Deploying multiple beyond diagonal reconfigurable intelligent surfaces (BD-RISs) can potentially improve the communication performance thanks to inter-element connections of each BD-RIS and inter-surface cooperative beamforming gain among BD-RISs. However, a major issue for multi-BD-RISassisted communication lies in the channel estimation overhead - the channel coefficients associated with the off-diagonal elements in each BD-RIS's scattering matrix as well as those associated with the reflection links among BD-RISs have to be estimated. In this paper, we propose an efficient channel estimation framework for double-BD-RIS-assisted multi-user multipleinput multiple-output (MIMO) systems. Specifically, we reveal that high-dimensional cascaded channels are characterized by five low-dimensional matrices by exploiting channel correlation properties. Based on this novel observation, in the ideal noiseless case, we develop a channel estimation scheme to recover these matrices sequentially and characterize the closed-form overhead required for perfect estimation as a function of the numbers of users and each BD-RIS's elements and channel ranks, which is with the same order as that in double-diagonal-RIS-aided communication systems. This exciting result implies the superiority of cooperative BD-RIS-aided communication over the diagonal- RIS counterpart even when channel estimation overhead is considered. We further extend the proposed scheme to practical noisy scenarios and provide extensive numerical simulations to validate its effectiveness.

翻译：部署多个超对角可重构智能表面（BD-RIS）有望提升通信性能，这得益于每个BD-RIS内部的单元间连接以及多个BD-RIS之间的表面协作波束成形增益。然而，多BD-RIS辅助通信面临的一个主要问题在于信道估计开销——不仅需要估计每个BD-RIS散射矩阵中非对角元素相关的信道系数，还需估计BD-RIS间反射链路对应的信道参数。本文针对双BD-RIS辅助的多用户多输入多输出（MIMO）系统，提出一种高效的信道估计框架。具体而言，我们通过挖掘信道相关性特征，揭示高维级联信道可由五个低维矩阵表征。基于这一新发现，在理想无噪声场景下，我们设计了一种顺序恢复这些矩阵的信道估计方案，并推导出实现完美估计所需闭式开销的表达式，该表达式是用户数、各BD-RIS单元数及信道秩的函数，其量级与双对角RIS辅助通信系统相同。这一重要结果表明：即使考虑信道估计开销，协作式BD-RIS辅助通信仍优于对角RIS方案。我们进一步将所提方案扩展至实际含噪场景，并通过大量数值仿真验证了其有效性。