Shadowing models
Log normal shadowing
Pathloss models predict the mean path loss as a function of transmission and reception parameters such as frequency, antenna heights, and distance, etc. Therefore, the predicted path loss between a transmitter and a receiver is constant, in a given environment and for a given distance.
However, different types of clutter may exist in the transmitter-receiver path. Therefore, the path losses for the same distance could be different along paths that pass through different types of environments. The location of the receiver in different types of clutter causes variations with respect to the mean path loss values given by the path loss models. Some paths undergo more loss while others are less obstructed and may have higher received signal strength. The variation of path loss with respect to the mean path loss values predicted by the propagation models, depending on the type of environment is called shadow fading (Shadowing) or slow fading. "Slow" fading implies that the variations in the path loss due to shadow fading occur comparatively slower than the fast fading effect (Fading), which is due to the mobile receiving multipath copies of a signal.
Measurements have shown that at any value of d, the path loss PL (d) at a particular location is random and distributed log-normally about the mean distance-dependent value i.e.
Where \(\chi\) is a zero-mean Gaussian distributed random variable (in dB) with standard deviation \(\sigma\ \)(in dB). The default value for \(\sigma\ is\ 5\ dB\), and the range of \(\sigma\) (in dB) is \(5 \leq \sigma \leq 12.\)