⚡ electrical engineering

Angularly-Resolved 3D Foliage Modeling and Measurements at 60 and 80 GHz: From Stochastic Geometry to Deterministic Channel Characterization

This paper presents a stochastic geometry-based approach to generate 3D foliage models for deterministic ray-tracing channel characterization, which is experimentally validated through 60 and 80 GHz measurements to analyze path-loss and RMS delay spread as functions of receiver angle and interpretable tree parameters.

Original authors: Jiri Blumenstein, Radek Zavorka, Josef Vychodil, Tomas Mikulasek, Jaroslaw Wojtun, Jan M. Kelner, Cezary Ziolkowski, Rajeev Shukla, Markus Hofer, Thomas Zemen, Christoph F Mecklenbrauker, Aniruddha Ch

Published 2026-03-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jiri Blumenstein, Radek Zavorka, Josef Vychodil, Tomas Mikulasek, Jaroslaw Wojtun, Jan M. Kelner, Cezary Ziolkowski, Rajeev Shukla, Markus Hofer, Thomas Zemen, Christoph F Mecklenbrauker, Aniruddha Chandra, Ales Prokes

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to send a high-speed message (like a 4K video stream) using invisible radio waves that are incredibly fast but also very fragile. These are millimeter waves (60 and 80 GHz). They are like super-fast, super-precise laser pointers.

The problem? If a tree stands between you and your friend, these waves don't just "go around" the tree like water flowing around a rock. They get blocked, scattered, or absorbed. To fix this, engineers need to know exactly how the tree messes up the signal.

This paper is about building a digital twin of a tree to predict exactly how these signals behave when they hit leaves and branches.

Here is the breakdown of their work using simple analogies:

1. The Goal: Predicting the "Tree Effect"

Think of the wireless signal as a swarm of tiny, invisible bees trying to fly from a transmitter (TX) to a receiver (RX).

The Challenge: If there is a tree in the middle, the bees hit the leaves, bounce off, get stuck, or slow down.
The Old Way: Previous models treated trees like simple hollow boxes or smooth balloons. This is like trying to predict how a swarm of bees reacts to a tree by pretending the tree is just a smooth, empty cardboard box. It's too simple and misses the chaos of real leaves.
The New Way: The authors built a 3D digital tree that looks like a cloud of thousands of tiny, randomly floating triangular shards (representing leaves and branches). It's not a perfect photo-realistic tree, but it captures the statistical chaos of a real tree.

2. How They Built the Digital Tree (The "Stochastic" Part)

Instead of measuring every single leaf on a real tree (which would take forever), they used a "recipe" to grow a fake tree that behaves like a real one.

The Shape: They started with a perfect sphere and then "shook" it with a virtual hand to make it lumpy and irregular, just like a real tree crown.
The Leaves: Inside this lumpy shape, they dropped thousands of tiny triangles (the leaves). They didn't place them neatly; they scattered them randomly, rotated them in different directions, and adjusted how crowded they were.
The Parameters: You can tweak the recipe to change the "tree's personality":
- Volume: How big is the tree?
- Density: Is it a sparse sapling or a thick oak?
- Leaf Size: Are the leaves tiny or huge?

3. The Experiment: Real vs. Virtual

The team didn't just stay in the computer. They went outside to Bangalore, India, with a real tree and high-tech equipment.

The Setup: They placed a transmitter 15 meters away from a real tree. They then walked a receiver in a half-circle around the tree (like a camera crew filming a movie scene).
The Frequencies: They tested two "colors" of light (radio waves): 60 GHz and 80 GHz. Think of 80 GHz as a slightly higher-pitched, more fragile sound than 60 GHz.
The Comparison: They ran their "Digital Tree" simulation on a laptop and compared the results to the real data they collected outside.

4. What They Discovered (The "Aha!" Moments)

A. The "Backscatter" Surprise
When the receiver was directly behind the tree (looking straight through the trunk), the signal was very weak (high loss). But when the receiver moved to the side (90 degrees), the signal got stronger.

