###### Abstract  
Atmospheric turbulence has an impact on the transmission of electromagnetic vortex waves with an orbital angular momentum (OAM) mode. In this paper, based on the joint atmospheric turbulence model, we examine the influence of atmospheric turbulence on the transmission of electromagnetic vortex waves. First, a mathematical model is established to formulate the transmission characteristics of electromagnetic vortex waves under joint atmospheric turbulence. Subsequently, in order to mitigate the influence of the atmospheric turbulence on the electromagnetic vortex waves, an adaptive compensation on phase is proposed. Finally, we analyzed the transmission performance of an OAM-mode multiplexing system using an adaptive compensation method through the wireless communication channel. By means of numerical simulation, the effect of atmospheric turbulence on the transmission characteristics and mode crosstalk of OAM is analyzed. The simulation results show that electromagnetic vortex waves could perform well on the wireless communication system with a low mode crosstalk, which provides the theoretical support to optimizing the mode division multiplexing technology in a free space communication system. electromagnetic vortex wave; orbital angular momentum; wireless communication; adaptive compensation 2019 9 901 000 0000 0000 0000 0000 00000 0000 00000 00000 00000 00000 00000 00000 000000 000000 000000 0000000 0000000 0000000 00000  
OAM modes at the same frequency, and each OAM mode is orthogonal to each other. Therefore, the application of electromagnetic vortex wave in free-space communication has the unique advantages of high-spectrum utilization and anti-interference. On the basis of OAM-mode multiplexing, a new dimension could be used by the orthogonality of the OAM mode as the basis of multichannel multiplexing [4; 5; 6]. However, it is important to consider how to realize multiplexing of a multi-vortex beam, a change of OAM mode after transmission through a turbulent channel, and the mode crosstalk problem caused by multiplexing among various beams [7]. Research on and application of the vortex beams have recently generated great research interest, which has resulted in a new branch of vortex beams in wireless communication systems. In 1992, [PERSON] and [PERSON] found that the Laguerre-Gaussian beam could carry an OAM mode [8], and the application of vortex beams in communication has attracted much attention. In 2004, [PERSON] et al. successfully demonstrated the free space optical (FSO) communication based on OAM sending and receiving data [9]. Later, [PERSON] et al. [10] experimentally produced this beam with a computer-generated hologram (CGH) displayed on a spatial light modulator. Subsequently, [PERSON] et al. used multiple phase screen simulation technology for studying the topology of vortex beam propagation in atmospheric turbulence, pointing out that a vortex beam carrying the OAM mode through atmospheric turbulence has greater robustness [11]. [PERSON] et al. found that a spectrum efficiency can be achieved of 25.6 (bit/s)/Hz with OAM multiplexing. [PERSON] and [PERSON] found the pure vortex beam carrying OAM transmissions through free space communication systems, by the propagation in the receiving port and the function between the difference intensity of atmospheric turbulence [12]. [PERSON] et al. discussed the expansion of the spiral spectrum of the Laguerre-Gaussian beam in the non-Kolmogorov turbulence [13]. Further, [PERSON] proposed that the divergence of the OAM mode was related to the beam waist type [14]. In 2016, [PERSON] studied the damage to the radial distribution of the Laguerre-Gaussian beam carrying OAM mode with weak-to-strong atmospheric turbulence [15]. The results show that the turbulence induces signal fading, and crosstalk deterioration even leads to link interruption. Therefore, it is necessary to develop a method to compensate the effects of atmospheric turbulence on spatial communication channels.