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arxiv: 2603.23727 · v2 · submitted 2026-03-24 · 📡 eess.SP · physics.ao-ph· physics.optics

End-to-End Optical Propagation Modeling for Water-to-Air Channels under Sea Surface and UAV Effects

Mohamed Nennouche , Mohammad-Ali Khalighi , Alexis Alfredo Dowhuszko , Djamal Merad This is my paper

Pith reviewed 2026-05-15 00:12 UTC · model grok-4.3

classification 📡 eess.SP physics.ao-phphysics.optics
keywords optical wireless communicationswater-to-air channelsMonte Carlo ray-tracingair bubbles scatteringsea surface modelingUAV instabilitybit-error rateunderwater sensors
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The pith

Monte Carlo ray-tracing shows optical links can carry 1 Mbps from 47 m underwater to a UAV with acceptable error rates.

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

The paper builds a simulation framework to predict how light travels from an LED on an underwater sensor up through the water surface to a sensitive receiver on a UAV. It folds in three main effects: light scattered by air bubbles, the random tilt and height of waves drawn from measured sea statistics, and the small position shifts of the drone caused by wind. The authors then run the model across realistic depths and wind speeds to check whether the link can deliver data at useful rates with low errors. Their calculations indicate that a bit-error rate of 10 to the minus 3 remains reachable at 1 Mbps even when the transmitter sits 47 meters down and winds reach 13 meters per second. This suggests that wireless optical muling could let floating drones collect data from fixed ocean sensors without physical cables or surface stations.

Core claim

A Monte Carlo ray-tracing algorithm that traces individual photon paths while incorporating Mie scattering from air bubbles, sea-surface elevations generated from the JONSWAP spectrum, and analytically derived loss from UAV motion under wind produces channel statistics that support practical water-to-air optical communication, specifically a bit-error rate of 10^{-3} at 1 Mbps for a 47 m transmitter depth and wind speeds up to 13 m/s.

What carries the argument

Monte Carlo ray-tracing algorithm that propagates photons through a volume containing Mie-scattering bubbles, a statistically generated JONSWAP sea surface, and time-varying UAV receiver positions derived from wind-induced perturbations.

If this is right

  • Underwater sensors can send data to nearby UAVs at 1 Mbps with a bit-error rate of 10^{-3} under the modeled conditions.
  • The link remains usable for transmitter depths up to 47 m and wind speeds up to 13 m/s.
  • Marine observatories can use optical wireless muling instead of cables or surface relays to reach aerial nodes.

Where Pith is reading between the lines

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

  • Periodic UAV overflights could replace fixed surface buoys for data collection from distributed underwater sensor arrays.
  • The same modeling approach could be reused to explore trade-offs when LED power or receiver field-of-view is changed.
  • Combining the channel model with UAV trajectory planning might allow coverage of larger ocean areas with fewer flights.

Load-bearing premise

The Monte Carlo ray-tracing simulation captures every important loss and correlation caused by bubbles, waves, and UAV motion without missing significant interactions or extra attenuation mechanisms.

What would settle it

A field measurement of actual bit-error rate using an LED transmitter at 47 m depth, a silicon photo-multiplier receiver on a UAV, and wind speeds near 13 m/s would directly test whether the modeled 10^{-3} error rate at 1 Mbps is observed.

Figures

Figures reproduced from arXiv: 2603.23727 by Alexis Alfredo Dowhuszko, Djamal Merad, Mohamed Nennouche, Mohammad-Ali Khalighi.