The Analogy: Imagine throwing a ball at a wall of leaves. If you throw it straight through, it hits everything and loses energy. If you throw it at the side, it might bounce off the first layer of leaves and come back to you. The simulation showed that signals bouncing off the outer layer of leaves (when you are on the side) lose less energy than signals trying to punch through the entire tree.

B. The "Echo Chamber" Effect (Delay Spread)
The paper measured how "spread out" the signal becomes.

The Analogy: Imagine shouting in a canyon. Sometimes you hear one clear echo. Sometimes you hear a messy, long rumble because the sound bounced off many different rocks at different times.
The Finding: When the receiver is on the side of the tree, the signal bounces around inside the "leaf cloud" and takes longer to arrive. This creates a "smear" in time (called RMS Delay Spread). The further around the tree you go, the more the signal bounces back and forth, making the "echo" longer and messier.

C. Frequency Matters
The 80 GHz signal was slightly more "fragile" than the 60 GHz signal. It lost about 3-4 dB more energy going through the tree. It's like trying to push a heavy box (80 GHz) through a crowd vs. a light box (60 GHz); the heavier one gets stopped more easily.

5. Why Does This Matter?

We are moving toward 6G and super-fast wireless networks. These networks will rely on high frequencies that struggle with obstacles like trees, buildings, and even rain.

The Takeaway: By creating a "smart, random" 3D model of a tree, engineers can now simulate how their networks will behave in a forest or a park without needing to build a physical prototype every time.
The Metaphor: It's like a flight simulator for radio waves. Before you build a real airport (network), you can fly a virtual plane (signal) through a virtual forest (the model) to see if it crashes.

In short: This paper teaches us how to build a "virtual forest" in a computer that is so realistic (statistically speaking) that we can predict exactly how fast our internet will be when we are standing behind a tree.

1. Problem Statement

The proliferation of millimeter-wave (mmWave) communications (30–300 GHz) offers high data rates but faces significant challenges regarding signal propagation, specifically high path loss, low diffraction, and high penetration losses. A critical scenario for 5G/6G deployment is the obstruction of the Line-of-Sight (LOS) by vegetation.

The Gap: Existing channel modeling techniques often rely on simplified geometric representations (e.g., hollow cubes or spheres) or point scatterers that lack physical realism. These abstractions fail to capture the complex scattering and attenuation mechanisms within the foliage volume, leading to inaccuracies in Channel State Information (CSI), particularly at mmWave frequencies where wavelength-scale details matter.
The Goal: To develop a physically interpretable, stochastic 3D foliage model that bridges the gap between simple geometry and complex reality, enabling deterministic ray-tracing simulations that accurately predict channel behavior (path loss and delay spread) when LOS is obstructed by trees.

2. Methodology

A. Stochastic 3D Foliage Modeling

The authors propose a methodology to generate a 3D tree crown model composed of randomly positioned and oriented triangular faces (scattering objects) within a defined envelope.

Envelope Generation: The tree crown shape is defined by a set of vertices and faces. To create an irregular, natural shape, a deformation function is applied to a unit sphere using random displacements sampled from a 3D normal distribution. The volume is scaled to match a target volume ( $V_D$ ).
Internal Structure (Scattering Faces): The interior of the crown is filled with triangular faces representing leaves and branches.
- Geometry: Each face is an equilateral triangle with a user-defined area ( $A$ ).
- Placement: Faces are randomly rotated using Rodrigues' rotation matrices and translated to random positions within the crown volume, following a uniform distribution.
- Parameters: The model is controlled by interpretable parameters: target volume ( $V_D$ ), triangle area ( $A$ ), internal density ( $\rho$ ), and deformation strength ( $\xi$ ).

B. Ray-Tracing Simulation

Tool: The open-source ray tracer Sionna (v1.0.2) is used.
Material Properties: Based on ITU-R P.833 recommendations, the foliage is modeled with a scattering coefficient ( $\mu_s = 0.50$ ), relative permittivity ( $\epsilon_r = 17$ ), and conductivity ( $\kappa = 0.05$ S/m).
Bandwidth: Simulations utilize a 2 GHz bandwidth centered at 60 GHz and 80 GHz.
Scenario: The transmitter (TX) is fixed 15m from the tree. The receiver (RX) moves along a half-circular trajectory around the tree, covering angles ( $\alpha$ ) from $0^\circ$ (directly behind the tree) to $180^\circ$ (directly facing the tree, though LOS is suppressed in analysis).

