Shadowing

Shadowing is a fading process caused by obstacles in the path between transmitter and receiver. The signal is being reflected, diffracted and scattered by these objects resulting in a randomly distributed variation in signal strength at a given distance. Due to the large amount of obstacles affecting the shadow fading it is often modeled with an statistical model [2,4].

The 802.11n channel model [3] includes the shadow fading by superimposing its path loss with a log-normal distribution which has been shown to be a well suited approximation [2]. Mathematically the log-normal distribution with variance $\sigma^2$ and standard deviation $\mu$ can be described as: $$ p_{\mathrm{ln}}(x) = \begin{cases} \frac{1}{\sqrt{2\pi}\sigma x} \exp{\left(-\frac{(\ln{(x)}-\mu)^2}{2\sigma^2}\right)} & x > 0 \\ 0 & x \le 0 \\ \end{cases} $$ Superimposing it with the path loss model results in the following equation: $$ L(d)(\mathrm{dB}) = \begin{cases} 20\log{\left(\frac{\lambda}{4\pi d}\right)} + 10\log{(p_{\mathrm{ln}}(x))} & d \le d_{\mathrm{bp}} \\ 20\log{\left(\frac{\lambda}{4\pi d}\right)} + 35\log{\left(\frac{d}{d_{\mathrm{bp}}}\right)} + 10\log{(p_{\mathrm{ln}}(x))} & d \ge d_{\mathrm{bp}} \\ \end{cases} $$ Each of the 6 scenarios have different $\sigma$ which are listed in the table below:

scenario |
$\mathbf{\sigma}$(dB)(LOS) |
$\mathbf{\sigma}$(dB)(NLOS) |

Flat-Fading | 3 | 4 |

Typical residential environment | 3 | 4 |

Typical residential or small office environment | 3 | 5 |

Typical office environment | 3 | 5 |

Typical large open space and office environments | 3 | 6 |

Large open space (indoor and outdoor) | 3 | 6 |