Matched detector in the presence of interference subspace uncertainty

The problem of the detection of a signal in the presence of broad-band noise and interferences that lie in a subspace that is imperfectly known is considered. It is assumed that a basis (or generating set) of the interference subspace is known up to additive white Gaussian noise. This amounts to assuming that each of these basis vectors lies in a cone, the aperture of which depends upon the level of uncertainty. This feature should drastically reduce the dimension of the subspace required to model the interferences and hence improve the performance of the detector. The maximum likelihood estimator of the different unknowns are first obtained, then the generalized likelihood ratio (GLR) is build and approximate probability density functions for the GLR under both hypotheses obtained. They allow to set the threshold to achieve a desired probability of false alarm.