Transient signal detection using prior information in the likelihood ratio test

A uniform approach to the problem of detecting a deterministic transient signal of unknown waveshape in Gaussian noise that is applicable for a general class of signals is provided. It is assumed that the vector representation consists of a group of zero coefficients plus a group of unknown nonzero coefficients, starting at a certain index. Performance indices for a likelihood-ratio-test detector of such a generalized transient signal are derived for three cases: (a) both the starting index and the number of unknown nonzero signal coefficients are known; (b) only the number of unknown nonzero signal coefficients is known; and (c) neither of these is known. It is shown that the performance of detector (a) is always better than that of (b) and (c), and conditions under which the performance of detector (b) is better than that of (c) are derived. The theoretical results are demonstrated by considering signals of different assumed structures