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

David William Marques Guerra, Taufik Abrao

TL;DR

Problem: channel estimation for XL-MIMO in a hybrid-field environment where FF and NF components coexist. Approach: a unified HF channel model and a sparsity-driven estimator called epsilon-OMP-SSIGW, using a combined FF/NF dictionary and a residual-based stopping rule that does not require prior knowledge of sparsity L or NF/FF ratio gamma. Contributions: (i) closed-form single-column LS gain update, (ii) gridless refinement via scalar gradient updates with Armijo backtracking, (iii) automatic path counting through residual stopping, and (iv) demonstrated NMSE gains across LoS and NLoS with favorable complexity. Significance: provides a practical, robust HF CE solution for XL-MIMO enabling reliable high-rate wireless in future networks.

Abstract

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

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

TL;DR

Problem: channel estimation for XL-MIMO in a hybrid-field environment where FF and NF components coexist. Approach: a unified HF channel model and a sparsity-driven estimator called epsilon-OMP-SSIGW, using a combined FF/NF dictionary and a residual-based stopping rule that does not require prior knowledge of sparsity L or NF/FF ratio gamma. Contributions: (i) closed-form single-column LS gain update, (ii) gridless refinement via scalar gradient updates with Armijo backtracking, (iii) automatic path counting through residual stopping, and (iv) demonstrated NMSE gains across LoS and NLoS with favorable complexity. Significance: provides a practical, robust HF CE solution for XL-MIMO enabling reliable high-rate wireless in future networks.

Abstract

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
Paper Structure (7 sections, 28 equations, 2 figures, 2 tables, 1 algorithm)

This paper contains 7 sections, 28 equations, 2 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Sparse Channel Estimation Formulation
  4. Proposed Solution and Algorithm
  5. Numerical Results and Discussions
  6. Conclusions
  7. Gradient for Single-Column Refinement

Figures (2)

  • Figure 1: NMSE and runtime of LS, MMSE, FF-OMP, HF-OMP variants, SD-OMP, HF SGP with $\gamma$, HF SGP without $\gamma$, and the proposed $\epsilon$-OMP-SSIGW for (a) NLoS, (b) mixed LoS/NLoS, and (c)–(d) runtime results.
  • Figure 2: (a) Complexity results based on Table \ref{['tab:complexity_updated']}; (b) NMSE and the resulting $L_{\rm est}$ (mean iteration count of the $\epsilon$-OMP-SSIGW) for different values of $\epsilon$.