PaperlayerView exact revision on arXiv

Source-linked AI summary

Sea-State-Induced Performance Transition in Maritime Networks: A Roughness-Aware Stochastic Geometry Framework

Wen-Yu Dong, Shaoshi Yang, Song Zhao, Rui-Si Han, Qi Bi, Sheng Chen

arXiv:2609.27897v1cs.NI

TL;DR

Maritime network analyses often assume smooth seas or simplify propagation, leaving the network effects of changing sea states insufficiently characterized. This paper incorporates a Rayleigh-based roughness-sensitive reflection model into stochastic geometry to derive uplink coverage expressions. It reports a non-monotonic trade-off: moderate roughness can improve reliability-oriented coverage, while stronger roughness degrades high-SINR performance.

  • Problem

    Maritime network analyses often fix sea conditions, while existing tractable models may omit important maritime propagation mechanisms and high-fidelity link models can be too complex for network-scale analysis.

    Source: §I · pp. 1–2

  • Method

    The paper derives a Rayleigh-criterion-based effective reflection coefficient and integrates the roughness-aware propagation model into stochastic geometry for uplink coverage analysis.

    Source: §I · p. 2

  • Results

    Moderate roughness can improve reliability-oriented coverage by mitigating destructive interference nulls, whereas stronger roughness attenuates coherent reflection and degrades high-SINR performance.

    Source: §I · p. 2, B. Coverage Performance Analysis · p. 6

  • Takeaways & Limitations

    Under the adopted propagation abstraction, sea roughness has a non-monotonic impact on maritime network performance, so its effect depends on the performance regime considered.

    Source: §I · p. 2, §VI · p. 6

Abstract

from arXiv · show

Analytical studies of maritime wireless networks commonly assume a deterministic smooth sea surface, leaving unclear how realistic ocean conditions reshape network-level reliability. Unlike conventional intuition that sea roughness always deteriorates propagation, this work reveals a non-monotonic sea-state-induced performance transition caused by the competition between interference-null mitigation and coherent reflection loss. This paper develops a physically grounded, sea-state-aware stochastic geometry framework for maritime networks by incorporating sea surface roughness into propagation modeling. Specifically, we derive an effective reflection coefficient based on the classical Rayleigh roughness criterion, where the significant wave height explicitly characterizes the attenuation of the coherent specular reflection component caused by surface roughness. By integrating the proposed channel model into a stochastic geometry framework, we derive tractable expressions for uplink coverage probability under different sea states. Our analysis reveals a non-monotonic impact of sea roughness on network performance under the considered propagation model: moderate roughness can improve reliability-oriented coverage by mitigating destructive interference nulls, whereas stronger roughness attenuates coherent reflected energy and degrades high-SINR performance. Measurement comparisons support the underlying roughness-sensitive reflection mechanism, while rough-sea VHF results are interpreted as wavelength-specific model predictions rather than direct empirical validation.

I. INTRODUCTION

The paper addresses the gap between physically realistic maritime propagation and tractable network analysis by modeling sea-state-dependent reflection within stochastic geometry. It finds that roughness can improve reliability at moderate levels but degrade high-SINR performance when coherent reflected energy is attenuated.

I. INTRODUCTION

  • Existing maritime network analyses often fix sea conditions, while high-fidelity link models can be too complex for large-scale network analysis.The paper identifies a gap between physical channel realism and tractable network-level modeling.Source: §I · pp. 1–2
  • A Rayleigh-criterion-based effective reflection coefficient connects significant wave height, carrier wavelength, and grazing angle to the transition from coherent interference to rough-surface scattering.The proposed physical model is integrated into stochastic geometry to derive uplink coverage expressions under roughness-aware propagation.Source: §I · p. 2
  • Moderate sea roughness can improve reliability-oriented coverage by mitigating destructive interference nulls, while stronger roughness attenuates coherent reflection and degrades high-SINR performance.This is the reported reliability–rate trade-off under the proposed framework.Source: §I · p. 2

A. Spatial and Network Model

  • Vessel locations are modeled by an isotropic non-homogeneous Poisson point process whose radial intensity can peak offshore in a shipping lane and decline farther out.The intensity profile combines a power-law term and exponential decay, with parameters controlling the peak location and concentration.Source: A. Spatial and Network Model · p. 2
  • Uplink vessels transmit independently with probability p_a, producing a thinned non-homogeneous Poisson point process of active interferers.The supplied text introduces the thinning model but does not provide its resulting intensity expression.Source: A. Spatial and Network Model · p. 2

B. Channel and SINR Model

The channel and SINR model represents a typical vessel’s uplink using large-scale path gain, Nakagami-m fading, interference from active vessels, and receiver noise.

