Average reflected power from a one-dimensional slab of discrete scatterers

Reflection from a one-dimensional random medium of discrete scatterers is considered. The discrete scattering medium is modeled by a Poisson impulse process with concentration lambda. By employing the Markov property of the Poisson impulse process, an exact functional integro-differential equation of the Kolmogorov-Feller type is found for the average reflected power. Approximate solutions to this equation are obtained by regular perturbation and two variable expansion techniques in the limit of small lambda. The regular perturbation results is valid for small slab thicknesses, while the two-variable result is uniformly valid for any thickness. The two-variable result shows that as the slab size becomes infinite all of the incident power is reflected on the average.