2.3.2. Delay Spread

One of the characteristics of the deterministic 3D RL algorithm is the capability to provide multipath characterization, a feature seldom considered in previous models. In Figure 4 it is presented the simulation results of the Delay Spread (DS) as seen at different 2D height planes, for the single tree scenario simulated in Section 3 with the pine and oak tree models. A 2D plane of DS indicates the values of DS detected at each point of a plane located at a specific height, assuming a static transmitter positioned as in the simulations of Section 3, at a height of 2m. DS values depend on the tree species, the distance of the observation point to the transmitter, the percentage of signal blockage, and the observation 2D height plane. A range between 2 and 12 ns was obtained for the simulated scenarios. It is important to note that in the presented results, the RF power level estimations within obstacles (trunk and mainly the vegetation part of the oak) have not been represented in order to show clearer the radio propagation zones around the trees.

For instance, at height 1 m, the points of the observation plane located after the tree show low-medium values of DS: 6–8 ns for the pine and 6–10 ns for the oak. This situation is due to the tree trunk, which is the most influent part in signal blockage.

However, for the pine case at 3 m height plane, the signal blockage is weaker due to the many air gaps of the pine tree top. Therefore, while pine tree behaves like a low density medium, the oak tree shows the behavior of a homogeneous medium. Generally, the obtained results are in accordance with [43,44]. Specifically, [43] presents UHF radio propagation estimations through a trunk-dominated area, for distances greater than 100 m. The work presented in [44] is closer to the case analyzed in this

paper: the authors compute the RMS delay spread of the measured power delay profiles at 5 GHz band along different trails within different forests. They obtained delay spread mean values between 60 ns and 90 ns depending on the trail (and therefore, the distance). These values agree with our simulation results, which correspond to shorter distances (less than 8 m in any case).

**Figure 4.** Simulation results of the Delay Spread, for both pine tree (**left**) and oak tree (**right**).

Similarly to the results in [45], it is noticed that, for any 2D height plane, the presence of vegetation contributed to the received signal level enhancement, predominantly in the side- and back-scattering regions, contrasted with the significant attenuation caused by absorption and scattering in the forward-scattering region produced after the tree [45].

Furthermore, delay spread values achieved along a linear path reflect a two-zone model similarly to path loss in Section 2.1: in the diffraction predominant zone, the number of signal components coming from scattering inside the tree is larger, and once mostly-coherently added produce larger values of DS; in the OLoS zone, away from the tree, the number of multipath components decrease considerably.

### *2.4. Experimental Measurements*

In order to complete the simulation outcomes for path loss, measurements were carried out in a forest and one medium size specimen of oak was chosen. The measurements were carried out using devices operating at the band of 2.4 GHz. The specific forest, composed of different type of trees, is called Chandebrito and is situated in Galicia, Spain. As shown in Figure 5a, the chosen tree's dimensions are larger in height and width than the model used for simulations: 5.5 m tall and 4.25 m wide. The larger width compensates the lesser homogeneity of the canopy that presents considerably more air gaps than in the simulated model becoming a polidispersive medium [46]. Figure 5b shows the surroundings of the chosen isolated tree, which is at least around 10 m away from any other tree.

The transmitter consisted of a programmable signal generator (WindFreak SynthHD) connected to a directional log-periodic antenna with vertical polarization, model Electro-Metrics EM6952, via a low-loss coaxial cable. The antenna radiation pattern shows 70◦ of azimuth (E-plane) and 125◦ of elevation (H-plane). The frequency of the transmitted tone was 2.4 GHz, and its power was 0 dBm. The antenna gain at this frequency is 5.5 dBi.

For acquiring the received signal we used a spectrum analyzer (SA) Rohde Schwarz FSH-6 that registered the RF signal via an antenna identical to the one used in transmission. No amplifiers or filters were used in transmission or reception.

The transmitter antenna was placed on a tripod at a height of 2m, in a fix location at a distance of 3.5 m from the tree trunk base. The receiver antenna was also fixed on the top of a tripod at 2 and 3 meters high, moving along a radial from the tree trunk base to 4.6m apart. Both the transmitter and receiver antennas pointed to the tree canopy.

**Figure 5.** (**a**) Oak tree specimen chosen for experimental measurements. (**b**) Surroundings of the isolated oak tree.

The measurement was done moving the tripod with the receiver antenna along a linear path from near (0.25 m) to far (4.6 m) the tree. The initial distance to the tree is 0.25 m. This initial distance was increased in steps of 0.10 m (>λ/4 increments) until the final position at 4.6 m from the tree was reached. At each position of the receiver antenna along the linear path the SA was configured to acquire a data trace of 301 power samples at 2.4 GHz, with a resolution bandwidth of 1 KHz and zero span, in order to average temporal power variations. Measurements were completed for receiver antenna heights of 2 m and 3 m given that in these cases the influence of the tree canopy is what creates the situation of a double propagation zone. A picture of the employed equipment is shown in Figure 6.

**Figure 6.** Employed equipment for the measurement campaigns.
