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Intelligent Reflecting Surface Aided Multicasting with Random Passive Beamforming

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 \emph{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.