In this letter, we consider a multicast system where a single-antenna transmitter sends a common message to multiple single-antenna users, aided by an intelligent reflecting surface (IRS) equipped with ${N}$ passive reflecting elements. Prior works on IRS have mostly assumed the availability of channel state information (CSI) for designing its passive beamforming. However, the acquisition of CSI requires substantial training overhead that increases with ${N}$ . In contrast, we propose in this letter a novel random passive beamforming scheme, where the IRS performs independent random reflection for ${Q} \geq $ 1 times in each channel coherence interval without the need of CSI acquisition. For the proposed scheme, we first derive a closed-form approximation of the outage probability, based on which the optimal ${Q}$ with best outage performance can be efficiently obtained. Then, for the purpose of comparison, we derive a lower bound of the outage probability with traditional CSI-based passive beamforming. Numerical results show that a small ${Q}$ is preferred in the high-outage regime (or with high rate target) and the optimal ${Q}$ becomes larger as the outage probability decreases (or as the rate target decreases). Moreover, the proposed scheme significantly outperforms the CSI-based passive beamforming scheme with training overhead taken into consideration when ${N}$ and/or the number of users are large, thus offering a promising CSI-free alternative to existing CSI-based schemes.

中文翻译：

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具有随机无源波束成形的智能反射面辅助多播

在这封信中，我们考虑了一个多播系统，其中一个单天线发射机向多个单天线用户发送一条公共消息，并辅以配备有智能反射面 (IRS) ${N}$ 被动反射元件。IRS 之前的工作主要假设信道状态信息 (CSI) 的可用性来设计其无源波束成形。然而，获取 CSI 需要大量的训练开销，随着 ${N}$ . 相反，我们在这封信中提议写一部小说随机无源波束成形 方案，其中 IRS 执行独立的随机反射 ${Q} \geq $ 每个信道相干间隔1次，无需CSI获取。对于所提出的方案，我们首先推导出中断概率的封闭形式近似值，基于该近似值，最优 ${Q}$ 可以有效地获得最佳停机性能。然后，为了进行比较，我们推导出传统基于 CSI 的无源波束成形的中断概率下限。数值结果表明，小 ${Q}$ 在高停电情况下（或具有高速率目标）和最佳 ${Q}$ 随着中断概率的降低（或速率目标降低）而变得更大。此外，当考虑到训练开销时，所提出的方案明显优于基于 CSI 的无源波束成形方案 ${N}$ 和/或用户数量很大，因此为现有的基于 CSI 的方案提供了一种有前途的无 CSI 替代方案。