Globally Optimal Resource Allocation Design for IRS-Assisted Multiuser Networks with Discrete Phase Shifts

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.