## 3 Results and Discussion
### Propagation Path Loss  
Propagation path loss is caused by the radiation diffusion of transmitting power and the propagation characteristics of a wireless channel, which reflects the change of the average power of a received signal in the macro range. It can be used to characterize the logarithmic relation between the power reduction and the Tx-Rx distance. In the analysis of wireless channel, some channel models have been built, such as free space model, Okumura-Hata model. Based on the actual propagation environment of the sea, [PERSON] et al. [31; 32] proposed a quasi-deterministic path loss propagation model for the open sea environment, which have considered the reflection from the water surface, divergence, and earth curvature effect and built a round earth loss model for the wireless channel over the sea.  
In this paper, we also use the round earth loss (REL) model to analyze the path loss based on the measurement data. Figure 5 plots the relationship between main influencing factors and Tx-Rx distance. It can be found that the effective reflection coefficient from the water surface increases with the increase of distance, while the divergence coefficient, shadowing coefficient, and diffraction loss caused by earth curvature decrease. The shadowing coefficient is also affected by the different surface slopes, where a larger slope results in a smaller shadowing coefficient at the same Tx-Rx distance. The diffraction loss caused by earth curvature appears beyond the 0.6 First Fresnel Zone \(D_{06}=1.94\) km, as shown in Figure 5. In addition, the divergence coefficient and the shadowing coefficient will decay to zeros due to the totally shadowed of the reflected rays. The distance for the totally shadowed is 12.63 km for \(h_{tx}=3.13\) m and \(h_{rx}=3.12\) m in this paper. However, our measurement distance is within this critical distance; the divergence coefficient and the shadowing coefficient are not reached 0 in this paper. As well, due to our short measurement distance, we obtain a small diffraction loss caused by earth curvature, shown in Figure 5.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Measurement** & \multicolumn{3}{c}{**RMS Delay Spread (ns)**} \\  & **50\%** & **75\%** & **90\%** \\ \hline S2I & 17.52 & 75.2 & 265.8 \\ S2S & 15.9 & 70.76 & 146.1 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistical result of the RMS delay spread.  
By including the factors mentioned above in the two-ray geometrical model [33], the REL model shown in Equation (4) can characterize the propagation path loss comprehensively.  
\[PL(d)=20\cdot\log_{10}\biggl{(}\frac{\lambda}{4\pi D_{\text{los}}}\biggr{)}+20 \cdot\log_{10}(\eta)+L_{\text{diff(e)}} \tag{4}\]  
where \(\eta=\left|1+S_{\text{c}}\cdot Div_{\text{eff}}\cdot R_{\text{rough}}\cdot e^{ \left|(2\pi/\lambda)D_{\text{diff}}\right|}\right|\). \(S_{\text{c}}\), \(Div_{\text{eff}}\), \(R_{\text{rough}}\), \(D_{\text{diff}}\), \(L_{\text{diff(e)}}\) are shadowing coefficient, divergence coefficient, effective reflection coefficient, the phase difference between reflected wave and line of sight (LOS) wave and the diffraction loss derived from earth curvature effect, respectively.  
Figure 6 plots the measurement path loss and the fitted results from typical models, including the free space model, one-slope model, ITU-R P.1411 model and REL model. It can be found that the measurement propagation path loss follows the REL model better than other classical models. Moreover, based on the REL model, the comparison result shows that the reflection effect is more obvious on the long-distance S2I measurement than that on the short-distance S2S measurement.  
Figure 5: Effect factors. (**a**) effective reflection coefficient from water surface, (**b**) divergence coefficient, (**c**) shadowing coefficient, and (**d**) diffraction loss caused by earth curvature.