Adaptive polarimetric detection in compound-Gaussian clutter

In this paper we deal with the problem of polarization diversity detection in compound-Gaussian clutter with unknown covariance matrix. To this end we assume that a set of secondary data, free of signal components and with the same covariance structure of the cell under test, is available. Due to the lack of a Uniformly Most Powerful (UMP) detector, we resort to a design procedure based upon the Rao test and the Wald test. Specifically, we first derive the Rao and the Wald tests assuming that the covariance matrix is known, then we plug into the derived decision rules a suitable estimate of the clutter covariance. Interestingly, the newly proposed detectors share the Constant False Alarm Rate (CFAR) property with respect to the texture statistical characterization. Moreover simulation results have shown that the Wald test based detector ensures a performance level higher than the Rao test. We have also conducted a further performance analysis, in the presence of real radar data and in comparison with the previously proposed Generalized Likelihood Ratio Test (GLRT) based receivers, which highlights that in general the Wald test receiver outperforms its counterparts. Finally, since the newly proposed decision rules as well as the previously designed GLRT's do not ensure the CFAR property with respect to the clutter covariance matrix, we have conducted a sensitivity analysis on the probability of false alarm (Pfa), based on simulated clutter with covariance matrix estimated from real radar data. The results have shown that Pfa is only slightly affected by variations in the clutter correlation properties and hence the CFARness is substantially achieved