167 research outputs found
On Ergodic Secrecy Capacity for Gaussian MISO Wiretap Channels
A Gaussian multiple-input single-output (MISO) wiretap channel model is
considered, where there exists a transmitter equipped with multiple antennas, a
legitimate receiver and an eavesdropper each equipped with a single antenna. We
study the problem of finding the optimal input covariance that achieves ergodic
secrecy capacity subject to a power constraint where only statistical
information about the eavesdropper channel is available at the transmitter.
This is a non-convex optimization problem that is in general difficult to
solve. Existing results address the case in which the eavesdropper or/and
legitimate channels have independent and identically distributed Gaussian
entries with zero-mean and unit-variance, i.e., the channels have trivial
covariances. This paper addresses the general case where eavesdropper and
legitimate channels have nontrivial covariances. A set of equations describing
the optimal input covariance matrix are proposed along with an algorithm to
obtain the solution. Based on this framework, we show that when full
information on the legitimate channel is available to the transmitter, the
optimal input covariance has always rank one. We also show that when only
statistical information on the legitimate channel is available to the
transmitter, the legitimate channel has some general non-trivial covariance,
and the eavesdropper channel has trivial covariance, the optimal input
covariance has the same eigenvectors as the legitimate channel covariance.
Numerical results are presented to illustrate the algorithm.Comment: 27 pages, 10 figure
On the Coherence Properties of Random Euclidean Distance Matrices
In the present paper we focus on the coherence properties of general random
Euclidean distance matrices, which are very closely related to the respective
matrix completion problem. This problem is of great interest in several
applications such as node localization in sensor networks with limited
connectivity. Our results can directly provide the sufficient conditions under
which an EDM can be successfully recovered with high probability from a limited
number of measurements.Comment: 5 pages, SPAWC 201
Matrix Completion in Colocated MIMO Radar: Recoverability, Bounds & Theoretical Guarantees
It was recently shown that low rank matrix completion theory can be employed
for designing new sampling schemes in the context of MIMO radars, which can
lead to the reduction of the high volume of data typically required for
accurate target detection and estimation. Employing random samplers at each
reception antenna, a partially observed version of the received data matrix is
formulated at the fusion center, which, under certain conditions, can be
recovered using convex optimization. This paper presents the theoretical
analysis regarding the performance of matrix completion in colocated MIMO radar
systems, exploiting the particular structure of the data matrix. Both Uniform
Linear Arrays (ULAs) and arbitrary 2-dimensional arrays are considered for
transmission and reception. Especially for the ULA case, under some mild
assumptions on the directions of arrival of the targets, it is explicitly shown
that the coherence of the data matrix is both asymptotically and approximately
optimal with respect to the number of antennas of the arrays involved and
further, the data matrix is recoverable using a subset of its entries with
minimal cardinality. Sufficient conditions guaranteeing low matrix coherence
and consequently satisfactory matrix completion performance are also presented,
including the arbitrary 2-dimensional array case.Comment: 19 pages, 7 figures, under review in Transactions on Signal
Processing (2013
- …