode and the corresponding bit rate has its own set of BER thresholds [10]. In this paper, we use the threshold values belonging to \(BER=10^{-6}\). Please note that \(BER=10^{-3}\) thresholds are also often used. From a system design point of view, any gain due to error correction coding (e.g., FEC, forward error correction) is already considered in the given thresholds. It is important to mention that an alternative system gain definition also includes the gains of the transmit (TX) and receive (RX) antennas (please see Reference [33]). \[SG_{\text{a}}(BER)^{\left[\text{dB}\right]}=P_{\text{TX}}{}^{\left[\text{dBm} \right]}+G_{\text{TXa}}{}^{\left[\text{dBi}\right]}+G_{\text{RXa}}{}^{\left[ \text{dBi}\right]}-P_{\text{RXth}}(BER)^{\left[\text{dBm}\right]}, \tag{2}\]  
where \(G_{\text{TXa}}\) and \(G_{\text{RXa}}\) stand for the transmit and receive antenna gains, respectively. As indicated with the \"dBi\" unit, at microwave and at millimeter-wave frequencies--by definition--the antenna gains are compared to the gain of the isotropic antenna. To distinguish between the two alternative definitions of system gain, in Equation (2), we note \(SG_{\text{a}}\) to indicate that both TX and RX antenna gains are added already. The two system gain definitions are illustrated in Figure 6, where only the \(\upmu\)/mmW parts are indicated. The payload and modulator/demodulator blocks shown in Figure 5 are not repeated in Figure 6.  
Using the alternative system gain definition \(SG_{\text{a}}\) is convenient when the transceiver has either an integrated antenna built together with the ODU (Figure 7a) or a flip-mount antenna directly attached to the ODU (Figure 7b). For dual-polarization and multi-channel links, additional signal combiners and/or feeder waveguides are required (Figure 7c,d) that introduce additional losses into the entire system.