Matched Detector and Estimator with Signature Uncertainty

We consider the detection and estimation of a signal, whose associated spatial signature is imperfectly known, in the presence of broad-band noise. While in most cases, the spatial signature (or steering vector) is assumed to be known, i.e., lies along a known direction, we consider the case where the signature is known up to additive white Gaussian noise. This amounts to assuming that it somehow lies in a cone, the aperture of which depends upon the level of uncertainty. We consider the multiple snapshots case and assume the unknown signature to remain constant over the whole set of snapshots. We develop the maximum likelihood estimator of the different unknowns, build the generalized likelihood ratio (GLR). We then evaluate the statistical properties of the associated test under both hypotheses and check the validity of the asymptotic analysis on simulations..