Dynamic Metasurface Antenna (DMA) is a cutting-edge antenna technology offering scalable and sustainable solutions for large antenna arrays. The effectiveness of DMAs stems from their inherent configurable analog signal processing capabilities, which facilitate cost-limited implementations. However, when DMAs are used in multiple input multiple output (MIMO) communication systems, they pose challenges in channel estimation due to their analog compression. In this paper, we propose two model-based learning methods to overcome this challenge. Our approach starts by casting channel estimation as a compressed sensing problem. Here, the sensing matrix is formed using a random DMA weighting matrix combined with a spatial gridding dictionary. We then employ the learned iterative shrinkage and thresholding algorithm (LISTA) to recover the sparse channel parameters. LISTA unfolds the iterative shrinkage and thresholding algorithm into a neural network and trains the neural network into a highly efficient channel estimator fitting with the previous channel. As the sensing matrix is crucial to the accuracy of LISTA recovery, we introduce another data-aided method, LISTA-sensing matrix optimization (LISTA-SMO), to jointly optimize the sensing matrix. LISTA-SMO takes LISTA as a backbone and embeds the sensing matrix optimization layers in LISTA's neural network, allowing for the optimization of the sensing matrix along with the training of LISTA. Furthermore, we propose a self-supervised learning technique to tackle the difficulty of acquiring noise-free data. Our numerical results demonstrate that LISTA outperforms traditional sparse recovery methods regarding channel estimation accuracy and efficiency. Besides, LISTA-SMO achieves better channel accuracy than LISTA, demonstrating the effectiveness in optimizing the sensing matrix.

翻译：动态超表面天线（DMA）是一种前沿天线技术，可为大规模天线阵列提供可扩展且可持续的解决方案。DMA的有效性源于其固有的可配置模拟信号处理能力，这有助于降低实现成本。然而，当DMA用于多输入多输出（MIMO）通信系统时，由于其模拟压缩特性，给信道估计带来了挑战。本文提出两种基于模型的学习方法来克服这一挑战。我们的方法首先将信道估计问题建模为压缩感知问题，其中感知矩阵由随机DMA加权矩阵结合空间网格字典构成。随后，我们采用学习型迭代收缩与阈值算法（LISTA）来恢复稀疏信道参数。LISTA将迭代收缩与阈值算法展开为神经网络，并训练该网络成为与先前信道高度匹配的高效信道估计器。由于感知矩阵对LISTA恢复精度至关重要，我们引入另一种数据辅助方法——LISTA感知矩阵优化（LISTA-SMO），以实现感知矩阵的联合优化。LISTA-SMO以LISTA为骨干网络，在其神经网络中嵌入感知矩阵优化层，使感知矩阵的优化与LISTA的训练同步进行。此外，我们提出自监督学习技术来解决无噪声数据获取困难的问题。数值结果表明，LISTA在信道估计精度和效率上均优于传统稀疏恢复方法。同时，LISTA-SMO比LISTA实现了更好的信道精度，验证了其在感知矩阵优化中的有效性。