Shadow Fading Map

The map enforces spatial consistency, ensuring that fading values for closely spaced points are correlated. This is typically achieved through 2D Gaussian filtering of an uncorrelated random map. The de-correlation distance—the distance at which the autocorrelation falls to 0.5—is a key parameter, often set between 10m and 100m depending on the environment (urban micro vs. rural macro). Without this, a moving UE would experience physically impossible, abrupt jumps in received power.

Shadow fading is modeled as a zero-mean Gaussian random variable in the logarithmic (dB) domain. The map's pixel values represent the deviation from the deterministic path loss, following a log-normal distribution. The standard deviation (σ) is environment-specific:

• Urban macro-cell: 8-10 dB
• Rural macro-cell: 4-6 dB
• Indoor office: 3-5 dB This statistical property directly impacts cell-edge coverage probability.

A single statistical map is insufficient for high-fidelity simulation. Advanced digital twins use 3D environment reconstruction and ray tracing to generate deterministic shadowing maps. This involves:

• Building footprint overlays: Assigning higher attenuation values to pixels behind large structures.
• Diffraction modeling: Calculating the shadow boundary behind sharp edges.
• Vegetation attenuation: Adding seasonal fading variations for foliage. This hybrid approach combines deterministic prediction with a stochastic residual component.

A signal from a UE is often received by multiple base stations. A realistic shadow fading map must model the cross-correlation between the fading experienced on these different links. The correlation coefficient (ρ) depends on:

• The angle of arrival difference at the UE.
• The site-to-site distance.
• Whether the sites are co-located or geographically separated. A typical model sets ρ = 0.5 for intra-site sectors and ρ = 0.0 for widely separated sites, ensuring consistent handover margin analysis.

While often treated as static, a shadow fading map can be dynamic in a digital twin to reflect environmental changes:

• Vehicular obstruction: Moving buses or trucks create temporary, deep fades (10-20 dB) that track with the vehicle's mobility model.
• Construction changes: The map is updated when new buildings are added to the 3D environment reconstruction.
• User mobility: The map is sampled along a user mobility model trajectory, converting a spatial process into a time-series for link-level simulation.

The shadow fading map is an additive overlay on the path loss map. The total channel gain at a location (x,y) is calculated as: G_total(x,y) = G_pathloss(x,y) + SF_map(x,y) + F_fast Where F_fast is the small-scale fading from a geometry-based stochastic channel model (GSCM). This separation of scales allows system-level simulators to apply shadow fading as a slow, location-dependent offset while computing fast fading per transmission time interval.