  In this paper, we study power allocation for secure communication in a
multiuser multiple-input single-output (MISO) downlink system with simultaneous
wireless information and power transfer. The receivers are able to harvest
energy from the radio frequency when they are idle. We propose a
multi-objective optimization problem for power allocation algorithm design
which incorporates two conflicting system objectives: total transmit power
minimization and energy harvesting efficiency maximization. The proposed
problem formulation takes into account a quality of service (QoS) requirement
for the system secrecy capacity. Our designs advocate the dual use of
artificial noise in providing secure communication and facilitating efficient
energy harvesting. The multi-objective optimization problem is non-convex and
is solved by a semidefinite programming (SDP) relaxation approach which results
in an approximate of solution.
  A sufficient condition for the global optimal solution is revealed and the
accuracy of the approximation is examined. To strike a balance between
computational complexity and system performance, we propose two suboptimal
power allocation schemes. Numerical results not only demonstrate the excellent
performance of the proposed suboptimal schemes compared to baseline schemes,
but also unveil an interesting trade-off between energy harvesting efficiency
and total transmit power.
