42 research outputs found
Signal from noise retrieval from one and two-point Green's function - comparison
We compare two methods of eigen-inference from large sets of data, based on
the analysis of one-point and two-point Green's functions, respectively. Our
analysis points at the superiority of eigen-inference based on one-point
Green's function. First, the applied by us method based on Pad?e approximants
is orders of magnitude faster comparing to the eigen-inference based on
uctuations (two-point Green's functions). Second, we have identified the source
of potential instability of the two-point Green's function method, as arising
from the spurious zero and negative modes of the estimator for a variance
operator of the certain multidimensional Gaussian distribution, inherent for
the two-point Green's function eigen-inference method. Third, we have presented
the cases of eigen-inference based on negative spectral moments, for strictly
positive spectra. Finally, we have compared the cases of eigen-inference of
real-valued and complex-valued correlated Wishart distributions, reinforcing
our conclusions on an advantage of the one-point Green's function method.Comment: 14 pages, 8 figures, 3 table
Complete diagrammatics of the single ring theorem
Using diagrammatic techniques, we provide explicit functional relations
between the cumulant generating functions for the biunitarily invariant
ensembles in the limit of large size of matrices. The formalism allows to map
two distinct areas of free random variables: Hermitian positive definite
operators and non-normal R-diagonal operators. We also rederive the
Haagerup-Larsen theorem and show how its recent extension to the eigenvector
correlation function appears naturally within this approach.Comment: 18 pages, 6 figures, version accepted for publicatio
On the Transmit Beamforming for MIMO Wiretap Channels: Large-System Analysis
With the growth of wireless networks, security has become a fundamental issue
in wireless communications due to the broadcast nature of these networks. In
this work, we consider MIMO wiretap channels in a fast fading environment, for
which the overall performance is characterized by the ergodic MIMO secrecy
rate. Unfortunately, the direct solution to finding ergodic secrecy rates is
prohibitive due to the expectations in the rates expressions in this setting.
To overcome this difficulty, we invoke the large-system assumption, which
allows a deterministic approximation to the ergodic mutual information.
Leveraging results from random matrix theory, we are able to characterize the
achievable ergodic secrecy rates. Based on this characterization, we address
the problem of covariance optimization at the transmitter. Our numerical
results demonstrate a good match between the large-system approximation and the
actual simulated secrecy rates, as well as some interesting features of the
precoder optimization.Comment: Published in Lecture Notes in Computer Science 8317, pp. 90-102,
2014. (Proceedings of International Conference on Information-Theoretic
Security (ICITS), Singapore, November 2013
Large dimensional analysis of Maronna's M-estimator with outliers
International audienceBuilding on recent results in the random matrix analysis of robust estimators of scatter, we show that a certain class of such estimators obtained from samples containing outliers behaves similar to a well-known random matrix model in the limiting regime where both the population and sample sizes grow to infinity at the same speed. This result allows us to understand the structure of such estimators when a certain fraction of the samples is corrupted by outliers and, in particular, to derive their asymptotic eigenvalue distributions. This analysis is a first step towards an improved usage of robust estimation methods under the presence of outliers when the number of independent observations is not too large compared to the size of the population