# Bit Error Rate of Multi-Gaussian Correlated Asymmetric Bessel Beam Through Turbulent Ocean
## 3 Numerical Simulations and Discussion
When \(\sigma\) tends to infinity, the partially coherent beam grows to the fully coherent one. Therefore, a laser source with higher coherence and longer wavelength is beneficial to signal transmission in oceanic turbulent channels. Figure 9 reports the relationship between BER and the waist radius \(\omega_{0}\) of the MGCAB beam under different basal signal-to-noise ratios \(SNR_{0}\). There exists an optimal value for the selection of \(\omega_{0}\). The severe spreading brought by small \(\omega_{0}\) and wide initial waist brought by large \(\omega_{0}\) both result in a larger spot size during propagation, which makes the beam suffer more turbulence disturbances and the consequent modal crosstalk. Therefore, a moderate \(\omega_{0}\) is preferable to mitigate turbulence effects and reduce BER. Apart from the crosstalk noise induced by oceanic turbulence, the system background noise also has an impact. As for given transmitted power, a larger \(SNR_{0}\) means smaller background noise and thus lower BER. When \(SNR_{0}\) exceeds about 30 dB, the background noise is extremely low and its impact can be negligible. Figure 8: Effects of wavelength \(\lambda\) and source coherence width \(\sigma\) on the BER of the MGCAB beam. Figure 7: Effects of the topological charge \(l_{0}\) on the BER of the MGCAB beam under different (**a**) beam index \(N\) and (**b**) signal modulation \(M\). Figure 9: Effects of beam waist radius \(\omega_{0}\) and basal signal-to-noise ratio \(SNR_{0}\) on the BER of the MGCAB beam. In summary, oceanic turbulence and the basal signal-to-noise ratio of the communication system both have impacts on the BER of the MGCAB beam. Oceanic turbulence can affect beam wavefront and cause modal crosstalk of the MGCAB beam. When the transmission distance increases, the cumulation of turbulence effects will increase the BER. It is worth noting that the high-temperature and high-salinity oceanic environment further exacerbates the turbulence perturbations, causing the BER to be at a high level and seriously affecting the signal transmission quality. In terms of the optimization of signal modulation strategy, we find that, compared with the traditional OOK modulation, the MGCAB beam under low-order QAM exhibits better anti-turbulence characteristics. The BER can also be reduced by adjusting the beam parameters such as wavelength, coherence width, and beam waist radius. In addition, the transverse spectral density distribution of the beam can be made more diverse by adjusting beam asymmetry, thus meeting the requirements of different application scenarios. Based on the above-mentioned research results, the subsequent research in the future can focus on the effective transmission of beams in extreme oceanic environments of high temperature and high salinity concentrations. The research directions may include designing new types of light beams with special anti-turbulence structures, exploring more suitable modulation strategies, which are expected to promote the development of underwater optical communication in complex oceanic environments.