  This paper considers simultaneous wireless information and power transfer
(SWIPT) in a multiple-input single-output (MISO) downlink system consisting of
one multi-antenna transmitter, one single-antenna information receiver (IR),
multiple multi-antenna eavesdroppers (Eves) and multiple single-antenna
energy-harvesting receivers (ERs). The main objective is to keep the
probability of the legitimate user's achievable secrecy rate outage as well as
the ERs' harvested energy outage caused by channel state information (CSI)
uncertainties below some prescribed thresholds. As is well known, the secrecy
rate outage constraints present a significant analytical and computational
challenge. Incorporating the energy harvesting (EH) outage constraints only
intensifies that challenge. In this paper, we address this challenging issue
using convex restriction approaches which are then proved to yield rank-one
optimal beamforming solutions. Numerical results reveal the effectiveness of
the proposed schemes.
