A Safe Approximation Approach to Secrecy Outage Design for MIMO Wiretap Channels

Consider a multi-input multi-output (MIMO) channel wiretapped by multiple multi-antenna eavesdroppers. Assuming imperfect eavesdroppers´ channel state information (CSI) at the transmitter, an outage-constrained secrecy rate maximization (OC-SRM) problem is considered. Specifically, we aim to design the transmit covariance matrix such that the outage secrecy rate is maximized for a given outage probability. The OC-SRM problem is challenging, and as a compromise, we resort to a recently developed Bernstein-type inequality approach to obtain a safe (conservative) approximate solution for OC-SRM. The merit of the proposed safe design lies in its tractability. In particular, a safe solution can be efficiently computed by alternately solving two convex conic optimization problems. The efficacy of the proposed design is demonstrated by simulations.