  This paper considers an angle-domain intelligent reflecting surface (IRS)
system. We derive maximum likelihood (ML) estimators for the effective angles
from the base station (BS) to the user and the effective angles of propagation
from the IRS to the user. It is demonstrated that the accuracy of the estimated
angles improves with the number of BS antennas. Also, deploying the IRS closer
to the BS increases the accuracy of the estimated angle from the IRS to the
user. Then, based on the estimated angles, we propose a joint optimization of
BS beamforming and IRS beamforming, which achieves similar performance to two
benchmark algorithms based on full CSI and the multiple signal classification
(MUSIC) method respectively. Simulation results show that the optimized BS beam
becomes more focused towards the IRS direction as the number of reflecting
elements increases. Furthermore, we derive a closed-form approximation, upper
bound and lower bound for the achievable rate. The analytical findings indicate
that the achievable rate can be improved by increasing the number of BS
antennas or reflecting elements. Specifically, the BS-user link and the
BS-IRS-user link can obtain power gains of order $N$ and $NM^2$, respectively,
where $N$ is the antenna number and $M$ is the number of reflecting elements.
