A large‑scale propagation model that represents slow, spatial variations of received power around a deterministic path‑loss mean by treating the multiplicative deviations as a log‑normal random variable, i.e., the received power in dB is modelled as the mean path loss plus a zero‑mean Gaussian random term with specified standard deviation.

Principle

Obstructions and large objects produce multiplicative attenuation on linear power; taking logarithms converts these multiplicative effects into additive, approximately Gaussian variations in dB over distances large compared with wavelength but small compared with cell size.

Demonstration

Illustrative scenario: along a suburban drive, the deterministic path‑loss curve gives an average received level; measured values scatter about that curve with a roughly Gaussian distribution in dB; fitting a Gaussian residual yields a standard deviation parameter used to compute the probability that received power falls below a threshold at a given distance.

Misapplication

Confusing log‑normal shadowing with small‑scale (fast) fading or assuming its samples are spatially independent at arbitrarily small separations misapplies the model; shadowing is a slow process with spatial correlation over tens to hundreds of metres in many environments.

Consequence

The model supplies a simple stochastic description for outage probabilities and link margins in system design and simulation; using it without environment‑specific parameter estimation or ignoring spatial correlation can understate or overstate outage and handover rates.

Reversal

In environments dominated by fast multipath (e.g., rich indoor scattering at small scales) or when shadowing statistics are non‑stationary (time‑varying geometry or moving obstructions), the log‑normal assumption and stationarity break down and require alternative or time‑dependent models.

Boundary

Within: large‑scale, slow variations of received power over distances where site geometry is roughly stationary and multiplicative obstruction effects dominate. Boundary case: mixed scenarios where both shadowing and strong small‑scale fading contribute equally. Outside: instantaneous fading at sub‑wavelength scales or deterministic site‑specific propagation dominated by single‑path obstructions.

Semantic Tension

Statistical tractability (single‑parameter variance in dB) ↔ need for spatially and temporally resolved, site‑specific models; model simplicity aids analysis but can obscure local non‑Gaussian or non‑stationary behavior.

Synthesis

Log‑normal shadowing isolates macroscopic, multiplicative variability into a Gaussian term in dB, providing a compact stochastic layer on top of mean path‑loss models that is powerful for probabilistic planning but must be calibrated and interpreted at the appropriate spatial and temporal scales.