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| The '''log-distance path loss model''' is a [[radio propagation model]] that predicts the [[path loss]] a [[Wiktionary:signal|signal]] encounters inside a building or densely populated areas over distance.
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| ==Applicable to / Under conditions==
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| The model is applicable to indoor propagation modeling.
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| ==Mathematical formulation==
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| ===The model===
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| Log-distance path loss model is formally expressed as:
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| : <math>PL\;=P_{Tx_{dBm}}-P_{Rx_{dBm}}\;=\;PL_0\;+\;10\gamma\;\log_{10} \frac{d}{d_0}\;+\;X_g,</math>
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| where
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| : <math>{PL}</math> is the total [[path loss]] measured in [[Decibel]] (dB)
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| : <math>P_{Tx_{dBm}}\;=10\log_{10} \frac{P_{Tx}}{1mW}</math> is the transmitted power in [[dBm]], where
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| : <math>P_{Tx}</math> is the transmitted power in [[watt]].
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| : <math>P_{Rx_{dBm}}\;=10\log_{10} \frac{P_{Rx}}{1mW}</math> is the received power in dBm, where
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| : <math>{P_{Rx}}</math> is the received power in watt.
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| : <math>PL_0</math> is the [[path loss]] at the reference distance ''d''<sub>0</sub>. Unit: [[Decibel]] (dB)
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| : <math>{d}</math> is the length of the path.
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| : <math>{d_0}</math> is the reference distance, usually 1 km (or 1 mile).
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| : <math>\gamma</math> is the [[path loss]] exponent.
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| : <math>X_g</math> is a [[normal random variable|normal (or Gaussian) random variable]] with zero [[mean]], reflecting the attenuation (in decibel) caused by [[flat fading]]{{Citation needed|date=October 2011}}. In case of no fading, this variable is 0. In case of only [[shadow fading]] or [[slow fading]], this random variable may have [[Gaussian distribution]] with <math>\sigma\;</math> [[standard deviation]] in [[Decibel|dB]], resulting in [[log-normal distribution]] of the received power in Watt. In case of only fast fading caused by multipath propagation, the corresponding gain in Watts <math>F_g\;=\;10^{\frac{-X_g}{10}}</math> may be modelled as a random variable with [[Rayleigh distribution]] or [[Ricean distribution]].<ref>{{cite book|title=Handbook of Propagation Effects for Vehicular and Personal Mobile Satellite Systems|author=Julius Goldhirsh|coauthors=Wolfhard J. Vogel|url=http://www.utexas.edu/research/mopro/papercopy/chapter11.pdf|chapter=11.4}}</ref>
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| ===Corresponding non-logarithmic model===
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| This corresponds to the following non-logarithmic gain model:
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| : <math>\frac{P_{Rx}}{P_{Tx}}\;=\;\frac{c_0F_g}{d^{\gamma}} </math>
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| where
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| <math>c_0\;=\;{d_0^{\gamma}}10^{\frac{-L_0}{10}}</math> is the average multiplicative gain at the reference distance <math>d_0</math> from the transmitter. This gain depends on factors such as carrier frequency, antenna heights and antenna gain, for example due to directional antennas; and
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| <math>F_g\;=\;10^{\frac{-X_g}{10}}</math> is a [[stochastic process]] that reflects [[flat fading]]. In case of only slow fading (shadowing), it may have [[log-normal]] distribution with parameter <math>\sigma\;</math> dB. In case of only [[fast fading]] due to [[multipath propagation]], its amplitude may have [[Rayleigh distribution]] or [[Ricean distribution]].
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| ==Empirical coefficient values for indoor propagation==
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| Empirical measurements of coefficients <math>\gamma</math> and <math>\sigma</math> in dB have shown the following values for a number of indoor wave propagation cases.<ref name = "Ref 1">''Wireless communications principles and practices'', T. S. Rappaport, 2002, Prentice-Hall</ref>
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| {| class="wikitable"
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| ! Building Type !! Frequency of Transmission !! <math>\gamma</math> !! <math>\sigma</math> [dB]
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| | Vacuum, infinite space || || 2.0 || 0
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| | Retail store || 914 MHz || 2.2 || 8.7
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| | Grocery store || 914 MHz || 1.8 || 5.2
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| | Office with hard partition || 1.5 GHz || 3.0 || 7
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| | Office with soft partition || 900 MHz || 2.4 || 9.6
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| | Office with soft partition || 1.9 GHz || 2.6 || 14.1
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| | Textile or chemical || 1.3 GHz || 2.0 || 3.0
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| | Textile or chemical || 4 GHz || 2.1 || 7.0, 9.7
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| | Metalworking || 1.3 GHz || 1.6 || 5.8
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| | Metalworking || 1.3 GHz || 3.3 || 6.8
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| |}
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| ==References==
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| <references/>
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| ==Further reading==
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| * ''Introduction to RF propagation'', John S. Seybold, 2005, Wiley.
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| * ''Wireless communications principles and practices'', T. S. Rappaport, 2002, Prentice-Hall.
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| ==See also==
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| *[[ITU Model for Indoor Attenuation]]
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| *[[Radio propagation model]]
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| *[[Young model]]
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| [[Category:Radio frequency propagation]]
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Greetings! I am Myrtle Shroyer. North Dakota is her beginning location but she will have to transfer one day or an additional. In her professional life she is a payroll clerk but she's always wanted her own company. The thing she adores most is physique building and now she is attempting to earn cash with it.
Here is my homepage std testing at home