  Intelligent reflecting surface (IRS) is an emerging technology to enhance
spatial multiplexing in wireless networks. This letter considers the discrete
passive beamforming design for IRS in order to maximize the minimum
signal-to-interference-plus-noise ratio (SINR) among multiple users in an
IRS-assisted downlink network. The main design difficulty lies in the discrete
phase-shift constraint. Differing from most existing works, this letter
advocates a convex-hull relaxation of the discrete constraints which leads to a
continuous reformulated problem equivalent to the original discrete problem.
This letter further proposes an efficient alternating projection/proximal
gradient descent and ascent algorithm for solving the reformulated problem.
Simulation results show that the proposed algorithm outperforms the
state-of-the-art methods significantly.
