Atomic Hybrid Sparse/Diffuse Channel Estimation and Cramér-Rao Bounds Analysis

2026-05-03

AI Summary

This work addresses the challenge of wireless channel estimation in the presence of both sparse specular paths and diffuse scattering components in the frequency domain. To this end, the authors propose an atomic hybrid sparse/diffuse (aHSD) channel model and develop a hybrid atomic least squares (HALS) algorithm that jointly estimates the delay parameters of both components in a gridless manner by combining atomic norm and ℓ² regularization. The study establishes, for the first time, a unified atomic hybrid framework, derives theoretical conditions via duality theory to guarantee the feasibility of gridless estimation, and formulates a Cramér–Rao bound (CRB) dependent on the minimum frequency separation, substantially improving performance prediction accuracy. Experimental results demonstrate that HALS significantly outperforms existing methods on both synthetic and real-world data, and the proposed CRB more accurately characterizes the fundamental performance limits of the estimation algorithm.

Abstract

In this paper, an atomic hybrid sparse/diffuse (aHSD) channel model in the frequency domain is proposed. Based on a structural analysis of the resolvable paths and diffuse scattering statistics, the Hybrid Atomic-Least-Squares (HALS) algorithm is designed to estimate sparse/diffuse components with a combined atomic and $\ell_2$ regularization. A theoretical analysis of the Lagrange dual problem is conducted, and the conditions required for primal and dual solutions are provided, supporting an off-the-grid delay-time estimator. The Cramér--Rao Bound (CRB) analysis in this paper focuses on the estimation of the channel parameters, resulting in a bound on the aggregate channel. Lower and upper bounds for the CRB on parameters are derived as functions of the minimum separations between frequency parameters. Numerical results via simulations on synthetic and real data validate the efficacy of the HALS estimation strategy and show the improved predictive ability of the CRB analysis for the performance of HALS versus previously considered bounds.

Problem

• channel estimation
• sparse/diffuse channel
• Cramér-Rao bound
• atomic norm
• hybrid channel model

Innovation

• atomic norm
• hybrid sparse/diffuse channel
• off-the-grid estimation
• Cramér–Rao bound
• HALS algorithm