50 research outputs found
Secure Degrees of Freedom of MIMO X-Channels with Output Feedback and Delayed CSIT
We investigate the problem of secure transmission over a two-user multi-input
multi-output (MIMO) X-channel in which channel state information is provided
with one-unit delay to both transmitters (CSIT), and each receiver feeds back
its channel output to a different transmitter. We refer to this model as MIMO
X-channel with asymmetric output feedback and delayed CSIT. The transmitters
are equipped with M-antennas each, and the receivers are equipped with
N-antennas each. For this model, accounting for both messages at each receiver,
we characterize the optimal sum secure degrees of freedom (SDoF) region. We
show that, in presence of asymmetric output feedback and delayed CSIT, the sum
SDoF region of the MIMO X-channel is same as the SDoF region of a two-user MIMO
BC with 2M-antennas at the transmitter, N-antennas at each receiver and delayed
CSIT. This result shows that, upon availability of asymmetric output feedback
and delayed CSIT, there is no performance loss in terms of sum SDoF due to the
distributed nature of the transmitters. Next, we show that this result also
holds if only output feedback is conveyed to the transmitters, but in a
symmetric manner, i.e., each receiver feeds back its output to both
transmitters and no CSIT. We also study the case in which only asymmetric
output feedback is provided to the transmitters, i.e., without CSIT, and derive
a lower bound on the sum SDoF for this model. Furthermore, we specialize our
results to the case in which there are no security constraints. In particular,
similar to the setting with security constraints, we show that the optimal sum
DoF region of the (M,M,N,N)--MIMO X-channel with asymmetric output feedback and
delayed CSIT is same as the DoF region of a two-user MIMO BC with 2M-antennas
at the transmitter, N-antennas at each receiver, and delayed CSIT. We
illustrate our results with some numerical examples.Comment: To Appear in IEEE Transactions on Information Forensics and Securit
On SDoF of Multi-Receiver Wiretap Channel With Alternating CSIT
We study the problem of secure transmission over a Gaussian multi-input
single-output (MISO) two receiver channel with an external eavesdropper, under
the assumption that the state of the channel which is available to each
receiver is conveyed either perfectly () or with delay () to the
transmitter. Denoting by , , and the channel state information
at the transmitter (CSIT) of user 1, user 2, and eavesdropper, respectively,
the overall CSIT can then alternate between eight possible states, i.e.,
. We denote by the
fraction of time during which the state occurs. Under these
assumptions, we first consider the Gaussian MISO wiretap channel and
characterize the secure degrees of freedom (SDoF). Next, we consider the
general multi-receiver setup and characterize the SDoF region of fixed hybrid
states , , and . We then focus our attention on the symmetric
case in which . For this case, we establish bounds
on SDoF region. The analysis reveals that alternating CSIT allows synergistic
gains in terms of SDoF; and shows that, by opposition to encoding separately
over different states, joint encoding across the states enables strictly better
secure rates. Furthermore, we specialize our results for the two receivers
channel with an external eavesdropper to the two-user broadcast channel. We
show that, the synergistic gains in terms of SDoF by alternating CSIT is not
restricted to multi-receiver wiretap channels; and, can also be harnessed under
broadcast setting.Comment: To Appear in IEEE Transactions on Information Forensics and Securit
On the Secrecy Degrees of Freedom of Multi-Antenna Wiretap Channels with Delayed CSIT
The secrecy degrees of freedom (SDoF) of the Gaussian multiple-input and
single-output (MISO) wiretap channel is studied under the assumption that
delayed channel state information (CSI) is available at the transmitter and
each receiver knows its own instantaneous channel. We first show that a
strictly positive SDoF can be guaranteed whenever the transmitter has delayed
CSI (either on the legitimate channel or/and the eavesdropper channel). In
particular, in the case with delayed CSI on both channels, it is shown that the
optimal SDoF is 2/3. We then generalize the result to the two-user Gaussian
MISO broadcast channel with confidential messages and characterize the SDoF
region when the transmitter has delayed CSI of both receivers. Interestingly,
the artificial noise schemes exploiting several time instances are shown to
provide the optimal SDoF region by masking the confidential message to the
unintended receiver while aligning the interference at each receiver.Comment: 5 pages, 1 figure, 1 table. This work has been presented at ISIT
2011. The current version fixes several bugs in the Proceeding