Safe convex approximation to outage-based MISO secrecy rate optimization under imperfect CSI and with artificial noise

Consider a scenario in which an MISO channel is overheard by multiple single-antenna eavesdroppers. The transmitter has perfect channel state information (CSI) with the legitimate channel, but has imperfect CSI with the eavesdroppers' channels. The CSI uncertainties are assumed stochastic. We formulate an artificial-noise (AN)-aided secrecy-rate maximization problem where the CSI uncertainties are handled using an outage-based formulation. Our aim is to find, for this problem, tractable designs for the transmit and AN covariances. Unfortunately, outage-based optimization problems are generally difficult to solve. The main contribution here is to derive a safe, convex optimization-based, approximation to the considered problem. The advantages of the method are shown by simulations.