⚡ electrical engineering

Air-Sea Surface Modeling and Operating Link Range Evaluation for AUV-to-UAV Optical Wireless Communication Links

This paper evaluates the impact of air-sea surface roughness on autonomous underwater vehicle-to-unmanned aerial vehicle optical wireless communication links by deriving a tractable analytical model for the ECKV sea surface and analyzing key performance metrics such as ergodic capacity, operating range, and pointing errors to provide practical system design insights.

Original authors: Ikenna Chinazaekpere Ijeh, Mohammad Ali Khalighi, Wasiu O. Popoola

Published 2026-05-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ikenna Chinazaekpere Ijeh, Mohammad Ali Khalighi, Wasiu O. Popoola

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 have a conversation with a friend. You are underwater in a submarine (an AUV), and your friend is hovering in a drone in the sky (a UAV). You want to send them a huge file of data, like a video or a map, instantly.

You can't use sound (like sonar) because it bounces off the water's surface and gets stuck. You can't use radio waves (like Wi-Fi) because water swallows them instantly. The only way to talk across the water-air boundary is with light—specifically, a very bright, focused beam from an LED.

This paper is about figuring out how to keep that light beam on target when the ocean surface is acting like a wobbly, moving mirror.

The Problem: The Wobbly Mirror

The biggest challenge isn't the distance; it's the sea surface. The ocean isn't flat; it's covered in waves caused by the wind.

Think of the sea surface like a funhouse mirror that is constantly shaking.

When the wind is calm, the mirror is mostly flat, and your light beam goes straight up to the drone.
When the wind blows, the waves tilt the "mirror." This tilts your light beam, sending it off-course. It's like trying to shine a flashlight at a moving target while standing on a boat that is rocking back and forth.

If the beam misses the drone's camera (the receiver), the message is lost. If the beam hits the camera but at a weird angle, the signal gets weak.

The Old Way vs. The New Way

Scientists have been trying to predict how much the waves will tilt the light for a long time.

The Old Model (Cox-Munk): This is like using a simple rule of thumb: "If the wind is 10 mph, the waves tilt the light by X amount." It's easy to use, but it's a bit rough. It doesn't capture the complex, choppy nature of real waves, especially when the wind is strong.
The Complex Model (ECKV): This is a super-detailed, physics-heavy model that accounts for every tiny ripple and how waves interact with each other. It's very accurate, but it's so complicated that it's like trying to solve a calculus equation just to aim a flashlight. It's too hard to use for designing real systems.

The Paper's Solution:
The authors looked at real photos of the ocean taken from different parts of the world (like the Black Sea and the Adriatic Sea) under various wind speeds. They compared the "Old Model" and the "Complex Model" against these real photos.

They discovered that the complex data looked a lot like a specific mathematical curve called the Weibull distribution. So, they created a new, simplified model (called the MW model) that uses this Weibull curve.

The Analogy: Think of the Complex Model as a 10,000-page instruction manual on how to bake a cake. The Old Model is a sticky note that says "add flour." The New Model is a perfect recipe card: it's simple enough to use quickly, but accurate enough to make a delicious cake every time.

What They Found Out

Using this new, easy-to-use model, they simulated how well the underwater-to-sky light link would work. Here are their main findings, explained simply:

Wind is the Enemy: The stronger the wind, the more the sea surface tilts, and the harder it is to keep the light beam on the drone. The capacity (how much data you can send) drops as the wind picks up.
Distance Matters: The further the drone flies away, the weaker the signal gets. Eventually, no matter how good your model is, the signal just fades away if you go too far.
The "Field of View" Trade-off (The Umbrella Analogy):
- Imagine the drone's camera has a "Field of View" (FoV). This is like an umbrella catching the light.
- A Wide Umbrella (Large FoV): Good if the wind is blowing hard and the light beam is wobbling all over the place. It catches the beam even if it's off-center. However, a wide umbrella also catches a lot of sunlight (noise), which drowns out your signal.
- A Narrow Umbrella (Small FoV): Good if the sun is bright. It blocks out the sunlight noise, making the signal clearer. However, if the wind blows the beam even a little bit, the beam misses the umbrella entirely.
- The Sweet Spot: The paper shows that for short distances, a wide umbrella is okay. But as you get further away or if the sun is bright, a narrower umbrella (smaller FoV) actually works better because it blocks the noise, provided the beam is reasonably stable.

The Bottom Line

This paper gives engineers a better, simpler tool to design communication systems between underwater robots and flying drones. By using their new "recipe card" model (the MW model) instead of the overly complex one or the too-simple one, they can predict exactly how far a drone can fly and how much wind it can handle before the light connection breaks.

They found that to get the best performance, you have to balance how wide your camera looks (to catch the wobbly beam) against how much sunlight it lets in (which creates noise). It's a delicate dance between catching the signal and blocking the noise.

