arxiv: 2605.13661 · v1 · submitted 2026-05-13 · 📡 eess.SP

Recognition: unknown

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

Ikenna Chinazaekpere Ijeh , Mohammad Ali Khalighi , Wasiu O. Popoola

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Pith reviewed 2026-05-14 17:54 UTC · model grok-4.3

classification 📡 eess.SP

keywords optical wireless communicationAUV-UAV linkssea surface roughnessECKV modelergodic capacityair-sea interfacepointing errorssolar noise

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The pith

A simplified analytical model of ocean waves enables range and capacity predictions for light-based links from underwater drones to aerial drones.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives a closed-form version of the ECKV sea surface roughness spectrum that matches measured ocean data. It applies this model to vertical optical wireless links between an autonomous underwater vehicle and an unmanned aerial vehicle. Both analytical formulas and Monte Carlo simulations are used to find the average data rate the link can support. The study focuses on how distance, misalignment, receiver angle, and sunlight noise reduce performance. This gives concrete guidance for building reliable air-sea optical communication systems.

Core claim

We present a tractable analytical representation of the ECKV model for sea-surface roughness and validate it against measured sea-state data. Using this representation together with the Cox-Munk model, we evaluate the ergodic capacity of AUV-to-UAV optical wireless communication links via analytical expressions and Monte Carlo methods, with emphasis on the effects of operating range, pointing errors, receiver field-of-view, and solar noise level.

What carries the argument

The tractable analytical form of the Elfouhaily-Chapron-Katsaros-Vandemark (ECKV) sea-surface spectrum, which models wave-induced distortions to the optical beam in the vertical air-sea path.

If this is right

The derived analytical model allows rapid computation of link performance without extensive simulations.
Link capacity decreases with increasing operating range and solar noise.
Pointing errors and limited receiver field-of-view impose additional constraints on achievable rates.
Both Cox-Munk and simplified ECKV models provide consistent insights into sea surface effects for system design.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Designers could use the model to optimize wavelength or power for different sea conditions.
The approach may extend to links involving surface vehicles or multiple hops.
Real-time adaptation based on measured sea state could improve link reliability in varying conditions.

Load-bearing premise

The Cox-Munk and ECKV statistical models continue to accurately represent the optical distortions caused by sea surface roughness in vertical underwater-to-air paths.

What would settle it

Direct measurement of the ergodic capacity in a real AUV-UAV optical link over a range of sea states, compared against the model's predictions for the same conditions.

Figures

Figures reproduced from arXiv: 2605.13661 by Ikenna Chinazaekpere Ijeh, Mohammad Ali Khalighi, Wasiu O. Popoola.

**Figure 1.** Figure 1: Considered direct water-to-air OWC scenario. II. SYSTEM MODEL AND CHANNEL ASSUMPTIONS A. AUV-UAV Optical Link Geometry [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Figure 2: PDF of φt, fφt (φt) for various seas and wind speeds ([*ref]: Data for both stereo images and ECKV were reproduced from [1]). TABLE I: MSE comparison of ECKV data with considered PDFs at various wind speeds U [MSE values are in ×10−6 ] Fig. U (m/s) Lognormal Gamma Weibull B-S 2a 6.1 47.27 4.25 3.75 109.21 2b 8.7 58.76 7.60 2.42 95.29 2c 12.9 61.54 7.67 0.94 141.92 2d 12.9 72.01 4.01 9.83 139.28 2e 15.2 54.… view at source ↗

**Figure 3.** Figure 3: Normalized PDF of transmitter tilt angle φt for wind speeds, U = 6, 10 and 14 m/s under CM and MW sea-surface models. speed increases from 6 to 14 m/s, angular variance increases, resulting in broader PDFs with lower peaks, indicative of rougher surfaces and steeper slopes. Quantitatively, the most probable tilt angle shifts from about 11◦ to 17◦ for CM and from 10◦ to 11◦ for MW, while heavier tails indic… view at source ↗

**Figure 4.** Figure 4: Effect of wind speed, Rx FoV, and operating range on ergodic capacity; m = 20, σφr = 10◦ , Lt(λ) = 0.025 Wm−2 nm−1 sr−1 . A. Effect of Wind Speed and Link Range on Ergodic Capacity [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: For small misalignment (σφr = 10◦ ), a bow-shaped decay with link range is observed, where capacity is high at low ranges (e.g., > 7 bps/Hz at Z = 20 m) and decreases rapidly with Z, suggesting suitability for applications in shortto-moderate link range. In this regime, a smaller FoV consistently outperforms a larger FoV, regardless of beam divergence (15◦ and 11◦ for m = 20 and 40 respectively), due to … view at source ↗

