Robust Optimization with Probabilistic Constraints for Power-Efficient and Secure SWIPT

In this paper, we propose beamforming schemes to simultaneously transmit data to multiple information receivers (IRs) while transfering power wirelessly to multiple energy-harvesting receivers (ERs). Taking into account the imperfection of the instantaneous channel state information, we introduce a probabilistic-constrained optimization problem to minimize the total transmit power while guaranteeing data transmission reliability, secure data transmission, and power transfer reliability. As the proposed optimization problem is non-convex and has an infinite number of constraints, we propose two robust reformulations of the original problem adopting safe-convex-approximation techniques. The derived robust formulations are in semidefinite programming forms, hence, they can be effectively solved by standard convex optimization packages. Simulation results confirm the superiority of the proposed approaches to a baseline scheme in guaranteeing transmission security.