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 closedform 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.

中文翻译：

---

通过封闭形式的两尺度模型从各向异性粗糙表面进行双静态散射

近年来，由于引入了新的双基地（和多基地）配置，包括基于全球导航卫星系统 (GNSS) 机会性开发的配置，双基地雷达已成为越来越受关注的话题。双基地电磁散射模型的研究在这些系统的分析、模拟和性能预测中起着重要作用。两尺度模型 (TSM) 是一种广泛用于计算粗糙表面散射的方法，因为它能够解释由于表面倾斜引起的去极化效应。然而，在其原始公式中，它需要计算密集的数值积分，以便在表面随机斜率上执行适当的平均。为了克服这个限制，开发了一种封闭形式的极化 TSM (PTSM)，最近也将其扩展到各向异性粗糙表面 (A-PTSM) 的情况，重点是海面。A-PTSM 可以有效地用于计算各向异性粗糙表面的反向散射，并可以支持单基地雷达任务的开发和分析。为了将其范围扩展到双基地和多基地配置的一般情况，在本文中，我们将 A-PTSM 扩展到双基地电磁散射的情况，展示了对双基地极化协方差矩阵的所有元素的评估。由于圆偏振信号在机会主义 GNSS 反射计应用中的相关性，线性和圆偏振基都被考虑。讨论了获得的元素的行为，对于入射平面内散射的情况，提供了协方差矩阵元素的简化表达式。提供了相关的数值示例，并与通过更精细但计算量更大的二阶小斜率近似 (SSA2) 方法获得的数值示例进行了比较。在示例中，我们考虑了风力驱动的海面和耕作土壤，以及 L 波段和 X 波段频率。然而，所提出的方法可用于微波遥感和所有观测几何的所有感兴趣频率，除了近掠入射和/或散射。但计算量更大的二阶小斜率近似 (SSA2) 方法。在示例中，我们考虑了风力驱动的海面和耕作土壤，以及 L 波段和 X 波段频率。然而，所提出的方法可用于微波遥感和所有观测几何的所有感兴趣频率，除了近掠入射和/或散射。但计算量更大的二阶小斜率近似 (SSA2) 方法。在示例中，我们考虑了风力驱动的海面和耕作土壤，以及 L 波段和 X 波段频率。然而，所提出的方法可用于微波遥感和所有观测几何的所有感兴趣频率，除了近掠入射和/或散射。