Area-to-area Lee model

The Lee model for area-to-area mode is a radio propagation model used to predict a path loss over flat terrain.^[1] The model provides a modified power law with correction factors for antenna heights and frequency.^[2]

This model is suitable for using in data collected. The model predicts the behaviour of all links that has ends in specific areas.

Originally developed for use at 900 MHz, the model includes an adjustment factor to increase the frequency range.^[2]

The Lee model is formally expressed as:

${\displaystyle L\;=\;L_{0}\;+\;\gamma \log d\;-10\log {F_{A}}}$

where,

L = The median path loss. Unit: decibel (dB)

L₀ = The reference path loss along 1 km. Unit: decibel (dB)

${\displaystyle \gamma \;}$ = The slope of the path loss curve. Unit: decibels per decade

d = The distance on which the path loss is to be calculated.

F_A = Adjustment factor.

The reference path loss is usually computed along a 1 km or 1 mile link. Any other suitable length of path can be chosen based on the applications.

${\displaystyle L_{0}\;=\;G_{B}\;+\;G_{M}\;+\;20\;(\log \lambda \;-\;\log d)\;-\;22}$

where,

G_B = Base station antenna gain. Unit: decibel with respect to isotropic antenna (dBi)

${\displaystyle \lambda }$ = Wavelength. Unit: meter (m).

G_M = Mobile station antenna gain. Unit: decibel with respect to isotropic antenna (dBi).

The adjustment factor is calculated as:

${\displaystyle F_{A}\;=\;F_{BH}\;F_{BG}\;F_{MH}\;F_{MG}\;F_{F}}$

where,

F_BH = Base station antenna height correction factor.

F_BG = Base station antenna gain correction factor.

F_MH = Mobile station antenna height correction factor.

F_MG = Mobile station antenna gain correction factor.

F_F = Frequency correction factor

${\displaystyle F_{BH}\;=\;\left(\;{\frac {h_{B}}{30.48}}\;\right)^{2}}$

where,

h_B = Base-station antenna height. Unit: meter (m).

or

${\displaystyle F_{BH}\;=\;\left(\;{\frac {h_{B}}{100}}\;\right)^{2}}$

where,

h_B = Base-station antenna height. Unit: foot (ft).

${\displaystyle F_{BG}\;=\;{\frac {G_{B}}{4}}}$

where,

G_B = Base-station antenna gain. Unit: decibel with respect to half wave dipole antenna (dBd)

${\displaystyle F_{MH}\;=\;{\begin{cases}\;\;{\frac {h_{M}}{3}}\;\;\;\;{\mbox{ if, }}h_{M}>3\\{\Big (}{\frac {h_{M}}{3}}{\Big )}^{2}{\mbox{ if, }}h_{M}\leq 3\end{cases}}}$

where,

h_M = Mobile-station antenna height. Unit: meter(m).

${\displaystyle F_{MG}\;=\;G_{M}}$

where,

G_M = Mobile-station antenna gain. Unit: Decibel with respect to half wave dipole antenna (dBd).

${\displaystyle F_{F}\;=\;{\big (}{\frac {f}{900}}{\big )}^{-n}{\mbox{ for }}2<n<3}$

where,

f = Frequency. Unit: megahertz (MHz)

• Hata model
• Okumura model
• COST 231 model
• Young model
• Point-to-point Lee model