# Effects of Atmospheric Turbulence on OAM-POL-FDM Hybrid Multiplexing Communication System
## 1 Introduction  
The requirement of communication links with high data capacity is propelled by the exponential increase of data traffic [1]. Different multi-level modulation formats such as m-ary quadrature amplitude modulation (m-QAM) and multiplexing techniques (e.g., wavelength division multiplexing (WDM), time-division multiplexing (TDM), polarization division multiplexing (PDM), and OAM multiplexing) have been used to improve transmission capacity and spectral efficiency [2; 3; 4; 5; 6]. In addition, many multi-channel communication systems based on hybrid multiplexing have been proposed [1], such as the OAM-POL hybrid multiplexing system and the 26-OAM mode multiplexing system proposed by [PERSON] [7; 8]. It has been proven that hybrid multiplexing can increase the transmission rate of communication systems [9]. Based on this, we propose a 32-channel-hybrid-multiplexing system that consists of OAM, polarization, and frequency division multiplexing (FDM) hybrid multiplexing [10; 11]. Compared with the above-mentioned OAM-POL multiplexing, the system adds a dimension (i.e., FDM), which enables the system to be well integrated with existing communication networks and achieves larger data capacity.  
Introducing the hybrid multiplexing system into the atmospheric turbulence channel and discussing the influence of turbulence on it will provide new ideas for improving the performance of free-space optical (FSO) communication systems. As a result, hybrid multiplexing has now become a focus in current FSO communication research [12; 13; 14; 15; 16]. In this paper, we used a hybrid multiplexingsystem that combines different multiplexing methods to transmit information in the atmospheric turbulence channel and studied the effects of atmospheric turbulence on the system [17; 18; 19]. Compared with the communication system in atmospheric turbulence that adopts the sole modulation method, the interaction between multiple multiplexing methods is considered in this study, which is derived from the superposition of different effects. Therefore, it is closer to the practical transmission environment and more practical in real scenarios. We simulated the propagation of an OAM beam under the influence of atmospheric turbulence by MATLAB and Optisystem. The influence of different atmospheric turbulence intensities for the hybrid multiplexed system were compared from phase, spectrum, OAM crosstalk, and BER. Consequently, the research conclusions can guide the realization of a hybrid multiplexed system under turbulence to a certain extent.  
The content of the article is arranged as follows. In Section 2, we introduce the expressions of atmospheric turbulence and vortex beam transmission [20] as well as the schematic diagram of the 32-channel OAM-POL-FDM multiplexing system [8]. Next, in Section 3, we introduce the effects of different atmospheric turbulence intensities on the phase, spectrum, OAM crosstalk, and BER of OAM-POL-FDM hybrid multiplexing systems. Finally, the influences of different turbulence intensities on the system are discussed in Section 4. For example, in the state of strong turbulence (\({\rm C_{n}}^{2}=10^{-14}\)\({\rm m^{-2/3}}\)), 46.8% of the energy leaks to the neighbor OAM mode and becomes noise when multiple topological states are transmitted simultaneously.