Comparison of optimization procedures for the 2×2 Sinclair and the 4×4 Mueller matrices in coherent radar polarimetry and its application to radar target versus background clutter discrimination

Basic principles of radar polarimetry are introduced. The target characteristic polarization state theory is developed first for the coherent case using the three-step, the basis transformation, and the power (Mueller) matrix optimization procedures. Kennaugh´s and Huyen´s theories of radar target polarimetry are verified for the monostatic reciprocal case. It is shown that there exist in total five unique pairs of characteristic polarization states for the symmetric scattering matrix, of which two pairs, the cross-polarization null and the copolarization max pairs, are identical, whereas the cross-pol max and the cross-pol saddlepoint pairs are distinct. The fifth pair, the co-pol null pair, lies in the plane spanned by the co-pol max/cross-pol null and the cross-pol max pairs, which determines the target characteristic circle on the polarization sphere reestablishing Huynen´s polarization fork concept. The theory is verified by an example in which the co-polarized and cross-polarized power density plots are presented next to the polarization fork