6,150 research outputs found
Improved subspace estimation for multivariate observations of high dimension: the deterministic signals case
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 and the number of snapshots converge to
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 and .
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.Comment: New version with minor corrections. The present paper is an extended
version of a paper (same title) to appear in IEEE Trans. on Information
Theor
Performance analysis of an improved MUSIC DoA estimator
This paper adresses the statistical performance of subspace DoA estimation
using a sensor array, in the asymptotic regime where the number of samples and
sensors both converge to infinity at the same rate. Improved subspace DoA
estimators were derived (termed as G-MUSIC) in previous works, and were shown
to be consistent and asymptotically Gaussian distributed in the case where the
number of sources and their DoA remain fixed. In this case, which models widely
spaced DoA scenarios, it is proved in the present paper that the traditional
MUSIC method also provides DoA consistent estimates having the same asymptotic
variances as the G-MUSIC estimates. 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 G-MUSIC estimates are still able to consistently separate the
sources, while it is no longer the case for the MUSIC ones. The asymptotic
variances of G-MUSIC estimates are also evaluated.Comment: Revised versio
Interpolating sequences for weighted Bergman spaces of the ball
Let be the space of holomorphic in the unit ball of
such that , where ,
(weighted Bergman space). In this paper we study the
interpolating sequences for various . The limiting cases
and are respectively the Hardy spaces and
, the holomorphic functions with polynomial growth of order
, which have generated particular interest.
In \S 1 we first collect some definitions and well-known facts about weighted
Bergman spaces and then introduce the natural interpolation problem, along with
some basic properties. In \S 2 we describe in terms of and the
inclusions between spaces, and in \S 3 we show that most of
these inclusions also hold for the corresponding spaces of interpolating
sequences. \S 4 is devoted to sufficient conditions for a sequence to be
-interpolating, expressed in the same terms as the conditions
given in previous works of Thomas for the Hardy spaces and Massaneda for
. In particular we show, under some restrictions on and
, that finite unions of -interpolating sequences coincide
with finite unions of separated sequences.
In his article in Inventiones, Seip implicitly gives a characterization of
interpolating sequences for all weighted Bergman spaces in the disk. We spell
out the details for the reader's convenience in an appendix (\S 5)
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