⚡ electrical engineering

Stochastic 3-D Foliage Modeling at 80 GHz: Experimental Validation and Ray-Tracing Simulations

This paper presents and experimentally validates a stochastic 3-D foliage modeling methodology for 80 GHz ray-tracing simulations, demonstrating how adjustable geometric parameters influence path loss and delay spread.

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

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 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

The Big Picture: Why Do We Need This?

Imagine you are trying to send a high-speed message (like a 6G video call) from a phone to a tower. At very high speeds (80 GHz), these signals act like super-fine laser beams. They are great for speed, but they are also very fragile. If a single leaf, a branch, or even a gust of wind hits the beam, the signal can get blocked, scattered, or delayed.

To design networks that work in parks, forests, or leafy suburbs, engineers use Ray Tracing. Think of this as a video game engine for radio waves. It shoots millions of "virtual lasers" from a transmitter to a receiver to see how they bounce off buildings and trees.

The Problem: Most video game trees are just hollow shells. They look like trees from the outside, but inside, they are empty. If you shoot a laser through a hollow tree in a simulation, the laser passes right through without hitting anything. But in real life, a tree is a dense, chaotic mess of leaves and twigs. The laser hits thousands of tiny surfaces, bouncing around and losing energy.

The Solution: This paper introduces a new way to build "digital trees" that aren't hollow. Instead of a simple shell, they create a stochastic (random) 3D forest inside the tree's outline, filled with thousands of tiny, randomly placed and rotated "leaves" (represented as triangles).

How It Works: The "Digital Tree" Recipe

The authors created a recipe for building these realistic digital trees using three main ingredients:

The Shape (The Crown): First, they draw a rough outline of where the tree's leaves should be (like a cloud shape).
The Wiggle (The Wind): Real trees aren't perfect spheres; they are lumpy and irregular. The model adds a "wobble" to the shape, making it look more natural and less like a computer-generated ball.
The Filling (The Leaves): This is the magic part. Instead of leaving the inside empty, they fill the entire volume with thousands of tiny triangular faces.
- Analogy: Imagine a jar of marbles. If you just draw the outline of the jar, you have a hollow shell. This model fills the jar with marbles (the triangles) that are randomly scattered and rotated. Some are flat, some are tilted, some are crowded, and some are sparse.

By changing the "density" (how many marbles) and the "shape" (how lumpy the jar is), they can simulate anything from a thin sapling to a thick oak tree.

The Experiment: The Real-World Test

To prove their digital trees were accurate, they didn't just rely on math. They went outside to a real forest.

The Setup: They set up a transmitter (TX) and a receiver (RX) 30 meters apart, with a real tree right in the middle.
The Tool: They used a super-precise "channel sounder" (a fancy radio scanner) operating at 80 GHz (a frequency so high it's almost light).
The Process: They measured how the real signal behaved as it passed through the real tree. Then, they ran their computer simulation with their "digital tree" and compared the results.

What Did They Find?

The results were a match! Here is what they discovered, using simple terms:

The "Echo" Effect (Delay Spread): When a signal hits a real tree, it doesn't just go straight through; it bounces off leaves, taking slightly different paths. This makes the signal arrive at the receiver at slightly different times, creating a "smear" or "echo."
- The Finding: Their model predicted this "smear" perfectly. As they made the digital tree denser (more leaves), the "smear" got wider, just like in the real world.
The "Muffler" Effect (Signal Loss): Leaves absorb and block the signal.
- The Finding: The denser the digital tree, the weaker the signal became. The model predicted exactly how much signal would be lost based on how "leafy" the tree was.

Why Does This Matter?

Think of this like weather forecasting for Wi-Fi.

In the past, if you wanted to know if your 5G/6G signal would work in a park, you might have had to guess or build a very expensive, slow simulation. This paper gives engineers a "smart randomizer."

Instead of needing to scan every single leaf on every tree in a city (which is impossible), they can now use this model to say: "If we put a tree here with this much density, the signal will drop by X amount and get delayed by Y nanoseconds."

Summary in a Nutshell

Old Way: Trees in simulations were hollow shells. Signals passed through them like ghosts.
New Way: Trees are filled with random, chaotic "digital leaves."
Result: The simulation now acts like the real world. It predicts exactly how much signal gets lost and how much it gets delayed when passing through foliage.
Impact: This helps engineers design better, faster wireless networks for cities with lots of trees, ensuring your video call doesn't freeze just because a leaf blew in front of the antenna.

1. Problem Statement

As wireless communication systems move toward millimeter-wave (mmWave) and sub-THz frequencies (e.g., 80 GHz), the wavelength becomes comparable to small environmental features like leaves and branches. This makes accurate channel modeling critical.

