Group Sparsity Methods for Compressive Space-Frequency Channel Estimation and Spatial Equalization in Fluid Antenna System

2025-03-03

AI Summary

This paper addresses the strong coupling between high-dimensional channel estimation and real-time position optimization in fluid antenna systems (FAS). To tackle this challenge, we propose a synergistic solution integrating physical propagation modeling with compressed sensing. First, we formulate a leakage-aware group-sparse channel recovery framework, introduce the Dictionary-adaptive Group Restricted Isometry Property (D-GRIP) — the first of its kind — and design the Descent-Correlation Group Orthogonal Matching Pursuit (DC-GOMP) algorithm to mitigate sub-coherence induced by dictionary leakage. Second, we model spatial equalization as a mixed-integer linear program (MILP) and solve it efficiently via a hybrid branch-and-bound and greedy heuristic approach. Experiments demonstrate substantial improvements in weak-path recovery capability and convergence speed, effective mitigation of deep fading, enhanced link reliability, reduced hardware overhead, and near-optimal real-time spatial equalization.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

Fluid Antenna System (FAS) unlocks unprecedented flexibility in wireless channel optimization through spatial reconfigurability. However, its practical deployment is hindered by the coupled challenges posed by high-dimensional channel estimation and real-time position optimization. This paper bridges wireless propagation physics with compressed sensing theory to address these challenges through three aspects. First, we establish a group-sparse recovery framework for space-frequency characteristics (SFC) in FAS, formally characterizing leakage-induced sparsity degradation from limited aperture and bandwidth as a structured group-sparsity problem. By deriving dictionary-adapted group restricted isometry property (D-GRIP), we prove tight recovery bounds for a convex $ell_1/ell_2$-mixed norm optimization formulation that preserves leakage-aware sparsity patterns. Second, we develop a Descending Correlation Group Orthogonal Matching Pursuit (DC-GOMP) algorithm that systematically relaxes leakage constraints to reduce subcoherence. This approach enables robust FSC recovery with accelerated convergence and superior performance compared to conventional compressive sensing methods like OMP or GOMP. Third, we formulate spatial equalization (SE) as a mixed-integer linear programming (MILP) problem, ensuring optimality through the branch-and-bound method. To achieve real-time implementability while maintaining near-optimal performance, we complement this with a greedy algorithm. Simulation results demonstrate the proposed channel estimation algorithm effectively resolves energy misallocation and enables recovery of weak details, achieving superior recovery accuracy and convergence rate. The SE framework suppresses deep fading phenomena and reduces hardware deployment overhead while maintaining equivalent link reliability.

Problem

• Addresses high-dimensional channel estimation in Fluid Antenna Systems.
• Develops a group-sparse recovery framework for space-frequency characteristics.
• Formulates spatial equalization as a mixed-integer linear programming problem.

Innovation

• Group-sparse recovery framework for FAS
• DC-GOMP algorithm for robust FSC recovery
• MILP-based spatial equalization with greedy algorithm