## 2 Theory of Underwater Electric Field Communication
### Electric Dipole Field Strength  
Simulating underwater electric field application scenarios and validating the effect of frequency on electric field propagation helps determine the optimal communication frequency. Theoretical modeling, solving, and simulation analysis were performed using CST 2021 software. Based on the biomimetic principles, underwater electric field communication is a low-frequency electromagnetic field. Therefore, we utilized the CST EMSTUDIO software with a low-frequency time-domain solver for simulation. The electrode material was set to PEC (Perfectly Electric Conducting) with infinite conductivity. The dipole was symmetrically distributed on both sides of the origin on the \(x\)-axis, with the background environment set to freshwater. Table 1 displays the specific parameter settings.  
In order to analyze the electromagnetic field propagation characteristics of the dipole in the underwater electric field communication model, we simplified the analysis of the electric field strength along the perpendicular axis of the dipole. Due to the symmetry of the dipole's electric field, the analysis and calculations in this paper focused on one side of the model. The meshing of the model was conducted using tetrahedral elements, with mesh size tailored to the field strength. Densely packed meshes were used in regions of strong electric field, while sparse meshes were applied in areas with weaker field strength. This mesh strategy accelerated the solver's solution process and ensured a smoother data curve. Additionally, the grids near the perpendicular axis of the dipole were refined to guarantee accurate output at the axis. The simulation model employed an adaptive meshing approach. Through the software's adaptive mesh solver, the grid size was refined to obtain more precise simulation data.  
The distribution of the electric field strength was generated by the electric dipoles in a freshwater environment. The electric field strength distribution exhibits symmetry with respect to the \(xoz\) plane (\(y=0\)) and the \(xoy\) plane (z = 0). The attenuation of the electric field strength with increasing distance is observed when different frequency signals are applied to the electric dipoles. The signal frequencies used are 30 KHz, 50 KHz, 55 KHz, and 60 KHz.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Model dimensions & 800 m \(\times\) 800 m \(\times\) 1000 m \\ Electrical conductivity & \(\sigma=487\upmu\)S/cm \\ Relative permittivity & \(\varepsilon_{r}=74\) \\ Relative permeability & \(\mu_{r}=0.9999\) \\ Electric dipole size & 15 mm \(\times\) 15 mm \(\times\) 0.2 mm \\ Distance between electric dipoles & 1 m \\ Current between electric dipoles & 0.5 A \\ \hline \hline \end{tabular}
\end{table}
Table 1: Freshwater medium and electrode model parameters.  
Based on the analysis of the results in Figure 2, it is observed that the electric field strength at the same location undergoes a sharp attenuation when the frequency of the alternating electric field is above 50 kHz. The alternating electric field at 50 kHz experiences relatively small attenuation compared to the 30 kHz alternating electric field, and the signal has a higher bandwidth. Considering the rapid attenuation of the field strength with frequency and the communication system's communication rate requirements, a carrier frequency of 50 KHz is selected.