# A New Propagation Channel Synthesizer for UAVs in the Presence of Tree Canopies

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## Abstract

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## 1. Introduction

## 2. Theoretical Background

#### 2.1. PO

#### 2.2. Multiple Scattering Theory (MST)

#### 2.3. New Combined PO/MST Model

## 3. The Proposed Channel Synthesizer

#### 3.1. Inputs

#### 3.2. Coherent Scattered Field

#### 3.3. Incoherent Scattered Field

#### 3.4. Discussion and Workflow

## 4. Artificial Scenario Validation

## 5. Experimental Data Validation

- As the change of the UAV position in elevation and azimuth w.r.t. the Rx was less than 30°, thus, not very significant from the scattering characteristics point of view, only one value of $K$ and ${\sigma}^{eq}(-{\widehat{k}}_{\mathrm{inc}},{\widehat{k}}_{\mathrm{inc}})$ was calculated.
- Only two trees influencing the coherent field calculations the most were considered within the combined PO/MST part of the simulator, namely the third and fourth tree from the right in the bottom row of trees in Figure 9b.
- the UAV speed was kept below 10 m/s, respecting the data sampling rate of 10 kHz, the spatial distance between two adjacent samples is below 1 mm, which is too dense. To characterize the fast fading thoroughly, a sufficient step may be longer, e.g., about $0.1\mathsf{\lambda}\cong 15\text{}\mathrm{mm}$. Following this, we provide an output for every 10th experimental data sample, which translates into a step in the UAV distance below $~0.07\mathsf{\lambda}$.
- Tree canopies are modeled simply as cylinders with radius of 1.8 m and height of 8 m with the bottom cap at the height of 1.5 m, i.e., the same as the Rx height.
- Ground reflections are not included.
- The simulation is carried out for a vertically polarized incident field, although the experimental data were obtained for the circularly polarized field.
- Tree trunks were not considered.

## 6. Discussion

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The common PO approach. The incident plane wave fields ${E}_{\mathrm{inc}}$ and ${H}_{\mathrm{inc}}$ result into surface equivalent currents ${J}_{\mathrm{eq}}$ and ${M}_{\mathrm{eq}}$ on the illuminated outer surface of the object. In turn, these currents provide scattered fields resulting into the blockage fields behind the object and cause the final coherent fields behind the object to be ${E}_{\mathrm{B}}$ and ${H}_{\mathrm{B}}$ from Equations (3) and (4).

**Figure 2.**The MST approach. The field inside the canopy’s voxels ${E}_{\mathrm{coh}}^{\mathrm{in}}\left(r\prime \right)$ depends on the distance through the canopy ${s}_{1}\left(r\prime \right)$ along ${\widehat{k}}_{\mathrm{inc}}$ and the complex propagation constant $K$ inside the canopy. The coherent $\langle {E}_{\mathrm{scat}}\left(r\right)\rangle $ and incoherent $\langle {\left|{E}_{\mathrm{scat}}\left(r\right)\right|}^{2}\rangle $ scattered fields are obtained at $r$, which is in the ${\widehat{k}}_{\mathrm{out}}$ direction with respect to the canopy’s center.

**Figure 3.**The new combined PO/MST approach. The inner part of the canopy (green outlines) is supposed to be illuminated by the incident plane wave. The field propagating through the canopy ${E}_{\mathrm{aper}}$ is accounted for by utilizing the complex propagation constant $K$ inside the canopy, $\widehat{n}={\widehat{n}}_{\mathrm{aper}}$ and path through the canopy towards $r\prime $. The common PO blockage field ${E}_{\mathrm{block}}$ uses $\widehat{n}={\widehat{n}}_{\mathrm{block}}$ and ${k}_{0}$.

**Figure 4.**Workflow of the new proposed propagation channel synthesizer. The change of the UAV and/or terminal positions is denoted by the time input sampling. The blue entities symbolize the input data while the yellow processes denote the corresponding calculations performed by the synthesizer. The resulting output field is symbolized by ${E}_{\mathrm{tot}}$.

