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WEKP-PLP: A Wireless Environment Knowledge Pool-Enhanced Path Loss Prediction Framework for Shore-to-Ship Communication

Jikun Du, Lei Tian, Jianhua Zhang, Pan Tang, Zihang Ding, Bin Ao, Zhen Zhang, Jialin Wang, Yuanzhi He

arXiv:2609.19066v1eess.SP

TL;DR

Sparse maritime measurement coverage and dynamic sea-surface conditions complicate shore-to-ship path-loss prediction and its uncertainty characterization. WEKP-PLP builds a ray-tracing-derived quantile prior and adapts it with measurement-based residual correction. The reported framework combines accurate point prediction with compact intervals and reliable coverage.

  • Problem

    Maritime measurements cover limited environmental conditions, while deterministic point-prediction methods do not characterize path-loss uncertainty under dynamic sea-surface conditions.

    Source: §I · p. 2

  • Method

    WEKP-PLP learns residual quantiles from ray-tracing data and uses a small number of measurements with GPR to correct the discrepancy from the WEKP median prediction.

    Source: §I · p. 2

  • Results

    The WEKP prior with GPR yields a much lower RMSE and more compact interval than the two-ray prior with the same residual correction.

    Source: E. Ablation Study of WEKP-PLP Framework · p. 12

  • Takeaways & Limitations

    The WEKP prior provides point-prediction and interval information, while measurement-based residual correction adapts that prior to real shore-to-ship scenarios.

    Source: E. Ablation Study of WEKP-PLP Framework · p. 12

Abstract

from arXiv · show

Accurate shore-to-ship path loss prediction is essential for maritime mobile communication systems, but it remains challenging because dynamic sea surface conditions can alter reflection paths and multipath effects, introducing uncertainty into the observed path loss. This paper proposes a wireless environment knowledge pool-enhanced path loss prediction (WEKP-PLP) method for point prediction and interval characterization of shore-to-ship path loss. The proposed method first constructs a wireless environment knowledge pool (WEKP) from ray tracing (RT) simulations under different wind speeds, temperatures, salinities, frequencies, antenna heights, and propagation distances. The WEKP learns the mapping from environmental and system parameters to path loss residual quantiles and provides a prior that contains both the median prediction and the associated prediction interval. To adapt this prior to real scenarios, a small number of measurement samples are used to learn the residual between the WEKP median prediction and the measured path loss through Gaussian process regression (GPR). The experimental results show that the WEKP-PLP provides accurate point prediction and compact intervals with reliable coverage. The proposed method achieves an MAE of 1.03 dB and an RMSE of 1.54 dB. The ablation results further confirm that both the WEKP prior and the residual correction using a small number of measurement samples are necessary for accurate and reliable shore-to-ship path loss prediction.

I. INTRODUCTION

Shore-to-ship prediction must contend with sparse maritime measurements and path-loss fluctuations caused by dynamic sea surfaces. WEKP-PLP combines a simulation-derived quantile prior with measurement-based residual correction to provide point predictions and intervals.

I. INTRODUCTION

  • Nearshore connectivity supports smart ports and environmental monitoring, motivating accurate propagation characterization for shore-to-ship system design and evaluation.Shore-to-ship communication can provide low-cost, high-rate broadband services for nearshore users compared with satellite communication.Source: §I · p. 1
  • Sparse maritime measurements and dynamic sea-surface effects leave shore-to-ship models with limited training coverage and insufficient characterization of path-loss uncertainty.Changing reflection points alter reflected path lengths and phase relationships, producing path-loss fluctuations that intervals can represent for link-budget design and coverage evaluation.Source: §I · pp. 1–2
  • Existing statistical, deterministic, and AI-based approaches face distinct constraints, including simplified reflection assumptions, computational cost, and large measurement-data requirements.RT simulation complexity grows with sea-surface discretization, while maritime measurement campaigns are less accessible than terrestrial ones.Source: §I · p. 2
  • WEKP-PLP learns residual quantiles from ray-tracing simulations across environmental and system conditions, then uses a small number of measurements to correct the WEKP median prediction.The pool maps conditions to residuals between RT-simulated path loss and the FSPL baseline; GPR learns the discrepancy between measured path loss and the WEKP-based median.Source: §I · p. 2
  • The framework provides a point estimate and prediction interval, using a WEKP prior from RT simulation data to reduce the requirement for large-scale measurements.The measurement-based GPR residual correction is described as improving point-prediction accuracy while maintaining reliable interval coverage.Source: §I · p. 2

