## 2 Isolated Single Tree Radio Channel Characterization
### Experimental Measurements
#### 2.4.1 Path Loss  
The SA measured values were processed. First, an averaging is applied to the 301 power samples composing each trace. Later all the data traces were normalized with respect to the power received at  
Figure 5: (a) Oak tree specimen chosen for experimental measurements. (b) Surroundings of the isolated oak tree. Figure 6: Employed equipment for the measurement campaigns. a reference distance of 1m from the transmitter, for each receiver height. In the case of the experimental data, the antenna gains are then compensated. The result is a set of 59 points that determines the signal level loss as a function of the distance between the tree and the receiver. The measured path loss is compared to simulated data in Figure 7 (corresponding datasets are provided as supplementary material). Only the portion of the distance axis corresponding to the forwarding zone (after the tree) matches for both datasets. The experimental outcomes corroborate the two-zone propagation model. The difference in dimensions between the virtual tree and the actual tree are primarily reflected in the lower power level received. Moreover, the radiation diagrams, and the power gains of the antennas used differ: omnidirectional in the virtual case and directive in the measurements. These and other factors are responsible for dissimilarities observed between the simulated and the experimental datasets. The not averaged multipath contributions observed in the simulation curves in Figure 7 are likely due to the lack of temporal averaging in the simulated data. The differences in the antenna radiation diagrams of the virtual and measurement cases can also explain the fit discrepancy. The following values of RMSE are observed between the experimental and simulated curves according to the antenna height and the propagation zone:  
* For diffuse zone: RMSE = 8.6370 dB at 2 m, and RMSE = 5.2804 dB at 3 m.
* For OLoS zone: RMSE = 5.8596 dB at 2 m, and RMSE = 6.2672 dB at 3 m.  
The diffuse scattering zone, located between 4m and around 5.5 m of the virtual distance axis, presents a less pronounced slope for both receiver heights. The slope of the OLoS zone decays faster than in the simulated scenario case. Finally, the averaging introduced in the SA acquisition and processing provided lower signal variability than in the simulation results. It is not possible to introduce averaging in the electric field results estimated by the simulation; however, in a simulator, the scenario is static and averaging does not seem necessary. In the measurement scenario, e.g., the wind blowing produces non trivial signal level variations that the averaging filters. The result is that the experimental curves are smoother than  
Figure 7: Comparison between simulation and measurement path loss for an isolated oak tree. the virtual ones. Spatial averaging was not applied; however, it is recommended for windy scenarios or irregularly shaped trees. Typically, the path loss variation as a function of distance is modeled by means of a log-distance or a linear regression. In Figure 8a the results of the model fitting are shown for the measured values, and in Figure 8b for the simulation case. It is noticed that depending upon the radio propagation zone a fit model is more suitable than any other, even despite the receiver height. The experimental and simulated path loss curves resulted in the following fitting:  
1. Diffuse scattering zone: it occurs near the tree, between 0.25 m and 1.6 m from the tree for 2 m height, and up to 1.8 m for 3 m case. In this zone only the fitting could be obtained by linear regression that meets the expression given in Equation (1): \[PL(d)=P_{0}+n\cdot d\] (1) where \(P_{0}\) is the reference power loss in dB at the start distance, 0.25 meter from the tree; \(d\) is the distance in meters between the start distance and receiver; \(n\) is the factor that determines the power decay rate with the distance. Parameters \(P_{0}\) and \(n\) in Equation (1) have been obtained for each one of the two receiver heights. 2.