Adaptive Radar Detection in Gaussian Disturbance With Structured Covariance Matrix via Invariance Theory

This paper deals with adaptive radar detection of targets in the presence of Gaussian disturbance sharing a block-diagonal covariance structure. The problem is formulated according to a very general signal model, which contains the point-like, range-spread, and subspace target (or targets) as special instances. Hence, a unified study on the resulting adaptive detection problem is handled with the use of the invariance theory. The obtained results, including an appropriate transformation group, a maximal invariant and an induced maximal invariant, are proven consistent with those existing in the literature for some simple scenarios. Meanwhile, since the widely-used generalized likelihood ratio detector does not admit a closed form expression, new invariant detectors and their CFAR versions are proposed in this general scenario. Finally, their detection performance is assessed and validated via numerical examples.