  We consider the problem of subspace estimation in situations where the number
of available snapshots and the observation dimension are comparable in
magnitude. In this context, traditional subspace methods tend to fail because
the eigenvectors of the sample correlation matrix are heavily biased with
respect to the true ones. It has recently been suggested that this situation
(where the sample size is small compared to the observation dimension) can be
very accurately modeled by considering the asymptotic regime where the
observation dimension $M$ and the number of snapshots $N$ converge to $+\infty$
at the same rate. Using large random matrix theory results, it can be shown
that traditional subspace estimates are not consistent in this asymptotic
regime. Furthermore, new consistent subspace estimate can be proposed, which
outperform the standard subspace methods for realistic values of $M$ and $N$.
The work carried out so far in this area has always been based on the
assumption that the observations are random, independent and identically
distributed in the time domain. The goal of this paper is to propose new
consistent subspace estimators for the case where the source signals are
modelled as unknown deterministic signals. In practice, this allows to use the
proposed approach regardless of the statistical properties of the source
signals. In order to construct the proposed estimators, new technical results
concerning the almost sure location of the eigenvalues of sample covariance
matrices of Information plus Noise complex Gaussian models are established.
These results are believed to be of independent interest.
