Secrecy analysis for forward link multi-user massive MIMO system with MRT precoding

The secrecy performance of forward link multi-user massive multiple-input multiple-output (MIMO) system is investigated in this paper. The base station (BS) equipped with a large number of transmit antennas sends mutually independent datas to multiple single-antenna legitimate users simultaneously. A passive multi-antenna eavesdropper is placed in the scenario to intercept the signals. We consider the case that the number of legitimate users and eavesdropper antennas increases proportionally with the number of BS antennas. Maximum ratio transmission (MRT) is used as linear precoder at the BS. Lower bounds on the ergodic achievable rate of legitimate users and upper bounds of the eavesdropper are derived. By minimizing the upper bounds on the achievable rates of the eavesdropper while satisfying the rate constraints of legitimate users, we present the corresponding optimal radiated power scaling (RPS) factor. In the limit of an infinite number of BS antennas, we prove that the optimal RPS factor converge to a different constant limit with that of the case in which the number of legitimate users and eavesdropper antennas is finite. We show that when the number of BS antennas grows large, the secrecy performance is mainly determined by the ratios between the number of BS antennas, legitimate users and eavesdropper antennas. A number of simulation results are presented to visualize the analysis.