Reconstruction of SINR Maps from Sparse Measurements using Group Equivariant Non-Expansive Operators

TL;DR

This paper introduces a novel, low-complexity method using Group Equivariant Non-Expansive Operators (GENEOs) to accurately reconstruct high-resolution SINR maps from sparse measurements, emphasizing topological fidelity over pixel-wise accuracy.

Contribution

The paper presents a new GENEO-based framework that embeds geometric priors for robust SINR map reconstruction from minimal data, outperforming traditional ML models in topological accuracy.

Findings

Outperforms ML baselines in topological metrics

Maintains competitive pixel-wise error (MSE)

Effective in realistic urban scenarios

Abstract

As sixth generation (6G) wireless networks evolve, accurate signal-to-interference-noise ratio (SINR) maps are becoming increasingly critical for effective resource management and optimization. However, acquiring such maps at high resolution is often cost-prohibitive, creating a severe data scarcity challenge. This necessitates machine learning (ML) approaches capable of robustly reconstructing the full map from extremely sparse measurements. To address this, we introduce a novel reconstruction framework based on Group Equivariant Non-Expansive Operators (GENEOs). Unlike data-hungry ML models, GENEOs are low-complexity operators that embed domain-specific geometric priors, such as translation invariance, directly into their structure. This provides a strong inductive bias, enabling effective reconstruction from very few samples. Our key insight is that for network management, preserving the topological structure of the SINR map, such as the geometry of coverage holes and interference patterns, is often more critical than minimizing pixel-wise error. We validate our approach on realistic ray-tracing-based urban scenarios, evaluating performance with both traditional statistical metrics (mean squared error (MSE)) and, crucially, a topological metric (1-Wasserstein distance). Results show that while maintaining competitive MSE, our method dramatically outperforms established ML baselines in topological fidelity. This demonstrates the practical advantage of GENEOs for creating structurally accurate SINR maps that are more reliable for downstream network optimization tasks.