  In this paper, we study the resource allocation algorithm design for
energy-efficient simultaneous wireless information and power transfer (SWIPT)
systems. The considered system comprises a transmitter, an information
receiver, and multiple energy harvesting receivers equipped with multiple
antennas. We propose a multi-objective optimization framework to study the
trade-off between the maximization of the energy efficiency of information
transmission and the maximization of wireless power transfer efficiency. The
proposed problem formulation takes into account the per antenna circuit power
consumption of the transmitter and the imperfect channel state information of
the energy harvesting receivers. The adopted non-convex multi-objective
optimization problem is transformed into an equivalent rank-constrained
semidefinite program (SDP) and optimally solved by SDP relaxation. Numerical
results unveil an interesting trade-off between the considered conflicting
system design objectives and reveal the benefits of multiple transmit antennas
for improving system energy efficiency.