C. Measurement Campaign

Setup: Measurements were conducted on a deciduous tree (summer, small leaves ~4-5 cm) in a real-world environment.
Equipment: A channel sounder operating at 60 GHz and 80 GHz with 2 GHz bandwidth. Both TX and RX used horn antennas (24.8 dBi gain).
Data Processing: The LOS component was removed from the data for specific RX positions (where the tree did not block the direct path) to isolate the interaction between the signal and the foliage.

3. Key Contributions

Stochastic-to-Deterministic Framework: A novel approach to generate 3D foliage models using stochastic geometry (random triangles) that serves as input for deterministic ray-tracing, offering both visualizability and physical interpretability.
Angularly-Resolved Characterization: Comprehensive analysis of how path loss and RMS delay spread vary as a function of the receiver's angle relative to the tree ( $\alpha$ ).
Experimental Validation: Rigorous comparison between the stochastic simulations and real-world measurements at 60 GHz and 80 GHz, validating the model's accuracy without requiring photorealistic rendering.
Parameter Sensitivity: Demonstration that the model can be tuned with physically meaningful parameters (volume, leaf density, shape) to match empirical data.

4. Key Results

A. Path Loss (PL) Analysis

Angular Dependency: Path loss is highest at $\alpha = 0^\circ$ (signal passes through the entire tree depth) and decreases as $\alpha$ increases toward $90^\circ$ and $180^\circ$ .
Quantitative Values:
- At $\alpha = 0^\circ$ , the additional attenuation caused by the tree is approximately 40 dB (total PL ~140 dB at 80 GHz).
- At $\alpha = 180^\circ$ , the additional attenuation is approximately 20 dB.
- At $\alpha = 90^\circ$ , the mean PL is ~130 dB (60 GHz) and ~133 dB (80 GHz).
Frequency Comparison: The 80 GHz band exhibits 3–4 dB higher attenuation than the 60 GHz band. This difference is slightly larger than the theoretical 2 dB difference in Free Space Path Loss (FSPL), indicating frequency-dependent foliage interaction.

B. RMS Delay Spread (DS) Analysis

Range: The DS ranges from 5 ns to 15 ns.
Angular Trend: DS increases almost linearly with the angle $\alpha$ $α$ .
- At $\alpha = 0^\circ$ (direct transmission), the DS is lower.
- At $\alpha = 180^\circ$ (reflection), the DS is higher.
Physical Explanation: At $\alpha = 180^\circ$ , multipath components (MPCs) reflect off the far side of the tree, effectively traveling through the foliage volume twice (in and out), resulting in longer delays and higher dispersion. At $\alpha = 0^\circ$ , signals pass through only once.
Variance: The variance of the DS is approximately 3 ns and remains relatively stable across different angles.

C. Model Validation

CDF Comparison: Cumulative Distribution Functions (CDFs) of the Power Delay Profile (PDP) for simulated and measured data show a strong qualitative match at both 60 GHz and 80 GHz.
Triangle Size: The study found that using triangle areas significantly larger than real leaves (e.g., $2 m^2$ ) still yields good agreement with measurements, suggesting that reducing triangle size further does not significantly improve model accuracy for these frequency bands.

5. Significance

This paper addresses a critical need for accurate channel modeling in mmWave networks where vegetation is a primary obstruction.

Practical Application: The proposed stochastic model allows network planners to simulate channel conditions in vegetated environments without needing complex, computationally expensive photorealistic scans of every tree.
Interpretability: By linking channel metrics (PL, DS) to physical parameters (tree volume, leaf density), the model provides insights into why the channel behaves a certain way, aiding in the design of robust mmWave systems.
Frequency Scaling: The validation at both 60 GHz and 80 GHz confirms the model's scalability across the mmWave spectrum, supporting the development of future 6G networks.
Open Science: The use of the open-source Sionna ray tracer and the publication of the methodology encourage reproducibility and further research in stochastic channel modeling.