27 research outputs found
On the Secrecy Degress of Freedom of the Multi-Antenna Block Fading Wiretap Channels
We consider the multi-antenna wiretap channel in which the transmitter wishes
to send a confidential message to its receiver while keeping it secret to the
eavesdropper. It has been known that the secrecy capacity of such a channel
does not increase with signal-to-noise ratio when the transmitter has no
channel state information (CSI) under mild conditions. Motivated by Jafar's
robust interference alignment technique, we study the so-called staggered
multi-antenna block-fading wiretap channel where the legitimate receiver and
the eavesdropper have different temporal correlation structures. Assuming no
CSI at transmitter, we characterize lower and upper bounds on the secrecy
degrees of freedom (s.d.o.f.) of the channel at hand. Our results show that a
positive s.d.o.f. can be ensured whenever two receivers experience different
fading variation. Remarkably, very simple linear precoding schemes provide the
optimal s.d.o.f. in some cases of interest.Comment: to appear in Proc. of IEEE International Symposium on Information
Theory (ISIT2010
Secret Key Agreement from Correlated Gaussian Sources by Rate Limited Public Communication
We investigate the secret key agreement from correlated Gaussian sources in
which the legitimate parties can use the public communication with limited
rate. For the class of protocols with the one-way public communication, we show
a closed form expression of the optimal trade-off between the rate of key
generation and the rate of the public communication. Our results clarify an
essential difference between the key agreement from discrete sources and that
from continuous sources.Comment: 9 pages, no figure, Version 2 is a published version. The results are
not changed from version 1. Explanations are polishe
Optimal Beamforming for Gaussian MIMO Wiretap Channels with Two Transmit Antennas
A Gaussian multiple-input multiple-output wiretap channel in which the
eavesdropper and legitimate receiver are equipped with arbitrary numbers of
antennas and the transmitter has two antennas is studied in this paper. Under
an average power constraint, the optimal input covariance to obtain the secrecy
capacity of this channel is unknown, in general. In this paper, the input
covariance matrix required to achieve the capacity is determined. It is shown
that the secrecy capacity of this channel can be achieved by linear precoding.
The optimal precoding and power allocation schemes that maximize the achievable
secrecy rate, and thus achieve the capacity, are developed subsequently. The
secrecy capacity is then compared with the achievable secrecy rate of
generalized singular value decomposition (GSVD)-based precoding, which is the
best previously proposed technique for this problem. Numerical results
demonstrate that substantial gain can be obtained in secrecy rate between the
proposed and GSVD-based precodings.Comment: Accepted for publication in IEEE Transactions on Wireless
Communication
Waveform Design for Secure SISO Transmissions and Multicasting
Wireless physical-layer security is an emerging field of research aiming at
preventing eavesdropping in an open wireless medium. In this paper, we propose
a novel waveform design approach to minimize the likelihood that a message
transmitted between trusted single-antenna nodes is intercepted by an
eavesdropper. In particular, with knowledge first of the eavesdropper's channel
state information (CSI), we find the optimum waveform and transmit energy that
minimize the signal-to-interference-plus-noise ratio (SINR) at the output of
the eavesdropper's maximum-SINR linear filter, while at the same time provide
the intended receiver with a required pre-specified SINR at the output of its
own max-SINR filter. Next, if prior knowledge of the eavesdropper's CSI is
unavailable, we design a waveform that maximizes the amount of energy available
for generating disturbance to eavesdroppers, termed artificial noise (AN),
while the SINR of the intended receiver is maintained at the pre-specified
level. The extensions of the secure waveform design problem to multiple
intended receivers are also investigated and semidefinite relaxation (SDR) -an
approximation technique based on convex optimization- is utilized to solve the
arising NP-hard design problems. Extensive simulation studies confirm our
analytical performance predictions and illustrate the benefits of the designed
waveforms on securing single-input single-output (SISO) transmissions and
multicasting
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
Optimal Inputs for Some Classes of Degraded Wiretap Channels
International audienceIn this paper, an analysis of an input distribution that achieves the secrecy capacity of a general degraded additive noise wiretap channel is presented. In particular, using convex optimization methods, an input distribution that achieves the secrecy capacity is characterized by conditions expressed in terms of integral equations. The new conditions are used to study the structure of the optimal input distribution for three different additive noise cases: vector Gaussian; scalar Cauchy; and scalar exponential
Robust Secure Transmission in MISO Channels Based on Worst-Case Optimization
This paper studies robust transmission schemes for multiple-input
single-output (MISO) wiretap channels. Both the cases of direct transmission
and cooperative jamming with a helper are investigated with imperfect channel
state information (CSI) for the eavesdropper links. Robust transmit covariance
matrices are obtained based on worst-case secrecy rate maximization, under both
individual and global power constraints. For the case of an individual power
constraint, we show that the non-convex maximin optimization problem can be
transformed into a quasiconvex problem that can be efficiently solved with
existing methods. For a global power constraint, the joint optimization of the
transmit covariance matrices and power allocation between the source and the
helper is studied via geometric programming. We also study the robust wiretap
transmission problem for the case with a quality-of-service constraint at the
legitimate receiver. Numerical results show the advantage of the proposed
robust design. In particular, for the global power constraint scenario,
although cooperative jamming is not necessary for optimal transmission with
perfect eavesdropper's CSI, we show that robust jamming support can increase
the worst-case secrecy rate and lower the signal to interference-plus-noise
ratio at Eve in the presence of channel mismatches between the transmitters and
the eavesdropper.Comment: 28 pages, 5 figure