## 1 Introduction
The effectiveness of the algorithm was verified within a communication distance of 6 m. In [3], a time-domain hybrid pulse-amplitude-modulation (TDHP) scheme is proposed for the first time in a UWOC system, achieving a maximization of transmission capacity and distance. When the transmitting power is 0.5 W and the wavelength is 450 nm, the communication distance is kept between approximately 11 m and 100 m by changing the generation ratio of different modulation methods, the receiver field of view, etc. Due to the complexity of the propagation environment, orthogonal frequency division multiplexing (OFDM) has gradually become a research hotspot because of its high reliability and stability. Given the limitations of single quadrature amplitude modulation (QAM) in terms of its rate and communication distance [9; 10], in [11], a joint power adaptation and adaptive QAM scheme is proposed. It optimizes the transmission efficiency of the system under channel variations, allowing each user to achieve the maximum transmission rate at high SNRs. In [12], the bit power loading method combined with wavefront shaping technology results in a 30.7% increase in the transmission rate. However, it is also unable to reduce the distance to the Shannon limit to achieve maximum rate optimization. In recent years, constellation probabilistic shaping (CPS) technology has gradually been applied to this problem. This technique converts uniformly distributed input bits into non-uniform, Gaussian-like, distributed constellation symbols. It not only reduces the distance to the Shannon limit but also allows for rate adaptability by adjusting the information entropy, achieving flexible rate adaptation [13]. In [14], it is verified that the probabilistic optimal solution for constellation points in an additive white Gaussian noise (AWGN) channel is Maxwell-Boltzmann (MB) distribution. In [15], a distance-based rate-adaptive VLC system is proposed by adding CPS. The shaping factor is adaptively changed according to the SNR, achieving a finer-grained rate adjustment, with the total capacity increased by up to 28%. In [16], an entropy loading technology based on CPS is proposed. In indoor downlink application scenarios, the appropriate bit rate is selected by estimating the received SNR of different users. This method achieves data rates of 26 to 46 Gbps over a communication distance of 0.5 to 2 m. In [17], in order to improve the transmission rate of VLC, an adaptive spatial modulation scheme based on CPS is proposed. In [18], it is proven that CPS can also increase the transmission distance, with probabilistic shaping 64 QAM (PS\(-\)64 QAM) providing at least a 40% improvement over uniform 64 QAM (UN\(-\)64 QAM). However, most of this technology is focused on VLC, and there is less research on UWOC systems. In order to provide a clearer and more concise overview of the above literature and the method proposed in this paper, the key features of these methods, such as their modulation method, link distance, etc., are summarized in Table 1. In UWOC, light experiences severe attenuation, which limits the communication distance. However, CPS optimizes symbol distribution, reducing the BER and enhancing system reliability. Compared to uniformly distributed input signals, CPS can extend the communication distance under the same conditions. Moreover, by adjusting the shaping degree, the information rate can be flexibly controlled and spectral efficiency improved. Different from existing schemes, the adaptive method proposed in this paper not only integrates CPS into its electrical domain but also controls the incident power in the optical domain. In order to adapt to the changing channel conditions and the dynamic range of the PMT, this paper first proposes a uniform QAM rate-adaptive control strategy in the electrical domain. Based on the link conditions, the modulation scheme is adaptively adjusted among BPSK, 4 QAM, 16 QAM, 64 QAM, and 256 QAM.