II. SYSTEM MODEL AND PROBLEM FORMULATION

Dynamic sea-surface interactions can make received path loss fluctuate, so the formulation predicts both a representative value and a range. Environmental and system inputs determine conditional path-loss quantiles, with lower and upper quantiles defining an interval.

A. Shore-to-Ship Propagation Scenario

  • The shore-to-ship scenario places a coastal transmitter and a vessel receiver over the sea, where direct and sea-surface-reflected components dominate the received signal.Rough sea surfaces, coastal buildings, and harbor facilities may add scattering, reflected, diffracted, or scattered paths.Source: A. Shore-to-Ship Propagation Scenario · p. 3
  • Dynamic sea-surface variation shifts reflection points and changes reflected-path lengths and phase relationships, producing short-term path-loss fluctuations even when the vessel is nearly stationary.The cited example shows measured variation within one minute while propagation distance changes by less than 1 m.Source: §II · p. 2, A. Shore-to-Ship Propagation Scenario · p. 3, Figure 1 · p. 3

B. Path Loss Prediction Formulation

  • Rather than predicting only one deterministic value, the formulation estimates conditional path-loss quantiles for each input feature vector.The median is the predicted path loss, while the lower and upper quantiles define the prediction interval.Source: B. Path Loss Prediction Formulation · p. 3, §II · p. 3
  • The input vector includes propagation distance, carrier frequency, wind speed, seawater temperature, and salinity.These variables represent the system settings and maritime environmental conditions considered in the formulation.Source: B. Path Loss Prediction Formulation · p. 3
  • For target coverage 1−α, the interval bounds are the predicted α/2 and 1−α/2 quantiles, and the median quantile supplies the point prediction.The conditional quantile is defined relative to the probability that path loss does not exceed a candidate value under the given inputs.Source: B. Path Loss Prediction Formulation · p. 3
  • Prediction intervals trade reliability against sharpness: wider intervals can cover measured path loss more often, but overly conservative intervals are less useful.The stated objective is an accurate representative prediction with a reliable, compact interval.Source: B. Path Loss Prediction Formulation · pp. 3–4

III. WIRELESS ENVIRONMENT KNOWLEDGE POOL CONSTRUCTION

The WEKP is built from ray-tracing data to map shore-to-ship conditions to path-loss quantiles. Its simulation dataset varies environmental and system parameters, while using a simplified propagation setup and a finite distance range shaped by computational cost.

III. WIRELESS ENVIRONMENT KNOWLEDGE POOL CONSTRUCTION

  • The WEKP maps environmental and system parameters to quantiles of the residual between RT-simulated path loss and the FSPL baseline.The resulting pool is intended to characterize shore-to-ship propagation conditions and path-loss quantiles.Source: §III · p. 4

A. Dataset Construction Based on Ray Tracing

  • Sea surfaces are simulated with the PM wave spectrum, using linear filtering with IFFT to generate wave characteristics across wind speeds.The simulated wave patterns characterize wave conditions rather than reproducing the precise sea surface during measurement.Source: A. Dataset Construction Based on Ray… · p. 4
  • Seawater dielectric properties use the Double Debye equation with salinity, temperature, and frequency as inputs, while a roughness coefficient modifies Fresnel reflection.The roughness adjustment represents weaker specular reflection and more diffuse energy as sea-surface roughness increases.Source: A. Dataset Construction Based on Ray… · p. 4
  • The RT dataset models direct and first-order sea-surface-reflected paths across wind speed, frequency, antenna-height combinations, distance, seawater temperature, and salinity.The sampled ranges include wind speeds of 2–8 m/s, frequencies of 2–14 GHz, and horizontal distances of 200–2000 m; the dataset contains 58,800 unique samples.Source: A. Dataset Construction Based on Ray… · pp. 4–5
  • RT simulation distances extend to approximately 2 km, compared with measurement distances up to 9.41 km, because discretizing the continuous sea surface makes longer-range simulation computationally burdensome.The number of sea-surface grids grows rapidly as simulation distance increases.Source: A. Dataset Construction Based on Ray… · p. 5

