Underwater Optical Channel Modeling

Updated 9 December 2025

Underwater optical channel (UWOC) is defined as the medium for propagating light where physical factors like absorption, scattering, and beam divergence cause exponential attenuation.
The channel model integrates deterministic losses with stochastic turbulence-induced fading using statistical frameworks such as WGG, EGG, and Gamma–Gamma laws to predict link performance.
High-fidelity simulation and analytical tools, including wave-optics methods and RTE solvers, are employed to optimize system design for long-range, high-data-rate underwater communications.

An underwater optical channel (UWOC) refers to the physical and statistical model governing the propagation of modulated optical signals through water, accounting for both deterministic attenuation (absorption, scattering, geometric factors) and stochastic turbulence-induced fading. The UWOC channel sets fundamental limits on achievable link distance, data rate, reliability, and system design. Channel characterization, physical-layer modeling, and performance evaluation are crucial for emerging high-speed, long-range, and multi-hop underwater wireless optical communication systems.

1. Physical Mechanisms: Absorption, Scattering, and Beam Geometry

The fundamental deterministic losses in UWOC stem from:

Absorption and Scattering: The total extinction coefficient at wavelength λ is $c(\lambda)=a(\lambda)+b(\lambda)$ , combining the molecular absorption coefficient $a(\lambda)$ and scattering coefficient $b(\lambda)$ . Typical values for clear ocean and coastal waters at 450 nm are $c\approx0.02$ m $^{-1}$ and $c\approx0.4$ m $^{-1}$ , respectively. Light intensity decays exponentially with propagation distance $d$ , following

$T(d,\lambda)=\exp[-c(\lambda)d].$

This underpins all path-loss computations (Jamali et al., 2016, Zhang et al., 2023).

Geometric Losses: Beam divergence and receiver aperture further limit the received fraction. A Gaussian beam with divergence half-angle θ and receiver aperture $A_r$ over distance $L$ loses power geometrically:

$L_{geom}(L)=\frac{A_r}{\pi(\theta L)^2}.$

The total received power is then

$P_r(L,\lambda)=P_t(\lambda)\,L_{geom}(L)\,e^{-c(\lambda)L}$

as in deep-sea demonstrations where geometry can reduce maximum range by a factor of 2 compared to losses alone (Zhang et al., 2023).

2. Stochastic Fading: Turbulence and Statistical Channel Laws

UWOC channels exhibit severe random signal fluctuations due to:

Turbulence-Induced Fading: Refractive index inhomogeneities caused by temperature, salinity, or air bubbles generate irradiance fluctuations.
- In weak turbulence and for homogeneous links, irradiance is usually assumed log-normal: $h=e^{2X}$ , $X\sim\mathcal{N}(\mu_X,\sigma_X^2)$ , with
$\mathrm{S.I.}=\exp(4\sigma_X^2)-1$

as the scintillation index (Jamali et al., 2016, Tayebnaimi et al., 2 Dec 2025). - For stratified or strongly inhomogeneous conditions, multi-lobe statistical mixtures provide superior fit: - Mixture Weibull–Generalized Gamma (WGG): For vertical links, $f_I(I)=\omega f_{Wb}(I;\beta,\eta)+(1-\omega)f_{GG}(I;a,d,p)$ captures both broad and peaked histograms, with excellent GoF metrics, $R^2\ge0.96$ in deep-ocean data (Xu et al., 2023). - Mixture Exponential–Generalized Gamma (EGG): Used under strong bubble and gradient effects; the EGG model yields analytically tractable closed forms for PDF, CDF, BER, and fits both fresh and salty water experimental data ( $R^2\to1$ ) (Zedini et al., 2018). - Gamma–Gamma law: For high turbulence/long path, the intensity PDF $f_H(h)$ involves Bessel functions and shape parameters derived from Rytov statistics (Zhou et al., 2020). - Multi-Layer and NLOS Channels: Vertically inhomogeneous links are best modeled as a cascade of independent layers, each following a generalized Gamma or EGG law (Das et al., 2022, Rahman et al., 2022, Lou et al., 2020). For NLOS, the impulse response is dominated by scattering, typically captured by a weighted double gamma (WDGF) law fitted to Monte Carlo histograms (Yue et al., 22 Jan 2025).

3. Numerical and Simulation Techniques

High-fidelity modeling and performance prediction leverage:

Wave-Optics Simulation (WOS): The vertical link is divided into $N_p$ slabs, each represented by a phase screen generated via a depth-dependent oceanic spectrum. Free-space propagation between screens uses low-pass-filtered Fourier transforms; screen parameters are set to rigorously avoid phase-factor aliasing [ $\delta$ , $N$ , $\Delta d$ , $N_p$ tuned as per sampling theorems in (Xu et al., 2023)].
Radiative Transfer Equation (RTE) Solvers: The RTE is discretized by high-order upwind finite differences and optimized quadratures (Lloyd–Max angular scheme + 7-point Newton–Cotes for in-scattering) to obtain accurate, energy-conserving channel impulse responses, delay spreads, and SNR profiles. Implementation details are crucial for matching Monte Carlo results (Illi et al., 2019).
Monte Carlo for Impulse Response and CIR: NLOS and scattering-dominated geometries require photon tracing using full interaction and survival statistics, combined with surface reflection models (Preisendorfer–Mobley) for sea surface (Yue et al., 22 Jan 2025).
ANN-Based Equalizers for Long Links: To compensate for high ISI and nonlinearities over hundreds of meters, experimenters deploy cascaded linear and low-complexity neural network equalizers, as in the first 1 Gbps over 250 m demonstration (Dong et al., 16 Nov 2024).