**Figure 5.** Figure 5: Effect of Rx angular misalignment σφr , beam size m, FoV φFoVr, and range Z on Cerg; U = 10 m/s, Lt(λ) = 0.025 Wm−2 nm−1 sr−1 . 20 40 60 80 100 120 140 160 180 200 Z (m) 0 1 2 3 4 5 6 7 8 L t ( ) = 0.025 Wm-2nm-1sr-1 (Simulation) L t ( ) = 0.25 Wm-2nm-1sr-1 (Simulation) L t ( ) = 0.025 Wm-2nm-1sr-1 (Simulation) L t ( ) = 0.25 Wm-2nm-1sr-1 (Simulation) FoVr = 15o (Analytical - MW Model) FoVr = 30o (Analytic… view at source ↗

**Figure 6.** Figure 6: Effect of upwelling solar radiance Lt(λ), FoV φFoVr, and range Z on Cerg; m = 20, U = 10 m/s, σφr = 10◦ . FoV configurations yield comparable performance, indicating an optimal operating range without adaptive parameter tuning; and (iii) at large distances (> 60m), smaller FoV and narrower beam become advantageous, as solar noise and geometric loss dominate, albeit with increased sensitivity to misalignmen… view at source ↗

read the original abstract

Air-sea surface interactions play a critical role in underwater-to-air optical wireless communication (OWC) links, particularly in vertical autonomous underwater vehicle (AUV) to unmanned aerial vehicle (UAV) scenarios, where the stochastic nature of the sea surface introduces optical distortions that impair link reliability. This work investigates the impact of air-sea surface roughness on AUV-to-UAV OWC systems using two experimentally validated models: the classical Cox-Munk and the Elfouhaily-Chapron-Katsaros-Vandemark (ECKV). A tractable analytical representation of the ECKV model is derived and validated against measured sea-state data. Using both analytical and Monte Carlo approaches, the link ergodic capacity is evaluated with particular emphasis on operating range, pointing errors, receiver field-of-view, and solar noise level, providing practical system design insights.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

A practical incremental model that simplifies the ECKV spectrum for AUV-UAV optical links and supplies usable capacity numbers under real impairments.

read the letter

The main point is that the authors derived a closed-form analytical approximation to the ECKV sea-surface spectrum, checked it against measured wave data, and then used both that formula and Monte Carlo runs to compute ergodic capacity for vertical AUV-to-UAV optical links. They focus on operating range, pointing jitter, receiver field of view, and solar background noise, which produces concrete design numbers rather than just another simulation study. That combination of tractability and dual verification is the useful part. The work sits squarely on the established Cox-Munk and ECKV roughness models, so the advance is mainly the simplification step and its application to this geometry. The capacity curves and sensitivity plots should be directly usable by link designers who need quick estimates without running full wave optics each time. The soft spots are limited but real. The abstract and available text do not show the exact fitting residuals or the range of sea states where the approximation holds within a stated error bound, so it is still possible that the analytical form drifts for the steepest waves or the exact vertical path. The paper also does not revisit whether the underlying slope statistics remain accurate when the transmitter is underwater and the receiver is airborne; that assumption is inherited rather than re-tested. No circular fitting is visible, and the Monte Carlo cross-check helps. This is the kind of paper that belongs in a specialized optical communications or underwater systems venue. Engineers who actually build AUV-UAV optical terminals will find the range and margin numbers worth pulling, while theorists looking for new physics will not. I would send it to peer review. The analytical reduction plus the validation data and the Monte Carlo comparison give referees something concrete to check, and the practical outputs justify the effort even if the model assumptions need tightening.

Referee Report

3 major / 2 minor

Summary. The paper models air-sea surface roughness for vertical AUV-to-UAV optical wireless communication links using the Cox-Munk and ECKV spectra. It derives a tractable analytical simplification of the ECKV model, validates this representation against measured sea-state data, and evaluates link ergodic capacity via both analytical expressions and Monte Carlo simulation, with emphasis on operating range, pointing errors, receiver field-of-view, and solar noise.

