Log-distance path loss model

The log-distance path loss model is a radio propagation model that predicts the path loss a encounters inside a building or densely populated areas over distance.

Applicable to / Under conditions

The model is applicable to indoor propagation modeling.

Mathematical formulation

The model

Log-distance path loss model is formally expressed as:

: $L;=10log\_\{10\}\; frac\{P\_\{Tx\{P\_\{Rx;=;L\_0;+;10gamma;log\_\{10\}\; frac\{d\}\{d\_0\};+;X\_g,$

where

: $\{L\}$ = The total path loss. Unit:Decibel (dB)

: $\{P\_\{Tx$ = transmitted power in watt or volt².

: $\{P\_\{Rx$ = received power in watt or volt².

: $L\_0$ = path loss at the distance "d"₀. Unit: Decibel (dB)

: $\{d\}$ = the length of the path.

: $\{d\_0\}$ = the reference distance, usually 1 km (or 1 mile).

: $gamma$ = the path loss distance exponent.

: $X\_g$ = a Gaussian random variable with zero mean and $sigma;$ standard deviation in dB, reflecting the shadow fading or slow fading.

Corresponding non-logarithmic model

This corresponds to the following non-logarithmic gain model:

: $frac\{P\_\{Rx\{P\_\{Tx;=;frac\{c\_0F\_g\}\{d^\{gamma$

where

$c\_0;=;\{d\_0^\{gamma10^\{frac\{-L\_0\}\{10$ is the average multiplicative gain at the reference distance $d\_0$ from the transmitter. This gain depends on factors such as carrier frequency, antenna heights and antenna gain, for example due to directional antennas; and

$F\_g;=;10^\{frac\{-X\_g\}\{10$ reflects the slow shadow fading, and is a stochastic process with log-normal distribution, with parameter $sigma;$ dB.

Empirical coefficient values for indoor propagation

Empirical measurements of coefficients $gamma$ and $sigma$ in dB have shown the following values for a number of indoor wave propagation cases. "Wireless communications principles and practices", T. S. Rappaport, 2002, Prentice-Hall]

References

Further reading

* "Introduction to RF propagation", John S. Seybold, 2005, Wiley.
* "Wireless communications principles and practices", T. S. Rappaport, 2002, Prentice-Hall.

ee also

*ITU model for indoor attenuation
*Radio propagation model