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To confirm the presence of water on the moon, many scientists of the world are making continuous efforts through remote sensing data of different missions. In this direction, the Dual Frequency Synthetic Aperture Radar (DFSAR) sensor of the Chandrayaan-2 mission adds a very important chapter which is the world's first Planetary SAR mission of fully polarimetric capability with L- and S-band. This study utilizes the L-band fully polarimetric DFSAR data of Chandrayaan-2 mission for the PolSAR parameters-based analysis and ice detection in permanently shadowed regions (PSRs) of the lunar South Polar craters. The PSR IDs SP_875930_3125710, SP_837670_3387710, and SP_874930_3578760 of the lunar South Pole were selected for the polarimetric analysis using DFSAR L-band. Based on previous studies ((Li et al., 2018), two out of three PSR Ids (SP_875930_3125710 and SP_874930_3578760) were easy to identify for surface ice. That is why only two PSR IDs were used for polarimetric SAR analysis of DFSAR data for surface ice characterization and detection. The hybrid polarimetric simulation was also performed to the fully polarimetric L-band data to study stokes vectors and associated child parameters for the selected study area. The analysis of polarimetric distortions confirms the persistence of the polarimetric quality of the SAR data and for this, the polarimetric distortion analysis was performed with co-pol and cross-pol channels. Wave dichotomy-based Huynen decomposition and Barnes decomposition models were implemented to the fully polarimetric quad-pol DFSAR data. The eigenvalue-eigenvector-based decomposition model was also implemented to characterize the scattering behavior of the PSRs. A high correlation was obtained between Circular Polarization Ratio (CPR), entropy, and alpha for the 200 hundred points randomly collected from the image. Diversity index also showed a high positive correlation with CPR. The polarimetric quality of the data was evaluated with the scatterplot between the cross-polarimetric channels and it was observed that the L-band quad-pol data of DFSAR satisfies the criteria for PolSAR data of a monostatic SAR system. Analysis of the results obtained from the polarimetric SAR data indicated that the high volumetric scattering and CPR for the PSR ID SP_875930_3125710 may be due to ice clusters within the permanently shadowed region. Polarimetric analysis of the PSR (SP_874930_3578760) at Howarth Crater using L-band DFSAR data shows a low amount of volumetric scattering and a low CPR for most locations in the PSR. The different ranges of CPR and volume scattering for both craters indicate that polarimetric parameters and indices should be studied in conjunction with geomorphological parameters of the lunar surface, for unambiguous identification of surface ice clusters in the PSR. [ABSTRACT FROM AUTHOR]