  This paper adresses the statistical behaviour of spatial smoothing subspace
DoA estimation schemes using a sensor array in the case where the number of
observations $N$ is significantly smaller than the number of sensors $M$, and
that the smoothing parameter $L$ is such that $M$ and $NL$ are of the same
order of magnitude. This context is modelled by an asymptotic regime in which
$NL$ and $M$ both converge towards $\infty$ at the same rate. As in recent
works devoted to the study of (unsmoothed) subspace methods in the case where
$M$ and $N$ are of the same order of magnitude, it is shown that it is still
possible to derive improved DoA estimators termed as Generalized-MUSIC with
spatial smoothing (G-MUSIC SS). The key ingredient of this work is a technical
result showing that the largest singular values and corresponding singular
vectors of low rank deterministic perturbation of certain Gaussian block-Hankel
large random matrices behave as if the entries of the latter random matrices
were independent identically distributed. This allows to conclude that when the
number of sources and their DoA do not scale with $M,N,L,$ a situation
modelling widely spaced DoA scenarios, then both traditional and Generalized
spatial smoothing subspace methods provide consistent DoA estimators whose
convergence speed is faster than $\frac{1}{M}$. The case of DoA that are spaced
of the order of a beamwidth, which models closely spaced sources, is also
considered. It is shown that the convergence speed of G-MUSIC SS estimates is
unchanged, but that it is no longer the case for MUSIC SS ones.
