The reconfigurable intelligent surface (RIS), which consists of a large number of passive and low-cost reflecting elements, has been recognized as a revolutionary technology to enhance the performance of future wireless networks. This paper considers an RIS assisted multicast transmission, where a base station (BS) with multiple-antenna multicasts common message to multiple single-antenna mobile users (MUs) under the assistance of an RIS. An equivalent channel model for the considered multicast transmission is analyzed, and then an optimization problem for the corresponding channel capacity is formulated to obtain the optimal covariance matrix and phase shifts. In order to solve the above non-convex and non-differentiable problem, this paper first exploits the gradient descent method and alternating optimization, to approach the locally optimal solution for any number of MUs. Then, this paper considers a special case, which can obtain the global optimal solution, and shows the sufficient and necessary condition for this special case. Finally, the order growth of the maximal capacity is obtained when the numbers of the reflecting elements, the BS antennas, and the MUs go to infinity.

中文翻译：

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可重构智能表面辅助多天线组播的容量表征


可重构智能表面（RIS）由大量无源且低成本的反射元件组成，被认为是增强未来无线网络性能的革命性技术。本文考虑了RIS辅助的多播传输，其中具有多天线的基站（BS）在RIS的协助下向多个单天线移动用户（MU）多播公共消息。分析所考虑的多播传输的等效信道模型，然后制定相应信道容量的优化问题以获得最佳协方差矩阵和相移。为了解决上述非凸且不可微的问题，本文首先利用梯度下降法和交替优化来逼近任意数量MU的局部最优解。然后，本文考虑了一种可以获得全局最优解的特殊情况，并给出了这种特殊情况的充分必要条件。最后，当反射单元、BS天线和MU的数量趋于无穷大时，获得最大容量的阶增长。