I did my research but I did not get a satisfying answer.
We have a transmitter and a receiver over a wireless communication channel. The channel's path loss is modeled as
$ 128 + 37 \log_{10} (d)$, with a shadowing standard deviation of $10$ dBs.

I am assuming that this path loss equation is expressed with dBs (nothing explicitly says that).

I have read that the combined path loss and the shadowing model is just the addition of the path loss model and a normally distributed random variable with mean $0$ and std. $10$ dBs.

  • Is this addition of path loss and shadowing is the same as the channel gain ?
  • If not, how to calculate the channel gain $\vert h \vert$ from the path loss model, combined with the shadowing ?
  • $\begingroup$ Do you know how to calculate channel gain based on path loss? $\endgroup$
    – ddddd
    Mar 29, 2019 at 4:58

2 Answers 2


To answer the literal questions you asked:

  • yes
  • see above

To Frame Challenge your question and give you what you were probably looking for:

The path loss equation you cited: $$ 128+37\log_{10}(d) , $$ is equivalent to: $$ \frac{P_r}{P_t} = \frac{10^{-12.8}}{d^{3.7}}, $$ where $P_r$ is the received power in Watts, and $P_t$ is the transmit power in Watts. From this equation it can be seen that the path loss exponent is 3.7.

Under log-normal shadowing, the random shadowing component is modeled as a zero-mean Gaussian random variable (in dB) added to the path loss.


The answers are

  • No.
  • You cannot.

Small scale (channel gain) and large scale (path loss + shadowing) fading effects cannot be deduced from each others. They have independent characterizations. The channel gain characteristics must be given. Usually in rich multi-path fading with no line-of-sight (LOS), Rayleigh fading is assumed, while if there is a strong LOS, Rician fading is assumed.


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