Bistatic Scattering From Anisotropic Rough Surfaces via a Closed-Form Two-Scale Model

Bistatic radars have been a topic of increasing interest in recent years, thanks to the introduction of new bistatic (and multistatic) configurations, including those based on the opportunistic exploitation of global navigation satellite systems (GNSSs). The research on bistatic electromagnetic scattering models plays an important role in the analysis of these systems, in their simulation, and in the prediction of their performance. The two-scale model (TSM) is a widely used approach for the computation of scattering from rough surfaces, since it is able to account for depolarization effects due to surface tilting. However, in its original formulation, it requires a computationally intensive numerical integration, in order to perform appropriate average over surface random slopes. To overcome this limitation, a closed-form polarimetric TSM (PTSM) was developed, which has been also recently extended to the case of anisotropic rough surfaces (A-PTSM), with a focus on the sea surface. The A-PTSM can be efficiently used to compute the backscattering from anisotropic rough surfaces and can support the development and analysis of monostatic radar missions. In order to extend its scope to the general case of bistatic and multistatic configurations, in this article, we extend the A-PTSM to the case of bistatic electromagnetic scattering, presenting the evaluation of all the elements of the bistatic polarimetric covariance matrix. Due to the relevance of circularly polarized signals in opportunistic GNSS reflectometry applications, both the linear and the circular polarization bases are considered. The behavior of the obtained elements is discussed, and simplified expressions of the elements of the covariance matrix are provided for the case of scattering within the incidence plane. Relevant numerical examples are provided and compared to those obtained by the more refined, but more computationally intensive, second-order small-slope approximation (SSA2) method. In the examples, we consider both a wind-driven sea surface and a tilled soil, and both L-band and X-band frequencies. However, the presented method can be used at all frequencies of interest for microwave remote sensing and for all observation geometries, except for near grazing incidence and/or scattering.