Joint pilot design and beamforming optimization in massive MIMO surveillance systems

This paper proposes a novel joint channel estimation and beamforming scheme for the massive multiple-input-multiple-output (MIMO) frequency-division duplexing (FDD) wireless legitimate surveillance system. With the proposed scheme, the monitor with the full duplex capability realizes the proactive eavesdropping of the suspicious link by leveraging the pilot attack approach. Specifically, exploiting the effective eavesdropping rate and the mean square error as performance metrics and setting a total power budget at the training and transmission phases, while guaranteeing the information from suspicious source can be successfully decode, joint pilot design, power allocation and beamforming strategy are formulated as optimization problems for the two objective functions: MSE and effective eavesdropping rate. A closed-form expression of the optimal pilot with the limited length can be obtained via the channel correlation. The optimal power problem at the training phase can be solved by a simple bisection method. Then, based on the obtained imperfect estimated channel, the jamming beamforming at monitor optimization algorithm is proposed by utilizing the convex Semidefinite Programming approach to maximize the effective eavesdropping rate. Numerical results show that the proposed joint pilot design, power allocation and beamforming optimization scheme can improve the surveillance performance of the legitimate monitor as compared to the existing passive eavesdropping and jamming-assisted eavesdropping.