Bistatic Radar Equation for Signals of Opportunity Revisited

The bistatic radar equation currently used for simulating surface-reflected waveforms or delay-Doppler maps (DDMs), produced by signals of opportunity from global navigation satellites system (GNSS) or communication satellites, was previously derived under some limiting assumptions. One of them was the use of the Kirchhoff approximation in a geometric optics limit that assumes strong diffuse (noncoherent) scattering typical for very rough surfaces. This equation would produce an incorrect result for the case of weak diffuse scattering, or in the presence of coherent reflection. In this paper, it is shown that the assumption of strong diffuse scattering is not necessary in deriving such an equation. The derivation of a generalized bistatic radar equation is now based only on the assumption of roughness statistics being spatially homogeneous, and thus this equation is applicable for a much wider range of surface conditions and scattering geometries. This approach allows to correctly describe the transition from partially coherent scattering to completely noncoherent, strong diffuse scattering. It is demonstrated for the case of the GNSS-R DDMs simulated for a wide range of surface winds, and their transitional behavior is discussed.