Hybrid-Field Channel Estimation for XL-MIMO Systems: Dictionary-based Sparse Signal Recovery

Extremely large-scale multiple-input multiple-output (XL-MIMO) systems are a key technology for future wireless networks, but the large array aperture naturally creates a hybrid-field (HF) propagation regime in which far-field (FF) planar-wave and near-field (NF) spherical-wave components coexist. This work considers the problem of HF channel estimation (CE) and introduces a unified model that superimposes FF and NF contributions according to the Rayleigh distance boundary. By exploiting the inherent sparsity of the channel in the angular and polar domains, we formulate the estimation task as a sparse recovery problem. Unlike conventional approaches that require prior knowledge of the channel sparsity level, the proposed method operates without requiring knowledge of the sparsity level L and the NF/FF ratio γ, which are used only for synthetic channel generation in simulations. The channel estimator determines the number of paths adaptively through a residual-based stopping rule. A combined FF/NF dictionary is employed to initialize the support, and each selected atom undergoes continuous parameter refinement to mitigate grid mismatch. Simulation results demonstrate that the proposed estimator achieves accurate HF channel reconstruction under both line-of-sight (LoS) and non-line-of-sight (NLoS) conditions, offering a practical and computationally efficient solution for XL-MIMO systems. Extremely Large-Scale MIMO (XL-MIMO); Channel State Information (CSI); Channel estimation (CE); hybrid-field (HF) wave propagation; near-field (NF) spherical wave model; far-field (FF) planar wave model

💡 Research Summary

This paper addresses the challenging problem of channel estimation (CE) in extremely large‑scale multiple‑input multiple‑output (XL‑MIMO) systems, where the massive array aperture inevitably creates a hybrid‑field (HF) propagation environment: far‑field (FF) planar‑wave components coexist with near‑field (NF) spherical‑wave components. The authors first develop a unified channel model that explicitly separates the FF and NF contributions based on the Rayleigh distance (D_{\text{Rayleigh}} = 2R^{2}/\lambda). The FF part is represented in the angular domain using a conventional DFT‑based dictionary (U) (size (N\times Q_{F})), while the NF part is represented in a polar (angle‑distance) domain using a second dictionary (V) (size (N\times Q_{N})). By concatenating the two dictionaries into a single matrix (A=