Significance. If the derivations and validations hold, the work supplies concrete system-design guidance for maritime OWC links by quantifying how sea-surface statistics limit capacity and range, which is useful for AUV-UAV operations where optical links must contend with dynamic surface distortions.

major comments (3)

[ECKV simplification section] The derivation of the tractable ECKV representation (likely §3 or equivalent) must include an explicit side-by-side comparison of key statistics (slope variance, PDF moments) between the simplified form and the original ECKV spectrum to demonstrate that essential propagation statistics are preserved; without this, the claim that the simplification introduces no material error remains unverified.
[Validation section] Validation against measured sea-state data (likely §4) reports agreement but omits quantitative metrics (RMSE, Kolmogorov-Smirnov statistic, or error bars on fitted parameters) and the exact sea-state conditions (wind speed range, fetch) used; these details are required to confirm that the model is not over-fitted and that the subsequent capacity curves are not sensitive to post-hoc parameter choices.
[Capacity evaluation section] The ergodic-capacity evaluation (analytical vs. Monte Carlo) assumes the Cox-Munk and ECKV roughness models remain accurate descriptors for the vertical geometry; a sensitivity test or literature citation addressing whether these spectra, calibrated for horizontal paths, introduce bias in the vertical AUV-UAV case is needed to support the operating-range claims.

minor comments (2)

Figure captions should explicitly state the wind-speed values and sea-state parameters corresponding to each plotted curve.
Notation for the pointing-error angle and receiver FOV should be defined consistently in the text and equations.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which help improve the clarity and rigor of our work on air-sea surface modeling for AUV-to-UAV optical links. We address each major comment point by point below.

read point-by-point responses

Referee: [ECKV simplification section] The derivation of the tractable ECKV representation (likely §3 or equivalent) must include an explicit side-by-side comparison of key statistics (slope variance, PDF moments) between the simplified form and the original ECKV spectrum to demonstrate that essential propagation statistics are preserved; without this, the claim that the simplification introduces no material error remains unverified.

Authors: We agree that an explicit comparison strengthens the claim. In the revised manuscript, we will add a table in the ECKV simplification section comparing slope variance, PDF moments, and other key statistics between the original ECKV spectrum and our tractable analytical form, confirming that essential propagation statistics are preserved with negligible deviation. revision: yes
Referee: [Validation section] Validation against measured sea-state data (likely §4) reports agreement but omits quantitative metrics (RMSE, Kolmogorov-Smirnov statistic, or error bars on fitted parameters) and the exact sea-state conditions (wind speed range, fetch) used; these details are required to confirm that the model is not over-fitted and that the subsequent capacity curves are not sensitive to post-hoc parameter choices.

Authors: We thank the referee for this observation. The revised validation section will incorporate quantitative metrics including RMSE and Kolmogorov-Smirnov statistics, error bars on fitted parameters, and explicit details on the sea-state conditions such as wind speed range and fetch lengths from the measured data. revision: yes
Referee: [Capacity evaluation section] The ergodic-capacity evaluation (analytical vs. Monte Carlo) assumes the Cox-Munk and ECKV roughness models remain accurate descriptors for the vertical geometry; a sensitivity test or literature citation addressing whether these spectra, calibrated for horizontal paths, introduce bias in the vertical AUV-UAV case is needed to support the operating-range claims.

Authors: The Cox-Munk and ECKV spectra model intrinsic surface slope statistics that are independent of link geometry. To address the concern directly, the revised capacity evaluation section will include relevant literature citations on vertical maritime OWC applications and a brief sensitivity discussion confirming applicability to the AUV-UAV vertical case. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation uses external models with independent validation

full rationale

The paper starts from the established Cox-Munk and ECKV roughness spectra (externally validated in prior literature), derives a tractable analytical simplification of ECKV, and validates that simplification directly against measured sea-state data. Ergodic capacity is then computed from the resulting model via both closed-form analysis and Monte Carlo simulation; no parameters of the capacity expression are fitted back to the same sea-state data used for model validation, and no self-citation chain is invoked to justify the core modeling choices. The derivation chain therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only abstract available; ledger therefore limited to the two roughness spectra treated as domain-standard inputs. No new free parameters, invented entities, or ad-hoc axioms are visible in the summary.

axioms (1)

domain assumption Sea-surface roughness statistics are adequately captured by the Cox-Munk and ECKV spectra for optical propagation calculations
Invoked when the paper adopts these models to represent air-sea interface distortions.

pith-pipeline@v0.9.0 · 5460 in / 1307 out tokens · 42790 ms · 2026-05-14T17:54:12.984996+00:00 · methodology

discussion (0)

Reference graph

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