Secrecy rate maximization for MISO multicasting SWIPT system with power splitting scheme

This paper considers transmit covariance matrix design for secrecy rate maximization problem in a multiple-input single-output (MISO) multicasting simultaneous wireless information and power transfer (SWIPT) system. In order to enhance the performance of the system, artificial noise (AN) is added to the transmit signal in the design for the following purposes: to reduce the received signal-to-noise ratio (SNR) at the eavesdroppers and increase the harvested energy. We assume that all the channel-state-information (CSI) is perfectly known at the transmitter and all legitimate users are capable of simultaneously receiving information and harvesting energy. In addition, all the eavesdroppers are passive and they can harvest energy only when they are not intercepting or eavesdropping the messages intended for the legitimate users. The original secrecy rate maximization problem is not convex in terms of transmit and artificial covariance matrices as well as the power splitting (PS) ratio. In order to circumvent this non-convexity issue, we exploit the Charnes-Cooper Transformation and semidefinite relaxation (SDR) to convert this original problem into a convex one. However, this convex problem does not always yield the rank-one transmit and AN covariance matrices to obtain the solution of the original problem. Therefore, we analyze the optimal conditions and utilize a Gaussian randomization (GR) method to construct the rank-one solutions from the non-rank one results. Simulation results have been provided to demonstrate the performance of the proposed transmit covariance matrices design for MISO multicasting SWIPT system.