A robust signal detection scheme

We consider the detection of a signal in the presence of both interferences that lie in a known subspace and white noise. The signal to be detected is the product of an unknown amplitude and a known signature-vector that is itself subject to additive white Gaussian noise. We develop the maximum likelihood estimates (MLE) of the problem in order to apply the generalized maximum likelihood test (GLRT) to our detection problem. The performances of the proposed detector are illustrated by means of numerical simulations and it is compared to the standard matched subspace detector.