# Wireless Channel Models for Over-the-Sea Communication: A Comparative Study
## 1 Introduction  
Wireless channels for the radio wave propagation over the sea surface are different from the usual channels used in ground-to-ground wireless communication due to the unique nature of the marine environment. For example, neither the refraction of wave propagation, nor the effect of the evaporation duct is present in the ground-to-ground scenarios. Existing approaches to the modeling of over-the-sea channels vary with frequencies, technology used, and implementation scenario. While some approaches used millimeter waves and wide band technology, others used frequencies such as 1.9, 2, and 10 GHz, etc. Some approaches considered vessel-to-vessel mobile communication on the sea. Ship-to-ship and ship-to-shore wireless communication scenarios were also considered and implemented. So far, there are two preliminary minor approaches [1; 2], that briefly describe a few models of channels for over-the-sea communication; however, with inadequate analysis and limited discussion on various models, applications, future improvements, and research directions. Readers can prompt references [1; 2] for further details. Typically, the over-the-sea wave propagation environment can be divided into two types: One is \"near the sea surface\" and the other is \"hundreds of meters abovethe sea surface or higher.\" In the near the sea surface environment, the transceiver platform remains close to the sea surface. For example, communication between a ship and a base station is maintained ashore. Figure 1 shows such a scenario when communication occurs near the sea surface. Studies conducted in [3] show that for modeling channels in such an environment, special attention is paid to refraction caused by a possible evaporation duct, as well as a direct ray and sea surface-reflected ray. An evaporation duct affects frequencies around 1 GHz and higher. In principle, an evaporation duct is formed due to variation in humidity across the air and sea boundary. This phenomenon is rather dominant in all kinds of seas. For example, the evaporation duct remains prevalent in equatorial and tropical sea regions in 90% of cases. Therefore, to design any channel model for the near-the-sea environment, careful considerations should be given to the effects of the evaporation duct. Moreover, there may be possible communication scenarios where the propagation distance exceeds 3000 m. In this case, a two-ray propagation model of a direct ray and a reflected ray cannot predict the interference zeroes. To deal with this, one should consider a three-ray propagation model consisting of a direct ray, a reflected ray from the sea surface, and a refracted ray caused by the evaporation duct. Two- and three-ray models of wave propagation will be further discussed in the upcoming sections of the paper. In a scenario where wireless transmission takes place hundreds of meters above the sea surface, the transceiver is deployed on an airborne device or platforms, such as unmanned aerial vehicles (UAVs) or any other aircrafts. It is possible for the elevated duct in the troposphere region to cause an attenuation of the signal and affect air-to-ground communication through the sea wave propagation. The elevated duct is an atmospheric canal that consists of a layer with highly dense air [4]. It starts and remains at high altitudes and mainly affects transmission with a very high frequency. Figure 2 shows a scenario for wireless transmission taking place hundreds of meters above the sea surface. As shown earlier in Figure 1, in near-the-sea transmission, the signal mainly propagates through the evaporation duct. Compared to such an environment, the airborne propagations must pass  
Figure 1: Radio wave propagation near the sea surface. Figure 2: Radio wave propagation in air-to-ground communication for over-the-sea channels. through the evaporation duct layer, the air layer (free space layer), and the elevated duct layer, as shown in Figure 2.  
In this paper, a comprehensive and comparative study of over-the-sea channel models for radio wave propagation is presented.