9,728 research outputs found
Almost sure localization of the eigenvalues in a gaussian information plus noise model. Applications to the spiked models
Let be a random matrix defined by
where
is a uniformly bounded deterministic matrix and where
is an independent identically distributed complex Gaussian
matrix with zero mean and variance entries. The purpose of this
paper is to study the almost sure location of the eigenvalues
of the Gram matrix
when and converge to
such that the ratio converges towards a constant
. The results are used in order to derive, using an alernative approach,
known results concerning the behaviour of the largest eigenvalues of
when the rank of
remains fixed when and converge to .Comment: 19 pages, 1 figure, Accepted for publication in Electronic Journal of
Probabilit
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
Optical fiber Sagnac interferometer for sensing scalar directional refraction: application to magnetochiral birefringence
We present a set-up dedicated to the measurement of the small scalar
directional anisotropies associated to the magnetochiral interaction. The
apparatus, based on a polarization-independent fiber Sagnac interferometer, is
optimized to be insensitive to circular anisotropies and to residual
absorption. It can thus characterize samples of biological interests, for which
the two enantiomers are not available and/or which present poor transmission.
The signal-to-noise ratio is shown to be limited only by the source intensity
noise, leading to a detection limit of Df = 500 nrad.Hz-1/2. It yields a limit
on the magnetochiral index nMC < 4 10-13 T-1 at 1550 nm for the organic
molecules tested.Comment: 17 pages, 8 figure
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
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