ISTA-Based Joint Dictionary Learning and Channel Estimation for XL-MIMO Systems

Channel estimation in extra-large multiple-input multiple-output systems is challenging due to near-field propagation, where the array response depends on both the angle and distance of the propagation paths. Existing near-field channel estimation methods typically rely either on fixed angle-distance grids, which suffer from grid mismatch effects, or on multi-stage refinement procedures with increased computational complexity. To address these limitations, this paper proposes the \textit{dictionary-learning iterative soft-thresholding algorithm (DL-ISTA)}, a method for joint near-field dictionary learning and channel estimation based on the iterative soft-thresholding algorithm. The proposed method jointly estimates the sparse channel coefficients and the continuous angle-distance parameters through alternating optimization, thereby avoiding discretization errors associated with fixed grids. To promote robust convergence, the angle-distance parameters are initialized using Sobol sequences, which provide uniform coverage of the parameter space. Numerical results show that DL-ISTA outperforms a baseline with comparable computational complexity and attains comparable or better accuracy than a substantially more complex benchmark.