Outage-Constrained Secrecy Energy Efficiency Optimization for CRNs With Non-Linear Energy Harvesting

In this paper, we investigate a robust transmit design in underlay energy harvesting (EH) cognitive radio networks (CRNs), where the malicious energy receivers (ERs) can be treated as potential eavesdroppers (Eves) due to their ability of wiretapping the desired information. Considering a general case of statistical Eves' channel state information (CSI), to transmit signals in a secret and energy-efficient manner, an outage-constrained secrecy energy efficiency (OC-SEE) optimization problem is formulated to design transmit beamforming vectors. The original problem is non-convex and challenging to solve. To make it more tractable, we first rewrite this problem by semi-definite relaxation (SDR), and Bernstein-type inequality (BTI) approach is resorted to conservatively approximate the probabilistic constraints. Then, based on the fractional programming theory, an equivalent parametric reformulation is proposed to convert the original problem into a subtractive form. Furthermore, by introducing auxiliary variables, with the aid of Sphere Bounding method, the tractable solution of this OC-SEE maximization problem can be obtained through solving a two-stage optimization problem. Finally, numerical results are provided to validate the efficacy of the proposed design.