Log Distance Path Loss Model

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The Log Distance Path Loss Model is a radio propagation model that predicts the path loss a signal encounters inside a building or densily populated areas over distance.

Contents

[edit] Applicable to / Under conditions

The model is applicable to indoor propagation modeling.

[edit] Mathematical formulation

[edit] The model

Log Distance Path Loss model is formally expressed as:

L\;=10\log_{10} \frac{P_{Tx}}{P_{Rx}}\;=\;L_0\;+\;10\gamma\;\log_{10} \frac{d}{d_0}\;+\;X_g

where,

L = The total path loss. Unit:Decibel (dB)

PTx = Transmitted power in Watt or Volt2.

PRx = Received power in Watt or Volt2.

L0 = The path loss at the distance d0. Unit: Decibel (dB)

d = The length of the path.

d0 = The reference distance, usually 1 km (or 1 mile).

γ = The path loss distance exponent.

Xg = A Gaussian random variable with zero mean and \sigma\; standard deviation in dB, reflecting the shadow fading or slow fading.

[edit] 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^{\gamma}}10^{\frac{-L_0}{10}} is the average multiplicative gain at the reference distance d0 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.

[edit] Empirical coefficient values for indoor propagation

Empirical measurements of coefficients γ and σ in dB have shown the following values for a number of indoor wave propagation cases. [1]

Building Type Frequency of Transmission γ σ [dB]
Vacuum, infinite space 2.0 0
Retail store 914 MHz 2.2 8.7
Grocery store 914 MHz 1.8 5.2
Office with hard partition 1.5 GHz 3.0 7
Office with soft partition 900 MHz 2.4 9.6
Office with soft partition 1.9 GHz 2.6 14.1
Textile or chemical 1.3 GHz 2.0 3.0
Textile or chemical 4 GHz 2.1 7.0, 9.7
Metalworking 1.3 GHz 1.6 5.8
Metalworking 1.3 GHz 3.3 6.8

[edit] References

  1. ^ Wireless communications principles and practices, T. S. Rappaport, 2002, Prentice-Hall

[edit] Further reading

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

[edit] See also

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