## 2 Ray Launching Technique and Simulation Scenario
Parameters such as frequency of operation, radiation patterns of the antennas, number of multipath reflections, separation angle between rays, and cuboid dimension can be taken into account. Additionally, the material properties for all the elements within the scenario can also be considered, given the dielectric constant and the loss tangent at the frequency range of operation of the system under analysis. The simulation scenario implemented for calculation by means of the in-house developed 3D Ray Launching code corresponds to the inhomogeneous vegetation environment represented in Figure 3, which is an outdoor location of the Campus of the Public University of Navarra. A view of the complete schematic vegetation model developed for simulation is depicted in Figure 4 with the position of the transmitter. All the material properties for all the elements within the scenario have been considered, given the dielectric constant and the loss tangent at the frequency range of operation of the system under analysis. Due to the continuous changes of the considered environment because of the weather, it is relevant to consider different conditions for the material properties of the trees. The top portion of the tree exhibits high variability depending on the season; for example in winter, there is little foliage whereas in summer the vast totality of the volume of the top of the trees is  
Figure 3: Vegetation scenario under consideration for simulation in the 3D Ray Launching algorithm **(a)** Real view **(b)** Schematic view for simulation. Figure 2: Schematic representation of the principle of operation of the in-house developed 3D Ray Launching algorithm. foliage. In addition, the humidity of the wood of the trunk of the trees strongly varies depending on the weather. This has led us to consider maximum and minimum conditions for the material properties of the foliage and the trunk of the trees. For that purpose, the values obtained in [27] for the material properties of the wood and the foliage have been used. The dielectric constant and conductivity of the wood of the ash tree, which are the trees of the considered scenario is variable with the temperature, as it is shown in Equations (4) and (5) with the parameter \(t\), and the dielectric constant and conductivity of the foliage of the trees is variable with humidity, as shown in Equations (6) and (7) with the parameter \(h\):  
\[\varepsilon_{r\;ash\;wood}=-4*10^{-6}t^{3}+0.0002t^{2}-0.0212t+21.483 \tag{4}\]  
\[\sigma_{ash\;wood}=3*10^{-7}t^{3}-0.0003t^{2}-0.004t+7.3238 \tag{5}\]  
\[E_{l}^{\perp}=\sqrt{\frac{P_{rad}D_{t}(\theta_{t},\phi_{t})\eta_{0}}{2\Pi}}\; \frac{e^{-j\beta_{0}r}}{r}\;\mathrm{X}^{\perp}L^{\perp} \tag{1}\]0  
\[E_{l}^{\perp}=\sqrt{\frac{P_{rad}D_{t}(\theta_{t},\phi_{t})\eta_{0}}{2\Pi}}\; \frac{e^{-j\beta_{0}r}}{r}\;\mathrm{X}^{\perp}L^{\perp} \tag{1}\]1  
To set up the dielectric constant and conductivity of the ash wood and the foliage, thresholds for the maximum and minimum humidity and temperature have been considered. These values have been fixed in the interval (0%, 30%) for the humidity and (20\({}^{\circ}\), 40\({}^{\circ}\)) for the temperature, according to [27]. Simulations have been performed for the minimum, medium and maximum values and the results shown in this work correspond with the medium values for the humidity and temperature. **\[E_{l}^{\perp}=\sqrt{\frac{P_{rad}D_{t}(\theta_{t},\phi_{t})\eta_{0}}{2\Pi}}\; \frac{e^{-j\beta_{0}r}}{r}\;\mathrm{X}^{\perp}L^{\perp} \tag{1}\]2** Schematic vegetation environment for simulation in the 3D Ray Launching algorithm. The material parameters used in the simulation are defined in Table 1[28,29]. **\[E_{l}^{\perp}=\sqrt{\frac{P_{rad}D_{t}(\theta_{t},\phi_{t})\eta_{0}}{2\Pi}}\; \frac{e^{-j\beta_{0}r}}{r}\;\mathrm{X}^{\perp}L^{\perp} \tag{1}\]3** Material properties in the ray launching simulation.