# Fronthaul Design for Wireless Networks
## 3 Fronthaul Design Methodology
### Link Design Algorithm
#### 3.1.1 Communication Technologies Models
Formally and given the rain intensity not exceeded in 0.01% of the time (\(R_{i}^{(0.01\%)}\)), the rain attenuation for that percentage of the time is given by (in dB):  
\[A_{rain}^{0.01\%}=\beta\times\left(R_{i}^{(0.01\%)}\right)^{\alpha}\times d _{ef}, \tag{6}\]  
where \(\beta\) and \(\alpha\) denote coefficients that depend on the carrier frequency and on the considered temperature and \(d_{ef}\) corresponds to the effective distance through a rainy path, which is computed as:  
\[d_{ef}=\max\left\{2.5\,d\;;\;\frac{d}{0.477\,d_{\rm[km]}^{0.633}\times\left(R _{i}^{(0.01\%)}\right)^{0.073\,\alpha}\times\int_{\rm[GHz]}^{0.123}-10.579 \left(1-e^{-0.024\,d_{\rm[km]}}\right)}\right\}; \tag{7}\]  
finally, the rain attenuation exceeded for a percentage of time \(U_{max}\) other than 0.01% is obtained as:  
\[A_{rain}=A_{rain}^{0.01\%}\times 0.12\,U_{max}^{-(0.546+0.043\log_{10}U_{ max})}. \tag{8}\]  
Turning the attention now to FSO systems, the term \(A_{sys}\) encompasses the attenuation induced by atmospheric absorption (\(A_{abs}\)), the attenuation due to atmospheric turbulence (\(A_{turb}\)), and the attenuation caused by scattering (\(A_{sca}\)). All these attenuation factors can be computed as described in the related literature [26; 27]; a summary is given as follows. Considering the atmospheric absorption (which is mainly caused by the presence of gaseous molecules), it can be given by (in dB):  
\[A_{abs}=\gamma_{abs}\times d, \tag{9}\]  
where \(\gamma_{abs}\) stands for the absorption attenuation coefficient, which depends on the considered temperature and on the relative humidity. The attenuation due to atmospheric turbulence (i.e., small and random variations of the refractive index of the Earth's atmosphere, which are responsible for wave front distortion) can be described by (in dB):  
\[A_{turb}=2\,\sigma_{scin}, \tag{10}\]where \(\sigma_{scin}\) refers to the scintillation index, which can be expressed as:  
\[A_{0}=92.4+20\log_{10}(d_{\rm[km]})+20\log_{10}(f_{\rm[GHz]}), \tag{2}\]0  
where \(\lambda\) corresponds to the operating wavelength and \(C_{n}^{2}\) represents the index of refraction structure parameter, which is computed as (in m\({}^{-2/3}\)):  
\[A_{0}=92.4+20\log_{10}(d_{\rm[km]})+20\log_{10}(f_{\rm[GHz]}), \tag{2}\]1  
where \(h_{a}\) denotes the transmitter altitude. With respect to \(A_{sca}\), which is caused by the occasional presence of fog (including mist and haze) and rain, it is important to stress that fog is the major contributor regarding the attenuation due to scattering; hence, and noticing that the respective attenuation coefficient is computed as a function of the visibility, this type of attenuation also depends on the desired time availability for the FSO link. More specifically, one has to take into account the value of the visibility that is not exceeded for a given percentage of the time in the location of interest. Since the ITU-R recommendations for FSO systems' design do not provide a metric to compute the visibility distribution, one alternative is to use one of the visibility distribution models presented in a related work [28]--e.g., the simplified model introduced therein and adopted in this methodology--which rely on the average number of foggy days (per year) and the average duration of fog events (in hours). Accordingly, the visibility value can be obtained and used to compute the respective attenuation that ensures that the planned FSO link may still suffer from fog outage, but no longer than the maximum percentage of the time regarding tolerated link unavailability, thus enabling fulfilling the SLR; it is important to mention that, in order to ensure the fulfillment of the same SLR regardless of the specific adopted wireless technology, the software tool considers the same percentage of the time for link unavailability regarding the attenuations related to both rain and fog.