# Effects of Atmospheric Turbulence on OAM-POL-FDM Hybrid Multiplexing Communication System
## 4 Conclusions  
When the vortex beam is transmitted in free space, the phase of the beam undergoes interference from the random phase error of atmospheric turbulence. We designed a 32-channel hybrid multiplexed communication system and discussed the impact of different turbulence intensities on the communication system by simulation. The spot size and deviation angle of the beam became larger after long-distance transmission. Mutual interference will occur between multiplexed OAM beams under the effect of turbulence. When the OAM beam passes through weak (\({\rm C_{n}}^{2}\) = 10\({}^{-16}\) m\({}^{-2/3}\)) and strong (\({\rm C_{n}}^{2}\) = 10\({}^{-14}\) m\({}^{-2/3}\)) turbulence, 7.2% and 46.8% of the energy leaked into the neighbor OAM mode, respectively. The larger the turbulence intensity, the more scattered the distribution of leaked energy in the adjacent OAM modes. When the OAM modes were \(l\) = +4 and \(l\) = +8, 3% and 1.6% energy leaked to the adjacent OAM mode and became noise under strong turbulence. Different frequency intervals will have different effects on the hybrid communication system when FDM is adopted. When the frequency interval decreases from 0.5 THz to 0.1 THz, the quality of eye diagrams will deteriorate. When the system transmits information, the performance improvement of BER from strong turbulence (\({\rm C_{n}}^{2}\) = 10\({}^{-14}\) m\({}^{-2/3}\)) to moderate turbulence can reach 0.8776 orders of magnitude, while the BER under weak turbulence (\({\rm C_{n}}^{2}\) = 10\({}^{-16}\) m\({}^{-2/3}\)) outperforms the BER under moderate turbulence (\({\rm C_{n}}^{2}\) = 10\({}^{-15}\) m\({}^{-2/3}\)) for up to 1.86 orders of magnitude. Based on the above results, it can be proven that atmospheric turbulence has a serious impact on the hybrid communication system. When the vortex beam with a topological charge of +8 is transmitted at a distance of 3 km, its phase is completely distorted at a turbulence intensity of \({\rm C_{n}}^{2}\) = \(5\times 10^{-15}\) m\({}^{-2/3}\). Consequently, when the vortex beam of \(l\) = +8 is transmitted under the turbulence intensity of \({\rm C_{n}}^{2}\) = 10\({}^{-15}\) m\({}^{-2/3}\), the distance must be less than 3 km to ensure that the phase can be successfully distinguished. Only when the phase is distinguishable can the signal be separated according to different phases at the receiving end. Figure 9: (**a**) Eye diagram of the received signal at a frequency interval of 0.5 THz. (**b**) Eye diagram of received signal at a frequency interval of 0.1 THz. (**c**) BER of the received signal at different signal intervals under weak turbulence (\({\rm C_{n}}^{2}\) = 10\({}^{-16}\) m\({}^{-2/3}\)) and without turbulence. Vortex optical communication is an effective method to solve the problem of shortage of spectrum resources. Atmospheric turbulence is an important factor affecting the signal quality of the FSO communication. It is of great significance to study the transmission of a vortex beam in atmospheric turbulence. In this paper, we not only combined FDM with an OAM communication system, but also studied the influences of turbulence on this system. This is an attempt to combine OAM multiplexing technology with the existing FDM communication system. Our new proposed OAM-POL-FDM hybrid multiplexing communication system not only promotes the application of vortex optical communication, but also solves the actual demand, which makes it possible to further increase communication capacity with limited bandwidth. In our research in the future, we will continue to study the signal transmission of a vortex beam under atmospheric turbulence based on this work. More discussions will be focused on combining new technologies with our systems in order to reduce the effects of turbulence on vortex beam transmission and mitigate crosstalk between different OAM modes. Conceptualization, H.L. ; Formal analysis and writing, L.Z. ; Investigation, Y.H. ; Software, H.S. ; Validation, Z.W.