# Wireless Channel Models for Over-the-Sea Communication: A Comparative Study
## 4 Channel Models for Over-the-Sea Wave Propagation
### Marine Communication Channel Modeling Based on the Finite Difference Time Domain (FDTD)  
The work presented in [9] aims to gain a more complete understanding of the communication channels in which UAVs are deployed for low-level maritime operations. The channel modeling  
Figure 10: Vessel-to-vessel communication scenario for the channel model. scheme was also presented using the FDTD method [28]. It also made a great effort to assess the effects of shadowing conditions on the sea surface on marine communication channels. The authors developed a 2-D EM simulator using a modified Pierson-Moscowitz (PM) spectral model [29]. The simulator was used to produce multipath scattering by generating a random sea surface in a deep water location. After analyzing the data retrieved from the simulation results, it was found that the simulation results gave a generalized path loss exponent, standard deviation, mean excess delay, and RMS delay as the functions of the frequency and the observable sea surface height for the stationary transmitter and receiver locations. Figure 11 presents a simple case scenario in which a UAV is communicating with a mobile vessel at a low-altitude, above-sea location. It is inevitable to lose the aircraft in the sea or have vehicular collision due to the loss of communication [30]. To establish a safe operation protocol for airborne maritime surveillance operations, path loss and multipath effects [31; 32] of the communication channels are key concerns. In the study presented in [9], the FDTD method is introduced to quantify the relevant parameters of maritime communication channels, through the simulation of the electromagnetic phenomena that contribute to the received waveform envelope in shadowing conditions. The work is mainly aimed at proposing a novel approach to the choice of a maritime communication channel. However, the authors claimed that the obtained research result is applicable to any sea-surface vehicle or sensor that uses wireless communications in the range of very high frequency (VHF) to 3 GHz. There are two reasons why the authors chose to apply the FDTD method for propagation analysis. One of them is the high accuracy of the method, and the other is the direct transient solution of [PERSON]'s equations [33]. Using this method, [PERSON]'s equations were solved through transient recursive calculations for EM analysis. The EM simulation engine developed by the authors in this paper contained three segments. These are random generation of the sea surface, implementation of the FDTD algorithm for analyzing EM propagation, and channel modeling based on the transient simulation results. The channel was simulated as a 2-D cross section [9]. The sea surface in the simulation was implemented as a perfectly conducting boundary condition. The transient impulse response for a random sea surface was numerically estimated using FDTD simulation, Next, this process was repeatedly used for multiple sea surfaces with different heights. These repetitive processes were undertaken to produce a significant set of population data. [PERSON] free space path loss equation [34] was used as a foundation for signal attenuation for wireless transmission. It can be described as:  
\[L_{s}(d)=(4\pi d/\lambda)^{2} \tag{9}\]  
where \(d\) is the physical distance between the TX and receiver (RX), and \(\lambda\) is the wavelength. A critical parameter for modeling wireless channels over the sea surface area is the path loss exponent. Figure 11: Scenario of marine communication between an unmanned aerial vehicle (UAV) and a mobile vessel at low altitude. This parameter is critical in the system design process. The basic path loss calculation [9] can be formulated as:  
\[L_{p}(d)=L_{s}(d_{o})+10 nlog\bigg{(}\frac{d}{d_{o}}\bigg{)}+X_{f}, \tag{10}\]  
where \(L_{s}(d_{o})\) is the measurement of the path loss at a particular location, which is at a distance of \(d_{o}\) from TX [35]. Here \(d\) is used to denote the distance of interest, and \(n\) is the path loss exponent.