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 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:


**Figure 7.** Comparison between simulation and measurement path loss for an isolated oak tree.

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 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.

**Figure 8.** Comparison of path loss curves fitting for an isolated oak tree: (**a**) experimental results and (**b**) simulation-based results.

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):

$$PL(d) = P\_0 + n \cdot d \tag{1}$$

where *P*<sup>0</sup> 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*<sup>0</sup> and *n* in Equation (1) have been obtained for each one of the two receiver heights.

2. OLoS zone: it occurs for a distance from the tree beyond 1.6 m for 2 m height, and beyond 1.8 m for 3 m case. In this zone the path loss admits a linear regression according to the floating intercept (FI) model Equation (2) applied in [15,20]:

$$PL(d) = \alpha + 10 \cdot \beta \cdot \log\_{10}(d) \tag{2}$$

where *d* is the distance, β the line slope, and α the floating-intercept in dB. The slopes β are −0.818 for 2 m and −0.7047 for 3 m, and the fit errors are 1.053 and 0.2681 dB, respectively. A linear regression was tried with smaller fit errors than the FI model.

As noticed in Figure 8a,b, the division into two propagation zones is more remarkable for the experimental data. The values of the parameters α, β, *P*<sup>0</sup> and *n* obtained for each zone and height are summarized in Table 3. The RMS error was used as an estimation of the error of the models.


**Table 3.** Path loss fitting parameters for measurement and simulation results.

### 2.4.2. Signal to Noise Ratio

Following the procedure described in [15], it is possible to estimate the coverage distance for an IEEE 802.15.4 connection if the Signal to Noise Ratio (SNR) is obtained as a function of distance. As described in [15], for a 22 byte frame length and a PER of 2%, then a BER < 1.14 <sup>×</sup> 10−<sup>4</sup> would be needed. According to [15] and Figure 9 the SNR required is 0 dB approximately. The noise power is measured using the SA, at a central frequency of 2.45 GHz and for a span of 5 MHz that simulates a 5 MHz bandwidth ZigBee channel. The value measured was −82 dBm.

**Figure 9.** Signal to Noise Ratio (SNR) vs. distance to transmitter for a ZigBee device.

The resulting SNR is shown in Figure 9. It can be deduced that for a ZigBee system with a threshold of SNR = 0 dB connectivity is possible in the vicinity of the tree. The connectivity is kept for both simulated and experimental cases, even if 2·5.5 dB are subtracted to compensate the antenna gain used in the measurements. This result agrees with [15,20].

This result reinforces the conclusion given in Section 2.3.2 in which it was indicated that the presence of the tree, thanks to the diffraction phenomenon, reinforced the signal reached in certain points around the tree, as also stated in [45].

### **3. Non-Isolated Single Tree Radio Channel Characterization**

Once the radio channel characterization of an isolated single tree has been performed by means of measurements and simulations, in this section a step towards a more realistic scenario has been taken. Specifically, simulations and measurements of a single tree nearby a dense forest zone with thick in-leaf trees have been performed. This scenario is located in the Orgi Forest. This forest is a 77-hectares millennial forest with a high ecological value which extends into the Ultzama Valley (Navarra). The oak groves populated the Navarra valleys 4000 years ago. Orgi Forest was declared a Natural Recreational Area in 1996, after the intense forest exploitation of wood, pasture for livestock and hunting. This was to encourage the natural regeneration of forest´s flora and fauna, while regulating the use of people.

Orgi has been included in the European Natura 2000 network. Natura 2000 is the largest network of protected areas in the world and it offers protection to most valuable and threatened species in Europe. In the case of Orgi, the oak (Quercus robur) is the main species protected. There are oak trees of two types where many of them are centenarians: the common oak and the American oak.

The forest is organized into three zones (shown in Figure 10). The first called Arigartzeta, is the welcome zone that gives access for the oak grove. It has parking and picnic areas. The second zone is called Tomaszelaieta, and has a large walk area, where the visitor can discover other tree species such as holly and elms as well as some animal species such as birds or amphibians. The third zone is called Muñagorri, which is a conservation area. The public cannot access this last zone due to restrictions in order to facilitate the process of natural regeneration. The measurements have been performed within the accessible Tomaszelaieta zone (see zoomed zone in Figure 10), which is prepared for visitors (see Figure 11).
