# Wireless Channel Models for Over-the-Sea Communication: A Comparative Study
## 4 Channel Models for Over-the-Sea Wave Propagation
### Channel Fading Margin for a Wireless Link  
Radio waves can easily get trapped within evaporation ducts and the sea surface. The propagation of signals and the estimation of refractivity are well studied in many existing models of the ocean surface channel. The fading characteristics of the evaporation ducts are a relatively newer topic in this area and should be analyzed and studied well to find the appropriate fading margin required for reliable wireless communication. To solve this problem, [PERSON] et al. presented a method for calculating the complete fading margin for a wireless link over the surface of the South China Sea [14].  
Based on the recent reports on the evaporation duct measurements, the authors of [14] calculated the statistical distribution of path loss at different distances in the South China Sea. The calculated path loss distributions vary from time to time and depend on the weather. They also suffer due to the slow and fast fading characteristics. After determining the fading characteristics, a complete fading margin was deduced. For 100 km, it was found that approximately 99% availability can be achieved with an 88-dB fading margin. For a shorter distance of 50 km, the necessary value of fading margin for 99% availability is only 50 dB.  
To calculate the fading margin, the first refractivity profile data is produced as follows:  
\[M(z)=\ M_{0}+0.125z-0.1258\ln\left(\frac{z+z_{0}}{z_{0}}\right) \tag{25}\]where \(M\) is the modified refractivity, \(z\) is the height in meters, \(z_{0}\) is the aerodynamic roughness in length, and \(\delta\) is the evaporation duct height. The PE tool [41] analyzed the data, including other parameters, to calculate the path loss. The antenna height for both the receiver and the sender was 4 m, which helped them continue transmission within the evaporation duct at 10.5 GHz. Since we know that the average signal-to-noise ratio is highly necessary for finding the fading margin, the mean path loss at a given distance must first be obtained. It was calculated using the following equation:  
\[\overline{PL(d)}=\ \gamma(d)+\ E\big{(}x^{\prime}_{dB}\big{)},\ d\geq 0 \tag{26}\]  
where \(\gamma(d)\) is the location parameter that varies with distance \(d\), and \(E\big{(}x^{\prime}_{dB}\big{)}\) is the expectation of path loss in dB. The fading margin for slow fading and fast fading can be calculated by the formulae:  
\[f_{m,slow}=\ X_{0}(P_{avail})-\ E\big{(}x^{\prime}_{dB}\big{)} \tag{27}\]  
\[f_{m,fast}=\ -10\ log\ [-ln\ (1-P_{out})] \tag{28}\]  
where \(P_{avail}\) is the probability of availability of slow fading for a given threshold value of \(X_{0}\), and \(P_{out}\) is the outage probability. Finally, the fading margin was calculated by summing up the slow and fast fading.  
The work presented in [14] is unique because no one has critically analyzed the calculation of the fading margin for over-the-sea wireless communication in the evaporation duct layer. The contribution is high, but there are a few areas for improvement that could be considered. However, it is not clearly mentioned whether the transmitter or receiver is mobile or static. This is important because, mostly, the transmitter is mobile in such a scenario and mobility can be a big concern. In addition, calculating the fading margin for other types of ducts can be performed in the future together with an implementation scenario.