It is well-known that the MUSIC method for DoA estimation degrades when the number of samples N and the array dimension M are large and of the same order of magnitude. In this context, several improvements have been proposed, among which the G-MUSIC method, which was shown to be consistent in the asymptotic regime where M, N converge to infinity at the same rate, and under an additional separation condition between noise and signal subspaces of the SCM. Nevertheless, this subspace separation condition is only fulfilled for sufficiently high SNR. Dimension reduction techniques are a classical way to partially circumvent this condition. In this paper, we provide an asymptotic analysis in terms of consistency and MSE in the aforementioned regime, of the Beamspace MUSIC, which is one popular technique to reduce the dimension of the observations.