# Aerial Coverage Analysis of Cellular Systems at LTE and mmWave Frequencies Using 3D City Models
## 2 System Model
### Network Model
#### 2.1.2 Link Model
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**\# 5 sectors per BS** & **3** & **6** & **9** & **12** & **15** & **18** & **21** & **24** & **27** & **30** & **33** & **36** & **39** & **42** & **45** \\ \hline \(\phi_{3}\)[\({}^{\circ}\)] & 65 & 32.5 & 21.67 & 16.25 & 13 & 10.83 & 9.29 & 8.13 & 7.22 & 6.5 & 5.91 & 5.42 & 5 & 4.64 & 4.33 \\ \(G_{0}\) [\(dBi\)] & 18 & 21.01 & 22.77 & 24.02 & 24.99 & 25.78 & 26.45 & 27.03 & 27.54 & 28 & 28.41 & 28.79 & 29.14 & 29.46 & 29.76 \\ \(P_{tx}\) [\(dBm\)] & 46 & 42.99 & 41.23 & 39.98 & 39.01 & 38.22 & 37.55 & 36.97 & 36.46 & 36 & 35.59 & 35.21 & 34.86 & 34.54 & 34.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Antenna parameters for different number of sectors per base station. Figure 2: A 2D representation of the line of sight. Blue lines indicate the serving base station, while orange lines indicate interfering base stations. A dashed line indicates NLOS and a full line indicates LOS. which is determined by UE altitude. For example, the formula for a user at an altitude above 22.5 m and with a LOS connection is defined as follows:  
\[PL=28.0+22\times log_{10}(d)+20 log_{10}(f_{c})+X_{\sigma}, \tag{2}\]  
where \(\sigma\) is defined as follows:  
\[\sigma=4.64\times exp(-0.0066\times h_{ut}), \tag{3}\]  
where \(h_{ut}\) is the UE altitude. To calculate the average building height, which the ground user model uses as an input [24], a line is drawn between user en BS and the average building height of all buildings intersecting this line is calculated. For mmWave, we consider the following close-in reference distance path loss model of [18]:  
\[PL(d)=PL(d_{0})+10 nlog_{10}(\frac{d}{d_{0}})+X_{\sigma}, \tag{4}\]  
where \(X_{\sigma}\) is a zero mean Gaussian random variable with standard deviation \(\sigma\) and \(n\) is the path loss exponent for a particular frequency band or a given environment. The standard deviation values for the LOS and NLOS cases are 10.3 and 14.6, respectively [17]. The path loss exponent values for the LOS and NLOS cases are 2.20 and 3.88, respectively [17], and \(PL(d_{0})\), the free space reference path loss at distance \(d_{0}\), is defined as:  
\[PL(d_{0})=10 log_{10}(\frac{4\pi d_{0}}{\lambda})^{2}, \tag{5}\]  
where \(\lambda\) is the wavelength and \(d_{0}\) is the reference distance. The reference path loss is taken at a distance of 1 m as proposed in [19] and thus results in 64 dB reference path loss. _SINR calculation_: When calculating the SINR at a specific location, all BSs are assumed to be transmitting on all sectors. Thus, for every sector, the received power is calculated as follows:  
\[P_{rx}=P_{tx}+G_{tx}+G_{rx}-PL, \tag{6}\]  
where \(P_{rx}\) is the received power, \(P_{tx}\) is the constant transmitted power, \(G_{tx}\) and \(G_{rx}\) are, respectively, the transmitting and receiving antenna gains in the direction of the user and PL is the corresponding path loss for that location, with all parameters in dB. Let A be the collection of all sectors. For one specific location, the SINRs of all sectors are calculated as follows:  
\[\forall a\in A:SINR_{a}=\frac{P_{rx,a}}{I_{a}+N}, \tag{7}\]  
where \(N=N_{0}BF\) (\(N_{0}\) is white noise density, \(B\) is signal bandwidth and \(F\) is noise figure, values in Table 1) is the noise power and \(I_{a}\) is the interference power considering \(a\) is the serving sector, which is defined as follows:  
\[I_{a}=\sum_{i\
eq a}^{A}P_{rx,i}. \tag{8}\]  
Out of all the resulting SINR values, the highest value is chosen as serving sector for every location, which allows us to determine a 3D sector assignment map that shows the sector assignment in a geographical area. Four slices of this assignment map at different heights are shown in Figure 3. Figure 3a-c shows that up to an altitude of around 35 m assignments happen in a cell-like manner, which means a UE is most likely to be assigned to the most nearby base station.