Invariance Theory for Radar Detectionin Disturbance With Kronecker ProductCovariance Structure—Part II: CompoundGaussian Environment

In this part of the paper, we consider the invariant framework and the novel constant false alarm rate (CFAR) detector design of Part I in compound Gaussian clutter. Specifically, the focus is on detecting range-spread targets embedded in compound Gaussian clutter that exhibits a Kronecker covariance structure. A suitable transformation group has been identified, ensuring that invariance implies the fully CFAR property, i.e., with respect to both the Kronecker covariance matrix and the texture. A maximal invariant is derived and used to gain insightful re-expressions of some established two-step adaptive CFAR detectors. At the stage of detector design, the pseudo-missing strategy proposed in Part I is adapted to the compound Gaussian case and then integrated into the test architectures to yield modified adaptive detectors. Furthermore, the one-step generalized likelihood ratio test is derived. Both detection strategies result in fully CFAR detectors under some mild technical conditions, as evidenced by their invariance with respect to the identified transformation group. For performance evaluation, their CFAR behavior and detection probability are assessed and analyzed across different experimental setups and signal models, highlighting the superior performance of the newly proposed detectors compared to some conventional counterparts and to those that do not leverage the prior (Kronecker) structure.