**Figure 5.**The selected artificial scenario with a terminal moving from $\left[0,\text{}0,\text{}1.5\right]$ to $\left[0,\text{}25,\text{}1.5\right]$ with a step of $0.2\lambda $: (

**a**) top view; (

**b**) front view. The alley of trees is selected so that there is one row on the left side and one row on the right side of the terminal, each at a distance of 4 m. The cylindrical tree canopies are separated by 5 m and have radius of 1.5 m and height of 6 m. The incident plane wave illuminates the scenario perpendicularly to the alley under the elevation angle of 45°. The dark green dashed line in (

**b**) indicates the inner part of the canopy illuminated by the incident plane wave as utilized by the combined PO/MST model.

**Figure 6.**The coherent scattered field (red) and total resulting field (black) for the scenario from Figure 5.

**Figure 7.**The coherent scattered field as obtained by PO in FEKO for the scenario from Figure 5 for the case of totally absorbing tree canopies.

**Figure 8.**The selected measurement scenario at Fleming Square in Prague, the Czech Republic: (

**a**) location of the receiver marked by the magenta dot; (

**b**) UAV during a flight, the Tx antennas placed on the 3D positioner are marked by the magenta circle.

**Figure 9.**The selected measurement scenario represented by cylindrical tree canopies: (

**a**) Tx positions (black line) and tree canopies (green cylinders); (

**b**) detail of the alley with Rx marked by the red asterisk, tree canopies represented by the green cylinders and Tx–Rx directions shown by the black lines. The Cartesian coordinate system is aligned so that the origin is at the Rx position, the x, y, and z axes point towards the east, north and zenith, respectively. Tx moving direction is denoted by the arrow.

**Figure 10.**The resulting received signal time series as provided by the synthesizer (black line) together with the actual experimental data (cyan line). A detail for the time from 5 s to 5.5 s is shown to demonstrate the continuity characteristic of the synthesizer’s output.

**Figure 11.**The coherent (red) and incoherent (magenta) scattered field as obtained inside the synthesizer. Faster changes in the incoherent scattered field result from more significant changes in the incidence direction within the particular time intervals.

**Figure 12.**Generated CIR for the experimental scenario under LoS propagation conditions as achieved at the flight time 5 s. The direct signal (black line) dominates while the coherent fields (blue lines) scattered from the two canopies closest to Rx are negligible. The total incoherent scattered fields from each canopy (red dashed lines) are stronger than the coherent scattered fields as they dominate in other than the forward scatter direction. The power levels and time delays are normalized with respect to the direct signal between Tx and Rx.

**Figure 13.**Generated CIR for the experimental scenario under NLoS propagation conditions as achieved at the flight time 25 s. The direct signal is blocked and, thus, not shown. The coherent field (blue lines) scattered from the canopy closest to Rx dominates and is responsible for the attenuation behind the canopy. The coherent field contribution from the second closest canopy is negligible. The total incoherent scattered fields from each canopy (red dashed lines) have levels about the same as in the LoS case, as they are not supposed to be blocked by any canopy. The power levels and time delays are normalized with respect to the direct signal between Tx and Rx. As Tx was at the farthest distance from the trees at the end of the alley, the observed maximum time delay is longer than in the LoS case.

Scatterer | Radius (cm) | Length/Thickness (cm) | Number Density (m^{−3}) |
---|---|---|---|

Branch category 1 | 11.4 | 131 | 0.2 |

Branch category 2 | 6.0 | 99 | 0.2 |

Branch category 3 | 2.8 | 82 | 2 |

Branch category 4 | 0.7 | 54 | 20 |

Branch category 5 | 0.2 | 12 | 100 |

Leaf | 3.7 | 0.02 | 500 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Kvicera, M.; Perez-Fontan, F.; Pechac, P.
A New Propagation Channel Synthesizer for UAVs in the Presence of Tree Canopies. *Remote Sens.* **2017**, *9*, 151.
https://doi.org/10.3390/rs9020151

**AMA Style**

Kvicera M, Perez-Fontan F, Pechac P.
A New Propagation Channel Synthesizer for UAVs in the Presence of Tree Canopies. *Remote Sensing*. 2017; 9(2):151.
https://doi.org/10.3390/rs9020151

**Chicago/Turabian Style**

Kvicera, Milan, Fernando Perez-Fontan, and Pavel Pechac.
2017. "A New Propagation Channel Synthesizer for UAVs in the Presence of Tree Canopies" *Remote Sensing* 9, no. 2: 151.
https://doi.org/10.3390/rs9020151