Transient Signal Detection Using Prior Information in the Likelihood Ratio Test

This paper provides a uniform approach to the problem of detecting a deterministic transient signal of unknown waveshape in Gaussian noise. By defining a transient signal as a signal which is localized in a certain vector representation, our analysis is applicable for a general class of signals. We assume that the vector representation consists of a group of zero coefficients plus a group of unknown nonzero coefficients, starting at a certain index. We derive performance indices for a likelihood-ratio-test detector of such a generalized transient signal for three cases: a) where both the starting index and the number of unknown nonzero signal coefficients are known; b) where only the number of unknown nonzero signal coefficients is known; c) and when neither of these is known. We show that the performance of detector a) is always better than that of b) and c) and we derive conditions under which the performance of detector b) is better than c). We demonstrate the theoretical results by considering signals of different assumed structure. We show that if the prior information about the signal structure is translated, using a proper signal representation, into a generalized transient signal of type a) or b), then a better detection performance can be achieved.