sinr map reconstruction in urban wireless networks using group equivariant non-expansive operators (GENEO)

High-resolution Signal-to-Interference-Noise Ratio (SINR) maps are a key enabler for radio environment mapping, coverage planning, and intelligent resource allocation in next-generation (6G-oriented) urban wireless networks, but dense measurement acquisition is often impractical. This thesis investigates SINR map reconstruction from extremely sparse and irregular samples (1–3%) using Group Equivariant Non-Expansive Operators (GENEOs), a parameter-efficient operator-learning framework that embeds geometric symmetries (notably rotation equivariance) and stability (non-expansiveness) directly into the reconstruction model. The proposed GENEO-based methodology combines rotation-equivariant kernel operators with similarity-based weighting to propagate sparse measurements over a 2-D urban grid while preserving structural regularities of radio propagation. The approach is validated on realistic ray-traced urban datasets (Munich and Paris) and benchmarked against classical interpolators (IDW, RBF), a statistical baseline (Gaussian Process Regression), and a deep learning baseline (U-Net), using pixel-wise metrics (RMSE, SSIM) and topological fidelity measures (e.g., persistence-diagram distances). At 2% sampling, GENEO achieves RMSE 3.42 ± 0.18 dB (vs. IDW 4.87 ± 0.24 dB and RBF 4.23 ± 0.21 dB), remaining functional down to 1% sampling with RMSE 4.52 ± 0.28 dB; U-Net yields the best accuracy (2.94 ± 0.16 dB) but with ~2M parameters, while GENEO uses ~100 parameters and substantially lower memory footprint. Cross-city transfer (Munich→Paris) shows moderate degradation (RMSE 4.15 ± 0.24 dB vs. 3.28 ± 0.17 dB within-city), indicating useful generalization without target-city retraining. Overall, GENEOs offer a mathematically grounded and computationally efficient alternative for SINR reconstruction in data-scarce settings, balancing accuracy, robustness, and interpretability.