Log Path Loss Model with Directivity Accounted

Question

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.

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]