Two Ray model is one of the ray tracing models. While free space propagation model is inaccurate for most mobile RF channels, Two ray model comes into the picture.

While transmitting a radio signal effects like path loss, multipath fading, shadowing, doppler effects etc. are taken into consideration.

Two ray model is useful when a single ground reflection of signal dominates multipath effect.

The main reasons due to which multipath effect is generated could be reflection, diffraction and scattering. Because of this, multiple replicas of a signal are generated and power gain decreases.

On the receiver end, transmitted signal and multipath are added together which produces distortion in the signal received.

Ray tracing models, assume a finite number of reflectors with known locations and dielectric properties and using maxwell equation, received power is estimated.

Two ray model considers two components of received signal at receiver side. One of them is LOS component which is same as transmitted signal propagating in free space. The other component is reflected component which transmitted signal reflected from ground. This model is more useful in rural area. Following figure shows diagram of the model.

Power of received signal can be determined using following formula:

$ p_r = p_t {\left[ \frac{\lambda}{4\pi}\right]}^2 {\left| \frac{\sqrt{G_l}}{l} + \frac{R\sqrt{G_r} e^{j\Delta\phi}}{x+x'}\right|}^2 $

where,

$ \Delta\phi = 2 \pi \frac{\left( x + x' - l\right)}{\lambda} \approx \frac{4 \pi h_th_r}{\lambda d} $

$ x+x' = \sqrt{ (h_t + h_r)^2 + d^2} $

$ l = \sqrt{ (h_t - h_r)^2 + d^2} $

$P_r(dBm) =P_t(dBm) \,+\, 10 log_{10}(Gl)\,+\,20log_{10}(h_th_r)−40 log_{10}(d)$