Invariant adaptive detection of range-spread targets under structured noise covariance

The invariance principle is adopted to develop an exhaustive study for adaptive detection of range-spread targets in Gaussian noise sharing a block-diagonal covariance structure. For this problem, the usual generalized likelihood ratio principle is intractable. In this paper, we first determine the largest group of affine transformations that does not alter the decision problem. Then, amaximal invariant identified by this groupisderived, which can characterize the totality of the invariant detectors and extends the existing results for the point-target case. A theoretical performance analysis of the maximal invariant is also given. Finally, we propose two classes of invariant detectors, which are distinguished by whether a constant false alarm rate (CFAR) is maintained. Numerical experiments are provided for a comparison of the proposed detectors, where a tradeoff between the CFARness and the improved performance has been observed and studied.