Intelligent reflecting surface (IRS) is a cost-effective solution for achieving high spectrum and energy efficiency in future wireless networks by leveraging massive low-cost passive elements that are able to reflect the signals with adjustable phase shifts. Prior works on IRS mainly consider continuous phase shifts at reflecting elements, which are practically difficult to implement due to the hardware limitation. In contrast, we study in this paper an IRS-aided wireless network, where an IRS with only a finite number of phase shifts at each element is deployed to assist in the communication from a multi-antenna access point (AP) to multiple single-antenna users. We aim to minimize the transmit power at the AP by jointly optimizing the continuous transmit precoding at the AP and the discrete reflect phase shifts at the IRS, subject to a given set of minimum signal-to-interference-plus-noise ratio (SINR) constraints at the user receivers. The considered problem is shown to be a mixed-integer non-linear program (MINLP) and thus is difficult to solve in general. To tackle this problem, we first study the single-user case with one user assisted by the IRS and propose both optimal and suboptimal algorithms for solving it. Besides, we analytically show that as compared to the ideal case with continuous phase shifts, the IRS with discrete phase shifts achieves the same squared power gain in terms of asymptotically large number of reflecting elements, while a constant proportional power loss is incurred that depends only on the number of phase-shift levels. The proposed designs for the single-user case are also extended to the general setup with multiple users among which some are aided by the IRS. Simulation results verify our performance analysis as well as the effectiveness of our proposed designs as compared to various benchmark schemes.

中文翻译：

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离散相移智能反射面辅助无线网络波束成形优化

智能反射面 (IRS) 是一种经济高效的解决方案，通过利用能够以可调相移反射信号的大量低成本无源元件，在未来的无线网络中实现高频谱和能源效率。IRS 的先前工作主要考虑反射元件处的连续相移，由于硬件限制，这实际上很难实现。相比之下，我们在本文中研究了 IRS 辅助无线网络，其中部署了一个在每个元素上只有有限数量相移的 IRS 以协助从多天线接入点 (AP) 到多个单天线的通信。天线用户。我们的目标是通过联合优化 AP 的连续发射预编码和 IRS 的离散反射相移来最小化 AP 的发射功率，受用户接收器处一组给定的最小信干噪比 (SINR) 约束的约束。所考虑的问题被证明是一个混合整数非线性规划 (MINLP)，因此通常难以解决。为了解决这个问题，我们首先研究了一个由 IRS 协助的用户的单用户案例，并提出了解决这个问题的最优和次优算法。此外，我们分析表明，与具有连续相移的理想情况相比，具有离散相移的 IRS 在渐近大量反射元件方面实现了相同的平方功率增益，而产生的恒定比例功率损耗仅取决于关于相移电平的数量。为单用户案例提出的设计也扩展到具有多个用户的一般设置，其中一些由 IRS 提供帮助。与各种基准方案相比，仿真结果验证了我们的性能分析以及我们提出的设计的有效性。