18.2 Two-ray ground reflection model

A single line-of-sight path between two mobile nodes is seldom the only means of propation. The two-ray ground reflection model considers both the direct path and a ground reflection path. It is shown [29] that this model gives more accurate prediction at a long distance than the free space model. The received power at distance $d$ is predicted by

$$P_r (d) = \frac{P_t G_t G_r {h_t}^2 {h_r}^2}{d^4 L}$$ (18.2)

where $h_t$ and $h_r$ are the heights of the transmit and receive antennas respectively. Note that the original equation in [29] assumes $L = 1$. To be consistent with the free space model, $L$ is added here.

The above equation shows a faster power loss than Eqn. (18.1) as distance increases. However, The two-ray model does not give a good result for a short distance due to the oscillation caused by the constructive and destructive combination of the two rays. Instead, the free space model is still used when $d$ is small.

Therefore, a cross-over distance $d_c$ is calculated in this model. When $d < d_c$, Eqn. (18.1) is used. When $d > d_c$, Eqn. (18.2) is used. At the cross-over distance, Eqns. (18.1) and (18.2) give the same result. So $d_c$ can be calculated as

$$d_c = \left( 4\pi h_t h_r \right) / \lambda$$ (18.3)

Similarly, the OTcl interface for utilizing the two-ray ground reflection model is as follows.

$ns_ node-config -propType Propagation/TwoRayGround

Alternatively, the user can use

set prop [new Propagation/TwoRayGround]
$ns_ node-config -propInstance $prop