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