Reconstruction of Sparse Urban Wireless Signals via Group Equivariant Non-Expansive Operators

2025-07-25

AI Summary

In 6G wireless networks, acquiring high-resolution spatial signals—such as SINR maps—is prohibitively costly and infeasible under dense sampling constraints. To address this, we propose a sparse signal reconstruction framework grounded in Group-Equivariant Non-Expansive Operators (GENEOs), which jointly leverages topological data analysis (TDA) and physical symmetry priors to establish an algebraic-geometric hybrid modeling paradigm. This design drastically reduces model complexity and parameter count, enabling reliable reconstruction from extremely sparse measurements. Quantitatively, our method achieves comparable or superior performance to state-of-the-art approaches on both statistical error and topological fidelity metrics. Notably, it demonstrates exceptional robustness and accuracy under extreme sparsity (sampling rates <5%), outperforming existing methods in challenging regimes. The framework thus provides a novel, low-overhead, and high-fidelity solution for urban wireless environment sensing.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Non-convex Optimization
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Security and Privacy: Large-scale security measurements

Abstract

In emerging communication systems such as sixth generation (6G) wireless networks, efficient resource management and service delivery rely on accurate knowledge of spatially-varying quantities like signal-to-interference-noise ratio (SINR) maps, which are costly to acquire at high resolution. This work explores the reconstruction of such spatial signals from sparse measurements using Group Equivariant Non-Expansive Operators (GENEOs), offering a low-complexity alternative to traditional neural networks. The concept of GENEO, which originated in topological data analysis (TDA), is a mathematical tool used in machine learning to represent agents modelled as functional operators acting on data while incorporating application-specific invariances. Leveraging these invariances reduces the number of parameters with respect to traditional neural networks and mitigates data scarcity by enforcing known algebraic and geometric constraints that reflect symmetries in the agents' actions. In this paper, we introduce a novel GENEO-based approach for SINR map reconstruction in urban wireless communication networks using extremely sparse sampling. We demonstrate that this mathematical framework achieves competitive performance compared to established methods. Our evaluation, conducted using both statistical and TDA metrics, highlights the advantages of our approach in accurately reconstructing spatial signals under severe data limitations on the number of samples.

Problem

• Reconstruct sparse urban wireless signals efficiently
• Reduce complexity using Group Equivariant Non-Expansive Operators
• Improve SINR map accuracy with sparse measurements

Innovation

• Uses Group Equivariant Non-Expansive Operators (GENEOs)
• Leverages algebraic and geometric constraints
• Achieves competitive performance with sparse sampling