Uniformly most powerful cyclic permutation invariant detection for discrete-time signals

The uniformly most powerful invariant (UMPI) test is derived for detecting a target with unknown location in a noise sequence. This test has the property that for each possible target location it has the greatest power of all tests which are invariant to cyclic permutations of the observations. The test is compared to the generalised likelihood ratio test (GLRT), which is commonly used as a solution to this detection problem. Monte-Carlo simulations show that the powers of the two tests are comparable, thereby justifying near-optimality of the GLRT