# 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  
This subsection explains all the components out of which the link model exists. _Antenna patterns_: For both considered frequency bands, the BSs were equipped with antennas with 3D radiation patterns modeled as in [23], as it specifies two different models for sectoral antennas, one for below 3 GHz and one for from 3 GHz to 70 GHz. An electrical downtilt of eight degrees and no mechanical tilt was used throughout all simulations. The 3 dB beamwidth (\(\phi_{3}\)), maximum transmit power (\(P_{tx}\)) and maximum antenna gain (\(G_{0}\)) for the three-sector case were based on the values provided by BIPT [22] (values can be found in Table 2). For mmWave deployments, it was assumed that more directional antennas, hence deployments with more than three sectors, can be designed. For  
Figure 1: Surface map of the city of Ghent with region of interest marked by the white square and the locations of the considered base stations marked by the white dots. The numbers indicate the index of the base stations. the \(>\)3-sector cases, the values of \(\phi_{3}\) are derived from the three-sector case by proportionally dividing the 65\({}^{\circ}\) beamwidth. Using the formulas of ITU-R [23], the new maximum antenna gain, \(G_{0}\), could be derived for every case and the maximum transmit power, \(P_{tx}\), was adjusted proportionally to the new maximum gain as to keep the exposure for ground users constant, in line with current RF exposure regulatory constraints. Reducing the azimuth beamwidth of the antenna patterns increases the maximum gain, which results in the maximum transmit power gradually lowering with increasing number of sectors per base station, the goal is to keep the sum of the maximum gain and the maximum transmit power constant. The values of \(\phi_{3}\), \(P_{tx}\) and \(G_{0}\) for different number of sectors can be found in Table 2. As for the azimuth rotation of every sector, the first sector was pointed north, 0\({}^{\circ}\), and the other sectors were evenly spaced to other angles. For example, in the six-sector case, the angles of the sectors were [0\({}^{\circ}\), 60\({}^{\circ}\), 120\({}^{\circ}\), 180\({}^{\circ}\), 240\({}^{\circ}\), 300\({}^{\circ}\)]. For both ground user equipment (UE) and aerial user equipment (AUE), an omnidirectional antenna with maximum gain of 2.15 dBi was used. _Line of sight_: When checking whether a UE location is in LOS with a base station, a line is drawn between the base station and the user in the 3D environment. If there are no intersections with the 3D environment the link between user and base station is considered LOS and if obstructions do exist the link is considered non-line of sight (NLOS). A 2D representation can be seen in Figure 2.  
_Path loss model_: The path loss (PL) model for LTE is defined by combining the work in [24], which specifies an LTE urban macro cell path loss model for ground users up to 22.5 m AGL, and the work in [25], which defines an LTE urban macro cell path loss model for aerial users above 22.5 m AGL. The general expression is as follows:  
\[PL=C+D\times log_{10}(d)+2 log_{10}(f_{c})+X_{\sigma}, \tag{1}\]  
where \(C\) and \(D\) are scenario (i.e., environment and LOS/NLOS link) and altitude-dependent constants (for the values, refer to 3 GPP [24; 25]); d is the 3D distance to the basestation; \(f_{c}\) is the carrier frequency, in this case 1.8 GHz; and \(X_{\sigma}\) is a zero mean Gaussian random variable with standard deviation \(\sigma\)