- Log-distance path loss model
The log-distance path loss model is a
radio propagation model that predicts thepath 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 zeromean and sigma;standard deviation indB , reflecting theshadow fading orslow 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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