  The current literature on intelligent reflecting surface (IRS) focuses on
optimizing the IRS phase shifts to yield coherent beamforming gains, under the
assumption of perfect channel state information (CSI) of individual
IRS-assisted links, which is highly impractical. This work, instead, considers
the random rotations scheme at the IRS in which the reflecting elements only
employ random phase rotations without requiring any CSI. The only CSI then
needed is at the base station (BS) of the overall channel to implement the
beamforming transmission scheme. Under this framework, we derive the sum-rate
scaling laws in the large number of users regime for the IRS-assisted
multiple-input single-output (MISO) broadcast channel, with optimal dirty paper
coding (DPC) scheme and the lower-complexity random beamforming (RBF) and
deterministic beamforming (DBF) schemes at the BS. The random rotations scheme
increases the sum-rate by exploiting multi-user diversity, but also compromises
the gain to some extent due to correlation. Finally, energy efficiency
maximization problems in terms of the number of BS antennas, IRS elements and
transmit power are solved using the derived scaling laws. Simulation results
show the proposed scheme to improve the sum-rate, with performance becoming
close to that under coherent beamforming for a large number of users.
