In this paper, we propose beamforming schemes to simultaneously transmit data securely to multiple information receivers (IRs) while transferring power wirelessly to multiple energy-harvesting receivers (ERs). Taking into account the imperfection of the instantaneous channel state information (CSI), we introduce a chance-constrained optimization problem to minimize the total transmit power while guaranteeing data transmission reliability, data transmission security, and power transfer reliability. As the proposed optimization problem is non-convex due to the chance constraints, we propose two robust reformulations of the original problem based on safe-convex-approximation techniques. Subsequently, applying semidefinite programming relaxation (SDR), the derived robust reformulations can be effectively solved by standard convex optimization packages. We show that the adopted SDR is tight and thus the globally optimal solutions of the reformulated problems can be recovered. Simulation results confirm the superiority of the proposed methods in guaranteeing transmission security compared to a baseline scheme. Furthermore, the performance of proposed methods can closely follow that of a benchmark scheme where perfect CSI is available for resource allocation.
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