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In array processing, a common problem is to estimate the angles of arrival of$K$ deterministic sources impinging on an array of $M$ antennas, from $N$observations of the source signal, corrupted by gaussian noise. The problemreduces to estimate a quadratic form (called "localization function") of acertain projection matrix related to the source signal empirical covariancematrix. Recently, a new subspace estimation method (called "G-MUSIC") has beenproposed, in the context where the number of available samples $N$ is of thesame order of magnitude than the number of sensors $M$. In this context, thetraditional subspace methods tend to fail because the empirical covariancematrix of the observations is a poor estimate of the source signal covariancematrix. The G-MUSIC method is based on a new consistent estimator of thelocalization function in the regime where $M$ and $N$ tend to $+\infty$ at thesame rate. However, the consistency of the angles estimator was not adressed.The purpose of this paper is to prove the consistency of the angles of arrivalestimator in the previous asymptotic regime. To prove this result, we show theproperty that the singular values of M x N Gaussian information plus noisematrix escape from certain intervals is an event of probability decreasing atrate O(1/N^p) for all p. A regularization trick is also introduced, whichallows to confine these singular values into certain intervals and to usestandard tools as Poincar\'e inequality to characterize any moments of theestimator. These results are believed to be of independent interest.

Large information plus noise random matrix models and consistent subspace estimation in large sensor networks