Wave reflection from randomly inhomogeneous ionospheric layer: 1. The method of describing the wavefield in a reflecting layer with random irregularities

It has been previously proposed to describe wave propagation in inhomogeneous media in a small‐angle approximation with the aid of a double weighted Fourier transform (DWFT) method. This method agrees with the methods of geometrical optics, smooth perturbations, and phase screen in domains of their applicability; therefore, it can be employed to solve direct and inverse problems of radio wave propagation in multiscale inhomogeneous ionospheric plasma. In this paper, for the DWFT wide‐angle generalization a wave equation is preliminary reduced using the Fock proper‐time method to a parabolic equation that then is solved by the DWFT method. The resulting solution is analyzed for the case of wave reflection and scattering by a layer with random irregularities and linear profile of average permittivity. We show the transformation of this solution into strict results in the absence of irregularities and in the single‐scatter approximation, including backscattering, during weak phase fluctuations. Under certain conditions, the solution takes the form of the small‐angle DWFT with respect to refraction in the layer and backscatter effects. Spatial processing in source and observer coordinates brings a beam of received waves into one wave without amplitude fluctuations, which allows an increase in resolution of vertical ionospheric sounding systems.