Persymmetric adaptive detection of distributed targets in partially-homogeneous environment

In this paper we deal with the problem of detecting distributed targets in the presence of Gaussian noise with unknown but persymmetric structured covariance matrix. In particular, we consider the so-called partially-homogeneous environment, where the cells under test (primary data) and the training samples (secondary data), which are free of signal components, share the same structure of the interference covariance matrix but different power levels. Under the above assumptions, we derive the generalized likelihood ratio test (GLRT) and the so-called two-step GLRT. Remarkably, the new receivers ensure the constant false alarm rate property with respect to both the structure of the covariance matrix as well as the power level. The performance assessment, conducted by resorting to both simulated data and real recorded dataset, highlights that the proposed detectors can significantly outperform their unstructured counterparts, especially in a severely heterogeneous scenario where a very small number of secondary data is available.