Spatial Consistency

Channel parameters such as delay spread, angle of arrival, and shadow fading must evolve as a continuous function of the terminal's position. A movement of 1 cm should not cause a completely new set of scatterers to appear. This is typically achieved by generating parameters for a grid of virtual locations and interpolating between them, ensuring that the channel impulse response changes smoothly without abrupt jumps in power or timing.

The model must anchor scatterers and propagation paths to a fixed geometric environment. In a Geometry-Based Stochastic Channel Model (GSCM) , clusters of scatterers are placed on a 2D or 3D map. As a user moves, the angles and delays of these clusters update deterministically based on geometry. This creates natural birth-death processes for paths, where a reflection disappears only when it is physically occluded, not randomly.

Different large-scale parameters (LSPs) cannot vary independently. A terminal entering a deep shadow fading region likely also experiences increased delay spread due to obstruction. Spatially consistent models enforce a cross-correlation matrix between LSPs like delay spread, angular spread, and shadow fading. This ensures that the joint distribution of parameters at any location reflects physically measured interdependencies.

The concept of a stationarity region defines an area—typically a few meters to tens of meters wide—where the statistical properties of the channel (the wide-sense stationary uncorrelated scattering assumption) remain valid. A spatially consistent model explicitly defines these regions and ensures that the small-scale fading statistics are identical within a region but transition smoothly across region boundaries, preventing artificial discontinuities at the edges.

For multi-antenna systems, the channel seen by closely spaced antenna elements must be highly correlated. A spatially consistent model generates the propagation paths once for the antenna array center and then applies a deterministic spherical wavefront or plane-wave phase shift to each element. This guarantees realistic spatial correlation matrices and accurate beamforming gain predictions, avoiding the independent-fading-per-element flaw.

A model that is consistent in space is automatically consistent in time for a moving terminal. The spatial correlation distance maps directly to a coherence time via the user's velocity. A properly designed spatial consistency filter ensures that the resulting Doppler spectrum matches the expected Jakes or custom spectrum. This duality validates the model, proving that smooth spatial transitions produce realistic temporal fading without separate time-domain stitching.