# Wireless Channel Models for Over-the-Sea Communication: A Comparative Study
## 4 Channel Models for Over-the-Sea Wave Propagation
### Multipath Channel Model for Propagation of Radio Waves Over the Sea Surface  
This paper presents an analytical approach to the development of a multipath channel model for the propagation of radio waves above the sea surface. A modeling approach can be applied to establish a channel impulse response consisting of a specular multipath, produced by a smooth sea surface, and a diffuse multipath, produced by a rough sea surface. The authors in [5] showed that a diffuse multipath can be obtained by gathering diffuse scattering energy together from the glistening surface. Methods for formulating impulse response curves for specular and diffuse multipath propagations were also discussed in detail in [5]. The introduced channel model in [5] is actually a modification of [39]. However, the modeling approach in [39] did not lead to their findings for over-the-sea radio wave propagation. Therefore, the authors in [5] modified the channel model in [39] using the Fresnel reflection coefficient of the sea, dipole antenna pattern at the transmitter and receiver, and parameters of sea states. Finally, the developed channel model was tested using various sea states, carrier frequencies, and transmission distances.  
In [5], the ratio of the specular multipath and direct path can be expressed as:  
\[\frac{Specular\ path\ Voltage}{Direct\ Path\ Voltage}=\ \rho_{s}\sqrt{G_{ant}}| \Gamma_{v}| \tag{20}\]  
where \(\rho_{s}\) is the reflection coefficient of the specular point, \(G_{ant}\) is the relative antenna gain, and \(\Gamma_{v}\) denotes the Fresnel reflection coefficient. What part of the incident angle is absorbed by the surface depends on this coefficient. The scattering of the rough sea surface causes diffuse reflection of the transmitted radio waves. The strength of diffuse reflection depends on the strength of the direct path signal. It can be calculated as:  
\[\frac{Diffuse\ Voltage}{Direct\ Path\ Voltage}=\ \sqrt{\frac{1}{4\pi}(\frac{R}{R_{1}R_{2 }})^{2}\left(\frac{1}{\beta_{0}^{2}}\right)Fig\exp\left(\frac{\beta^{2}}{ \beta_{0}^{2}}\right)\ dA\cdot\rho_{roughness}\cdot\sqrt{G_{ant}}\cdot| \Gamma_{v}|\cdot\sqrt{S_{f}}} \tag{21}\]  
where \(R\) is the direct path length to the receiver, \(R_{1}\) is the path length from the transmitter to the differential path, and \(R_{2}\) is the path length from the differential patch to the receiver. \(\beta\) is the surface tilt, \(\beta_{0}\) is the mean square value of the surface of the region of interest, \(\rho_{roughness}\) is the roughness factor, and \(S_{f}\) is the shadowing factor.  
The main problem of previous studies on modeling a multipath channel in an oceanic environment is that the models are based only on measured data and; therefore, are applicable to particular frequencies and geographical situations. The approach in [5] overcomes this problem, because it presented a theoretical multipath wireless channel modeling approach applicable to different carrier frequencies, transmission conditions, sea states, and transmission distances. The only drawback of this work is that the measurement results are not validated by any real-time implementation.