  In this paper, we design a robust resource allocation algorithm for a
wireless-powered communication network (WPCN) taking into account residual
hardware impairments (HWIs) at the transceivers, the imperfectness of the
channel state information, and the non-linearity of practical radio frequency
energy harvesting circuits. In order to ensure power-efficient secure
communication, physical layer security techniques are exploited to deliberately
degrade the channel quality of a multiple-antenna eavesdropper. The resource
allocation algorithm design is formulated as a non-convex optimization problem
for minimization of the total consumed power in the network, while guaranteeing
the quality of service of the information receivers in terms of secrecy rate.
The globally optimal solution of the optimization problem is obtained via a
two-dimensional search and semidefinite programming relaxation. To strike a
balance between computational complexity and system performance, a
low-complexity iterative suboptimal resource allocation algorithm is then
proposed.
  Numerical results demonstrate that both the proposed optimal and suboptimal
schemes can significantly reduce the total system power consumption required
for guaranteeing secure communication, and unveil the impact of HWIs on the
system performance: (1) residual HWIs create a system performance bottleneck in
the high transmit/receive power regimes; (2) increasing the number of transmit
antennas can effectively reduce the system power consumption and alleviate the
performance degradation due to residual HWIs; (3) imperfect CSI increases the
system power consumption and exacerbates the impact of residual HWIs.
