On the consistency of the G-MUSIC DoA estimator

Recently, a new subspace DoA estimation method (called "G-MUSIC") has been proposed, in the context where the number of available snapshots N is of the same order of magnitude than the number of sensors M. In this context, the traditional subspace methods tend to fail because the empirical covari-ance matrix of the observations is a poor estimate of the true covariance matrix. G-MUSIC is based on a new consistent estimator of the localization function in the regime where M and N tend to +∞ at the same rate. However, the consistency of the DoA estimator was not adressed. The purpose of this paper is to prove the consistency of the angles estimator in the previous asymptotic regime.