Radar equations in the radio wave backscattering problem

We present a method for finding the relation between the singly scattered signal and the Fourier spectrum of dielectric permittivity fluctuations of a medium with regard to the scattering volume which is controlled by the antenna pattern and is not small. Using this method, we found a radar equation which relates the temporal Fourier spectrum of the scattered signal and the spatio-temporal spectrum of permittivity fluctuations. We also obtained a statistical radar equation to relate the statistically averaged spectral power of the scattered signal and the spectral density of permittivity fluctuations without the conventional assumption that the spatial correlation radius of irregularities is small compared with the Fresnel radius.