Channel Estimation for Wideband XL-MIMO: A Constrained Deep Unrolling Approach

Extremely large-scale multiple-input multipleoutput (XL-MIMO) enables the formation of narrow beams, effectively mitigating path loss in high-frequency communications. This capability makes the integration of wideband high-frequency communications with XL-MIMO a key enabler for future 6G networks. Realizing the full potential of such wideband XL-MIMO systems critically depends on acquiring accurate channel state information. However, this acquisition is significantly challenged by inherent wideband XLMIMO channel characteristics, including near-field propagation effects, beam split, and spatial non-stationarity. We formulate the channel estimation as a maximum a posteriori problem and propose an unrolled proximal gradient descent network. The network integrates learnable step sizes and replaces the proximal operator with a neural network to implicitly learn channel prior knowledge without requiring explicit regularization terms. To enhance the convergence behavior, we incorporated a monotonic descent constraint on the layer-wise estimation error during training. This constrained learning problem is addressed using a primal-dual training approach. Theoretical analysis is provided to characterize the duality gap and convergence behavior of the proposed method. Furthermore, simulation results are presented to validate its effectiveness, demonstrating gains in estimation accuracy over both traditional and deep learning-based methods.

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. 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.

Trainable Proximal Gradient Descent Based Channel Estimation for mmWave Massive MIMO Systems

In this letter, we focus on the problem of millimeter-Wave channels estimation in massive MIMO communication systems. Inspired by the sparsity of mmWave MIMO channel in the angular domain, we formulate the estimation problem as a sparse signal recovery problem. We propose a deep learning based trainable proximal gradient descent network (TPGD-Net) for mmWave channel estimation. Specifically, we unfold the iterative proximal gradient descent (PGD) algorithm into a layer-wise network. Different from the PGD algorithm, the gradient descent step size in TPGD-Net is set as a trainable parameter. Moreover, the proximal operator in PGD algorithm is replaced by a tailored neural network which incorporates data-driven prior channel information to perform proximal operator in an implicit manner. We further improve the performance of the TPGD-Net by introducing the inter-stage feature pathways module to alleviate the feature information transmission bottleneck between each two adjacent layers. Simulation results on the Saleh-Valenzuela channel model and the DeepMIMO dataset demonstrate its effectiveness compared to the state-of-the-art mmWave channel estimators.