Secrecy Performance Analysis for MIMO-DF Relay Systems With MRT/MRC and TZF/MRC Schemes

Transmit beamforming is a diversity technique in multiple-input multiple-output (MIMO) systems. It improves the diversity order and enhances the information security of the MIMO systems. In this paper, we mathematically analyze the secure performance of a MIMO decode-and-forward (DF) relay system under the presence of an eavesdropper and with the imperfect channel state information (CSI) of the eavesdropping channel. To enhance the secrecy performance, we employ multiple antennas at all legitimate nodes and utilize two linear beamforming schemes, i.e., maximal ratio transmission (MRT) and transmission zero-forcing (TZF), at the transmitter and maximal ratio combining (MRC) scheme at the receiver. The probability density function (PDF) of the output SNR for different numbers of antennas at the transmitter and receiver is plotted and discussed. After that, we apply this PDF to derive the closed-form expressions of the secrecy outage probability (SOP) and ergodic secrecy capacity (ESC) of the considered MIMO-DF relay system over Rayleigh fading channels for MRT/MRC and TZF/MRC schemes. In addition, based on the obtained analysis results, we provide the location of the relay that minimizes the system SOPs. All the analysis results are validated by Monte-Carlo simulations. The results show that the TZF/MRC scheme provides better SOP and ESC than the MRT/MRC scheme. Moreover, the number of antennas at the legitimate nodes and the location of the eavesdropper significantly impact the secrecy performance.