When shadowing is caused by a single object such as a hill or mountain, the attenuation caused by diffraction can be estimated by treating the obstruction as a diffracting knife edge. This is the knife edge diffraction model. It is the simplest of diffraction models and the diffraction loss in this case can be readily estimated by using the classical Fresnel solution for the field behind a knife edge.

Consider a receiver at point R, located in the shadowed region (also called the diffraction zone). The field strength at point R in the figure is the vector sum of the fields due to all of the secondary Huygens sources above the knife edge. The electric field strength, Ed of a knife edge diffracted wave is given by

$\dfrac{Ed}{Eo}=F\left(v\right)=\dfrac{\left(i+j\right)}{2} \displaystyle\int_v^{\infty{}}\exp{\left(\dfrac{\left(-j\pi{}t{^2}\right)}{2}\right)}\ dt$

Where Eo is the free space field strength in the absence of both ground and knife edge and F(v) is the complex Fresnel integral. The Fresnel integral F(v), is a function of the Fresnel Kirchoff diffraction parameter and is commonly evaluated using tables or graphs for given values of v. The diffraction gain due to presence of a knife edge, as compared to free space E field, is given by,

Gd(dB) = 20log|F(v)|

In practice, graphical or numerical solutions are relied upon to complete diffraction gain.