Figure 1
Figure 1. Figure 1: Illustration of the considered W2A wireless optical link environmental monitoring. These advantages, however, come at the cost of reduced link range, typically limited to a few tens of meters in clear waters [4]. This range limitation is attributed to several impairments, including absorption, scattering, point￾ing errors, background noise, and oceanic turbulence [5], [17], [18]. Here, to further reduce th… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison between the exact numerical integration and the proposed [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Axes and rotation angles of a typical quadcopter UAV that can be used for data muling in the considered coral reef monitoring scenario. [36]. Lastly, Nb(z) and Ψ in (19) are calculated as follows [64]: Nb(z) = Z rmax rmin n(r, z)dr ≈ (1.6 × 1010) r 4 ref 3 r 3 min  U10 13 3 exp  − z L(U10)  , (24) Ψ = Z rmax rmin n(r, z) Nb(z) πr2 dr = Z rmax rmin 3 r 3 min r 4 ref G(r, z) πr2 dr ≈ 3πr2 min. (25) Now, … view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of Snell’s law at photon arrival at the water-air interface. between the photon direction vector ⃗µ i = (µ i x , µi y , µi z ) and the normal vector as follows [44], see [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Flow chart of Monte Carlo photon propagation algorithm for the W2A link. are taken within the interval [−π/2, π/2] with a step size of ∆θ, see (9) in Subsection III-B. These parameters are listed in Table II, where the considered parameters in the four rightmost columns are taken from [59]. Finally, we consider in this study the DJI Matrice 300 RTK UAV platform [76]. This platform was selected because it i… view at source ↗
Figure 6
Figure 6. Figure 6: Simulation-based distribution of αUAV using (27) and its analytical distribution using (34) for wind speeds: (a) U10 = 5 m/s, and (b) U10 = 13 m/s . of the proposed approximate analytical PDF, fαUAV (α). Fig￾ures 6a and 6b contrast the simulation-based histograms of αUAV obtained from (27), with fαUAV (α) given by the closed￾form expression in (34), for the two cases of U10 = 5 and 13 m/s, respectively. Fi… view at source ↗
Figure 9
Figure 9. Figure 9: Evolution of the density number of bubbles Nb(z) with depth z based on the HN bubble population model for different wind speeds U10 [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Variations of the scattering coefficient of bubbles bbub with depth z based on the HN bubble population model for different wind speeds U10. of z, which clearly demonstrates the significant variation in bbub near the surface. This highlights the importance of accounting for the effect of air bubbles on photon propagation near the water surface. Also, reasonably, higher wind speeds result in a greater conc… view at source ↗
Figure 11
Figure 11. Figure 11: W2A channel gain for different wind speeds U10; (a) evolution over a time interval of 10 s; (b) distribution over 104 channel realizations. increased wind speed has three notable effects. First, it alters the height and wavelength of surface waves, as illustrated in [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Average channel gain as a function of the LED beam divergence θ1/2 for different wind speeds U. To better understand these results, we have shown in [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Spatial distribution of the average channel gains with different LED beam divergence angles θ1/2 and wind speeds U10; (a) U10 = 5 m/s, θ1/2 = 10◦ ; (b) U10 = 5 m/s, θ1/2 = 20◦ ; (c) U10 = 5 m/s, θ1/2 = 30◦ , (d) U10 = 13 m/s, θ1/2 = 10◦ , (e) U10 = 13 m/s, θ1/2 = 20◦ ; (f) U10 = 13 m/s, θ1/2 = 30◦ . The green circle in the center of all subplots represents the PD active area [PITH_FULL_IMAGE:figures/full… view at source ↗
Figure 14
Figure 14. Figure 14: Average channel gain as a function of the Tx depth dwater, θ1/2 = 10◦ and different wind speeds U10. from 10 to 40 m. A larger dwater leads to increased photon absorption and scattering during propagation in water, and furthermore, results in a larger beam size at the water-air interface, increasing the proportion of photons not captured on the Rx’s equivalent active area. To support these results, [PITH… view at source ↗
Figure 15
Figure 15. Figure 15: Spatial distribution of the average channel gain at the Rx plane for different wind speeds and Tx depths: (a) U10 = 5 m/s, dwater = 15 m; (b) U10 = 5 m/s, dwater = 30 m; (c) U10 = 5 m/s, dwater = 40 m; (d) U10 = 13 m/s, dwater = 15 m; (e) U10 = 13 m/s, dwater = 30 m; (f) U10 = 13 m/s, dwater = 40 m. θ1/2 = 10◦ , the green circle in the center of all subplots represents the equivalent Rx active area [PITH… view at source ↗
Figure 16
Figure 16. Figure 16: Average channel gain as a function of the Rx height dair above the sea surface for different wind speeds U10. of the underwater node or the UAV. In this paper, this effect is modeled by an offset horizontal displacement δm between the Tx and the Rx as illustrated in [PITH_FULL_IMAGE:figures/full_fig_p016_16.png] view at source ↗
Figure 18
Figure 18. Figure 18: Illustration of the Tx-Rx horizontal displacement error (spatial offset) δm [PITH_FULL_IMAGE:figures/full_fig_p017_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Average channel gain as a function of the Tx-Rx displacement [PITH_FULL_IMAGE:figures/full_fig_p017_19.png] view at source ↗
Figure 21
Figure 21. Figure 21: Geographical location of the three AODN temperature and salinity measurement stations studied in this work based on data from [83]. APPENDIX B TURBULENT WIND MODELING ACCORDING TO DRYDEN MODEL We consider in this work turbulent winds (i.e., with time￾varying wind speed), which are commonly encountered in analyses of airflow over the ocean. To model the effect of these phenomena, here we employ the Dryden … view at source ↗
Figure 22
Figure 22. Figure 22: Oceanic profiles of (a) temperature (b) salinity in three localizations near the New Caledonia Barrier reef indicated in [PITH_FULL_IMAGE:figures/full_fig_p019_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Variations of wind speed for average wind speed of ux = uy = 5 m/s (under moderate turbulence conditions) along the (a) x-axis and (b) y-axis. APPENDIX C DISTRIBUTIONS OF TURBULENT WIND COMPONENTS In this appendix, we derive the statistical distributions of the wind velocity components, i.e., V = (Vx, Vy, Vz), using the Dryden model. To this end, we recall the linear filters Hx, Hy, and Hz introduced in (… view at source ↗
read the original abstract

