We consider multi-antenna wireless systems aided by reconfigurable intelligent surfaces (RIS). RIS presents a new physical layer technology for improving coverage and energy efficiency by intelligently controlling the propagation environment. In practice however, achieving the anticipated gains of RIS requires accurate channel estimation. Recent attempts to solve this problem have considered the least-squares (LS) approach, which is simple but also sub-optimal. The optimal channel estimator, based on the minimum mean-squared-error (MMSE) criterion, is challenging to obtain and is non-linear due to the non-Gaussianity of the effective channel seen at the receiver. Here we present approaches to approximate the optimal MMSE channel estimator. As a first approach, we analytically develop the best linear estimator, the LMMSE, together with a corresponding majorization-minimization-based algorithm designed to optimize the RIS phase shift matrix during the training phase. This estimator is shown to yield improved accuracy over the LS approach by exploiting second-order statistical properties of the wireless channel and the noise. To further improve performance and better approximate the globally-optimal MMSE channel estimator, we propose data-driven non-linear solutions based on deep learning. Specifically, by posing the MMSE channel estimation problem as an image denoising problem, we propose two convolutional neural network (CNN)-based methods to perform the denoising and approximate the optimal MMSE channel estimation solution. Our numerical results show that these CNN-based estimators give superior performance compared with linear estimation approaches. They also have low computational complexity requirements, thereby motivating their potential use in future RIS-aided wireless communication systems.

中文翻译：

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可重构智能表面辅助MISO通信的信道估计：从LMMSE到深度学习解决方案

我们考虑了可重构智能表面（RIS）辅助的多天线无线系统。RIS提出​​了一种新的物理层技术，可通过智能控制传播环境来提高覆盖范围和能源效率。然而，在实践中，要实现RIS的预期收益需要准确的信道估计。解决该问题的最新尝试已经考虑了最小二乘（LS）方法，该方法简单但也不理想。基于最小均方误差（MMSE）准则的最优信道估计器很难获得，并且由于在接收机处看到的有效信道的非高斯性而呈非线性。在这里，我们提出了逼近最佳MMSE信道估计器的方法。作为第一种方法，我们将分析性地开发出最佳线性估计器LMMSE，以及设计用于在训练阶段优化RIS相移矩阵的相应的基于主要化-最小化的算法。通过利用无线信道和噪声的二阶统计特性，该估计器显示出比LS方法更高的准确性。为了进一步提高性能并更好地估计全局最优的MMSE信道估计器，我们提出了基于深度学习的数据驱动非线性解决方案。具体而言，通过将MMSE信道估计问题摆在图像降噪问题上，我们提出了两种基于卷积神经网络（CNN）的方法来进行去噪并逼近最佳MMSE信道估计解决方案。我们的数值结果表明，与线性估计方法相比，这些基于CNN的估计器具有出色的性能。