## 1. Introduction

[2] The method of radio wave backscattering due to dielectric permittivity fluctuations of the medium provides the basis for a wide variety of techniques for probing the ionosphere (the radio wave incoherent scattering method [*Kofman*, 1997]; scattering from artificial irregularities [*Belikovich et al.*, 1986]), the atmosphere (mesospheric-stratospheric-tropospheric sounding [*Woodman*, 1989]), and other media. Central to these techniques is the radar equation that relates the mean spectral power of the scattered signal to the statistical characteristic of the medium dielectric permittivity fluctuations, their spectral density [*Tatarsky*, 1967; *Woodman*, 1989; *Ishimaru*, 1981]. A standard method for constructing the statistical radar equation involves constructing the spectral power (or a received signal autocorrelation function) using two approximations. One of them, namely, the single-scattering approximation, is applicable when the dielectric permittivity fluctuations are weak and the scattered field is significantly weaker than the incident field. The other approximation is the approximation of the irregularities' spatial correlation radius smallness in comparison to the Fresnel radius.

[3] The single-scattering problem of the electromagnetic wave has been reasonably well studied in situations where the receiver and the transmitter are in the far-field region of the scatterer. In this case it is possible to obtain a simple linear relation between the scattered signal and the spatial Fourier spectrum of irregularities without recourse to a statistical averaging [*Newton*, 1969; *Ishimaru*, 1981]. However, in remote diagnostics of media, the scattering volume size is determined by the antenna pattern crossing. Hence it is impossible to use a classical approximation of the sounding volume smallness [*Ishimaru*, 1981] to obtain the radar equation relating the scattered signal to the Fourier spectrum of dielectric permittivity fluctuations. Therefore, when obtaining the statistical radar equation, one has to average the received signal power and to use the approximation of the spatial correlation radius smallness, which makes it possible to generalize results derived from solving a classical problem of wave scattering from a single small irregularity to the problem of scattering from a set of uncorrelated small irregularities [*Tatarsky*, 1967; *Ishimaru*, 1981].

[4] Here we have obtained the radar equation relating the scattered signal spectrum to the spatial spectrum of dielectric permittivity fluctuations for bistatic sounding. This expression was obtained without a traditional limitation on the smallness of the scattering volume size and describes essentially the scattering from an extended scatterer. An analysis of the expression revealed a selectivity of the scattering similar to the widely known Wolf-Bragg condition.

[5] We obtained the statistical radar equation for bistatic sounding, which relates the scattered signal mean power to the dielectric permittivity fluctuations' spectral density without a classical approximation of the spatial correlation radius smallness. This equation has a more extensive validity range when compared to the well-known equation [*Tatarsky*, 1967; *Ishimaru*, 1981], obtained by assuming the smallness of the irregularities' spatial correlation radii.

[6] It was pointed out earlier [*Doviak and Zrnic*', 1984] that there are difficulties in obtaining the equation for correlation radii or scattering volume bigger than Fresnel radius without exact antenna patterns, irregularities, and sounder signals. The suggested method does not contain those limitations.