We study channel estimation for a beyond diagonal reconfigurable intelligent surface (BD-RIS) aided multiple input single output system. We first describe the channel estimation strategy based on the least square (LS) method, derive the mean square error (MSE) of the LS estimator, and formulate the BD-RIS design problem that minimizes the estimation MSE with unique constraints induced by group-connected architectures of BD-RIS. Then, we propose an efficient BD-RIS design which theoretically guarantees to achieve the MSE lower bound. Finally, we provide simulation results to verify the effectiveness of the proposed channel estimation scheme.

翻译：本文研究了一种基于超对角可重构智能表面（BD-RIS）辅助的多输入单输出系统的信道估计问题。我们首先描述了基于最小二乘（LS）方法的信道估计策略，推导了LS估计器的均方误差（MSE），并构建了BD-RIS设计问题，该问题旨在最小化估计MSE，同时满足由BD-RIS的分组连接架构所引入的特殊约束。随后，我们提出了一种高效的BD-RIS设计方案，该方案在理论上能够达到MSE下界。最后，我们提供了仿真结果以验证所提信道估计方案的有效性。