Secrecy Outage Design in MIMO-SWIPT Systems Based on a Non-Linear EH Model

This paper consider a multiple-input multiple- output (MIMO) downlink system with simultaneous wireless information and power transfer (SWIPT). In this system, we provide secure communication by considering all non-linear energy receivers (ERs) as the potential eavesdroppers. We aim to design an optimal covariance matrix of the transmit signal based on the proposed outage-constrained secrecy rate maximization (OC-SRM) problem, where the proposed system keeps the probability of the secrecy rate outage and the harvested energy outage caused by uncertainties regarding the channel state information (CSI) below the given thresholds. The proposed maximization problem is non-convex and unlikely to be efficiently computable. To surmount the non-convexity of the proposed OC-SRM problem, we resort several transformations and approximations. In the partial channel uncertainty (PCU) model, we introduce auxiliary variables to transfer the Shannon capacity expressions into easy handled forms based on the concept of Fenchel conjugate arguments. As a compromise, we employ three safe approximation approaches to find the upper bounds of the probabilistic constraints. Moveover, an alternating optimization (AO) algorithm is proposed to solve the reformulated problem. The performance of the proposed design is efficiently validated by numerical results in our paper.