Technical Summary: Air-Sea Surface Modeling and Operating Range Evaluation for AUV-to-UAV Optical Wireless Communication Links

Problem Statement
The proliferation of autonomous marine and aerial platforms has created a demand for high-capacity, low-latency communication between underwater and above-water systems. Conventional acoustic and radio-frequency (RF) technologies are unsuitable for direct underwater-to-air links due to extreme attenuation and impedance mismatch at the interface. Optical Wireless Communication (OWC) offers a viable alternative; however, vertical links between Autonomous Underwater Vehicles (AUVs) and Unmanned Aerial Vehicles (UAVs) face significant challenges. The stochastic nature of the air-sea interface introduces dynamic surface roughness, refractive-index discontinuities, and wave-induced refraction. These factors cause beam distortion, pointing errors, and severe power fluctuations, which impair link reliability and capacity. While the classical Cox-Munk (CM) model is widely used to describe sea surface slope statistics, it lacks explicit representation of spatial and temporal correlations and multi-scale wave interactions, limiting its accuracy under moderate-to-high wind conditions. Conversely, the more physically consistent Elfouhaily-Chapron-Katsaros-Vandemark (ECKV) model is complex and difficult to integrate directly into analytical link performance evaluations.

Methodology
This work investigates the impact of air-sea surface roughness on AUV-to-UAV OWC systems by developing a tractable analytical representation of the ECKV model. The methodology proceeds as follows:

System Modeling: A vertical OWC link geometry is established where an AUV transmits via a Lambertian LED to a hovering UAV equipped with a Silicon Photomultiplier (SiPM). The channel model accounts for deterministic path loss, angular misalignment at both the transmitter (due to sea slope) and receiver (due to UAV motion), and the receiver's Field-of-View (FoV) constraints.
Surface Modeling and Validation: The authors utilize the ECKV model, validated against real stereo-image measurements from the Black, Adriatic, and Yellow Seas. To create an analytically tractable expression for the transmitter tilt angle probability density function (PDF), $f_{\phi_t}(\phi_t)$ , the authors perform curve fitting on ECKV data using various parametric distributions (Lognormal, Gamma, Weibull, etc.).
Proposed Model Derivation: The Weibull distribution is identified as providing the closest statistical approximation to the ECKV data across various wind speeds. The authors derive a "Modified Weibull" (MW) model where the shape ( $k$ ) and scale ( $\lambda$ ) parameters are linearly related to wind speed ( $U$ ). This allows for a generalized, wind-speed-dependent analytical expression for surface slope statistics.
Performance Evaluation: The link's ergodic capacity is evaluated using both analytical integration and Monte Carlo simulations. The analysis considers the joint impact of surface roughness (modeled by both CM and MW), pointing errors, receiver FoV, and solar background noise levels.

Key Contributions

Tractable ECKV Representation: The paper derives a simplified, analytically tractable Modified Weibull (MW) model based on the validated ECKV formulation. This model successfully captures the statistical behavior of sea-surface slopes under diverse wind conditions (6–15 m/s) while remaining suitable for analytical link design.
Comparative Analysis: The study compares the performance of the classical Cox-Munk model against the proposed MW model, demonstrating that the MW model offers a more accurate representation of surface roughness derived from real-world stereo imagery.
Capacity Evaluation Framework: The authors provide a comprehensive evaluation of the ergodic capacity for vertical AUV-to-UAV links, explicitly incorporating the effects of surface-induced pointing errors, receiver misalignment, and solar noise.
Design Insights: The work quantifies the trade-offs between receiver FoV, beam divergence, and operating range, highlighting how these parameters interact with environmental conditions to determine link viability.

Results
Numerical results indicate that link ergodic capacity decreases monotonically with increasing range ( $Z$ ) and wind speed ( $U$ ). Key findings include:

Wind Speed Impact: Higher wind speeds increase surface roughness, leading to broader tilt angle distributions and reduced capacity. The MW model predicts that as wind speed increases from 6 to 14 m/s, the most probable tilt angle shifts, and the probability of severe misalignment events increases.
FoV Trade-off: There is a critical trade-off between receiver FoV and solar noise. A narrower FoV (e.g., 15°) significantly outperforms a wider FoV (e.g., 30°) at moderate to long ranges by reducing solar background noise, provided the link is not severely misaligned.
Misalignment Sensitivity: Under low misalignment ( $\sigma_{\phi_r} = 10^\circ$ ), a narrow FoV consistently yields higher capacity. However, under high misalignment ( $\sigma_{\phi_r} = 20^\circ$ ), a wider FoV is advantageous at short ranges to relax alignment constraints, while a narrower FoV becomes superior at longer ranges where geometric loss and solar noise dominate.
Solar Radiation: Increased upwelling solar radiance significantly degrades performance, particularly for receivers with wide FoVs and high-gain detectors like SiPMs, which are sensitive to ambient noise.

Significance
The paper claims that its primary significance lies in bridging the gap between complex, physically accurate sea-surface models (ECKV) and practical, analytical link design. By providing a tractable MW model validated against experimental data, the work enables more accurate performance prediction for vertical OWC links than the classical Cox-Munk model allows. The study offers practical system design insights, specifically regarding the optimization of receiver FoV and beam parameters to mitigate the dual challenges of surface-induced pointing errors and solar noise. This facilitates the development of reliable, high-capacity communication links for coordinated AUV-UAV missions in realistic marine environments.

The Problem: The Wobbly Mirror

The Old Way vs. The New Way

What They Found Out

The Bottom Line

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