## 3 Simulation and Analysis  
In this section, first, we compared the transmission characteristics of electromagnetic vortex wave, which carry the single-mode and the multi-mode of OAM through an ideal channel and a turbulent channel, respectively. Then, the adaptive compensation technology was used to correct the turbulence influence exerted on the electromagnetic wave. Furthermore, we compared the transmission characteristics before and after adding the adaptive compensation. Last but not least, the results of signal-to-crosstalk ratio were given, and after adding adaptive compensation, the trend of communication capacity changing with the number of transmission modes was shown. For simulation analysis, the work was modeled on the Laguerre-Gaussian beam with the wavelength of Ku band sets of 2 cm. We used the example of the Laguerre-Gaussian beam for carrying the OAM mode of \(p=0\), \(l=5\). The received mode intensity and phase distribution of electromagnetic vortex waves are shown in Figure 1. It can be seen from the three-dimensional diagram of the intensity distribution that the strength ring of OAM mode with the same topological charge gradually diffuses in the ideal channel as the transmission distance increases. The phase distribution spirals with the change in transmission distance. At the center of the beam, the intensity is zero and the phase singularity occurs. Due to the atmospheric turbulence in the space communication channel, the spiral wavefront structure of OAM mode was easily distorted by it, which limited the performance of the free space  
Figure 1: Intensity and phase distribution of electromagnetic vortex waves with transmission distance (a) 1 km, (b) 5 km, and (c) 10 km through ideal conditions. communication system based on the OAM mode. Therefore, we needed to consider the effect of atmospheric turbulence on electromagnetic vortex waves in free space communication channels. [PERSON] was the first to propose a phase screen generation method based on Fourier transform [22]. We can express the changing phase caused by atmospheric turbulence in terms of a Fourier integral. Figure 2 displays the strength of the weak-to-strong atmospheric turbulence by using a series of random phase screens. Some major parameters are as follows: The large-scale \(l_{x}=10\) m, the small-scale \(l_{y}=0.01\) m, the length of one side of square phase screen is 0.2 m, and the number of grid points per side is 256. In the simulation process, we used the joint atmospheric turbulence model that corresponded to actual channel conditions. Electromagnetic vortex wave propagation in the atmosphere channels is affected by a variety of linear and nonlinear effects. The OAM mode is a spatial mode distribution, so the intensity and phase distortion of its wavefront are inevitably affected by atmospheric turbulence. Atmospheric turbulence causes a random fluctuation of the refractive index and distortions of the propagating beam wavefront. Figure 3 shows the intensity and phase distribution of electromagnetic vortex waves with transmission distances of 1 km, 5 km and 10 km under the conditions of moderate-to-strong turbulence. In a single channel transmission, using a single OAM mode, the circular intensity distribution of single mode vortex beam is distorted, and the intensity distribution in the ring is no longer uniform with the increasing propagation distance. The variance of phase distribution is increasingly untidy. Compared to the ideal channel transmission, burr defect appears on the surface of the intensity of electromagnetic vortex waves. The phase perturbation of the single mode vortex beam is gradually distorted, and the isophase lines are distorted by turbulence. The intensity of electromagnetic vortex waves has a weakening trend, and the diameter of the intensity ring gradually diffuses with the increase in propagation distance. The phase diverges outward as the transmission distance increases.