Invariant CFAR Detection in Gaussian Disturbance with Kronecker Covariance Structure

This paper studies the adaptive detection of range-spread targets in a Gaussian environment, assuming a Kronecker-product structure for the disturbance covariance matrix. Invoking the principle of invariance, we identify a transformation group that significantly reduces the dimensionality of nuisance parameters, ensuring the constant false alarm rate (CFAR) property for all invariant statistics. A maximal invariant (MI) is derived, providing the foundation for new CFAR detectors that are invariant tests functionally depending on the MI. At the stage of detector design, two adaptive detectors are devised: the former employs the two-step strategy and incorporates the Kronecker maximum likelihood estimate based on secondary data, while the latter is the one-step generalized likelihood ratio test realized via an alternating-optimization algorithm. Both are invariant tests, and thus their CFAR properties with respect to the Kronecker covariance matrix are naturally guaranteed. Numerical results demonstrate the superior detection performance and robust CFAR behavior of both the detectors compared to conventional methods designed for the unstructured case.