## 2 Isolated Single Tree Radio Channel Characterization
### Simulation Software  
In order to perform wireless channel estimation, in which multiple elements such as vegetation are considered, different approaches can be employed. These can be based on analytical models, usually employing first degree approximations to simplify them, or empirical/semi-empirical models, which rely on measurement-based regressions. Theoretical or analytical approaches are based on statistical theory and usually provide accurate propagation phenomena predictions [25; 26; 27; 28]. Two different types of theoretical models can be distinguished in the literature, namely the radiative energy transfer (RET) model [29] and the analytical theory approach by [PERSON] [30]. These two models have successfully been used to simulate radio wave propagation in vegetation environments but, due to the complexity of the mathematical equations on which they are based, and the difficulty to extract the input parameters of the models, such as density, area or thickness of leaves and branches, they tend to be unaffordable for real-sized scenarios, such as forests [31]. On the other hand, empirical techniques are based on extensive measurement campaigns in the considered environment [32; 33; 34; 35; 36]. They have successfully characterized path loss attenuation impact in diverse scenarios with inhomogeneous vegetation within them, and at different frequency bands. However, their main drawback is their lack of accuracy when different site-specific environments are analyzed. As an example, the work in [37] verifies that the well-known propagation empirical models can lead to an error percentage of 30% in propagation predicted values for a classic tomato greenhouse. To overcome these limitations, ray-tracing based methods have been proposed in the literature. In [38], a propagation model based on uniform theory of diffraction (UTD) has been presented for urban environments, considering the impact of propagation over buildings and the vegetation attenuation and scattering. In [39], another propagation model based on geometrical optics (GO) is presented to assess the scattered field caused by vegetation elements in the radio path. Methods based on GO such as ray tracing or ray launching achieve a good trade-off between simulations accuracy and computational cost [40]. Due to this fact, in this work, an in-house developed 3D Ray Launching (3D-RL) algorithm has been used to characterize inhomogeneous vegetation environments. The 3D-RL model is a deterministic technique based on GO and UTD and it is divided in three main steps:  
1. The first step consists in the design and creation of a realistic scenario, considering all the obstacles and scatterers within it. All the geometries and dimensions of all the objects within the scenario are taken into account, which lead to a realistic scenario which consider every detail of the environment. 2. The second step is the simulation procedure, in which the physical wavefront is approximated by a set of rays, which travel from the emitter in the same direction as the corresponding wave vector. The rays are launched following a solid angle, with angular resolution in both horizontal and vertical planes. These rays interact with the surrounding media following Fresnel equations, considering the frequency dispersive characteristics of the dielectric constant and conductivity of the corresponding materials of all the elements within the implemented scenario. 3. The last step deals with data processing from the complete 3D simulation volume, in order to extract power characterization as well as time domain characterization of the corresponding system within the simulation scenario. The ad-hoc 3D ray launching algorithm has been described in detail in [40] and validation in complex environments including vegetation has been described in [41]. In the algorithm, the consideration that the vegetation medium is homogeneous has been assumed, thus it has been treated as an isotropic dielectric material with constant permittivity and conductivity.