ingLSD-UnfoldNet: A Deep Unfolded Network with Learnable Sparse Dictionary for Near-Field Channel Estimation in Massive MIMO Systems

This paper tackles the problem of performance limitations on channel estimation accuracy in near-field massive MIMO systems resulting from the sparse reconstruction method with fixed spatial grid dictionaries. It presents a deep unfolded network with a learnable sparse dictionary (LSD-UnfoldNet) to address the grid mismatch, thereby obtaining high accuracy and low-complexity near-field channel estimation as the sparse dictionary and channel reconstruction parameters are jointly optimized using end-to-end learning. The iterative shrinking threshold algorithm is unfolded into an L-layer neural network with L learnable sparse dictionaries and linear transformation matrices in each layer of the network. Besides, to improve the correlation characteristics of the sensing matrix, an orthogonal regularization term is introduced. During training of the neural network, the Adam optimizer and cosine annealing learning rate scheduling are applied to jointly minimize the normalized mean square error and total loss of learned dictionary correlations. Experimental results demonstrate that the proposed method, at a representative signal-to-noise ratio of 20 dB, achieves normalized mean square errors of −24.5 dB. The root mean square errors for angle and distance estimation were 0.50° and 0.18 m, respectively, achieving superior performance relative to heuristic algorithms and deep learning-based algorithms. Beyond its strong robustness to different grid granularities and spatial distances, the proposed method also achieves competitive pilot overhead compared with other approaches.