Convolutional Dictionary Learning-Based Hybrid-Field Channel Estimation for XL-RIS-Aided Massive MIMO Systems

Extremely large reconfigurable intelligent surface (XL-RIS) is emerging as a promising key technology for 6G systems. To exploit XL-RIS’s full potential, accurate channel estimation is essential. This paper investigates channel estimation in XL-RIS-aided massive MIMO systems under hybrid-field scenarios where far-field and near-field channels coexist. To handle the high-dimensional nature of XL-RIS channels, a convolutional dictionary learning (CDL) problem is formulated, which is cast as a bilevel optimization problem. To compute the gradient of the upper-level objective, we introduce an unrolled optimization method based on proximal gradient descent (PGD) and its special case, the iterative soft-thresholding algorithm (ISTA). We propose two neural network architectures, Convolutional ISTA-Net (CISTA-Net) and its enhanced version CISTA-Net+, for end-to-end optimization of the CDL. To overcome the limitations of linear convolutional dictionary in capturing complex hybrid-field channel structures, we further replace linear convolution dictionary with convolutional neural network blocks in the gradient descent step, while employing a learnable proximal mapping module and incorporating cross-layer feature integration. Simulation results demonstrate the effectiveness of the proposed channel estimation algorithms for hybrid-field XL-RIS massive MIMO systems.