B. WEKP Implementation Using CatBoost Quantile Regression

The WEKP uses FSPL as a baseline and CatBoost quantile regression to estimate conditional quantiles of RT residual path loss. Adding those residual quantiles to FSPL yields path-loss quantiles and the WEKP prediction interval.

B. WEKP Implementation Using CatBoost Quantile Regression

  • The WEKP models conditional quantiles of the RT-simulated path-loss residual relative to FSPL, using environmental and system parameters as inputs.The residual is the RT path loss minus the FSPL baseline.Source: B. WEKP Implementation Using CatBoost… · p. 5
  • CatBoost quantile regression estimates multiple quantiles of the RT residual from the feature vector, with quantile loss minimized separately for each quantile level.The median residual supplies a point estimate, while lower and upper residual quantiles describe its uncertainty range.Source: B. WEKP Implementation Using CatBoost… · p. 5
  • Adding each predicted residual quantile to the FSPL baseline produces the corresponding WEKP-based path-loss quantile.The median path-loss quantile is the WEKP-based median prediction.Source: B. WEKP Implementation Using CatBoost… · p. 5
  • The lower and upper WEKP path-loss quantiles form the prediction interval, which is later refined through measurement-based residual correction.The WEKP supplies a median prediction and interval from RT residual characteristics before practical-scenario adaptation.Source: B. WEKP Implementation Using CatBoost… · p. 5

IV. MEASUREMENT-BASED RESIDUAL CORRECTION

The WEKP prior may mismatch real measurements because RT simulations include the direct and first-order sea-surface-reflected paths, while real conditions may include additional propagation effects. A small set of measurements is used to model the residual from the WEKP median and refine its output.

IV. MEASUREMENT-BASED RESIDUAL CORRECTION

  • Real measurements may include propagation effects not fully represented by the RT simulation’s direct and first-order sea-surface-reflected paths.This difference may create a mismatch when the WEKP prediction is applied to measurements.Source: §IV · p. 5
  • The correction models the residual between measured path loss and the WEKP-based median prediction.Source: §IV · p. 5
  • The WEKP prediction serves as prior information, and a small number of measurement samples are used to adapt it to real shore-to-ship conditions.Source: §IV · p. 5

A. Measurement Campaign

A shore-to-ship measurement campaign collected real path loss data around Taohua Island under practical maritime conditions. The section describes the measurement setup, ship route and conditions, and processing used to retain valid samples.

A. Measurement Campaign

  • The campaign around Taohua Island collected real path loss data for residual correction and final performance evaluation.Source: A. Measurement Campaign · pp. 5–6
  • Fig. 3 depicts the measurement platform, transmitter and receiver antennas, and the measurement route.Source: Figure 3 · p. 6
  • The transmitter used a horn antenna to send a pseudorandom code, while an omnidirectional receiver antenna captured it; GPS timing synchronized the units.The platform also included a vector signal generator, power amplifier, low-noise amplifier, and spectrum analyzer.Source: A. Measurement Campaign · p. 6
  • The ship followed a preset 1.40–9.41 km route, recording antenna motion and meteorological conditions including wind speed of 2.5–3.1 m/s.Seawater temperature was 15.3–16.0 °C and salinity was 32.4–34.6 ppt.Source: A. Measurement Campaign · p. 6
  • After back-to-back hardware calibration and IQ-data processing, 25,587 valid samples remained across three measured frequency points.Processing used FFT, division by the calibration signal, and IFFT to obtain the channel impulse response.Source: A. Measurement Campaign · p. 6

B. Gaussian Process Regression for Residual Correction

The correction stage uses Gaussian process regression to model the mismatch between measurements and the WEKP median prior. Its predicted residual mean adjusts the median, while residual uncertainty contributes to the corrected interval.

