Accurate estimation of the cascaded channel from a user equipment (UE) to a base station (BS) via each reconfigurable intelligent surface (RIS) element is critical to realizing the full potential of the RIS's ability to control the overall channel. The number of parameters to be estimated is equal to the number of RIS elements, requiring an equal number of pilots unless an underlying structure can be identified. In this paper, we show how the spatial correlation inherent in the different RIS channels provides this desired structure. We first optimize the RIS phase-shift pattern using a much-reduced pilot length (determined by the rank of the spatial correlation matrices) to minimize the mean square error (MSE) in the channel estimation under electromagnetic interference. In addition to considering the linear minimum MSE (LMMSE) channel estimator, we propose a novel channel estimator that requires only knowledge of the array geometry while not requiring any user-specific statistical information. We call this the reduced-subspace least squares (RS-LS) estimator and optimize the RIS phase-shift pattern for it. This novel estimator significantly outperforms the conventional LS estimator. For both the LMMSE and RS-LS estimators, the proposed optimized RIS configurations result in significant channel estimation improvements over the benchmarks.

翻译：在可重构智能表面（RIS）辅助通信中，通过每个RIS单元准确估计从用户设备（UE）到基站（BS）的级联信道，对于实现RIS控制整体信道能力的全部潜力至关重要。待估计参数的数量等于RIS单元的数量，除非能够识别出潜在的结构性特征，否则需要同等数量的导频。本文揭示了不同RIS信道固有的空间相关性如何提供这种所需的结构性特征。我们首先利用大幅缩减的导频长度（由空间相关矩阵的秩决定）来优化RIS相移模式，以最小化电磁干扰下信道估计的均方误差（MSE）。除了考虑线性最小均方误差（LMMSE）信道估计器外，我们提出了一种仅需已知阵列几何信息、无需任何用户特定统计信息的新型信道估计器。我们将其称为降子空间最小二乘（RS-LS）估计器，并为其优化了RIS相移模式。该新型估计器性能显著优于传统LS估计器。对于LMMSE和RS-LS两种估计器，所提出的优化RIS配置相较于基准方案均能带来显著的信道估计性能提升。