2,163 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 X-Channels with Feedback and Delayed CSI
The sum degrees of freedom (DoF) of the two-user MIMO X-channel is
characterized in the presence of output feedback and delayed channel state
information (CSI). The number of antennas at each transmitters is assumed to be
M and the number of antennas at each of the receivers is assumed to be N. It is
shown that the sum DoF of the two-user MIMO X-channel is the same as the sum
DoF of a two-user MIMO broadcast channel with 2M transmit antennas, and N
antennas at each receiver. Hence, for this symmetric antenna configuration,
there is no performance loss in the sum degrees of freedom due to the
distributed nature of the transmitters. This result highlights the usefulness
of feedback and delayed CSI for the MIMO X-channel.
The K-user X-channel with single antenna at each transmitter and each
receiver is also studied. In this network, each transmitter has a message
intended for each receiver. For this network, it is shown that the sum DoF with
partial output feedback alone is at least 2K/(K+1). This lower bound is
strictly better than the best lower bound known for the case of delayed CSI
assumption for all values of K.Comment: Submitted to IEEE ISIT 2012 on Jan 22, 201
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