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

arXiv: https://arxiv.org/abs/2409.16664 · HTML: https://mlsanity.com/paper/2409.16664/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2024.

## Built on by (most cited first, 1 of 1)

- [Lightweight Deep Learning-Based Channel Estimation for RIS-Aided Extremely Large-Scale MIMO Systems on Resource-Limited Edge Devices](https://mlsanity.com/paper/2507.09627/) (2025)

## Abstract (arXiv)

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. We formulate this problem using dictionary learning, which allows for joint optimization of the dictionary and estimated channel. To handle the high-dimensional nature of XL-RIS channels, we specifically adopt a convolutional dictionary learning (CDL) formulation. The CDL formulation is cast as a bilevel optimization problem, which we solve using a gradient-based approach. To address the challenge of computing 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 and its enhanced version Convolutional ISTA-Net+, for end-to-end optimization of the CDL. To overcome the limitations of linear convolutional filters in capturing complex hybrid-field channel structures, we propose the CNN-CDL approach, which enhances PGD by replacing linear convolution filters with CNN blocks in its gradient descent step, employing a learnable proximal mapping module in its proximal mapping step, and incorporating cross-layer feature integration. Simulation results demonstrate the effectiveness of the proposed methods for channel estimation in hybrid-field XL-RIS systems.