  Wireless communications via intelligent reflecting surfaces (IRSs) has
received considerable attention from both academia and industry. In particular,
IRSs are able to create favorable wireless propagation environments with
typically low-cost passive devices. While various IRS-aided wireless
communication systems have been investigated in the literature, thus far, the
optimal design of such systems is not well understood. In this paper,
IRS-assisted single-user multiple-input single-output (MISO) communication is
investigated. To maximize the spectral efficiency, a branch-and-bound (BnB)
algorithm is proposed to obtain globally optimal solutions for both the active
and passive beamformers at the access point (AP) and the IRS, respectively.
Simulation results confirm the effectiveness of deploying IRSs in wireless
systems. Furthermore, by taking the proposed optimal BnB algorithm as the
performance benchmark, the optimality of existing design algorithms is
investigated.
