  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 ${\cal S}\text{-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.
