Polarimetric Detection in Compound Gaussian Clutter with Kronecker Structured Covariance Matrix

In this paper, we consider polarimetric adaptive detection in compound Gaussian clutter whose covariance matrix (CM) has a Kronecker structure. We derive the Cramér-Rao bound of a Kronecker structured CM estimate and analyze the constant false alarm rate property of the adaptive subspace matched filter detector that uses Kronecker structured estimates. We provide a general expression for the average signal-to-clutter ratio loss (SCRL) as a function of the mean square error of the covariance estimate. The aforementioned expression is helpful in determining how many samples are required in order to achieve a desired average SCRL level in practical scenarios. Based on that expression, we show that the required sample size can be effectively reduced by exploiting the Kronecker structure of the clutter CM. We also derive the asymptotic detection performance of the adaptive subspace matched filter. The analysis of SCRL and detection performance can be extended to more general scenarios, especially when the maximum-likelihood estimate of the structured CM involves solving fixed point equations. Numerical simulations validate the merits of the proposed methods.