Adaptive Radar Detection in Low-Rank Heterogeneous Clutter via Invariance Theory

This paper addresses adaptive detection of a range distributed target in the presence of dominant heterogeneous clutter, which is (possibly) low-rank and lies in a known subspace, plus Gaussian thermal noise. First, this problem is transformed into an equivalent binary hypothesis test with observations having block-diagonal covariance matrices. Then an invariance analysis is conducted on the resulting hypothesis test. Data and unknown parameters are compressed into a maximal invariant and an induced maximal invariant, respectively, w.r.t. a suitable transformation group. This suggests to focus attention on invariant detectors and to establish the relationship between invariance and constant false alarm rate (CFAR) property. According to this guideline, two tunable invariant detectors exploiting the aforementioned covariance structure are devised, and they are shown to ensure bounded CFAR and standard CFAR properties, respectively. Finally, the CFAR behavior of the proposed detectors as well as their detection performance is assessed via numerical simulations.