Beyond diagonal reconfigurable intelligent surface (BD-RIS) is a new advance and generalization of the RIS technique. BD-RIS breaks through the isolation between RIS elements by creatively introducing inter-element connections, thereby enabling smarter wave manipulation and enlarging coverage. However, exploring proper channel estimation schemes suitable for BD-RIS aided communication systems still remains an open problem. In this paper, we study channel estimation and beamforming design for BD-RIS aided multi-antenna systems. We first describe the channel estimation strategy based on the least square (LS) method, derive the mean square error (MSE) of the LS estimation, and formulate the joint pilot sequence and BD-RIS design problem with unique constraints induced by BD-RIS architectures. Specifically, we propose an efficient pilot sequence and BD-RIS design which theoretically guarantees to achieve the minimum MSE. With the estimated channel, we then consider two BD-RIS scenarios and propose beamforming design algorithms. Finally, we provide simulation results to verify the effectiveness of the proposed channel estimation scheme and beamforming design algorithms. We also show that more interelement connections in BD-RIS improves the performance while increasing the training overhead for channel estimation.

翻译：超越对角可重构智能表面（BD-RIS）是RIS技术的新进展与泛化。BD-RIS通过创造性地引入元件间连接，突破了RIS元件之间的隔离性，从而实现更智能的波束操控并扩大覆盖范围。然而，探索适用于BD-RIS辅助通信系统的信道估计方案仍是一个开放性问题。本文研究了BD-RIS辅助多天线系统中的信道估计与波束成形设计。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估计的均方误差（MSE），并提出了受BD-RIS架构独特约束的联合导频序列与BD-RIS设计问题。具体而言，我们提出了一种高效的导频序列与BD-RIS设计方案，理论上保证了最小MSE的实现。基于估计的信道，我们进一步考虑了两种BD-RIS场景，并提出了波束成形设计算法。最后，我们通过仿真结果验证了所提信道估计方案与波束成形设计算法的有效性，并表明BD-RIS中更多元件间连接虽能提升性能，但也会增加信道估计的训练开销。