# path loss

Path loss is the effect that traveling through space has on the signal.

A simple model of path loss is

\begin{equation}
r(t) = \Re(\frac{\lambda \sqrt{G} e^{\frac{-jd2\pi}{\lambda}}}{4\pi d}u(t)e^{j2\pi f_c t})
\end{equation}

where \(G\) is the product of the antenna field radiation pattern in the LOS direction (has to do with antenna aperture)

From this eq, the ratio of transmit to recieve power is

\begin{equation}
\frac{P_r}{P_t} = (\frac{\sqrt{G}\lambda}{4 \pi d})^2
\end{equation}

Common model for large urban areas is the okumura model.

A simplified model is

\begin{equation}
P_r = P_t K \left[ \frac{d_0}{d} \right]^{\gamma}
\end{equation}

where \(K\) is a constant, \(d_0\) is the reference distance from farfield, and \(\gamma\) is the path loss exponent (comes from existing tables of empirical data).

This model is quite commonly used.