  Intelligent reflecting surface (IRS) is a promising technology for achieving
high spectrum efficiency in future wireless networks by leveraging massive
low-cost reflecting elements with each reflecting the incident signal with a
proper phase shift. However, prior works on IRS are mainly based on the
optimization of infinite-resolution phase shifters which are practically
infeasible due to hardware imperfections. In contrast, we study in this paper
an IRS-aided wireless network, where an IRS with only finite-resolution phase
shifter available at each element is deployed to assist in the communication
from a multi-antenna access point (AP) to a single-antenna user. We aim to
minimize the transmit power at the AP by jointly optimizing the transmit
beamforming at the AP and reflect beamforming at the IRS, subject to the
signal-to-noise ratio (SNR) constraint and practical discrete phase shift
constraints. We first propose a suboptimal but low-complexity algorithm by
exploiting the alternating optimization technique. Then, we reveal that as in
the case with continuous phase shifts, the IRS with discrete phase shifts also
achieves the squared power gain for asymptotically large number of reflecting
elements, despite suffering a performance loss that depends only on the
resolution of phase shifters.
