## 1 Introduction  
A modern underwater wireless sensor network (UWSN) often consists of widely distributed underwater sensors, relay buoys, autonomous underwater vehicles (AUVs), and remotely operated underwater vehicles (ROVs) to accomplish underwater sensing, monitoring, and communication tasks [1; 2; 3; 4; 5; 6; 7; 8]. To link the distributed nodes in an UWSN, underwater optical wireless communication (UWOC), underwater acoustic communication (UWAC), and underwater radio frequency (RF) communication (URFC) are leading candidates [1] delivering essential data around each node and providing various underwater services for scientific and commercial applications, such as water quality monitoring [5], maintaining of oil platforms [9], and life study [10]. UWOC links typically utilize green or blue light as the signal carrier, featuring the highest propagation speed in water compared to UWAC and URFC [1; 11]. The bandwidth of the light is in the range of hundreds of terahertz. Most UWOC systems employ a line-of-sight configuration, effectively avoiding signal diffusion scenarios common in UWAC and URFC. This configuration also significantly enhances the security of the communication system by inhibiting eavesdropping attacks. With the advantages of ultra-high bandwidth, low latency, and enhanced security, UWOC systems present considerable potential for applications in UWSNs, particularly for tasks requiring real-time data transmission. However, underwater optical channels encounter substantial interference due to severe absorption and scattering phenomena. Scattering occurs when light deviates from its original path due to interactions with small particles or objects in the water, thereby diffusing light throughout its propagation pathway. Meanwhile, absorption converts light energy into other energy forms, such as heat, in a UWOC channel. These factors inevitably impose constraints on the achievable link length of UWOC systems [1]. While other interferences, such as chromatic and spatial dispersions, exist within UWOC channels, they are ignored in this work due to their comparably lesser impact than the power loss induced by absorption and scattering. To alleviate this limitation, strategies to increase the optical signal-to-noise ratio (OSNR) or adapt to a noisy signal channel can be deployed. The utilization of a higher-power light source [12] or a more sensitive photon receiver [13] can improve the system's signal-to-noise ratio (SNR), thereby facilitating longer transmission distances in water. Nevertheless, the deployment of a high-power light source commonly results in a low modulation bandwidth, thereby constraining the overall transmission capacity. Additionally, highly sensitive photonic receivers, such as single-photon avalanche diodes and photomultiplier tubes, typically require exceedingly high driving voltages (ranging from ~100 V to 1000 V). Additionally, these sensitive photonic receivers are easily impacted by interference from background noise. Therefore, UWOC systems commonly require a delicate balance of the data rate and transmission distance. For example, in [14], a high-power optical source was applied and enabled a 138-m 1-Mbps UWOC transmission. The authors in [13] employed a high-sensitivity single-photon avalanche diode to achieve a 144-m 500-bps and a 117-m 2-Mbps UWOC transmission. Meanwhile, ultra-high-speed UWOC systems were demonstrated over shorter transmission distances. The authors in [15] proposed a 30-m 500-Mbps UWOC system, while the authors in [16] illustrated a 20-m 1.5-Gbps UWOC transmission, the authors in [17] utilized a laser-based white-light source to enable a 2.3-m 8.7-Gbps UWOC transmission, and a 90-m 560-Mbps UWOC system was demonstrated in [18]. Alternatively, the adoption of advanced signal processing algorithms in UWOC systems has been shown to enhance the system's adaptability to noise and attenuation in UWOC channels with low OSNR, thus enabling a high operation bandwidth and an optimal transmission rate [19; 20; 21; 22; 23; 24].