## 4 Simulation Result Analysis  
In this section, the performance of the proposed rate-adaptive control strategy is verified by simulation. Based on the above channel model and system, the information rate, reliability, spectral efficiency and throughput performance of the rate-adaptive control strategy are analyzed. As shown in Figure 6, the BER and communication distance before and after shaping are compared under the same spectrum efficiency. Specifically, (a) and (c), respectively, represent the performance comparison between UN\(-\)16 QAM and PS\(-\)64 QAM when the information entropy is 4, while (b) and (d) show the performance comparison between UN\(-\)64 QAM and PS\(-\)256 QAM when the information entropy is 6. The simulation results show that under the same spectral efficiency, the signal after shaping has better a BER performance and longer communication distance. Therefore, PS\(-\)64 QAM (H = 4) and PS\(-\)256 QAM (H = 6) are selected in the subsequent simulated adaptive control experiment and combined with PCS technology. The performance comparison of the communication distance of the uniform adaptive QAM and the joint regulation rate adaptation in the photoelectric domain is shown in Figure 7. The simulation results show that under the FEC threshold, when the communication distance is short and the received power is too high, the PMT is saturated and distorted and the BER is close to 0.5. When the LCLV is used to regulate the incident power, the communication distance is reduced by approximately 6 m, which can alleviate the influence of saturation distortion to a certain extent. Compared with a single high-order modulation mode, the adaptive modulation method can select the best modulation mode  
Figure 6: Performance comparison before and after shaping under the same spectral efficiency. (**a**) Comparison of BER performance between UN\(-\)16 QAM and PS\(-\)64 QAM (H = 4); (**b**) comparison of BER performance between UN\(-\)64 QAM and PS\(-\)256 QAM (H = 6); (**c**) comparison of communication distance between UN\(-\)16 QAM and PS\(-\)64 QAM (H = 4); (**d**) comparison of communication distance between UN\(-\)64 QAM and PS\(-\)256 QAM (H = 6). based to the channel's state and improve the communication distance. PS\(-\)256 QAM increases the communication distance by approximately 47% compared to UN\(-\)256 QAM, PS\(-\)64 QAM increases it by about 41% compared to UN\(-\)64 QAM, and PS\(-\)16 QAM extends the communication distance by around 18% compared to UN\(-\)16 QAM. It can be seen that when the communication distance changes, resulting in changes in the underwater channel, the adaptive modulation algorithm effectively extends the dynamic range of the communication distance and maintains the system's reliability. The performance comparison of the information rate (a) and spectral efficiency (b) between uniform adaptive QAM and joint regulation rate adaptation in the photoelectric domain is presented in Figure 8. The simulation results show that with the uniform adaptive QAM strategy, when the modulation mode changes from 256 QAM to 64 QAM, the information rate decreases from 15.36 Mbps to 11.52 Mbps and the spectrum efficiency decreases from 2 bps\(/\)Hz to 1.5 bps\(/\)Hz. In the photoelectric domain joint control strategy, PS\(-\)256 QAM with an information entropy of 7 can increase the rate to 13.44 Mbps and the spectral efficiency to 1.75 bps\(/\)Hz within the same communication distance. Similarly, the information rate and spectral efficiency of other signals after probability shaping are improved within some distance ranges. Figure 8: (**a**) Information rate comparison of different adaptive modulation modes; (**b**) spectral efficiency comparison of different adaptive modulation modes (modulation modes from top to bottom: blue line—256 QAM, 64 QAM, 16 QAM, 4 QAM and BPSK; red line—256 QAM, PS\(-\)256 QAM (H = 7), PS\(-\)256 QAM (H = 6), PS\(-\)64 QAM (H = 5), PS\(-\)64 QAM (H = 4), PS\(-\)16 QAM (H = 3), 4 QAM and BPSK).