Spatial-Temporal Interpolation

A geostatistical method that predicts unknown RF signal values at unmeasured locations by computing a weighted average of known neighboring measurements. The weights are derived from a modeled variogram, which quantifies spatial autocorrelation as a function of distance. Unlike simple inverse distance weighting, Kriging provides a statistically optimal, unbiased estimator with minimum variance.

• Produces both a predicted value and a kriging variance (uncertainty estimate)
• Requires modeling the experimental variogram from empirical data
• Types include Ordinary, Universal, and Co-Kriging for multivariate data

A non-parametric Bayesian machine learning method that defines a distribution over possible functions that fit observed spectrum data. GPR provides both a predicted mean and a quantified uncertainty (variance) at every spatial coordinate, making it ideal for REM construction where confidence intervals are critical for risk-aware spectrum access decisions.

• Defined by a mean function and a covariance kernel (e.g., Matérn, RBF)
• Naturally handles noisy observations through a Gaussian likelihood model
• Computationally intensive: O(n³) complexity requires sparse approximations for large sensor networks

A deep learning architecture that models distributed sensors as nodes in a graph, where edges represent spatial proximity or propagation paths. GNNs perform message passing between connected nodes to interpolate spectrum data across irregular sensor topologies, learning complex non-linear spatial dependencies that traditional geostatistical methods may miss.

• Captures non-Euclidean spatial relationships in urban canyons
• Supports inductive learning: generalizes to new sensor locations without retraining
• Variants include Graph Convolutional Networks (GCN) and Graph Attention Networks (GAT)

A core geostatistical function that quantifies the spatial autocorrelation of RF measurements as a function of separation distance. The experimental variogram plots the average squared difference between measurement pairs against their lag distance, revealing the range (distance beyond which measurements are uncorrelated), sill (maximum variance), and nugget (measurement noise).

• Foundational input for Kriging-based spectrum cartography
• Typical models: Spherical, Exponential, Gaussian, Matérn
• Anisotropic variograms account for directional dependence (e.g., along streets vs. through buildings)

A signal processing technique that reconstructs a wideband spectrum map from sub-Nyquist rate samples by exploiting the inherent sparsity of spectrum occupancy in the frequency domain. Instead of sampling at twice the maximum frequency, compressed sensing acquires a small number of random linear projections and recovers the full signal via ℓ₁-minimization.

• Enables wideband monitoring with affordable analog-to-digital converters
• Recovery algorithms: Basis Pursuit, OMP, LASSO
• Requires a sparsifying basis (e.g., Fourier, wavelet) where the signal is compressible

A discrete global grid system developed by Uber that partitions the Earth's surface into hierarchical hexagonal cells. H3 provides a standardized, distortion-minimizing spatial indexing system for aggregating and querying REM data, avoiding the angular distortion of rectangular grids at high latitudes.

• 15 resolution levels: from ~1,000 km² (level 0) to < 1 m² (level 15)
• Each hexagon has a unique 64-bit index for efficient database lookups
• Hexagons offer uniform adjacency: every cell has six equidistant neighbors, simplifying spatial interpolation