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.

中文翻译：

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角域智能反射面系统：设计与分析

本文考虑了一种角域智能反射面 (IRS) 系统。我们推导出从基站 (BS) 到用户的有效角度以及从 IRS 到用户的有效传播角度的最大似然 (ML) 估计量。结果表明，估计角度的精度随着基站天线数量的增加而提高。此外，将 IRS 部署得更靠近 BS 会增加从 IRS 到用户的估计角度的准确性。然后，基于估计的角度，我们提出了 BS 波束成形和 IRS 波束成形的联合优化，其性能分别与基于全 CSI 和多信号分类 (MUSIC) 方法的两种基准算法相似。仿真结果表明，随着反射元件数量的增加，优化后的 BS 光束变得更加聚焦于 IRS 方向。此外，我们推导出可实现速率的封闭形式近似值、上限和下限。分析结果表明，可通过增加基站天线或反射元件的数量来提高可实现的速率。具体来说，BS-user 链路和 BS-IRS-user 链路可以获得阶次的功率增益 $N$ 和 $NM^{2}$ , 分别, 其中 $N$ 是天线编号和 百万美元 是反射元素的数量。