  This paper investigates a secure wireless-powered multiantenna multicasting
system, where multiple power beacons (PBs) supply power to a transmitter in
order to establish a reliable communication link with multiple legitimate users
in the presence of multiple eavesdroppers. The transmitter has to harvest radio
frequency (RF) energy from multiple PBs due to the shortage of embedded power
supply before establishing its secure communication. We consider two different
scenarios. In the first, the PBs and the transmitter belong to the same
operator, where we formulate the resource allocation problem as the
minimization of the total transmit power subject to the target secure rate
constraint. The solution of this problem yields both the optimal power and
energy transfer time allocation. Due to the non-convexity of this problem, we
propose a two-level approach, where the inner level problem can be recast as a
convex optimization framework via conic convex reformulation, while the outer
level problem can be handled by using one-dimensional (1D) search. The second
scenario considers the case where the transmitter and the PBs belong to
different service suppliers. Hence, we formulate the resource allocation
problem where we consider incentives for the PBs to assist the transmitter.
This leads to the formulation of a Stackelberg game for the secure
wireless-powered multiantenna multicasting system. The transmitter has to pay
for the energy services from these multiple PBs in order to facilitate secure
communications. In this game, the transmitter and the PB are modelled as leader
and follower, respectively, in which both of them try to maximize their own
utility function. The closed-form Stackelberg equilibrium of the formulated
game is then derived. Finally, numerical results are provided to validate our
proposed schemes.
