Suppose that I have the log Path Loss distance model described here https://en.wikipedia.org/wiki/Log-distance_path_loss_model

$$PL(d,\gamma) = P_{t}-P_{r}=PL_{0}+10\gamma log_{10}\frac{d}{d_{0}}+X_{g}$$

Suppose that the receiver has some kind of directivity (i.e. it can be a Yagi Uda antenna), can I include or is there a way to include a term that takes into account that directivity??

My ultimate goal is to have something like

$$PL(d,\gamma,\theta,\phi) = P_{t}-P_{r}=PL_{0}+10\gamma log_{10}\frac{d}{d_{0}}+X_{g}+G(\theta,\phi)$$

where $G(\theta,\phi)$ is the directivity gain on the angle $(\theta,\phi)$, where $\theta, \phi$ are the azimuth and zenith angles with reference to the receiver.


1 Answer 1


Frankly, it is included in the $PL_0$ term. $PL_0$ term is the reference measurement where it is done in the far-field.

The expression below may used for theoretical calculations, gives slightly accurate results for real scenarios! In this case where the TX/RX antennas pointing each other, $PL_0$ can be written as $$PL_0 \approx P_TG_R(\phi,\theta) G_T(\phi,\theta)) \left( \frac{\lambda} {4\pi d_0} \right)^\gamma$$

Do not forget to translate $PL_0$ to [dB]

  • $\begingroup$ Interesting so the Antenna's directivity gain, can be incorporated by the directivity gain included at the Path Loss for the reference measurement? $\endgroup$ Nov 4, 2021 at 10:50
  • $\begingroup$ Also, is there some literature that I can look after for understanding in depth the equation that you provided ? $\endgroup$ Nov 4, 2021 at 11:15
  • $\begingroup$ I am not sure, but Rappaport's book may include these path loss models as I remember. $\endgroup$ Nov 5, 2021 at 11:27
  • $\begingroup$ Yes, it is based on yout reference measurement. The reference measurement must be performed when the two antenna perceftly points each other (and in the same polarization ofc.) $\endgroup$ Nov 5, 2021 at 11:28

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