## 2 System Design  
### Fresnel Lens Array  
At the receiver end of the traditional UOWC system, the Fresnel lens is often utilized in front of the photodetector to converge the received optical signal, as shown in Figure 2a. However, the focal point location of the Fresnel lens will change with the receiver's movement, which results in the degradation of the communication performance, and even the interruption of the data link. The alignment requirements are essential for the UOWC system, which results in restricted system mobility. After the transceiver is aligned, the receiver can only move in the horizontal direction to ensure the stability of the communication link, which means the system has one DOF in the horizontal direction. When the optical signal is incident horizontally, the received power of the signal after being transmitted through the water tank can be expressed as [28]:  
\[P_{r}(d)=P_{t}\times\eta_{t}\times\eta_{r}\times\frac{A_{r}}{\pi\Big{(}d\tan \frac{\theta}{2}\Big{)}^{2}}\times\exp[-c(\lambda)d] \tag{1}\]  
where \(P_{t}\) is the transmitting power, \(\eta_{t}\) is the optical efficiency of the transmitter, \(\eta_{r}\) is the optical efficiency of the receiver, \(A_{r}\) is the convergence area of the lens, \(d\) is the transmission distance, \(\theta\) is the divergence angle of the LED source, and \(c(\lambda)\) is the total attenuation  
To enhance the mobility of the UOWC system, we propose a Fresnel lens array structure to realize an effective convergence of multiple-incident optical signals from different directions, as shown in Figure 2b. The DOF available for the UOWC system will increase with the number of lenses used in the array. Considering the limited space inside the receiver, the area of each Fresnel lens decreases as the number of lenses added to the array increases, which leads to a degradation of the received power. Hence, we take a 6-lens array structure as an example to verify the flexibility and communication reliability. All the lenses are combined into a hemispherical shape according to the schematic diagram shown in Figure 3a. We designed a core frame of the lens array using a 3D printer (Z600 plus, HORI). A regular pentagonal Fresnel lens with a side length of 16 mm is placed in the center, and five regular hexagonal Fresnel lenses with the same side length are fixed on different sides by rotatable axes. All the lenses are produced from poly (methyl methacrylate), which has a refractive index of 1.49. The assembled 6-lens array is shown in Figure 3b. The focal length of all the lenses is set to 20 mm. The focal point of each Fresnel lens is assigned to 20 mm. By adjusting the angles of the lenses, the focal points of the incident optical signals from six different directions can be converged on the same photodetector. A positive-intrinsic-negative (PIN) photodiode (Hamamatsu S6967) with a large active photosensitive area of 26.4 mm\({}^{2}\) is employed to realize an optical-to-electro (O/E) conversion of the received signal. The \(-3\) dB bandwidth of the PIN is 50 MHz, and the photosensitivity at 450 nm can be 0.3 A/W.  
Figure 3: (**a**) Schematic diagram of a 6-lens array; (**b**) Assembled 6-lens array.  
Figure 2: Schematic diagram of the dynamic UOWC system. (**a**) With one lens; (**b**) With lens array.