B. Gaussian Process Regression for Residual Correction

  • GPR models the discrepancy between measured path loss and the WEKP-based median prediction rather than learning the full path-loss relationship from measurements alone.The WEKP prediction remains the prior, addressing mismatch between simulation settings and practical measurement conditions.Source: B. Gaussian Process Regression for… · pp. 6–7
  • GPR uses the original features together with WEKP-based interval width, which supplies uncertainty information under different propagation conditions.The training targets are residuals between measured path loss and the WEKP median prediction.Source: B. Gaussian Process Regression for… · p. 7
  • GPR models covariance between residual values at different inputs and estimates a predictive distribution for a new input.The kernel function specifies that covariance; larger kernel values indicate stronger covariance.Source: B. Gaussian Process Regression for… · p. 7
  • The GPR predictive mean corrects the WEKP median, and its residual variance helps construct the corrected prediction interval.For a 90% target coverage level, the fixed scaling factor k is 1.645.Source: B. Gaussian Process Regression for… · p. 7

V. EXPERIMENTAL RESULTS AND ANALYSIS

The evaluation covers both RT simulation data and measurement data, assessing point prediction alongside interval characterization. Its metrics include point errors, coverage, interval width, and Winkler score.

V. EXPERIMENTAL RESULTS AND ANALYSIS

  • The experiments evaluate the framework using RT simulation data for WEKP construction and measurement data for residual correction and validation.Source: §V · p. 7
  • Evaluation includes MAE, RMSE, and R2 for point prediction, plus coverage and interval width for interval characterization.Source: §V · p. 7
  • The Winkler score is highlighted because it jointly evaluates interval sharpness and penalties for observations outside the prediction interval.Source: §V · p. 7

A. Performance Analysis of WEKP Construction

CatBoost is selected for the WEKP because it balances interval coverage and width; feature analyses show that environmental parameters chiefly inform RT residual uncertainty.

A. Performance Analysis of WEKP Construction

  • RMSE values around 1.84 dB and R2 values around 0.95 are similar across candidate models, so point prediction alone does not select the WEKP implementation.The candidates learn the residual component rather than the entire path loss.Source: A. Performance Analysis of WEKP… · pp. 7–8
  • 90.03% coverage, 4.72 dB mean interval width, and the lowest Winkler score of 7.28: CatBoost provides the best interval balance and is selected for the WEKP.XGBoost, CatBoost, and NGBoost reach the 90% target, while the MLP's coverage is 68.05%.Source: Table II · p. 8, A. Performance Analysis of WEKP… · p. 8
  • Environmental inputs chiefly characterize RT residual uncertainty: distance dimensionality and antenna height add little, while wind, temperature, and salinity change interval behavior.Adding dielectric parameters to G4 yields limited improvement; environmental variables contribute mainly to uncertainty characterization.Source: A. Performance Analysis of WEKP… · pp. 8–9, Figure 4 · p. 8
  • Wind speed has the widest SHAP distribution and effects in both directions; salinity and temperature also affect learned residuals, but less strongly in the RT dataset.The paper relates wind's non-monotonic effects to sea-surface roughness and changes in reflected components.Source: A. Performance Analysis of WEKP… · pp. 8–9, Figure 5 · p. 9

B. Interval Behavior and Generalization Analysis of WEKP

WEKP retains target interval coverage under practical measurement-scenario parameters, though its point accuracy declines and intervals widen; interval width varies with distance and wind speed.

