# Fronthaul Design for Wireless Networks
## 3 Fronthaul Design Methodology
### Link Design Algorithm
#### 3.1.1 Communication Technologies Models  
For wireless communication technologies such as MRT and FSO, the received signal power, \(P_{Rx}\), is given by (in logarithmic units):  
\[P_{Rx}=P_{Tx}+G_{Tx}+G_{Rx}-A_{0}-A_{equil}-A_{sys}, \tag{1}\]  
where \(P_{Tx}\) corresponds to the transmitted power (in dBW or dBm), \(G_{Tx}\) and \(G_{Rx}\) stand for the transmitter and receiver antenna gains (in dBi), respectively, and \(A_{0}\) represents the free-space path loss (in dB), i.e.,  
\[A_{0}=92.4+20\log_{10}(d_{\rm[km]})+20\log_{10}(f_{\rm[GHz]}), \tag{2}\]  
where \(d\) denotes the link distance and \(f\) refers to the carrier frequency, \(A_{equil}\) denotes the losses (in dB) related to equipment like cables, modulators, etc. (which are typically lower than 3 dB), and \(A_{sys}\) corresponds to other losses (in dB) related to specific attenuation factors regarding the considered communication technology. With respect to MRT systems, the term \(A_{sys}\) incorporates the attenuation caused by obstacles in the line-of-sight path (\(A_{obs}\)), the attenuation induced by atmospheric gases (\(A_{gas}\)), and the attenuation due to rain (\(A_{rain}\)). All these attenuation factors can be computed as described in the related literature [13]; a summary is given as follows. The attenuation due to obstacles can be computed as (in dB):  
\[A_{obs}=\max\left\{0\;;\;6.9+20\log_{10}(\sqrt{(\
u-0.1)^{2}+1}+\
u-0.1) \right\}, \tag{3}\]  
where \(\
u\) is proportional to the amount of the Fresnel ellipsoid that is obstructed by the obstacle, i.e.,  
\[\
u=\frac{h_{obs}}{17.32}\sqrt{8\frac{f_{\rm[GHz]}}{d_{\rm[km]}}}, \tag{4}\]where \(h_{obs}\) denotes the height of the top of the obstacle above the straight line joining the two ends of the link (if the height is below this line, then \(h_{obs}\) is negative). The attenuation due to atmospheric gases (namely uncondensed water vapor and oxygen) can be computed as (in dB):  
\[A_{gas}=(\gamma_{o}+\gamma_{w})\times d, \tag{5}\]  
where \(\gamma_{o}\) and \(\gamma_{w}\) represent, respectively, the attenuation caused by oxygen and water by units of length; values for these parameters can be extracted from nonlinear curves as a function of the carrier frequency. With respect to \(A_{rain}\), it should be pointed out that since rain is highly variable over time and differs from place to place, the respective attenuation factor depends on the desired time availability for the MRT link. More specifically, the attenuation due to rain has to be computed taking into account the value of rain intensity that is not exceeded in a certain percentage of the time in the location of interest. Accordingly, and having in mind the Service Level Requirements (SLR)--which address service times, maintenance, availability, performance, etc.--an MRT system designer must first stipulate the minimum time availability of the link (e.g., 99.9% of the time, as adopted in this work); afterwards, by using the method suggested by an ITU-R (International Telecommunication Union - Radiocommunication Sector) recommendation [25], the rain attenuation is computed, thus ensuring that the planned MRT link may still suffer from rain outage, but no longer than the maximum percentage of time unavailability of the link (\(U_{max}\)), with \(U_{max}=100\%-\) minimum link availability percent.