Physical layer security of multiple-input-multiple-output systems with transmit beamforming in Rayleigh fading

This study analyses the physical layer security in the wiretap channel for multiple-input-multiple-output transmit-beamforming (TB) systems with maximal ratio combining (MRC) receivers. The TB is designed to maximise the signal-to-noise ratio (SNR) at the main receiver output. The authors assume that both legitimate and eavesdropper receivers have the knowledge of their own channel state information (CSI). Furthermore, they consider that the transmitter has the full CSI of the main channel and does not have the CSI of the eavesdropper's channel. At the eavesdropper, two combining methods are considered: (i) MRC technique and (ii) selection combining method. They derive closed-form expressions for the exact secrecy outage probability (SOP) and the probability of strictly positive secrecy capacity. Expressions of the asymptotic SOP and the asymptotic epsilon-outage secrecy capacity are also derived. The secrecy diversity order and the secrecy SNR gain are then obtained.