  This paper investigates robust and secure multiuser multiple-input
single-output (MISO) downlink communications assisted by a self-sustainable
intelligent reflection surface (IRS), which can simultaneously reflect and
harvest energy from the received signals. We study the joint design of
beamformers at an access point (AP) and the phase shifts as well as the energy
harvesting schedule at the IRS for maximizing the system sum-rate. The design
is formulated as a non-convex optimization problem taking into account the
wireless energy harvesting capability of IRS elements, secure communications,
and the robustness against the impact of channel state information (CSI)
imperfection. Subsequently, we propose a computationally-efficient iterative
algorithm to obtain a suboptimal solution to the design problem. In each
iteration, S-procedure and the successive convex approximation are adopted to
handle the intermediate optimization problem. Our simulation results unveil
that: 1) there is a non-trivial trade-off between the system sum-rate and the
self-sustainability of the IRS; 2) the performance gain achieved by the
proposed scheme is saturated with a large number of energy harvesting IRS
elements; 3) an IRS equipped with small bit-resolution discrete phase shifters
is sufficient to achieve a considerable system sum-rate of the ideal case with
continuous phase shifts.
