Exploiting Structured Sparsity in Near Field: From the Perspective of Decomposition

TL;DR

This work addresses whether the advantages of structured sparsity in far-field channels extend to near-field ELAA scenarios. It identifies physical and mathematical bottlenecks caused by spherical-wave propagation, notably power leakage and triple coupling of elevation, azimuth, and distance, which complicate sparse recovery. The authors propose the triple parametric decomposition (TPD) framework to decouple the three geometric parameters and enable robust near-field sparse-channel estimation that leverages structured sparsity, with Stepwise implementations that isolate angle and distance information. The approach offers robustness to cluster size and distance, broad compatibility with established algorithms (e.g., MUSIC), and significant reductions in computational and structural complexity, while outlining practical applications (AoA detection, recursive tracking, LDMA) and future directions including continuous-aperture HMIMO and two-module sparse-recovery algorithms. Overall, TPD provides a scalable pathway to efficient near-field channel estimation in ELAA and HMIMO systems, potentially enabling practical 6G deployments with reduced pilot overhead and processing burden.

Abstract

The structured sparsity can be leveraged in traditional far-field channels, greatly facilitating efficient sparse channel recovery by compressing the complexity of overheads to the level of the scatterer number. However, when experiencing a fundamental shift from planar-wave-based far-field modeling to spherical-wave-based near-field modeling, whether these benefits persist in the near-field regime remains an open issue. To answer this question, this article delves into structured sparsity in the near-field realm, examining its peculiarities and challenges. In particular, we present the key features of near-field structured sparsity in contrast to the far-field counterpart, drawing from both physical and mathematical perspectives. Upon unmasking the theoretical bottlenecks, we resort to bypassing them by decoupling the geometric parameters of the scatterers, termed the triple parametric decomposition (TPD) framework. It is demonstrated that our novel TPD framework can achieve robust recovery of near-field sparse channels by applying the potential structured sparsity and avoiding the curse of complexity and overhead.

Figures (6)

• Figure 1: Physical peculiarities caused by the spherical-wave-based modeling in near-field communications.
• Figure 2: Illustration of the weak sparseness in near-field communication with the ($64 \times 64$) UPA, number of scatterers is set to $L = 3$. $K$ denotes the number of non-zero entries.
• Figure 3: Capturing structured information in 3D space.
• Figure 4: The proposed TPD framework for near-field communications.
• Figure 5: NMSE of geometric parameters versus cluster concentration factor, array size: ($256\times 256$ for default, $256\times 1$ for ULA setting), distance set to $10\ {\rm m}$, $3$ clusters, each of which contains $2$ scatterers.