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：我们研究了一种基于超对角线可重构智能表面（BD-RIS）辅助的多输入单输出系统的信道估计问题。首先，我们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），并基于BD-RIS组连接架构的独特约束，构建了旨在最小化估计MSE的BD-RIS设计问题。接着，我们提出了一种高效的BD-RIS设计，该设计在理论上保证能够达到MSE下界。最后，我们通过仿真结果验证了所提信道估计方案的有效性。