This article considers an intelligent reflecting surface (IRS)-assisted point-to-point multiple-input single-output communication system. An IRS implemented by configurable phase shifters is used to assist the transmission from an access point (AP) equipped with multiple antennas to a user having a single antenna. We aim to jointly optimize the transmit beamforming at the AP and the reflect beamforming at the IRS to maximize the spectral efficiency of the system. The considered joint optimization problem can be decoupled into the transmit and reflect beamforming design problems by applying the maximum-ratio transmission strategy. The former has a closed-form expression, whereas the latter requires solving a nonconvex optimization problem. A known solution based on manifold optimization (MO) is proposed to solve the reflect beamforming design problem. Although the MO-based algorithm achieves higher spectral efficiency than the conventional semidefinite relaxation approach, it incurs high time complexity. On this basis, we address this issue by proposing a computationally efficient gradient projection (GP)-based algorithm for the reflect beamforming design problem. When low-resolution (e.g., 1–2 bits) phase shifters are adopted, we leverage an innovative probability learning technique on the basis of the cross-entropy (CE) framework to alleviate the performance loss caused by the use of low-resolution phase shifters. Simulation results demonstrate that the proposed GP-based algorithm nearly obtains the same spectral efficiency as the state-of-the-art MO-based algorithm at a low complexity. However, the running time is significantly reduced. When low-resolution phase shifters are employed, the proposed CE-based algorithm outperforms the test algorithms in terms of spectral and energy efficiency in various system configurations.

中文翻译：

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智能反射面辅助MISO通信系统的波束成形优化

本文考虑了一种智能反射面（IRS）辅助的点对点多输入单输出通信系统。由可配置移相器实现的IRS用于协助从配备有多个天线的接入点（AP）到具有单个天线的用户的传输。我们旨在共同优化AP处的发射波束成形和IRS处的反射波束成形，以最大程度地提高系统的频谱效率。通过应用最大比率传输策略，可以将考虑的联合优化问题分解为传输和反射波束成形设计问题。前者具有封闭形式的表达式，而后者则需要解决非凸优化问题。提出了一种基于流形最优化（MO）的已知解决方案来解决反射波束形成设计问题。尽管基于MO的算法比常规的半定性松弛方法具有更高的频谱效率，但它会带来较高的时间复杂度。在此基础上，我们针对反射波束成形设计问题提出了一种基于计算效率高的基于梯度投影（GP）的算法，从而解决了这一问题。当采用低分辨率（例如1-2位）移相器时，我们将在交叉熵（CE）框架的基础上利用创新的概率学习技术来缓解因使用低分辨率相位而导致的性能损失移位器。仿真结果表明，所提出的基于GP的算法在低复杂度下几乎可以获得与基于MO的最新算法相同的频谱效率。但是，运行时间大大减少了。当使用低分辨率移相器时，在各种系统配置中，基于频谱和能量效率的建议基于CE的算法优于测试算法。