Low-orbit quantum satellites are part of building a global secure communication network. However, as single quantum satellites move fast relative to ground terminals with limited service time and the satellite-ground quantum link is susceptible to atmospheric conditions (e.g. rain, snow, haze, etc.), ground end-users need to switch to other satellites available for service in time to meet the sustainable communication demands. In the common coverage area, if the user only chooses the currently proposed single-attribute decision strategy, such as the minimum communication elevation angle, the optimal entanglement degree or the minimum link attenuation, the optimal single attribute can be achieved with losing the advantage of other attributes. This will easily result in load imbalance and uneven resource allocation of quantum satellites, and even communications may be interrupted in serious cases. To this end, we consider the attenuation interference of snowfall on the satellite-ground link and the process of end-user-associated switching of quantum satellites, and build a multi-attribute evolutionary game switching model to achieve Nash equilibrium in the allocation of quantum satellite resources. Meanwhile, satellite resource allocation can be maximized to enhance the switching success rate of users in the low earth orbit (LEO) quantum satellite communication network.

Evolutionary game theory combines biological evolutionary properties with game theory to make the system stable through constant comparison and imitation in multiple choices. In actual quantum satellite switching, the users switching satellites at the same time do not know each other's state information in a completely rational way, which satisfies the non-rational conditions of evolutionary games. We analyze the quantum channel attenuation characteristics under snowfall and atmospheric turbulence according to the Gamma spectral distribution function of snow and obtain the variation of channel attenuation with transmission distance. The bandwidth that can be allocated to users by the quantum satellite corresponds to the current satellite load state, which means that more users result in fewer quantum satellite bandwidth resources available to each user. The longer remaining service time of the quantum satellite indicates that the selection of this strategy prolongs the service cycle of the user and reduces the user switching number. The communication elevation angle reflects the channel condition of the satellite-ground link, and the larger communication elevation angle leads to shorter communication distance, lower link attenuation, and better channel conditions. As the elevation angle is difficult to measure in real time with the terrain environment obstruction, the measured elevation angle cannot reflect the channel conditions, and thus the communication elevation angle is converted into the link attenuation characteristics which can directly represent the channel conditions. Therefore, we define a utility function based on the user's bandwidth, remaining satellite service time, and link attenuation, and define an overhead function based on the inter-satellite transmission delay and channel entanglement to obtain the user's payoff function. Finally, we derive the dynamic replication equation of the satellite to build an evolutionary game switching model.

Firstly, the effect of snowfall on the satellite-ground link attenuation is analyzed. Under certain snowfall intensity, the total attenuation suffered by the link increases as the light quantum propagation distance rises. In the case of a certain propagation distance of the light quantum signal, as the snowfall intensity increases, the total communication link attenuation grows due to the scattering and absorption effect between the light quantum signal and snow particles in the atmosphere. It results in the subsequent increase in the total communication link attenuation, and the atmospheric snowfall environment will exert a significant influence on quantum satellite communications (Fig. 1). The number of users to be switched simultaneously is 1000 and the number of available strategies is 2. In the six switching experiments, the number of users selected for Quantum LEO1 varies with the iteration number (Fig. 3), and the number of users plateaus with the increasing iteration number, which demonstrates that the proposed quantum satellite multi-user switching strategy has sound convergence stability. As the game proceeds, the gains gradually converge to the average gain of all users and reach equilibrium by the sixth iteration. Then the users revenue do not increase and stabilize to ensure the multi-user fairness during the quantum satellite switching (Fig. 4). The single-attribute judgment switching method converges faster than the multi-attribute switching decision, and the number of users connected to Quantum LEO1 increases when equilibrium is finally reached, but this is at the expense of the other attributes (Fig. 5). Experimental results show that the switching strategy based on the evolutionary game improves the switching success rate by 1.2% over the switching strategy based on the lowest link attenuation (Fig. 6) under the switching user number of 660. When the minimum entanglement threshold is set to 0.8, the switching success rate of the evolutionary game-based switching strategy improves by 1.5% over the switching strategy based on the optimal entanglement (Fig. 7) under the switching user number of 700.

An evolutionary game-based quantum satellite switching strategy is proposed for the multi-user switching scenario of quantum satellites under a snowfall environment. Various attributes affecting the quantum satellite switching decision are analyzed and combined with the attenuation characteristics between quantum star-ground links to obtain the effect function, the overhead function, and then the average gain function of users. An evolutionary game model is built by considering the transmission among users and between users and quantum satellites, and the performance of the switching strategy using this model is simulated. The results show that the proposed strategy not only has sound stability with the influence among multiple attributes considered but also can make the quantum satellite load relatively balanced. Finally, compared with the single-attribute quantum satellite switching strategy based on minimum link attenuation and optimal entanglement, the proposed strategy can also improve the success rate of user switching more effectively, providing references for future multi-user dynamic switching design of low-orbit quantum satellite networks under snowfall interference environment.