Eavesdropping Behavior Detection Algorithm Based On Large Dimensional Theory In Massive MIMO Systems

Massive MIMO systems are one of the indispensable technologies in the future 5G mobile network,from single-antenna MIMO,multi-antenna MIMO to the current massive MIMO.Massive MIMO technology has greatly increased the spatial multiplexing capability of mobile networks by using many receiving and transmitting antennas,and has achieved high spectrum efficiency and energy efficiency.However,massive MIMO technology has some security risks due to the openness of wireless networks,such as user signal eavesdropping and information leakage.This paper aims to study algorithms that can detect active eavesdropping behaviors in massive MIMO systems.This paper mainly studies the methods of detecting eavesdropping in two different situations.When the number of legitimate users is large,we use the Silverstein equation to find the theoretical endpoint value of the sample covariance matrix's eigenvalue and calculate the rejection domain of the hypothesis test by setting the test statistic.Thus,we would know whether there is eavesdropping.When the number of legitimate users is small,that is,the covariance matrix is a Spiked matrix model,this paper proposes two methods based on the improved matrix theory of MDL and noise M-P law to estimate the number of sources.We compare the number of non-noises sources with the number of legitimate user signals in null hypothesis to determine whether there is active eavesdropping.In the simulation experiments,it is found that when the signal-to-noise ratio is good,the improved MDL method has better detection performance even if the sample size is small,and the M-P law method should have better detection performance only when the sample size is large.When the ratio of sample size to dimension is good,the improved MDL method and the M-P method have better detection performance as long as the signal-to-noise ratio has a certain value.When the signal-to-noise ratio is small,the two methods are not ideal and the signal-to-noise ratio condition required by the M-P law is lower than that required by the MDL.