This paper deals with channel estimation in reconfigurable intelligent surface (RIS) aided multiple-input multiple-output (MIMO) time-division duplexing systems. In a typical RIS assisted communication, an RIS is deployed in the close proximity of communication devices, thus resulting in ill-conditioned low-rank channel matrices. To effectively estimate these channels, we propose a two-stage channel estimation method. Specifically, in the first stage, the direct MIMO channel between the end terminals is estimated by utilizing the conventional uplink training approach. In the second stage, after the training process, it is noticed that the RIS channel estimation problem becomes equivalent to a well-known dictionary learning problem. Therefore, we propose to use a bilinear adaptive vector approximate message passing (BAdVAMP) algorithm to estimate RIS channels, which has been shown to be accurate and robust for ill-conditioned dictionary learning problems in compressed sensing. We also propose a phase shift design (passive beamforming) for the RIS by formulating an optimization problem that maximizes the total channel gain at the receiver. Due to its non-convex nature, an approximate closed-form solution is proposed to obtain the phase shift matrix. Numerical results show that the proposed BAdVAMP based RIS channel estimation performs better than its counterpart bilinear generalized AMP (BiGAMP) scheme.

中文翻译：

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可重构智能表面辅助MIMO网络的信道估计方法和相移设计

本文涉及可重构智能表面 (RIS) 辅助多输入多输出 (MIMO) 时分双工系统中的信道估计。在典型的 RIS 辅助通信中，RIS 部署在靠近通信设备的位置，从而导致病态的低秩信道矩阵。为了有效地估计这些信道，我们提出了一种两阶段信道估计方法。具体地，在第一阶段，终端之间的直接MIMO信道利用传统的上行训练方法进行估计。在第二阶段，在训练过程之后，注意到 RIS 信道估计问题变成了一个众所周知的字典学习问题。所以，我们建议使用双线性自适应向量近似消息传递 (BAdVAMP) 算法来估计 RIS 通道，该算法已被证明对于压缩感知中的病态字典学习问题是准确和稳健的。我们还通过制定优化问题来为 RIS 提出相移设计（无源波束成形），以最大化接收器的总信道增益。由于其非凸性质，提出了一种近似封闭形式的解来获得相移矩阵。数值结果表明，所提出的基于 BAdVAMP 的 RIS 信道估计比其对应的双线性广义 AMP (BiGAMP) 方案表现更好。我们还通过制定优化问题来为 RIS 提出相移设计（无源波束成形），以最大化接收器的总信道增益。由于其非凸性质，提出了一种近似封闭形式的解来获得相移矩阵。数值结果表明，所提出的基于 BAdVAMP 的 RIS 信道估计比其对应的双线性广义 AMP (BiGAMP) 方案表现更好。我们还通过制定优化问题来为 RIS 提出相移设计（无源波束成形），以最大化接收器的总信道增益。由于其非凸性质，提出了近似封闭形式的解来获得相移矩阵。数值结果表明，所提出的基于 BAdVAMP 的 RIS 信道估计比其对应的双线性广义 AMP (BiGAMP) 方案表现更好。