Log Distance Path Loss or Log Normal Shadowing Model

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Log distance path loss model is a generic model and an extension to Friis Free space model. It is used to predict the propagation loss for a wide range of environments, whereas, the Friis Free space model is restricted to unobstructed clear path between the transmitter & the receiver.

Log Normal Shadowing image 1
In the far field region of the transmitter \((d ≥ d_f)\), if \(PL(d_0)\) is the path loss measured in \(dB\) at a distance \(d_0\) from the transmitter, then the path loss (the loss in signal power measure in dB when moving from distance \(d_0\) to \(d\) ) at an arbitrary distance \(d >d_0\) is given by

Log Normal Shadowing equation
\(PL(d_0)\) = Path Loss in \(dB\) at a distance \(d_0\)
\(PL_{d>d0}\)= Path Loss in \(dB\) at an arbitrary distance \(d\)
\(n\) = Path Loss exponent. See the table below that gives the path loss exponent for various environments.
\(\chi\) = A zero-mean Gaussian distributed random variable (in \(dB\)) with standard deviation – \(\sigma\). This variable is used only when there is a shadowing effect. If there is no shadowing effect, then this variable is zero. Taking log of the Normal (Gaussian)-variable results in the name “Log-Normal” fading.

Log Normal Shadowing Table
Usually to model real environments the shadowing effects cannot be neglected. If the shadowing effect is neglected, the Path Loss is simply a straight line (see the plot below). To add shadowing effect a zero-mean Gaussian random variable with standard deviation – \(\sigma\) is added to the equation. The actual path loss may still vary due to other factors. Thus the path loss exponent (modeling the slope) and the standard deviation of the random variable should be known precisely for a better modeling.

Log Normal Shadowing image 2
The Path Loss Exponent (PLE) table given above is for reference only. It may or may not fit the actual environment we are trying to model. PLE is an important parameter and it affects the system performance drastically. Usually PLE is considered to be known a-priori but mostly that is not the case. Care must be taken to estimate the PLE for the given environment before design & modeling. PLE estimation is done by equating the observed (empirical) values over several time instants to the established theoretical values. Refer [Srinivasa2009] for a literature on PLE estimation in large wireless networks.

Matlab Code:

Please refer the ebook Simulation of Digital communication Systems using Matlab – by Mathuranathan for the Matlab code.

Simulation Results:

Log Normal Shadowing image 3


[Srinivasa2009] Srinivasan, S.; Haenggi, M. “Path loss exponent estimation in large wireless networks”, Information Theory and Applications Workshop, On pages 124 – 129, Feb 2009.

  • Ahsan Javid

    log distance path loss model having a attenuation factor matlab code kindly help me

  • Mirza Ferdous

    Dear Mr. Mathuranathan Sir,

    May you please share the “log distance path loss matlab code” thanks

    Mirza Ferdous Rahman

  • shahid ullah

    How i can generate Hata Model for (1) Urban (2)Rural area when ht=30m ,hr=1m ,f=800Mhz and distance is 10 t0 200m…. plz snd me coding

  • Abdelrahman Salama Arbi

    how I can generate the shadowing samples at different locations in a cell when they are not independent , there is a correlation distance between them .