Active Eavesdropper Detection Based On Large Dimension Random Matrix Theory For Massive MIMO Systems

Massive multiple-input multiple-output(massive MIMO)is considered as the key technology of the physical layer specification of the fifth generation mobile network(5G).Due to the openness of the wireless communication environment,communication based on massive MIMO technology has some information security risks.Active eavesdropper can interfere with channel estimation results of the massive MIMO systems by contaminating the pilot signals transmitted in the uplink.In turn,the uplink signal transmitted by the legitimate user and the downlink beamforming of the base station are affected.This not only affects the quality of communication,but more seriously,will jeopardize the security of information transmission.To address these issues,this paper proposes two algorithms for the active eavesdropper detection.The two methods are applicable to the scenario where the number of samples is larger or smaller than the number of base station antennas,respectively.For the scenarios where the number of samples is larger than the number of base station antennas,this paper proposes an active eavesdropper detection algorithm based on large-dimensional random matrix theory.The algorithm is based on signal subspace and random sequences.Rand sequences transmitted by the user can create random signature that cannot be forged by eavesdropper.When the number of base station antennas and samples tend to be large,the eigenvalue distribution of the sample covariance matrix of random sequence received by the base station converges to the limit spectrum distribution which can be characterized by the matrix dimensions.In this paper,based on the large-dimensional random matrix theory,the limit distribution of the eigenvalues of legitimate user signals is derived,which is used to determine the distribution range of the eigenvalues of legitimate user's signal.This paper proposes to employ the large-dimensional random matrix theory,to determine whether there exists active eavesdropping in the system through hypothesis testing.At the same time,the Marcenko-Pastur law of the large-dimensional random matrix theory is used to remove the noise component from the received signal.Monte Carlo simulation results show that the proposed algorithm has stable detection performance with respective to different sample numbers,base station antennas and signal power levels.The propose method significantly outperforms the existing MDL&ERD.For the scenarios where the number of samples is smaller than the number of base station antennas,this paper proposes an active eavesdropper detection algorithm combining large-dimensional random matrix theory and linear shrinkage method.The traditional method of using information theoretic approach to detect active eavesdropper is not applicable to the case where the number of samples is smaller than the number of base station antennas.The method proposed in this paper combines the linear shrinkage method with the subspace method.It can detect active eavesdropper effectively in a small sample scenario,without significant increase of additional computational overhead.This paper proposes to use the large dimensional random matrix theory to estimate the noise variance.With the assistance of accurate noise estimation and linear shrinkage method,the proposed method can improve the detection performance under small samples.After linearly shrinked its eigenvalues,the sample covariance matrix can better fit the population matrix.The linearly shrinkaged sample eigenvalues are used in the subspace method for detection,which makes it possible to accurately detect the existence of active eavesdropper in the small sample scenarios.Monte Carlo simulation results show that the combination of large-dimensional random matrix theory and linear shrinkage detection algorithm is effectively with respect to different base station antenna numbers and signal power levels.