4. Analytical Performance Metrics

Closed-form predictions for link performance metrics are now standard, encompassing:

Average BER and Outage: For OOK with IM/DD and stochastic fading $f_I(I)$ ,

$\langle P_b \rangle = \frac{1}{2}\int_0^\infty \mathrm{erfc}\left( \frac{\gamma_0 I}{2\sqrt{2}} \right) f_I(I)\,dI$

with each law (WGG, EGG, Gamma–Gamma, cascade) yielding expansion in gamma or Fox–H functions (Xu et al., 2023, Zedini et al., 2018, Das et al., 2022, Lou et al., 2020).

Ergodic Capacity: For IM/DD or heterodyne detection,

$C = \mathbb{E}[\log_2(1+T\gamma)],$

again admitting exact Fox–H (or Meijer–G) representation for all major underwater fading models (Zedini et al., 2018, Das et al., 2022, Xu et al., 2023).

Diversity Order: Key for multi-layer channels—diversity order $DO=\sum_{i=1}^N \min\{d_i/2, \rho^2/2\}$ for N-layer GG with pointing error parameterized by $\rho^2$ ; smallest exponent in the Fox–H expansion sets the decay rate (Das et al., 2022).
Relay/Spatial Diversity Gains: Multi-hop and multi-aperture schemes break SNR bottlenecks. Dual-hop links and multi-aperture receivers provide order-10 to 40 dB SNR improvement at fixed BER, and linear scaling of diversity order with $N$ provided physical apertures or relays are sufficiently uncorrelated (Jamali et al., 2016, Jamali et al., 2015, Rahman et al., 2022, Jamali et al., 2015).

5. Channel Parameters, System Design, and Experimental Validation

Modern UWOC system design proceeds from:

Wavelength Selection: Minimize $c(\lambda)$ ; 450–550 nm window is optimal ( $c=0.02$ –$0.08$ m $^{-1}$ ) across clear to deep sea (Zhang et al., 2023, Kodama et al., 2021).
Aperture/Beam Control: Tuning beam divergence and receiver area is critical to mitigate geometry loss, especially at ranges >100 m (Zhang et al., 2023, Dong et al., 16 Nov 2024). Effects of misalignment enter via $A_0$ , $\rho^2$ in performance formulas.
Statistical Model Fit: WGG, EGG, and generalized gamma models (including N-layer and NLOS WDGF) realize $R^2$ near unity and $\mathsf{MSE}$ below $10^{-3}$ on broad experimental datasets; single-component and log-normal models are consistently outperformed (Xu et al., 2023, Zedini et al., 2018, Yue et al., 22 Jan 2025).
Deep-Sea Long-Term Experiments: 30 m LOS links at 1650 m depth provide BER $<10^{-5}$ for 125 Mbps; 117–231 m ranges are shown feasible under optimal geometry and high launch powers (Zhang et al., 2023).
Adaptivity and Equalization: For >250 m, 1 Gbps, ISI and nonlinearities require cascaded equalization—linear prefilters followed by low-complex ANN (10 neurons), yielding BER below the HD-FEC limit at otherwise prohibitive distances (Dong et al., 16 Nov 2024).
Multi-wavelength Diversity: Exploiting per-wavelength differences in turbulence and absorption, simultaneous multi-wavelength transmission exponentially reduces fade probability, mean fade duration, and increases MTBF (Tayebnaimi et al., 2 Dec 2025).

6. Multi-Layer, NLOS, and Bubble-Enhanced Channel Models

Advanced models explicitly handle:

Multi-Layer Stratification: Essential for accurate prediction in vertical UWOC; each layer's parameters can be derived from measured temperature, salinity, and turbulence spectra, and overall performance is dictated by the weakest (lowest-diversity) layer (Das et al., 2022, Rahman et al., 2022, Lou et al., 2020).
Non-Line-of-Sight (NLOS) Propagation: For surface-reflection or high-scatter environments, physically accurate Monte Carlo plus WDGF fits, combined with log-normal turbulence, provide a full impulse response and system-level BER and outage analysis for arbitrary geometry (Yue et al., 22 Jan 2025).
Bubble Obstruction: Air bubble statistics and induced blockage are handled via composite Weibull or mixture mass models (with zero, partial, and full blockage states), resulting in direct expressions for BER and capacity under bubble-turbulence channels (Shin et al., 2020).

7. Unified Perspective and Analytical Tools

The current state-of-the-art in UWOC channel modeling delivers a unified, mathematically tractable description:

Parametric Statistical Models: WGG and EGG mixtures enable accurate, scalable modeling from vertical stratification to multi-aperture and dual-hop architectures.
Analytical Metrics: Closed-form expressions for key system metrics via Fox–H (and Meijer–G) functions—outage, BER, ergodic capacity, and diversity order are directly computable once parametrization is achieved.
Design Implications: System optimization proceeds by fitting physical channel parameters to measured ocean profile, choosing geometry, and selecting modulation/equalization to match required performance margins. The toolkit is validated across experimental, simulation, and analytical predictions (Xu et al., 2023, Zedini et al., 2018, Das et al., 2022, Dong et al., 16 Nov 2024, Zhang et al., 2023).

In summary, underwater optical channels are characterized by exponential attenuation, scattering-induced impulse response dispersion, and multi-scale turbulence-induced fading. Recent research provides unified, physics-informed, and experimentally validated statistical models (WGG, EGG, GG, N-layer cascade, WDGF), supported by rigorous numerical and Monte Carlo methods, enabling closed-form analytical performance predictions over a wide range of UWOC system architectures. This framework supports robust, high-data-rate, and long-distance underwater wireless optical communications across both research and field-deployment contexts (Xu et al., 2023, Zedini et al., 2018, Das et al., 2022, Zhang et al., 2023, Dong et al., 16 Nov 2024, Yue et al., 22 Jan 2025, Rahman et al., 2022, Zedini et al., 2020).