Signal Detection with Noise Power Variation Between the Hypotheses

Detecting a known signal in additive noise is a widespread problem. Two different cases have been processed in the literature whether the noise power is known or not. Here we consider the case where the noise power could vary between the null and alternative hypothesis. This situation occurs if the receiver electronic behave differently if the signal of interest (SOI) is present or when the signal signature is not perfectly known or could change. We have developed the generalized likelihood ratio test (GLRT) for the problem at hand and compared its performances with the one which assumes the same noise power under the two hypotheses. We first present some numerical simulations to attest to the validity of the analysis. Then we experiment the new detector on real data to detect knocking for car engine management to show the improvement with the standard detector.