Log-distance path loss model

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


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