  We study the beamforming design for multiuser systems with simultaneous
wireless information and power transfer (SWIPT). Employing a practical
non-linear energy harvesting (EH) model, the design is formulated as a
non-convex optimization problem for the maximization of the minimum harvested
power across several energy harvesting receivers. The proposed problem
formulation takes into account imperfect channel state information (CSI) and a
minimum required signal-to-interference-plus-noise ratio (SINR). The globally
optimal solution of the design problem is obtained via the semidefinite
programming (SDP) relaxation approach. Interestingly, we can show that at most
one dedicated energy beam is needed to achieve optimality. Numerical results
demonstrate that with the proposed design a significant performance gain and
improved fairness can be provided to the users compared to two baseline
schemes.
