On The Ergodic Secrecy Capacity And Secrecy Outage Probability Of The Mimome Rayleigh Wiretap Channel

In this paper, we study the multiple-input multiple-output multiple-eavesdropper wiretap channel in the nonergodic and ergodic scenarios, both with stationary Rayleigh distributed fading channels. For the ergodic scenario, we derive a new closed-form expression for the ergodic secrecy capacity with full channel state information at the transmitter (CSIT) of the main and the eavesdropper channels, allowing the covariance matrix to be time-varying. A lower bound for the ergodic capacity with full CSIT, in which the covariance matrix is fixed for the entire transmission period is also derived. The first expression is restricted to the high signal-to-nose ratio (SNR) limit, with n(t) transmit antennas, n(r) receive antennas (nrnt) and n(e)=n(t) eavesdropper antennas (n(t)xn(r)xn(t) setup). The second expression is restricted to the n(t)xn(t)xn(t) antenna setup. For the nonergodic scenario, we derive a new closed-form expression for the secrecy outage probability in the high SNR limit, in a 2 x n(r)x2 setup with nr2. We are also able to calculate an upper bound for the secrecy outage probability in other antenna setups. Copyright (c) 2015 John Wiley & Sons, Ltd.28