## 2 System Architecture
### Maritime Channel  
The maritime communication channel model used in this paper is shown in Figure 3. When the sea surface is undulating due to sea winds and the transceivers are vibrating up and down due to waves, the electromagnetic wave signals, in addition to being affected by Gaussian white noise, also experience multipath interferences caused by reflections such as specular and diffuse reflections, as shown in Figure 3. Here we default that there is only one specular reflection path. However, due to the effect of wind, waves and sea climate on the sea surface, diffuse reflection points are randomly distributed around the specular reflection points, which makes an \"effective reflection region\". Therefore, it is necessary to determine the time-delay caused by the diffuse reflection point. According to the standard, in the 100 kHz maritime channel environment, reflections are mainly contained in the first 10.4 \(\upmu\)s of the symbol, but there are extreme cases where reflections occur at 50 \(\upmu\)s [20]. The literature [21] gives a maximum delay of 46.2848 \(\upmu\)s for a shore-based antenna of a 80 m height and a shipboard antenna of a 25 m height. Therefore, in this paper, the performance of the proposed TDOM system will be analyzed separately for two types of maritime communication channels, i.e., a single-path additive Gaussian white noise channel and a maritime multipath channel that includes one line of sight (LoS) path and multiple reflection paths. During simulation, three reflection paths are considered, i.e., two diffuse reflection paths which cause a delay of 50 \(\upmu\)s and 10 \(\upmu\)s at the maximum and minimum, respectively, and one specular reflection path which causes a negligible propagation delay. Meanwhile, during the simulation, in order to facilitate the understanding of the results under maritime multipath channels, the impact of system parameters on communication performance under the additive Gaussian white noise (AWGN) channel is firstly tested [22]. The ratio between the signal passing through the specular reflection path and the Los transmission signal is [23]  
\[\frac{V_{\text{Specular}}}{V_{\text{LoS}}}=\rho_{s}\sqrt{G_{\text{ant}}}|\Gamma _{v}|\rho_{\text{veg}}, \tag{6}\]  
where \(V_{\text{Specular}}\) and \(V_{\text{LoS}}\) represents the voltage of the signal passing through the specular reflection path and the LoS path, respectively. \(\rho_{s}\) is the specular reflection coefficient, and \(\Gamma_{v}\) is the Fresnel reflection coefficient, i.e.,  
\[\rho_{s}=\exp\left[-2\left(\frac{2\pi\sigma_{h}\sin(\varphi)}{\lambda}\right) ^{2}\right], \tag{7}\]  
Figure 3: Schematic diagram of the maritime communications channel model. \[\Gamma_{v}=\frac{\varepsilon_{c}\sin\varphi-\sqrt{\varepsilon_{c}-\cos^{2}\varphi}}{ \varepsilon_{c}\sin\varphi+\sqrt{\varepsilon_{c}-\cos^{2}\varphi}}. \tag{8}\]  
where \(\sigma_{h}\), \(\varphi\), \(\lambda\), and \(\varepsilon_{c}\) are, respectively, the rms surface height variation, the grazing angle, the wavelength, and the surface dielectric constant. In this paper, \(\sigma_{h}\) is set to be 0.3 m, assuming that the wave is gentle [23]. Moreover, the ratio between the strength of the signal passing the diffuse reflection path and the Los transmission signal is [23]  
\[\frac{V_{\text{Diffuse}}}{V_{\text{LoS}}}=\sqrt{\frac{1}{4\pi}\bigg{(}\frac{R }{R_{1}R_{2}}\bigg{)}^{2}\frac{1}{\beta_{0}^{2}}\exp\left(-\frac{\beta^{2}}{ \beta_{0}^{2}}\right)dA}\cdot|\Gamma_{v}|\cdot\rho_{\text{veg}}\cdot\sqrt{G_{ \text{ant}}}\cdot\rho_{\text{roughness}}\cdot\sqrt{S_{f}}. \tag{9}\]  
where \(R\), \(R_{1}\) and \(R_{2}\) are the distance of the LoS path, the distance from the transmitter to the reflection point and from the reflection point to the receiver, respectively. In this paper, \(R\) is set to be 5 km, and \(R_{1}\) and \(R_{2}\) are set to be 100 m and 10 m, respectively.