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.