A maximal invariant framework for adaptive detection with arrays

A framework for exploring array detection problems in a reduce dimensional space by exploiting the theory of invariance in hypothesis testing is introduced. 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. A locally most powerful test for the unstructured covariance case is obtained using this approach, and it is shown that the Kelly and adaptive matched filters (AMF) detectors form an algebraic span for any invariant detector. Several new detectors which incorporate insights gained from applying the same framework to structured covariance matrices, and which are shown to perform as well or better than existing detectors, are proposed