A sharp upper bound for the probability of error of the likelihood ratio test for detecting signals in white Gaussian noise

A new sharp upper bound for the probability of error of the likelihood ratio test is given for the detection in white Gaussian noise of any random vector whose norm is greater than, or equal to, a given value and whose probability of presence is less than, or equal to, one half. Also, a new test for the detection of such vectors is described. This test does not depend on the distribution of the signal vector but nevertheless its probability of error is less than, or equal to, the given upper bound.