B. Channel and SINR Model

  • Small-scale fading power gain is modeled with a Nakagami-m distribution for tractability and flexibility in representing line-of-sight-dominant maritime links.The passage does not specify a particular m value for this section.Source: B. Channel and SINR Model · p. 2
  • The typical vessel’s uplink SINR compares its transmit power, fading, and path gain with aggregate interference from other active vessels and additive white Gaussian noise.The desired link uses path gain G(D), while each interfering link contributes through its own path gain G(D_i).Source: B. Channel and SINR Model · p. 2

C. Baseline Large-Scale Path Loss Model

The baseline uses a smooth-sea piecewise path-loss model with a breakpoint separating two-ray propagation from a regime that includes an atmospheric evaporation-duct path.

C. Baseline Large-Scale Path Loss Model

  • The baseline piecewise path-loss framework assumes an ideal, perfectly smooth sea and sets its breakpoint using antenna heights and carrier wavelength.The breakpoint is d_break = 4h_thr/λ.Source: C. Baseline Large-Scale Path Loss Model · p. 2

1) Two-Ray Model (d < dbreak):

  • Below d_break, the two-ray model describes propagation as the coherent sum of direct and sea-reflected paths.This is the shorter-distance regime of the piecewise model.Source: 1) Two-Ray Model (d < dbreak) · pp. 2–3

2) Three-Ray Model (d ≥dbreak):

  • At or beyond d_break, the three-ray model adds a path associated with reflection and refraction within the atmospheric evaporation duct.The passage identifies this third path as significant beyond the breakpoint.Source: 2) Three-Ray Model (d ≥dbreak) · p. 3

A. Derivation of the Effective Reflection Coefficient

The effective reflection coefficient models sea roughness through Rayleigh-based attenuation of coherent specular reflection. The resulting path-loss model connects two-ray and three-ray propagation to a continuous transition between smooth-sea multipath and rough-sea direct-path regimes.

A. Derivation of the Effective Reflection Coefficient

  • The Rayleigh roughness factor attenuates the coherent specular component, with grazing angle ψ ≈ (ht + hr)/d.The effective reflection coefficient is the product of the ideal coefficient and the scattering factor; for a smooth sea it approaches −1, while rough seas reduce its magnitude.Source: A. Derivation of the Effective… · p. 3

B. Modified Path Loss Equations

  • The two-ray model forms the received field as the vector sum of the LOS and sea-reflected fields.For far-field scenarios, the direct and reflected path lengths are approximated by d for amplitude, with their difference used for phase.Source: B. Modified Path Loss Equations · p. 3
  • The roughness-aware path loss is free-space path loss divided by the multipath gain factor.Theorem 1 gives the linear path loss as a piecewise function for a non-ideal reflection coefficient.Source: B. Modified Path Loss Equations · p. 3
  • For d ≥ dbreak, the three-ray model adds an evaporation-duct-refracted path treated as a reflection from effective height he with coefficient −1.The model uses the duct ray’s path-length difference in calculating multipath gain.Source: B. Modified Path Loss Equations · p. 3
  • As Hs increases from zero toward infinity, the model transitions from conventional smooth-sea two-ray/three-ray propagation toward dominant direct-path propagation.At Hs → 0, ρs → −1; at Hs → ∞, ρs → 0.Source: B. Modified Path Loss Equations · p. 3

IV. SEA-STATE-AWARE UPLINK COVERAGE ANALYSIS

The uplink coverage analysis incorporates sea state into propagation modeling for both desired and interference links, making coverage depend on sea state as well as the SINR threshold.