B. Interval Behavior and Generalization Analysis of WEKP

  • The practical-parameter test examines whether WEKP can approximate RT predictions without rerunning simulations for measurement conditions, while also assessing its uncertainty estimates.The results indicate reliable coverage under these parameters despite moderately reduced point accuracy.Source: B. Interval Behavior and… · pp. 9–10
  • Interval width increases with distance in low-wind conditions and generally decreases as wind speed rises within a distance group.The paper attributes this pattern to changes in sea-surface reflection and path-loss fluctuations; the intervals therefore adapt to propagation conditions.Source: Figure 6 · p. 9, B. Interval Behavior and… · pp. 9–10
  • 2.77 dB RMSE, 91.70% coverage, 10.21 dB mean interval width, and 11.94 dB maximum width are reported for WEKP under measurement-scenario parameters.The coverage meets the 90% target, while point prediction accuracy is affected by the changed input parameters.Source: B. Interval Behavior and… · p. 9

C. Measurement-based Residual Correction

Measurement-based residual correction adapts the WEKP prior, with GPR outperforming QR in the reported correction tests. The proposed method also outperforms conventional path loss models and maintains useful intervals in cross-frequency prediction.

C. Measurement-based Residual Correction

  • As correction samples increase, GPR RMSE decreases while coverage stays above target and mean interval width remains stable; GPR also beats QR in error and interval width.For 300 correction samples, GPR provides a better balance of prediction accuracy and interval reliability than QR.Source: C. Measurement-based Residual Correction · p. 10
  • With 300 corrected samples, RMSE is 1.17 dB at 4 GHz, 1.29 dB at 4.5 GHz, and 1.89 dB at 5 GHz, with coverage above or near target.Interval widths remain relatively stable across frequencies; the reported differences mainly reflect propagation characteristics.Source: C. Measurement-based Residual Correction · p. 10

D. Comparison With Conventional Path Loss Models

C. Measurement-based Residual Correction

  • At 4 GHz and 4.5 GHz, most measurements fall inside the predicted intervals, but some long-distance 5 GHz samples fall outside amid larger path loss fluctuations.The intervals still provide uncertainty information across propagation conditions.Source: C. Measurement-based Residual Correction · p. 10, Figure 8 · p. 11
  • Training correction on 4 GHz and 5 GHz measurements improves 4.5 GHz accuracy as sample count rises, while coverage meets target despite wider intervals.The wider intervals reflect added frequency-transfer uncertainty when source-frequency residuals may not match the target frequency.Source: C. Measurement-based Residual Correction · p. 10, Figure 9 · p. 11

E. Ablation Study of WEKP-PLP Framework

The ablation results indicate that the WEKP prior and measurement-based residual correction both contribute to the framework. With 300 correction samples, the method reports an MAE of 1.03 dB and an RMSE of 1.54 dB while meeting target coverage.

E. Ablation Study of WEKP-PLP Framework

  • Applying the WEKP prior directly to measurements yields large prediction errors and low coverage, so it cannot serve as the final measurement-scenario prediction without correction.The stated mismatch is that RT simulation mainly includes direct and sea-surface-reflected components, while real measurements may contain additional propagation effects.Source: E. Ablation Study of WEKP-PLP Framework · p. 11, Table IV · p. 12
  • With the same GPR residual correction, the WEKP prior produces lower RMSE and a more compact interval than the two-ray prior.The ablation attributes the difference to prior quality and notes that a weak prior is difficult to correct with few measurements.Source: E. Ablation Study of WEKP-PLP Framework · p. 12

VI. CONCLUSION

  • The framework uses the WEKP prior for point prediction and interval information, then measurement-based residual correction to adapt it to real shore-to-ship scenarios.Future work will incorporate more diverse sea states and independent measurement routes to further validate prediction capability.Source: E. Ablation Study of WEKP-PLP Framework · p. 12, §VI · p. 12
  • With 300 correction samples, WEKP-PLP achieves an MAE of 1.03 dB and an RMSE of 1.54 dB while achieving the target coverage level.The conclusion identifies both the WEKP prior and measurement-based residual correction as necessary.Source: §VI · p. 12

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