Log-distance path loss model

The Log Distance Path Loss Model is a indoor Radio propagation model that predicts the path loss a signal encounters inside a building 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:

$L\;=\;L_{0}\;+\;N\;\log {\frac {d}{d_{0}}}\;+\;X_{g}$

where,

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

L₀ = The path loss at reference distance, usually, 1 km or 1 mile. Unit: Decibel (dB)

N = The path loss distance exponent times 10.

X_g = A Gaussian random variable with zero mean and $\sigma \;$ standard deviation.

Calculation of empirical coefficients

The coefficients N and sigma are calculated as follows.

Building Type	Frequency of Transmission	N	Sigma
Retail store	914 MHz	22	8.7
Grocery store	914 MHz	18	5.2
Office with hard paritition	1.5 GHz	30	7
office with soft partition	900 MHz	24	9.6
office with soft partition	1.9 GHz	26	14.1
Textile or chemical	1.3 GHz	20	3.0
Textile or chemical	4 GHz	21	7.0, 9.7
Metalworking	1.3 GHz	16	5.8
Metalworking	1.3 GHz	33	6.8

Further reading

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

See also

• ITU Model for Indoor Attenuation
• Radio propagation model