Cramer-Rao Lower Bound for Prior-Subspace Estimation

In the context of the localization of digital multi-source, we can sometimes assume that we have some a priori knowledge of the location/direction of several sources. In that situation, some works have proposed to tacking into account of this knowledge to improve the localization of the unknown sources. These solutions are based on an orthogonal deflation of the signal subspace. In this paper, we derive the Cramer-Rao lower bound for orthogonally deflated MIMO model and we show that the estimation schemes based on this model can help the estimation of the unknown DOA in some limit situations as for coherent or highly correlated sources but cannot totally cancel the influence of the known directions, in particular for uncorrelated sources with closely-spaced DOA with finite number of sensors