  The intelligent reflecting surface (IRS) is a planar array with massive
reconfigurable passive elements, which can align the reflecting signals at the
receivers via controlling the phase shifts at each element independently. Since
IRS can be implemented without RF chain, it is seen as a cost-effective
solution for boosting the spectral efficiency for the future communication
system. This work considers the IRS-aided multiuser multi-input single-output
downlink transmission, and our goal is to maximize the sum rate by jointly
optimizing the transmit beamformer at the base station and the phase shifts,
which can be either continuous or discrete, at the IRS. This sum rate
maximization (SRM) problem is challenging, especially for the discrete-phase
case. To tackle it, we first derive a more tractable equivalent formulation of
the SRM problem with structured convex constraints and a smooth objective. From
there, a custom-derived block-coordinated accelerated projected gradient
algorithm is developed. Simulation results demonstrate that the proposed design
outperforms state-of-the-art design in the sum rate performance.
