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.
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