A low-frequency spaceborne synthetic aperture radar (SAR) working system, e.g., operating at the $L$ -band or $P$ -band, has great advantages of military target detection and biomass monitoring. Nevertheless, it is more susceptible to ionospheric effects compared with the higher frequency system. A trans-ionospheric wave propagation model is established in this paper to incorporate ionospheric effects on SAR signals. As one of the significant distortion sources for the polarimetric SAR (PolSAR), Faraday rotation (FR) is mainly imposed by background ionosphere, and its spatial variation is discussed. FR estimators have been devised in succession to estimate FR angle (FRA), and various potential novel estimators can still be derived. But, from a viewpoint of theoretical expressions, the earliest estimator is bound to be the optimal one. Based on PolSAR real data, this mathematical conclusion is further validated via comprehensive performance analysis as to estimation bias and standard deviation rather than the existent root-mean-square principle. Finally, a step-by-step procedure of the FRA map is proposed and operated with an application of the airborne P-band PolSAR data. In particular, the ambiguity error of FRA estimates within a SAR observation is simulated and resolved. By processing the ALOS-2 real data, the spatial distribution of FRAs is retrieved and used to operate ionospheric total electron content soundings.
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