  In this paper, we study resource allocation for multiuser multiple-input
single-output secondary communication systems with multiple system design
objectives. We consider cognitive radio networks where the secondary receivers
are able to harvest energy from the radio frequency when they are idle. The
secondary system provides simultaneous wireless power and secure information
transfer to the secondary receivers. We propose a multi-objective optimization
framework for the design of a Pareto optimal resource allocation algorithm
based on the weighted Tchebycheff approach. In particular, the algorithm design
incorporates three important system objectives: total transmit power
minimization, energy harvesting efficiency maximization, and interference power
leakage-to-transmit power ratio minimization. The proposed framework takes into
account a quality of service requirement regarding communication secrecy in the
secondary system and the imperfection of the channel state information of
potential eavesdroppers (idle secondary receivers and primary receivers) at the
secondary transmitter. The adopted multi-objective optimization problem is
non-convex and is recast as a convex optimization problem via semidefinite
programming (SDP) relaxation. It is shown that the global optimal solution of
the original problem can be constructed by exploiting both the primal and the
dual optimal solutions of the SDP relaxed problem. Besides, two suboptimal
resource allocation schemes for the case when the solution of the dual problem
is unavailable for constructing the optimal solution are proposed. Numerical
results not only demonstrate the close-to-optimal performance of the proposed
suboptimal schemes, but also unveil an interesting trade-off between the
considered conflicting system design objectives.
