## 4 Proposed PDM-Based UWOC Link Description  
Figure 2 illustrates the proposed PDM-based UWOC link, which carries data from two independent channels, designed by using OptiSystemTM and MATLABTM software. The UWOC channel modeling was performed in MATLABTM, while the transmitters and receivers were designed in OptiSystemTM. Figure 2 depicts two channels in the UWOC link, each transmitting high-speed 1 Gbps NRZ/_RZ_ encoded data. In each channel, a continuous wave laser operating at a wavelength of 1550 nm and a power of 100 mW is used to modulate the 1 Gbps NRZ/RZ encoded data using a Mach-Zehnder modulator (MZM). The output of each channel is connected to a polarization controller, which applies a phase shift of 0\({}^{\circ}\) and 90\({}^{\circ}\) to each respective output. Figure 3 displays the optical spectrum for each polarization state, illustrating the RZ and NRZ encoding schemes. The outputs of the polarization controllers are combined and transmitted through the UWOC link. To model the UWOC link, [PERSON]'s law is used. [PERSON]'s law is commonly applicable to optical signals in any medium [38]. Two assumptions were made to validate the use of [PERSON]'s law in this analysis. Firstly, it was assumed that the transmitter and receiver are perfectly aligned. Furthermore, although scattered photons are theoretically considered lost, in real-time scenarios, some of these scattered photons can still be detected by the receiver due to multiple scattering. Since the numerical simulations were conducted within a limited range of communication, the alignment between the transmitter and receiver was considered to be perfect. With an increase in the link length, a noticeable  
Figure 2: Proposed 2 \(\times\) 1 Gbps PDM-based high-speed UWOC model. decrease in the received power was observed, indicating the occurrence of either photon scattering or absorption phenomena. Based on the numerical simulations, a simplified mathematical expression is proposed by fitting the data. This mathematical expression serves as an approximation for the received power \(p_{r}\) in the UWOC channel and is given as follows:  
\[p_{r}=c_{1}\times\exp(c_{2}\times d) \tag{6}\]  
where \(c_{1}\) and \(c_{2}\) are constants and \(d\) is the range of the UWOC channel. In the receiver stage of our proposed PDM-UWOC system, a polarization splitter is used to separate the received optical signal into its respective polarization states. Since our system employs polarization division multiplexing (PDM), where data are transmitted simultaneously in two orthogonal polarization states, this component plays a crucial role. By using a polarization splitter, we can effectively isolate the individual polarization components and independently process them for further signal analysis and decoding. For the optical detection of the received signals, an Avalanche Photo-Detector (APD) is employed in the receiver section. The selection of an APD is motivated by its ability to provide high sensitivity and gain. This is particularly advantageous in underwater  
Figure 3: Measured optical power spectra: (**a**) X polarization with NRZ encoding; (**b**) Y polarization with NRZ encoding; (**c**) X Polarization with RZ encoding; (**d**) Y polarization with RZ encoding. optical communication, where received optical power levels can be relatively low due to attenuation and scattering in the underwater medium. The APD's responsivity of 1 A/W indicates that for every watt of incident optical power, it generates an electrical current of 1 ampere, which enables efficient signal detection. To enhance the signal-to-noise ratio and suppress high-frequency noise components, a low-pass filter with a cut-off frequency of 750 MHz is employed. Underwater communication channels are susceptible to various sources of noise, including background noise and ambient light fluctuations.