Analysis on the Resolution of Polarimetric Radar and Performance Evaluation of the Polarimetric Bandwidth Extrapolation Method

Polarimetric radar provides useful information on scattering mechanisms, and advances in polarimetric synthetic aperture radar (POLSAR) technology have shown the effect of polarization information on various applications. The disadvantage of POLSAR is low azimuth resolution capability. Since the effective pulse repetition frequency (PRF) in each polarimetric channel of POLSAR is half the total PRF, the resolution is twice as low as the single-polarization SAR. This drawback may be mitigated by employing a superresolution method designed for polarimetric radar such as polarimetric bandwidth extrapolation (PBWE), previously proposed by the authors. Thus far, the authors only empirically showed that polarization information helps in improving resolution via numerical simulations. In this paper, theoretical analysis on the resolution of a polarimetric radar is provided. Along with the resolution, estimation accuracy of the polarization property of the target is studied. In the analysis, we employ the recently proposed metric called the statistical resolution limit (SRL) that provides the highest resolution achievable by any unbiased parametric spectral estimator. The SRL of polarimetric radar is derived and compared with that of single-polarization radar. The Cramér-Rao bound (CRB) of the polarization estimation error of the polarimetric radar is also derived. The complexified full Fisher information matrix and the CRBs of signal parameters are derived first for the general multichannel signal in nonwhite Gaussian noise. Then, the SRL and the polarization estimation error are derived using the CRBs of signal parameters for the cases where two point targets are closely located. It is shown analytically and numerically that the polarization information helps in improving the SRL. It is also shown that the polarimetric processing significantly improves the accuracy of the polarization estimation when two targets are located closer than the Fourier resolution cell. Finally, the performance of the PBWE is evaluated via simulations and is compared to the SRL and the CRB for the polarization estimation.