⚡ electrical engineering

Statistical Channel Model for FSO Systems Assisted by a UAV-Mounted IRS

This paper proposes a novel closed-form statistical channel model for free-space optical systems assisted by UAV-mounted intelligent reflecting surfaces, which accounts for random UAV fluctuations to derive beam misalignment statistics and provide design guidelines for minimizing outage probability.

Original authors: Ferdaous Tarhouni, Vasilis K. Papanikolaou, Laura Cottatellucci, Mohammad-Ali Khalighi, Robert Schober

Published 2026-08-12

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CC BY 4.0

Original authors: Ferdaous Tarhouni, Vasilis K. Papanikolaou, Laura Cottatellucci, Mohammad-Ali Khalighi, Robert Schober

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 trying to send a secret message using a super-bright laser pointer across a city. This is the world of Free Space Optical (FSO) communication, a technology that promises internet speeds far faster than the Wi-Fi or 5G signals we use today. Instead of invisible radio waves, it uses beams of light. But there's a catch: light travels in a straight line. If a building, a tree, or even a bird gets in the way, the message is lost. To fix this, scientists have been looking for ways to bounce the light around obstacles, much like a game of laser tag where you aim your beam at a mirror to hit a target behind a wall.

Enter the "Intelligent Reflecting Surface" (IRS). Think of this not as a regular mirror, but as a high-tech, programmable sheet of glass that can twist and turn the light beam exactly how you want it to, sending it precisely to its destination. Now, imagine putting this smart mirror on a drone (a UAV) hovering in the sky. This gives the system superpowers: it can fly to the perfect spot to catch the laser and bounce it over a building. However, drones aren't perfect; they wobble, shake, and drift in the wind. If the mirror moves even a tiny bit, the laser might miss the receiver entirely, turning a super-fast connection into a broken one. The big question is: how do we predict exactly how much the drone's wobble will mess up the signal, and where should we fly the drone to keep the connection alive?

This paper tackles that exact problem by building a new mathematical "rulebook" for these flying laser systems. The authors, a team of researchers from Germany and France, realized that while we know how to use mirrors on the ground, we didn't have a good way to calculate what happens when the mirror is on a shaky drone in the air, especially when the laser is coming from a weird angle. Previous models were too simple, often assuming the drone and the laser were perfectly aligned in a flat, 2D world, which doesn't match real life.

The researchers started by using a fundamental principle of physics called the Huygens-Fresnel principle (think of it as a rule that explains how light waves spread out like ripples in a pond) to write down new, more accurate equations for how the laser beam hits the drone's mirror and how it bounces off. They then created a detailed statistical model—a way to predict the odds of the signal failing. They treated the drone's wobbles (both its position moving up and down and its tilt) like random jitter, similar to how a hand holding a camera might shake. They figured out that these jitters create a specific pattern of "misalignment," where the laser beam lands slightly off-center on the receiver's lens.

Using their new math, the team simulated the system on a computer to see how it behaved under different conditions. They found that the amount of signal loss depends heavily on how much the drone shakes and how the mirror is programmed to bend the light. They tested two different ways of programming the mirror's surface: one that bends the light in a simple, straight-line way (Linear Phase) and another that bends it in a more complex, curved way (Quadratic Phase). Their simulations showed that the more the drone shakes, the worse the connection gets, but the new model predicts this drop-off very accurately.

Perhaps the most practical finding came when they asked, "Where is the best place to fly the drone?" They ran a digital search to find the perfect spot for the drone-mounted mirror to minimize the chance of the connection dropping out (called "outage probability"). They discovered a surprising trade-off: while the mirror helps focus the beam, it also makes the system very sensitive to movement. Their results suggest that to get the best performance, the drone should hover much closer to the receiver (the person catching the laser) than to the sender. By shortening the distance the light has to travel after it bounces off the drone, the system becomes less likely to miss the target, even if the drone is wobbling. In their specific test scenario, the optimal spot was found just a few meters away from the receiver, whereas placing the drone near the sender resulted in a much higher chance of failure.

The paper concludes that while we can't stop the wind from shaking the drone, we can use this new math to place the drone in the smartest possible spot to keep the laser link strong. The authors validated their formulas by running millions of computer simulations, which matched their new equations almost perfectly. This work doesn't just solve a math puzzle; it provides a blueprint for engineers who want to build real-world, drone-based laser internet systems that can survive the inevitable bumps and jitters of the sky.