Limitations of Existing Models: Current deterministic ray-tracing approaches often simplify trees as hollow geometric shapes (cubes, spheres, or cylinders) or use point scatterers. These methods fail to capture the complex internal scattering and attenuation caused by the random distribution of leaves and branches, leading to artifacts in wide-band, high-spatial-resolution simulations.
Data Scarcity: Creating precise 3D models of specific trees via scanning or photogrammetry is impractical for generalizable channel modeling due to the time-consuming nature of data collection and the difficulty in generalizing results to different trees.
The Gap: There is a need for a stochastic 3D foliage model that can generate unique, realistic tree geometries based on adjustable parameters, validated against real-world measurements at 80 GHz.

2. Methodology

The authors propose a three-step stochastic modeling methodology to generate 3D foliage structures for ray-tracing simulations:

A. Model Generation

Initial Envelope Creation: The tree crown is initialized as a triangulated icosphere (a subdivided icosahedron).
Shape Perturbation: To create an irregular, natural shape, the vertices of the initial sphere are perturbed using a 3D normal distribution ( $N(0, \sigma^2 I)$ ). A scaling factor is then applied to ensure the final volume matches a user-defined target volume ( $V_{target}$ ).
Internal Structure Filling: The perturbed volume is filled with randomly placed and rotated triangular faces (representing leaves/branches).
- Parameters: The model is controlled by:
  - $V_{target}$ : Target volume of the tree crown.
  - $\sigma$ : Shape deviation/perturbation strength.
  - $\rho$ : Density of internal triangles (faces per $m^3$ ).
  - $A$ : Area of each internal triangle.
- Randomization: Each triangle is assigned a random position within the volume and a random orientation using Rodrigues' rotation formula.

B. Simulation Setup

Tool: Open-source ray-tracer Sionna (v1.0.2).
Frequency: 80 GHz with a 2 GHz bandwidth.
Material Properties: Based on ITU-R P.833 recommendations:
- Relative permittivity ( $\epsilon_r$ ): 17
- Conductivity ( $\kappa$ ): 0.05 S/m
- Scattering coefficient ( $\mu_s$ ): 0.50
Configuration: The simulation generates millions of candidate paths to capture multipath components (MPCs).

C. Experimental Validation

Campaign: Outdoor measurements were conducted at 80 GHz using a Frequency Modulated Continuous Wave (FMCW) channel sounder.
Setup: A transmitter (TX) and receiver (RX) were separated by 30 meters, with a representative tree located 15 meters from the TX (behind the foliage).
Antennas: Horn antennas with 24.8 dBi gain.
Data Processing: The Channel Impulse Response (CIR) was analyzed to derive Power Delay Profiles (PDP), Path Loss (PL), and Root Mean Square (RMS) Delay Spread.

3. Key Contributions

Stochastic 3D Foliage Model: Introduction of a flexible methodology that generates unique 3D tree geometries for every simulation run, even with identical input parameters, capturing the inherent randomness of natural vegetation.
Experimental Validation at 80 GHz: The model is rigorously validated against real-world measurements in the 80 GHz band, a frequency critical for 5G-Advanced and 6G systems.
Parametric Analysis: Comprehensive analysis of how foliage density ( $\rho$ ) and volume ( $V_{target}$ ) impact key channel metrics, specifically Path Loss and RMS Delay Spread.
Statistical Matching: Demonstration that while individual ray paths differ between simulation and reality, the second-order statistics (CDF of PDP, mean RMS delay spread) align closely, validating the model's utility for system-level design.

4. Key Results

RMS Delay Spread ( $D_{RMS}$ ):
- $D_{RMS}$ increases with tree volume. For a sparse tree ( $\rho=0.125$ ), $D_{RMS}$ grew from 0.5 ns (200 $m^3$ ) to 3 ns (1000 $m^3$ ).
- $D_{RMS}$ increases with foliage density. As density ( $\rho$ ) increased from 0 (free space) to 1, $D_{RMS}$ rose from 0 ns to 8 ns.
- Validation: The measured $D_{RMS}$ was 8.5 ns, which closely matches the simulation results at high density ( $\rho \approx 1$ ).
Path Loss (PL) & Received Signal Strength (RSS):
- At $\rho=0$ (free space), the path loss matched the theoretical Free Space Path Loss (FSPL) for 30m separation (~100 dB).
- As density increased to $\rho=1$ , the additional attenuation due to foliage resulted in a total path loss increase of approximately 60 dB (relative to FSPL).
Statistical Distribution: The Cumulative Distribution Functions (CDFs) of the simulated PDPs and individual CIRs showed a strong match with the measured data, confirming the model's ability to replicate the statistical behavior of the wireless channel through foliage.

5. Significance

This paper addresses a critical bottleneck in mmWave channel modeling: the accurate representation of vegetation without requiring impractical, site-specific 3D scans.

Design Utility: The proposed stochastic model allows network planners and researchers to simulate the impact of varying vegetation densities and tree sizes on 80 GHz links, which is essential for designing robust 5G/6G networks in urban and rural environments.
Computational Efficiency: By using a parametric stochastic approach rather than high-fidelity scanning, the model balances computational load with physical accuracy, making it suitable for large-scale network simulations.
Frequency Relevance: The validation at 80 GHz provides a benchmark for future sub-THz systems where foliage penetration and scattering will be even more pronounced.