*3.2. Experimental Analysis*

In this case of non-isolated tree, measurements have been also performed in the real scenario. The transmitter has been placed at 2.5 m distance from the tree under analysis at a height of 1 m, supported by a plastic structure. The tree is 6 m height and 3.7 m of maximum width (see Figure 13). Measurements have been taken in a linear path (represented by a white dashed line in Figure 14) from the transmitter (red dot in Figure 14) to a distance of 15 m. The measured path loss values are depicted in Figure 15, where the simulation results have also been included in order to comparing them. As can be seen, in this non-isolated tree case, the simulator provides very accurate estimations. This good agreement is due to the multipath propagation, which starts gaining relevance because of the dense vegetation present in the nearer area of the tree under analysis.

**Figure 13.** Detail of the Non-Isolated tree under analysis with the dense forest background.

**Figure 14.** Upper view of the created scenario. The white dashed line represents the linear path where the measurements have been taken.

(**a**)

**Figure 15.** Measured vs. Simulated Path loss for the linear path corresponding to the white dashed line of Figure 14. (**a**) at 1m height; (**b**) at 2 m height.

### **4. Discussion**

Observing the values in Table 3, the rate of decay with distance, *n*, appears to be smaller than the value for open scenarios under free-space conditions that is around 2. This indicates the re-radiation effect probably due to the tree. The fitting of the simulation data for the 3 m case exhibits the decay rate value closest to the free-space condition, 1.863.

The parameters values summarized in Table 3, for linear or log-distance models are not in agreement with values reported in [14,15,20]. Reasons for this dissimilarity are found, among others, in the frequency, the scenario, and the radio link setup. Largest RMSE values are observed for the simulation results likely due to the lack of temporal averaging in the simulated data.

In [14], the transmitter antenna points to the top of the tree, and the receiver antenna is pointed upwards, so that the set simulates a transmitter – satellite or helicopter – located over the tree and the receiver. The frequency band analyzed was 8–12 GHz, so that the signal loss is stronger than for the 2.4 GHz: As explained in Section 3, this setup led to three-zone propagation.

In [15,20], the peer-to-peer transmission is analyzed, without blocking the radio link by a tree, only locating the transmitter on the tree trunk. Using a log-distance model, reported values of the decay rate *n* are larger than 2. In [15,20], a log-distance model is also applied for the radio link blocked by an undefined number of trunks, but not canopies.

In summary, with the exception of [14], most of the literature related to propagation in vegetation media does not reflect a scenario as described herein. Only the RET model [29] could be used to try to replicate the results presented here. However, the difficulty of programming this model, given the high number of parameters to be evaluated, has made this task unbearable.

For our study of an isolated tree, it is reasonable to consider that any signal fading analysis should not depend on the distribution of the foliage in the species or specimen of the tree considered as would occur for the case of a thin tree. It is for these cases that up-to-date prediction models may not fit the experimental results. For a case of an isolated tree as a vegetation obstacle, some models as ITU-R P.833-7 [13] consider the signal excess loss produced by the diffraction occurring on the obstacle top as well as on the left and right sides of the tree, and these diffractions are modeled according to a knife-edge case.

Our objective is not to offer a model for the components due to the diffraction or scattering phenomena. For modeling those components, a more exhaustive measurement campaign should be carried out, and a wideband channel sounder would be needed to provide power and delay metrics. In our present contribution we provide a path loss model that results sufficient to determine the quality of a D2D link in terms of probability error.

Regarding the results presented in this paper, a diffraction dominant zone in the vicinity of the tree has been identified. Near the tree the channel model corresponds to a multipath response or scattering situation. This region would be dominated by diffraction that is responsible for producing that the large attenuation introduced by the tree blockage starts recovering and continue as an open-space component.

In summary, compared to previous works, in this work experimental results achieved under anechoic chamber have been now demonstrated for outdoors. In addition, it has been also demonstrated that the neighborhood of trees affects the diffuse zone's positive effect on the received power level. This helps to understand the effect of the single trees on the SNR and the achieved results could find a practical applicability when deploying a network in forest areas.

As previously said, further research is required to deepening in the phenomenon of the propagation in vegetation media, and specifically, more experimental measurements should be carried out at different locations to complete the statistical analysis as well as the results presented in this work. Possible future work would be to analyze the effect of line of trees blocking the wireless propagation.

It is worth noting that the use of the presented 3D Ray Launching simulation tool gains importance when the scenario under analysis becomes more complex in terms of morphology and the number of elements/obstacles/vegetation present within it, as it can be seen in presented results. Thus, obtaining accurate path loss estimations will lead to optimized radio planning decisions in scenarios with dense vegetation such as parks and forests.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/1424-8220/19/21/4606/s1, Data set DS\_sim and DS\_meas corresponding to Figure 7: Comparison between simulation and measurement path loss for an isolated oak tree.

**Author Contributions:** Conceptualization, A.A.; Methodology, A.A., P.L.-I. and F.F.; Software and Simulations, P.L.-I., I.P., A.E., M.C.-E. and L.A.; writing—original draft preparation, A.A., L.A., I.P. and P.L.-I.; writing—review and editing, A.A., P.L.-I. and F.F.; Visualization, E.A., I.P., H.K. and A.A.; measurements, A.A., H.K.; Supervision, A.A.

**Funding:** This research was funded by Xunta de Galicia under grant ED431C-2019/26, Spanish Government under grant TEC2017-85529-C03-3R, AtlantTIC Research Center and project RTI2018-095499-B-C31, Funded by Ministerio de Ciencia, Innovación y Universidades, Gobierno de España (MCIU/AEI/FEDER, UE).

**Acknowledgments:** We would like to recognize the work, courage and sacrifice of the professionals and volunteers who worked hard against the terrifying fire that in October 2017 devastated the forest to which the tree of our study belonged. In the present, wonderful actions struggle to bring back the forest.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
