Log Distance-Normal Shadow Model and Friis Since I'm founding several but different results about this model, I would ask you if all it is OK with this formulas:

1) Friis Model --> $Pr_0 = Pt + Gt + Gr + 20\log_{10}\frac{\lambda}{4\pi d}$

2) Log Normal Shadow --> $Pr_L = Pr_0 - 10\eta\log_{10} d + \chi_{\sigma}$

where:


$Pr_0$ is the power received in the Friis Model as depicted above
$Pr_L$ is the power received in the Log Normal Shadow Model as depicted above
$Pt$ is the power transmission
$Gt$ and $Gr$ are the respective transmitter and receiver gains
$\lambda = c/f$, where $c$ is the light speed and $f$ is the frequency
$\eta$ is the Path Loss exponent
$\chi_{\sigma}$ is a Gaussian zero mean random variable with standard deviation $\sigma$.


I am a bit concerned about the signs and the $\log$ operations.
I verified all the steps and they are all correct.