A Modified Three-Ray Model for Maritime Wireless Communication With Evaporation Ducts

Evaporation ducts which extend long-distance coverage and enhance maritime communication quality hold significant potential for 6G broadband communications. The recent three-ray maritime channel model–incorporating rough sea reflections, wave-induced fading, Earth curvature divergence, and evaporation duct trapping–aligns well with high-frequency (5.25–12.74 GHz) measurements but exhibits significant errors at low-frequency (2.02–4.50 GHz) due to unaccounted evaporation duct leakage. To address this issue, a modified model has been developed. Guided by Huygens-Fresnel’s principle, the inherent correlation between evaporation duct leakage and electromagnetic wave angular spectrum expansion is analyzed. The parabolic equation method is then employed to quantitatively characterize this correlation, based on which an evaporation duct propagation attenuation factor is derived and further incorporated into a frequency-dependent modified three-ray path loss model. Shore-to-ship measurements verify this model, showing excellent agreement at high frequencies comparable to the latest three-ray model and better agreement at low frequencies, demonstrating superior predictive performance.