Underwater observatories have recently emerged as an efficient solution for marine biodiversity monitoring. The primary objective of this work is to enable efficient and cost-effective data muling from underwater sensors by investigating the use of optical wireless communications to transmit data from the underwater sensors to an aerial node close to the water surface, such as an unmanned aerial vehicle (UAV). More specifically, we utilize a direct water-to-air (W2A) optical communication link between the sensor node equipped with an LED emitter and the UAV equipped with an ultra-sensitive receiver, i.e., a silicon photo-multiplier. As a main contribution, we develop a comprehensive Monte Carlo-based ray-tracing algorithm to characterize this complex channel. This framework rigorously incorporates the impact of air bubbles modeled through the Mie scattering theory, a realistic sea surface representation derived from the JONSWAP spectrum, and an analytical derivation of the channel loss resulting from UAV instability under wind-induced perturbations. Furthermore, we conduct a comprehensive analysis of the W2A channel, examining the influence of key parameters such as wind speed, transmitter configurations, and receiver characteristics. The end-to-end performance evaluation demonstrates the practical feasibility of the proposed approach, achieving a bit-error rate of $10^{-3}$ at a data rate of 1 Mbps for a transmitter depth of 47 m and wind speeds up to 13 m/s.

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.

Referee Report

2 major / 2 minor

Summary. The paper claims to introduce a Monte Carlo-based ray-tracing algorithm for end-to-end modeling of water-to-air optical channels, incorporating Mie scattering from air bubbles, JONSWAP-derived sea surface statistics, and an analytical model for UAV instability under wind perturbations. Through parameter studies, it concludes that the approach is feasible, achieving a BER of 10^{-3} at 1 Mbps for a 47 m transmitter depth and wind speeds up to 13 m/s.

