  This paper investigates multiuser multi-input single-output (MISO) downlink
communications assisted by a self-sustainable intelligent reflection surface
(IRS), which can harvest power from the received signals. We study the joint
design of the beamformer at an access point (AP) and the phase shifts and the
power harvesting schedule at an IRS for maximizing the system sum-rate. The
design is formulated as a non-convex optimization problem taking into account
the capability of IRS elements to harvest wireless power for realizing
self-sustainability. Subsequently, we propose a computationally-efficient
alternating algorithm to obtain a suboptimal solution to the design problem.
Our simulation results unveil that: 1) there is a non-trivial trade-off between
the system sum-rate and self-sustainability in IRS-assisted systems; 2) the
performance gain achieved by the proposed scheme is improved with an increasing
number of IRS elements; 3) an IRS equipped with small bit-resolution discrete
phase shifters is sufficient to achieve a considerable system sum-rate of an
ideal case with continuous phase shifts.
