Application of maximal invariance to adaptive detection with structured and unstructured covariance matrices

The authors introduce a framework for exploring array detection problems in a reduced dimensional space by exploiting the theory of invariance in hypothesis testing. This involves calculating a low dimensional basis set of functions called the maximal invariant, the statistics of which are often tractable to obtain, thereby making analysis feasible and facilitating the search for tests with some optimality property. This approach obtains a locally most powerful test for unstructured covariance and shows that the Kelly and AMF detectors form an algebraic span for any invariant detector. With the same framework applied to structured covariance matrices, several new detectors are shown to perform as well or better than existing detectors