# Effects of Atmospheric Turbulence on OAM-POL-FDM Hybrid Multiplexing Communication System
## 3 Discussion on Transmission Performance under the Turbulence
When the difference between topological charge \(l_{1}\) and \(l_{2}\) becomes smaller, the crosstalk of the two OAM modes becomes more severe. Therefore, proper intervals between different OAM modes should be maintained to ensure the signal transmission is more effective. After the system transmits signals under different turbulence intensities, the results of BER and Q function are shown in Figure 7g. The BER were obtained under weak turbulence (\({\rm{C_{n}}^{2}=10^{-16}~{}m^{-2/3}}\)), moderate turbulence (\({\rm{C_{n}}^{2}=10^{-15}~{}m^{-2/3}}\)), and strong turbulence (\({\rm{C_{n}}^{2}=10^{-14}~{}m^{-2/3}}\)), respectively, and the transmission distance was 1 km. The BER was gradually reduced as the transmission power increased. On the other hand, the BER increased when the turbulence intensity increased. The difference in BER between the turbulence intensity \({\rm{C_{n}}^{2}=10^{-14}~{}m^{-2/3}}\) and \({\rm{C_{n}}^{2}=10^{-15}~{}m^{-2/3}}\) in the system can be up to 1.86 orders of magnitude, and the difference in BER between the turbulence intensity \({\rm{C_{n}}^{2}=10^{-15}~{}m^{-2/3}}\) and \({\rm{C_{n}}^{2}=10^{-16}~{}m^{-2/3}}\) in the system can reach 0.8776 orders of magnitude. FDM is added to this hybrid multiplexing system. We studied the effects of different frequency intervals on system performance. In the simulation, the communication system was under weak turbulence (\({\rm{C_{n}}^{2}=10^{-16}~{}m^{-2/3}}\)), and the frequency interval was set at 0.5 THz, 0.3 THz, and 0.1 THz, respectively. The obtained spectrum distribution is shown in Figure 8, where power suppression can reach up to 40.332 dB while the frequency interval was set as 0.5 THz. The extent to which the signal is affected depends on the frequency intervals. The eye diagram of the signals at the receiver with the frequency intervals set as 0.1 THz and 0.5 THz are illustrated in Figure 9a,b, respectively. The decrease in frequency intervals resulted in the increase of BER of received signals and deterioration of stability of the waveform. The result of the BER of the transmitted signal is shown in Figure 9c, which shows that the signal quality is better at a frequency interval of 0.5 THz than at 0.3 THz, and the signal quality is better at a frequency interval of 0.3 THz than at 0.1 THz. When the frequency interval descends, the signal quality is significantly affected and the BER gradually increases. Furthermore, at the same frequency interval, a greater turbulence intensity will lead to larger BER of the received signal. Therefore, different frequency intervals or turbulence intensities will  
Figure 8: The spectral distribution of the 32-channel OAM hybrid multiplexing communication system. The beam is divided into four different frequency ranges after FDM. The intervals between the four frequencies were 0.1 THz, 0.3 THz, and 0.5 THz, respectively. affect the BER of received signal even in the same OAM multiplexing link. When the OAM-POL-FDM hybrid multiplexing system is used in the atmospheric turbulence channel, the influence of spectrum efficiency, frequency interval, and turbulence intensity on the hybrid communication system should be considered comprehensively. In order to ensure that the OAM-multiplexed signal can be successfully de-multiplexed, the phase of the vortex beam in the receiver must be completely distinguished. Therefore, the transmission distance cannot exceed the limit of the transmission distance to ensure that the phase can be distinguished under the corresponding turbulence intensity.