Oblique projection for source estimation in a competitive environment: Algorithm and statistical analysis

In this paper, we study the problem where the aim is to estimate the source (complex amplitude) parameter of a single signal contaminated by a structured interference (constituted by the other signals) and by a background Gaussian noise. To solve this problem, we propose an estimator based on a partially estimated oblique projection. We derive closed-form expressions of the variance of this estimator and of the Cramér–Rao bound (CRB) associated with the considered model. In particular, we show that the proposed estimator is (i) asymptotically (for large number of sensors) efficient in the sense that its variance meets the CRB for a single signal in noise and (ii) for a small of moderate number of sensors, the variance remains close to the CRB without structured interference for well separated bearings.