# Log Distance-Normal Shadow Model and Friis

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.