Technical Summary: Statistical Channel Model for FSO Systems Assisted by a UAV-Mounted IRS

Problem Statement
Free Space Optical (FSO) communication offers high data rates suitable for 5G and beyond networks but is strictly constrained by the requirement for a Line-of-Sight (LoS) link. While Unmanned Aerial Vehicle (UAV)-mounted Intelligent Reflecting Surfaces (IRS) have been proposed to relax this constraint by providing flexible, non-LoS connectivity, practical deployment faces significant challenges. Specifically, the hovering of UAVs induces random fluctuations in both position and orientation. These misalignments degrade end-to-end channel quality, yet existing statistical channel models for IRS-assisted FSO links are limited. Prior works often rely on restrictive assumptions, such as specific phase-shift profiles, in-plane propagation only, or independent fluctuation statistics, which fail to capture the complexity of realistic, arbitrary deployment scenarios involving UAV jitter.

Methodology
The authors develop a comprehensive statistical channel model for a UAV-mounted IRS assisting an FSO link between a fixed Transmitter (Tx) and a fixed Receiver (Rx). The methodology proceeds through three main stages:

Electric Field Derivation: Based on the Huygens-Fresnel principle, the paper derives novel, closed-form expressions for the electric field incident on the IRS and the field reflected toward the receiver. Unlike previous studies limited to in-plane propagation, these expressions are valid for arbitrary incident and reflected beam directions ( $\theta_i, \phi_i, \theta_r, \phi_r$ ). The model accounts for the elliptical nature of the Gaussian beam on the IRS plane, deriving effective beam widths and wavefront curvature radii for general transmitter locations.
Conditional Geometric and Misalignment Loss (GML): The authors derive a closed-form expression for the conditional GML coefficient ( $h_{irs}$ ) as a function of the beam misalignment distance ( $u$ ) at the receiver lens. This derivation considers both Linear Phase (LP) and Quadratic Phase (QP) shift profiles on the IRS. The model approximates the received power without relying on common upper-bound approximations found in literature.
Statistical Modeling of Fluctuations: The paper models UAV-induced perturbations as zero-mean Gaussian random variables affecting the UAV's vertical position ( $z$ ) and the incident angles ( $\theta_i, \phi_i$ ). Using first-order Taylor series expansions, the authors derive the statistical relationship between incidence and reflection angles, establishing that the resulting beam misalignment at the receiver follows a Beckmann distribution. Consequently, a closed-form Probability Density Function (PDF) for the GML is derived, linking the physical fluctuations to the channel gain distribution.

Key Contributions

Generalized Electric Field Expressions: The paper provides the first derivation of incident and reflected electric field expressions valid for arbitrary Tx and Rx orientations, moving beyond the in-plane constraints of prior works.
Tractable Closed-Form GML PDF: A novel, closed-form statistical channel model for the GML is presented. This model is valid for both LP and QP phase-shift profiles and accounts for correlated fluctuations in UAV position and orientation, assuming Gaussian statistics.
Refined Power Approximation: The authors derive a tractable approximation for received power that avoids the upper-bound assumptions often used in existing literature, offering a more accurate representation of the channel gain.
Optimal Deployment Guidelines: The framework is utilized to analyze the outage probability, providing a numerical search method to determine the optimal placement of the UAV-mounted IRS to minimize system outage.

Results
The proposed analytical model was validated against Monte Carlo (MC) simulations using $10^7$ realizations. The results demonstrate:

Model Accuracy: The analytical PDF of the GML shows strong agreement with simulation data. The model accurately captures the "heavy tail" behavior of the channel distribution under high fluctuation scenarios, particularly for the Quadratic Phase profile.
Impact of Fluctuations: Increased UAV fluctuations (in both position and angle) significantly degrade channel quality. The analysis reveals that when fluctuation parameters exceed certain thresholds, the PDF of the GML exhibits a heavy tail, leading to a higher probability of deep fades.
Optimal Placement: Simulations regarding the optimal IRS location reveal a critical trade-off. While IRS deployment mitigates beam divergence, it increases sensitivity to misalignment. The results indicate that the optimal position for minimizing outage probability lies in the immediate vicinity of the Receiver (Rx). Placing the IRS closer to the Rx shortens the post-reflection propagation path, thereby reducing the probability of the beam deviating from the center of the receiver lens. However, the outage probability landscape near the optimal point is steep; small deviations from the optimal coordinates can lead to significant performance degradation.

Significance
The paper claims to address a gap in the literature by providing a general statistical channel model that jointly accounts for geometric losses and UAV fluctuations in both position and orientation, valid for arbitrary transmitter and receiver locations. The authors emphasize that tractable statistical models are essential for system-level analysis and optimization. By validating the model through simulations and deriving practical deployment guidelines, the work offers a foundation for designing robust, UAV-assisted FSO networks that can effectively mitigate the connectivity challenges posed by UAV hovering jitter.

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