# Fronthaul Design for Wireless Networks
## 3 Fronthaul Design Methodology
### Link Design Algorithm
#### 3.1.1 Communication Technologies Models
Formally, the attenuation caused by scattering is given by (in dB):  
\[A_{0}=92.4+20\log_{10}(d_{\rm[km]})+20\log_{10}(f_{\rm[GHz]}), \tag{2}\]2  
where \(\gamma_{fog}\) and \(\gamma_{rain}\) represent, respectively, the attenuation caused by fog and water by units of length. The former parameter can be expressed as (in dB/km):  
\[A_{0}=92.4+20\log_{10}(d_{\rm[km]})+20\log_{10}(f_{\rm[GHz]}), \tag{2}\]3  
where \(V\) stands for the visibility and \(q\) refers to a coefficient that is dependent on the size distribution of the scattering particles, which is given by:  
\[q=\left\{ \begin{array}{ll}1.6&V>50\text{ km}\\ 1.3&6\text{ km}<V<50\text{ km}\\ 0.16\,V_{[\text{km}]}+0.34&1\text{ km}<V<6\text{ km}\\ V_{[\text{km}]}-0.5&0.5\text{ km}<V<1\text{ km}\\ 0&V<0.5\text{ km}\end{array} \right.\,. \tag{15}\]  
With respect to the visibility, it can be computed as (in km):  
\[V=\frac{U_{max}}{100}\times\frac{365.25}{\overline{N_{fog}}_{[\text{days/year }]}}\times\frac{24}{\overline{D}_{[\text{h}]}}, \tag{16}\]where \(\overline{N_{fog}}\) and \(\overline{D}\) refer to the average number of foggy days and the average duration of fog events, respectively. Finally, the parameter related to the attenuation caused by water can be expressed as (in dB/km):  
\[\gamma_{train}=1.076\,\left(R_{i}^{(0.01\%)}\right)^{0.67}\times 0.12\,U_{max} ^{-(0.546+0.043\log_{10}U_{max})}. \tag{17}\]  
After computing the received signal power, the wireless link margin, \(W_{link}\), is obtained as (in dB):  
\[W_{link}=P_{Rx}-S_{Rx}, \tag{18}\]  
where \(S_{Rx}\) refers to the sensitivity of the receiver. In order to consider a wireless connection as viable and since the higher the link margin, the more robust the wireless link will be, as it will be prepared for potential extra attenuations, \(W_{link}\) must be greater than a user-specified minimum accepted link margin (e.g., 3 dB, as adopted in this work for both MRT and FSO links). Once the link margin requirement is satisfied, another requirement, namely the Bit Error Rate (BER), must be fulfilled in order to ensure that the wireless link is feasible (e.g., in this work, the BER must be lower than \(10^{-6}\)). The BER can be extracted from mapping curves as a function of the Signal-to-Noise Ratio (SNR) of the MRT link [13] or the FSO link [29]. With respect to the SNR of an MRT link, it can be given by (in dB):  
\[\text{SNR}^{\text{(MRT)}}=P_{Rx}-N_{f}-N_{0}, \tag{19}\]  
where \(N_{f}\) corresponds to the noise figure of the receiver and \(N_{0}\) denotes the thermal noise, which can be computed as (in dBW):  
\[N_{0}=-204+10\log_{10}(b_{w[\text{Hz}]}), \tag{20}\]  
where \(b_{w}\) represents the noise equivalent bandwidth of the receiver; it can be expressed as:  
\[b_{w}=\frac{B_{link}}{\log_{2}(M)}, \tag{21}\]  
where \(B_{link}\) and \(M\) stand for the link bit rate and the QAM (Quadrature Amplitude Modulation) signal constellation size, respectively. Considering an FSO link and making the typical assumption of a shot-noise-limited operation with On-Off Key (OOK) modulation, the SNR can be obtained as (in dB):  
\[\text{SNR}^{\text{(FSO)}}=P_{Rx}-\frac{P_{Rx}+A_{turb}}{2}-5\log_{10}\left(2\, h\times\frac{c}{\lambda}\times B_{link}\right), \tag{22}\]  
where \(h\) and \(c\) refer to the Planck constant and the speed of light, respectively. Considering now FO systems, the associated technology differs from the two wireless communication systems previously discussed (MRT and FSO) as it does not use the atmosphere as the propagation medium. More specifically, since the beam is confined to the fiber, there are no outside weather conditions that need to be taken into consideration when planning point-to-point transmission using the FO technology. Accordingly, evaluating a link budget for FO is equivalent to computing the total loss, suffered by a transmitted signal across various components and along the optical fiber, with reference to the minimum receiver power required to maintain normal operation.