Spectrum Cartography

The foundational geostatistical technique for spectrum cartography, Ordinary Kriging models the spatial correlation of received signal strength using a semivariogram. This method provides the best linear unbiased predictor (BLUP) of PSD at unobserved locations by weighting nearby sensor measurements based on their spatial covariance structure. Unlike simple inverse distance weighting, Kriging quantifies the estimation variance at each interpolated point, giving operators a confidence interval for the predicted spectrum occupancy.

A Radio Environment Map is the multi-dimensional output of spectrum cartography, integrating geolocated sensing data with propagation models and transmitter databases. A complete REM stores:

• Spatial coordinates (latitude, longitude, altitude)
• Frequency-specific PSD measurements
• Temporal metadata for time-varying analysis
• Transmitter locations and known emitter parameters This layered database enables cognitive radios to query real-time spectrum availability at their precise location before transmission.

Traditional Nyquist-rate sampling of wideband spectrum is hardware-prohibitive. Compressive spectrum cartography exploits the inherent sparsity of spectrum occupancy—most frequencies are idle at any location—to reconstruct complete spatial-spectral maps from sub-Nyquist samples. By solving an L1-minimization problem, the system recovers the full PSD map from dramatically fewer measurements, reducing sensor cost and data throughput requirements while maintaining high-fidelity spatial resolution.

Modern approaches replace classical Kriging with Graph Neural Networks (GNNs) that model spectrum sensors as nodes in a graph with edges weighted by spatial proximity and propagation characteristics. The GNN learns complex, non-linear spatial-spectral dependencies directly from data, outperforming linear estimators in environments with:

• Irregular terrain causing non-stationary shadowing
• Urban canyons with multi-path reflections
• Dynamic emitter populations with unknown spatial statistics Message passing between nodes enables accurate PSD prediction even in areas far from physical sensors.

Beyond PSD interpolation, advanced cartography estimates the channel gain map—the spatial distribution of path loss between any transmitter location and any receiver location. This is accomplished through tomographic techniques that invert received signal strength measurements to reconstruct the attenuation field. The resulting map enables:

• Interference footprint prediction for proposed new transmitters
• Optimal sensor placement to minimize estimation error
• Coverage hole detection for cellular network planning

Static sensor grids are suboptimal for dynamic spectrum environments. Adaptive cartography systems use active learning to direct mobile sensing agents toward areas of high estimation uncertainty or rapid temporal change. Multi-resolution techniques apply:

• Coarse mapping over quiescent rural areas with sparse sampling
• Fine-grained mapping in urban hotspots with dense, drone-mounted sensors This hierarchical approach minimizes sensing overhead while guaranteeing a maximum PSD estimation error bound across the entire region of interest.