# Wireless Channel Models for Over-the-Sea Communication: A Comparative Study
## 4 Channel Models for Over-the-Sea Wave Propagation
### Multipath Delay Profile and Doppler Spread of Millimeter Radio Waves Over the Sea Surface  
Millimeter waves usually have high bandwidth and capacity. In [17], [PERSON] et al. presented an LoS ship-to-ship wireless channel model for over-the-sea communication. They considered the small-scale behaviors of a channel model like Doppler spread, RMS delay spread, and coherence bandwidth. Thirty-five GHz and 94 GHz were the frequencies used in [17].  
The proposed channel model was based on a ray-tracing channel simulator named Wireless Insite [38]. Geometry of the sea surface environment, objects within the terrain dimension, transmitter and receiver specifications (such as heights and locations), types of antenna, carrier frequency, and specification of the sea water were designed using the mentioned tool. Next, the software was used to calculate the time of arrival, angle of arrival, and received power of each signal path. Finally, the data were processed to compute the Doppler spread, PDP, RMS delay spread, and coherence bandwidth.  
For considering reduction in the reflected energy in specular direction, the reflection coefficient \(R\) was formulated as:  
\[R=R_{0}\exp[-8(\frac{\pi(\Delta h)\cos\theta_{i}}{\lambda_{0}})^{2}] \tag{31}\]where \(R_{0}\) is the smooth surface coefficient, \(\theta_{i}\) is the angle of incidence, \(\Delta h\) is the standard deviation in the surface height, and \(\lambda_{0}\) is the wavelength. Statistical properties of mean excess delay and RMS delay spread were obtained from the average PDPs using Equations (1) and (2) in Section 2 of this paper. Authors of [17] showed the effect of receiver speed over the sea surface, which caused a shift in the Doppler frequency. For \(i\)-\(th\) propagation path, the Doppler Effect was given by:  
\[\Delta f_{i}=f_{0}[\frac{d_{i}V_{T}}{c}+\frac{a_{i}V_{R}}{c}] \tag{32}\]  
where \(V_{R}\) and \(V_{T}\) are velocities of the receiver and transmitter, \(a_{i}\) and \(d_{i}\) are the directions of arrival and departure of the \(i\)-\(th\) ray, \(f_{0}\) is the carrier frequency, and \(c\) is the speed of light. When the time correlation of the impulse response is 50%, the coherence time is formulated as:  
\[T_{c}=\frac{9}{16\pi f_{m}} \tag{33}\]  
where \(T_{c}\) is the coherence time. As another small-scale parameter, coherence distance is extracted from the angle of arrival. This parameter refers to the amount of separation in space where a fading channel does not confront any change. It was formulated as:  
\[D_{c}=\frac{\lambda\sqrt{ln2}}{A\sqrt{23(1-\gamma\cos[2(\theta-\theta_{max})] )}} \tag{34}\]  
where \(D_{c}\) is the coherence distance, \(A\) is the angular speed, \(\gamma\) is the angular constriction, \(\theta_{max}\) is the maximum fading in the azimuth direction, \(\lambda\) is the wavelength, and \(\theta\) is the direction of arrival.  
Even though the proposed channel model had a high capacity and data rate, only LoS propagations were considered. Authors of [17] did not consider nLoS and bLoS propagation links. In [17], the effects of atmospheric ducts were overcome but they failed to analyze the refractive profile of the rough sea surface.