# Bit Error Rate of Multi-Gaussian Correlated Asymmetric Bessel Beam Through Turbulent Ocean
## 3 Numerical Simulations and Discussion
It can be observed that the BER of low-order modulation decreases more significantly when turbulence weakens. Since high-order modulation can carry more data bits, the QAM modulation order should be selected adaptively to make a balance between information capacity and BER according to specific requirements. Considering the properties of the beam itself, Figure 6b,d shows the relationship between BER and modulation order \(M\) under different asymmetry factors \(c\) of the MGCAB beam. The BER increases with \(c\) due to the larger OAM modal crosstalk of asymmetric mode in turbulence. Low-order modulation has a lower BER and a smaller \(c\) is preferable under low-order modulation. By comparing Figure 6b,d, we find that the BER decreases significantly in weaker oceanic turbulence, which makes high-order modulation a viable alternative option. The variation in BER with \(c\) is relatively gentle under high-order modulation, which indicates that the change in \(c\) has a small impact on beam propagation  
Figure 5: Effects of temperature–salinity gradient ratio \(H\) on the BER of the MGCAB beam under different (**a**) temperature dissipation rates \(\chi_{T}\) and (**b**) kinetic energy dissipation rates \(\varepsilon\). in this condition. Since \(c\) is an important parameter controlling the transverse intensity pattern of the MGCAB beam, the optical field available is more flexible and diverse with the adjustment of beam asymmetry [23]. As a new degree of freedom of the vortex beam, the topological charge \(l_{0}\) affects the BER of the MGCAB beam given in Figure 7a. Generally, the spot size expands with topological charge [38], which is also applicable to the MGCAB beam. The larger spot makes the beam more vulnerable to oceanic turbulence perturbations and exacerbates crosstalk between OAM modes. As a result, the SNR of transmission link decreases and BER increases. Therefore, the construction of the MGCAB beam with lower topological charge is preferable in multiplexing systems, which reduces not only BER but also the size of receiving aperture. Aiming at the problem of higher BER caused by large topological charge, the approach of low-order modulation of QAM can be adopted to reduce BER, which is intuitively demonstrated in Figure 7b. In addition, by introducing the adaptive feedback correction technique to measure the wavefront distortion caused by turbulence and conduct phase compensation, the BER can also be reduced [38]. Compared to topological charge \(l_{0}\), the impact of beam index \(N\) on BER is relatively smaller. The beam index affects the far-field intensity distribution of the MGCAB beam. With the increase in \(N\), the perturbations of turbulence on the beam become larger and the BER gradually increases. On the other hand, a larger \(N\) brings a flatter center intensity profile and a steeper edge in the far field [14]. Therefore, it is advisable to select the beam index according to the adaptability of beam field to different receiving systems within the acceptable range of BER. The influences of wavelength \(\lambda\) and source coherence width \(\sigma\) on the BER of the MGCAB beam are shown in Figure 8. With the increment in wavelength, a lower BER is obtained. The wavefront distortion and OAM modal crosstalk of the long-wavelength beam are weaker than those of the short-wavelength one due to the larger beam spatial coherence radius, demonstrating better resistance of long wavelength to turbulence perturbations. On the other hand, the increment in source coherence width \(\sigma\) also reduces BER. A larger \(\sigma\)  
Figure 6: Effects of signal modulation on the BER of the MGCAB beam under different (**a**) transmission distances \(z\) and (**b**) beam asymmetry factors \(c\). The values of turbulence parameter \(\chi_{T}\) in (**a,b**) are set as \(\chi_{T}\)= \(10^{-7}\) K\({}^{2}\)/s, while in (**c,d**) are set as \(\chi_{T}\)= \(10^{-9}\) K\({}^{2}\)/s. corresponds to higher beam coherence, which mitigates the dispersal of the OAM spiral spectrum and decreases crosstalk.