  Intelligent reflecting surfaces (IRSs) have received considerable attention
from the wireless communications research community recently. In particular, as
low-cost passive devices, IRSs enable the control of the wireless propagation
environment, which is not possible in conventional wireless networks. To take
full advantage of such IRS-assisted communication systems, both the beamformer
at the access point (AP) and the phase shifts at the IRS need to be optimally
designed. However, thus far, the optimal design is not well understood. In this
paper, a point-to-point IRS-assisted multiple-input single-output (MISO)
communication system is investigated. The beamformer at the AP and the IRS
phase shifts are jointly optimized to maximize the spectral efficiency. Two
efficient algorithms exploiting fixed point iteration and manifold optimization
techniques, respectively, are developed for solving the resulting non-convex
optimization problem. The proposed algorithms not only achieve a higher
spectral efficiency but also lead to a lower computational complexity than the
state-of-the-art approach. Simulation results reveal that deploying large-scale
IRSs in wireless systems is more efficient than increasing the antenna array
size at the AP for enhancing both the spectral and the energy efficiency.
