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

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.