Significance. Should the Monte Carlo results prove robust, the framework would constitute a useful engineering tool for evaluating optical wireless links in challenging marine environments, potentially enabling cost-effective data collection from underwater observatories via UAVs. The explicit combination of established physical models (Mie, JONSWAP) with platform dynamics is a methodological strength.

major comments (2)
  1. [Abstract] Abstract: The performance claim of BER = 10^{-3} at 1 Mbps rests on an unvalidated Monte Carlo simulation; no information is given on the number of rays, convergence metrics, or sensitivity to random seed, which directly affects confidence in the reported error rate under the combined channel impairments.
  2. [Ray-tracing framework] Ray-tracing framework: The description of the ray-tracing framework does not address possible statistical dependence between the sea-surface wave field and the bubble distribution; since both are driven by wind, any correlation would change the joint distribution of received intensity and invalidate the quoted BER without additional modeling.
minor comments (2)
  1. The abstract refers to an ultra-sensitive receiver (silicon photo-multiplier) but does not specify key parameters such as quantum efficiency or dark count rate used in the BER calculation.
  2. Consider adding a table summarizing the simulation parameters (e.g., wavelength, LED power, receiver FOV) for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below and have revised the manuscript to improve clarity and robustness where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The performance claim of BER = 10^{-3} at 1 Mbps rests on an unvalidated Monte Carlo simulation; no information is given on the number of rays, convergence metrics, or sensitivity to random seed, which directly affects confidence in the reported error rate under the combined channel impairments.

    Authors: We agree that the Monte Carlo validation details were insufficient. In the revised manuscript we have added explicit parameters: 10^7 rays per realization, a convergence criterion requiring the sample variance of received intensity to stabilize below 1% across successive batches of 10^5 rays, and a sensitivity study across five independent random seeds showing BER variation remains below 8% for the reported operating point. These additions directly support the quoted 10^{-3} BER at 1 Mbps and 47 m depth. revision: yes

  2. Referee: [Ray-tracing framework] Ray-tracing framework: The description of the ray-tracing framework does not address possible statistical dependence between the sea-surface wave field and the bubble distribution; since both are driven by wind, any correlation would change the joint distribution of received intensity and invalidate the quoted BER without additional modeling.

    Authors: We acknowledge the potential for correlation. The current implementation generates the JONSWAP wave field and the wind-parameterized bubble size distribution independently, following common practice in the literature. In the revision we have inserted a dedicated paragraph explaining this modeling choice, quantifying the expected impact of neglected correlation via a first-order sensitivity bound, and stating that the reported BER holds under the independence assumption. Full joint stochastic modeling would require new empirical data and is noted as future work. revision: partial

Circularity Check

0 steps flagged

No circularity: simulation assembles independent external models

full rationale

The derivation chain constructs the W2A channel via Monte Carlo ray-tracing that directly imports Mie scattering, JONSWAP surface statistics, and an analytical UAV jitter term; none of these are defined in terms of the target BER or fitted to the simulation output. The reported 10^{-3} BER at 1 Mbps is a numerical result of the assembled model rather than a quantity that reduces to its own inputs by construction. No self-definitional loops, fitted-input predictions, or load-bearing self-citations appear in the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The model rests on standard scattering and wave theories plus an analytical UAV perturbation model; no new free parameters or invented entities are introduced beyond the simulation framework itself.

axioms (2)
  • domain assumption Mie scattering theory accurately describes bubble-induced light scattering in seawater
    Invoked to model air bubbles without additional justification or validation data in the abstract.
  • domain assumption JONSWAP spectrum provides a realistic statistical representation of sea surface elevation
    Used to generate the moving water surface geometry.

pith-pipeline@v0.9.0 · 5563 in / 1343 out tokens · 37985 ms · 2026-05-15T00:12:19.142022+00:00 · methodology

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Reference graph

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