## 6 Conclusions  
In this paper, we focus on the parameter optimization of POV's source for the underwater transmission system using M-QAM based on bandwidth-limited ABER and study the influence of seawater turbulence and seawater absorption on AIC of bandwidth-constrained communication systems under the optimal parameters of POV's source. The numerical analysis of the ABER and AIC of bandwidth-constrained link is obtained: There exists optimizing half beam-width \(\tilde{w}_{opt}(z_{0},m_{0})\) of POV that is the function of the topological charge \(m_{0}\) and transmission distance. The ABER of bandwidth-constrained link increases with the increase of bandwidth \(B\) and the decrease of \(P_{TX}/N_{0}\), that is the increase of signal-to-noise ratio (SNR) of the optical system \(P_{TX}/N_{0}\) enhances the ability of the communication system to resist turbulent channel disturbance. For communication links with short link length, weak seawater turbulence and narrow communication bandwidth, it is more beneficial to adopt QAM of low order \(M\). However, for communication systems with long links, strong seawater turbulence and wide communication bandwidth, QAM of high order \(M\) should be adopted. High-order modulation is less affected by the turbulent  
Figure 11: The capacity of the POV carrier link versus the inner scale for different outer scale under (**a**) 4-QAM, \(z=100\) m, and (**b**) 256-QAM, \(z=150\) m.  
Figure 10: The capacity of the POV carrier link versus the ratio of temperature and salinity fluctuation contributions to the refractive index spectrum for the structural constant of the salinity-temperature fluctuation \(C_{\varepsilon_{XT}}^{2}=5\times 10^{-15}\), \(C_{\varepsilon_{XT}}^{2}=10^{-14}\), \(C_{\varepsilon_{XT}}^{2}=5\times 10^{-14}\), \(C_{\varepsilon_{XT}}^{2}=10^{-13}\) under (**a**) 4-QAM, \(z=100\) m, (**b**) 256-QAM, \(z=150\) m.  
strength, which indicates that high-order modulation has better anti-interference ability than low-order modulation for long link. Bandwidth-limited ABER increases and AIC decreases with the increase of seawater turbulence strength, and the salinity fluctuation has a greater impact on the AIC than the temperature fluctuation. The decrease of the outer scale and increase of the inner scale as well as channel number have a positive gain for AIC. The results of this paper show that the loss of AIC of underwater transmission system can be reduced by selecting appropriate modulation order of QAM and optimized parameters of POV.  
Conceptualization, Y.Z. ([PERSON]); methodology, Y.Z. ([PERSON]); software, Q.Y.; validation, Y.Z. ([PERSON]), Q.Y. and Y.Z. ([PERSON]); formal analysis, Q.Y.; investigation, Q.Y.; resources, Y.Z. ([PERSON]); data curation, Q.Y.; writing--original draft preparation, Y.Z. ([PERSON]) and L.Y.; writing--review and editing, Y.Z. ([PERSON]); visualization, Q.Y.; supervision, Y.Z. ([PERSON]) and Y.Z. ([PERSON]); project administration, Y.Z. ([PERSON]) and Y.Z. ([PERSON]); funding acquisition, Y.Z. ([PERSON]) and L.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (61871202, 11904136).  
Not applicable.  
The authors declare no conflict of interest.