## 1 Introduction  
The exploration and utilization of the underwater environment have long been a significant focus in multiple fields, including marine biology, oceanography, national defense, and telecommunications [1, 2]. However, effective communication in underwater environments is significantly hindered by the complex and dynamic nature of aquatic conditions [3, 4, 5]. Currently, underwater wireless communication is primarily achieved through three main approaches: radio frequency (RF) communication, acoustic communication, and optical communication [6]. RF communication's effective communication range is limited due to the rapid attenuation of electromagnetic wave signals caused by the high conductivity of seawater. In addition, RF communication devices are usually large in size and not suitable for covert operation, which further limits their application in specific scenarios [7; 8]. In contrast, acoustic waves experience less attenuation in aquatic environments and can support stable communication over long distances. As a result, acoustic communication has become the main mode of underwater communication today [9]. However, acoustic communication is constrained by several inherent limitations, including relatively low data transmission rates and significant propagation delays. These limitations make it less suitable for applications requiring high-bandwidth or real-time communication capabilities [10]. With the increasing demand for underwater communication systems, both RF and acoustic communications are facing challenges in meeting the requirements for high-bandwidth and real-time data transmission. In this context, UWOC has emerged as a promising alternative [11; 12]. UWOC employs light waves for data transmission, offering significant advantages including high-bandwidth, low-latency, and high-speed communication capabilities [13; 14; 15]. The attenuation of light in underwater environments exhibits significant wavelength dependence. Experimental studies have demonstrated that the blue-green spectrum, particularly within the wavelength range of 470-525 nm, experiences substantially lower attenuation compared to other spectral regions. This characteristic makes the blue-green band the optimal wavelength range for UWOC [16]. In recent years, UWOC has garnered considerable attention owing to its distinctive advantages. Significant advancements in system performance have been achieved through comprehensive research efforts, encompassing channel modeling, modulation techniques, channel coding, and hardware design [17; 18; 19; 20; 21]. In terms of modulation, conventional techniques, including on-off keying (OOK) and pulse-position modulation (PPM), have been widely adopted by UWOC systems [22]. OOK is widely adopted in optical communication systems due to its simple hardware implementation, low resource consumption, high bandwidth efficiency, and low power consumption. However, its performance is significantly limited by poor interference resistance under low SNR conditions. In contrast, PPM demonstrates superior noise immunity by encoding information through temporal pulse positioning. Nevertheless, this modulation scheme imposes stringent requirements on timing synchronization accuracy. Even minor timing jitter or synchronization errors can substantially degrade the BER performance. Furthermore, the hardware implementation of PPM systems presents greater complexity compared to OOK-based systems [23; 24; 25]. Recently, advanced modulation techniques including quadrature amplitude modulation (QAM), orthogonal frequency division multiplexing (OFDM), and multiple-input multiple-output (MIMO) have been implemented in UWOC systems to enhance data transmission rates and spectral efficiency [26; 27; 28]. However, these techniques require substantial hardware resources, making their implementation challenging in resource-constrained underwater environments [29; 30].