293 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
Retrospective Interference Alignment
We explore similarities and differences in recent works on blind interference
alignment under different models such as staggered block fading model and the
delayed CSIT model. In particular we explore the possibility of achieving
interference alignment with delayed CSIT when the transmitters are distributed.
Our main contribution is an interference alignment scheme, called retrospective
interference alignment in this work, that is specialized to settings with
distributed transmitters. With this scheme we show that the 2 user X channel
with only delayed channel state information at the transmitters can achieve 8/7
DoF, while the interference channel with 3 users is able to achieve 9/8 DoF. We
also consider another setting where delayed channel output feedback is
available to transmitters. In this setting the X channel and the 3 user
interference channel are shown to achieve 4/3 and 6/5 DoF, respectively
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