Physics-Aware Huber-Log Differential Total Variation for Hybrid-Field Channel Estimation in 6G UM-MIMO Systems

Abstract

Ultra-massive multiple-input multiple-output (UM-MIMO) has emerged as a key physical-layer technology for 6G wireless networks. However, the coexistence of far-field and near-field propagation components poses significant challenges to accurate and robust channel estimation. Although existing angular-polar dual-dictionary methods can effectively represent hybrid-field channels, their concatenated dictionaries may incur considerable computational and storage overhead. Angular-domain block-sparse methods provide a more compact alternative, but often rely on predefined partitions or spatially invariant priors that may not adapt well to regime-dependent block structures. To overcome these limitations, we propose a physics-aware unified angular-domain estimation framework. Through discrete convolution analysis and Fresnel integral approximation, we demonstrate that hybrid-field channels exhibit regime-dependent angular block structures and a consistent two-scale bin-to-bin difference pattern. To capture this structure, we design a Huber-Log Differential Total Variation (HL-DTV) hyperprior to promote local continuity for mild variations while preserving large-scale structural differences. To address the coupling introduced by HL-DTV, we develop the Parity-Enabled Alternating Refinement with Lambert- $\mathcal {W}$ Sparse Bayesian Learning (PEARL-SBL) algorithm, which enables parallelizable scalar refinement through even-odd decoupling and closed-form updates. Simulation results show that the proposed approach outperforms existing far-field, near-field, and hybrid-field methods in channel estimation accuracy and spectral efficiency, validating its effectiveness for 6G UM-MIMO systems.