IV. SEA-STATE-AWARE UPLINK COVERAGE ANALYSIS

  • Unlike fixed-environment stochastic geometry analyses, this framework incorporates the environmental variable Hs into the propagation model.The model applies to both desired-signal and interference links.Source: §IV · p. 3
  • The roughness-aware path-loss model applies to desired-signal links under varying sea state.Source: §IV · p. 3
  • Uplink coverage probability is a function of both the SINR threshold and sea state.Source: §IV · p. 3

A. Interference Characterization under Roughness-Aware Propagation

The interference analysis separates aggregate interference into near-field and far-field components and derives their transforms using stochastic-geometry tools.

A. Interference Characterization under Roughness-Aware Propagation

B. Coverage Probability under Sea-State Variation

The section expresses uplink coverage under sea-state-dependent propagation and evaluates it through serving-distance conditioning and a Nakagami-m fading approximation.

B. Coverage Probability under Sea-State Variation

C. Sea-State-Induced Coverage Transition

Sea roughness changes coverage through competing effects: it can ease destructive multipath cancellation, but sufficiently rough seas reduce useful coherent reflected power. The framework identifies a reliability-specific wave height where those effects balance.

C. Sea-State-Induced Coverage Transition

  • For small Hs, weaker coherent reflection can reduce destructive multipath cancellation; at sufficient roughness, coherent-power loss instead reduces useful received power.The transition point balances the benefit of null mitigation against the loss of coherent reflected power.Source: C. Sea-State-Induced Coverage Transition · p. 4
  • For a given reliability requirement, the optimal significant wave height marks the balance between null-mitigation benefit and coherent-reflection loss.It provides an analytical link between environmental sea conditions and network-level reliability.Source: C. Sea-State-Induced Coverage Transition · p. 4
  • As Hs approaches zero, the model recovers coherent two-ray/three-ray propagation; under severe roughness, ρs approaches zero and direct and non-coherent components dominate.The model is described as consistent with existing propagation models in these limiting cases.Source: C. Sea-State-Induced Coverage Transition · p. 4, Figure 2 · p. 5

V. NUMERICAL RESULTS

The numerical evaluation uses a specified VHF carrier, link budget, fading model, antenna geometry, and vessel spatial distribution.

V. NUMERICAL RESULTS

  • Simulations use a 162 MHz carrier with 25 kHz bandwidth, 30 dBm vessel transmit power, and −174 dBm noise power.The stated settings also include OS and vessel antenna heights of 50 m and 10 m, respectively.Source: §V · p. 5
  • Small-scale fading follows a Nakagami-m distribution with m = 3, with an evaporation duct height of 30.5 m.Source: §V · p. 5
  • Vessels follow a Gamma-parameterized NHPPP with α = 3, β = 1/500, density μ0 = 1 × 10−4 m−2, and access probability pa = 0.2.Source: §V · p. 5

A. Model Validation against Empirical Data

The paper compares roughness-aware propagation predictions with measurements and finds a non-monotonic coverage response to sea roughness. Moderate roughness can improve reliability-oriented coverage, while stronger roughness reduces high-SINR performance under the adopted model.

A. Model Validation against Empirical Data

  • For Hs = 1 m, the roughness-aware model produces shallower fades and reduces RMSE from 7.73 dB to 6.41 dB against measured signal data.Source: Figure 3 · p. 5
  • Beyond the breakpoint, the refined model incorporating atmospheric ducting and surface roughness reduces overall RMSE from 11.40 dB to 8.94 dB against empirical data.The comparison concerns the full propagation range where the three-ray model is active.Source: A. Model Validation against Empirical… · p. 5

B. Coverage Performance Analysis

  • Moderate roughness benefits low-SINR reliability by mitigating deep fades, but scattering can weaken constructive peaks needed for high-SINR coverage.The paper states that a smooth-sea assumption yields pessimistic reliability estimates but optimistic peak-rate estimates.Source: B. Coverage Performance Analysis · p. 6
  • At T = −15 dB, coverage first rises to a peak at moderate Hs, then declines as coherent reflected power loss overtakes null mitigation.The peak marks the roughness level where null-mitigation gains are maximally leveraged before specular-power reduction dominates.Source: Figure 4 · p. 5, B. Coverage Performance Analysis · p. 6

VI. CONCLUSION

  • The conclusion frames the non-monotonic effect as applying under the adopted roughness-aware propagation abstraction and emphasizes realistic sea conditions in maritime network analysis.Source: §VI · p. 6
Loading 2609.27897v1…