A multiple-input single-output cognitive radio downlink network is studied with simultaneous wireless information and power transfer. In this network, a secondary user coexists with multiple primary users and multiple energy harvesting receivers. In order to guarantee secure communication and energy harvesting, the problem of robust secure artificial noise-aided beamforming and power splitting design is investigated under imperfect channel state information (CSI). Specifically, the transmit power minimization problem and the max-min fairness energy harvesting problem are formulated for both the bounded CSI error model and the probabilistic CSI error model. These problems are non-convex and challenging to solve.A one-dimensional search algorithm is proposed to solve these problems based on S-Procedure under the bounded CSI error model and based on Bernstein-type inequalities under the probabilistic CSI error model. It is shown that the optimal robust secure beamforming can be achieved under the bounded CSI error model, whereas a suboptimal beamforming solution can be obtained under the probabilistic CSI error model. A tradeoff is elucidated between the secrecy rate of the secondary user receiver and the energy harvested by the energy harvesting receivers under a max-min fairness criterion. USA (e-mail: lee880716@gmail.com).The research was supported by the Natural Science Foundation of China (61301179, 61501356, 61501354 and 61401338) and a scholarship from China Scholarship Council.
Index TermsCognitive radio, physical-layer secrecy, robust beamforming, wireless information and power transfer.
This work deals with Feigenbaum's functional equationwhere p ≥ 2 is an integer, g p is the p-fold iteration of g, and h is a strictly monotone odd continuous function on [−1, 1] with h(0) = 0 and |h(x)| < |x| (x ∈ [−1, 1], x = 0). Using a constructive method, we discuss the existence of continuous unimodal even solutions of the above equation.
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