Fresnel approximation for wave scattering in a random medium

In this paper, instead of introducing the scattering volume, we include the model of transmitting and receiving antennas in an explicit form. We consider these antennas as Gaussian (Gaussian attenuation across the antenna aperture). Such an approach works well with the description of scattering in the Fresnel approximation, in which we keep the quadratic terms in the phase expansion. The longitudinal scale of the scattering volume is determined by the electromagnetic pulse envelope, which we also assume to be Gaussian.