# A New Propagation Channel Synthesizer for UAVs in the Presence of Tree Canopies
## 4 Artificial Scenario Validation  
Having the new proposed synthesizer implemented in software, it is convenient to first test its proper functionality using an artificially-defined scenario with a very simple geometry. This allows us to predict the expected results up to a certain level prior to using the synthesizer. For these purposes, we have defined a simple alley of roadside trees, all of which have a cylindrical canopy of 1.5 m radius and 6 m height. In the _xyz_ Cartesian coordinate system, each canopy has the \(z\) component of its center point at 4 m, i.e., the canopies span in the \(z\) axis direction from 1 m to 7 m above ground level. The UAV is fixed under the elevation angle of 45\({}^{\circ}\) from the point of view of its ground terminal and, in azimuth, the incident plane wave is perpendicular to the alley. The terminal at a height of 1.5 m is supposed to be moving in the \(y\) direction inside the alley from 0 m to 25 m with a sampling step of 0.2\(\lambda\), where \(\lambda\) represents the wavelength of the incident plane wave which has the frequency set to 2 GHz and its polarization is vertical. The alley surrounds the terminal on its left and right side by four trees at a 4 m distance; the tree spacing is set to be 5 m. The branches and leaves parameters are the same as in [2; 4; 5; 6]. Please see Figure 5 below for more details. As the trees are quite separated from each other and the distance from their center points towards the terminal is long, we may expect LoS propagation conditions towards the UAV within some parts of the terminal route. On the other hand, diffraction effects caused by the coherent scattered field should be clearly identified when the propagation path towards the UAV is blocked by a particular canopy. In addition, the resulting time series should follow the symmetry of the scenario where the terminal starts to move 5 m before the beginning of the alley and stops 5 m behind the alley. As explained above in Section 3.3, to save the computation time, only the trees on the right side of the terminal are utilized within the coherent scattered field calculations. Further, the value of \(\sigma^{\alpha\beta}(-\mathbf{\hat{k}}_{\mathrm{inc}},\mathbf{\hat{k}}_{ \mathrm{inc}})\) for the very first \(\mathbf{\hat{k}}_{\mathrm{inc}}\) direction is utilized throughout the calculations. Figure 6 presents the results obtained by the proposed synthesizer. It should be noted that, on a PC with a 3.5 GHz quad-core processor and 16 GB RAM, the total computation time for the 834 terminal positions (distance of 25 m with a step of 0.2\(\approx\) 3 cm) was only about 50 s, including the surface and volume sampling of the canopies. Again, it should be stressed that this synthesizer provides a site-specific time series respecting the geometry of the scenario, as well as the physical parameters of the tree canopies. For the considered tree dimensions and their number, full-wave solutions using the multilevel fast multipole method (MLFMM) method in electromagnetic simulators would be impossible due to unrealistic memory requirements. Figure 5: The selected artificial scenario with a terminal moving from \([0,\ 0,\ 1.5]\) to \([0,\ 25,\ 1.5]\) with a step of 0.2\(\lambda\): (**a**) top view; (**b**) front view. The alley of trees is selected so that there is one row on the left side and one row on the right side of the terminal, each at a distance of 4 m. The cylindrical tree canopies are separated by 5 m and have radius of 1.5 m and height of 6 m. The incident plane wave illuminates the scenario perpendicularly to the alley under the elevation angle of 45\({}^{\circ}\). The dark green dashed line in (**b**) indicates the inner part of the canopy illuminated by the incident plane wave as utilized by the combined PO/MST model. To support the obtained results, the same scenario was simulated in FEKO [18] using the common PO for the case of completely absorbing canopies, i.e., not accounting for any field passing through dielectric objects.