  Intelligent reflecting surfaces (IRSs) are envisioned as a low-cost solution
to achieve high spectral and energy efficiency in future communication systems
due to their ability to customize wireless propagation environments. Although
resource allocation design for IRS-assisted multiuser wireless communication
systems has been exhaustively investigated in the literature, the optimal
design and performance of such systems are still not well understood. To fill
this gap, in this paper, we study optimal resource allocation for IRS-assisted
multiuser multiple-input single-output (MISO) systems. In particular, we
jointly optimize the beamforming at the base station (BS) and the discrete IRS
phase shifts to minimize the total transmit power. For attaining the globally
optimal solution of the formulated non-convex combinatorial optimization
problem, we develop a resource allocation algorithm with guaranteed convergence
based on Schur's complement and the generalized Bender's decomposition. Our
numerical results reveal that the proposed algorithm can significantly reduce
the BS transmit power compared to the state-of-the-art suboptimal alternating
optimization-based approach, especially for moderate-to-large numbers of IRS
elements.
