27 research outputs found
Quantization Bounds on Grassmann Manifolds and Applications to MIMO Communications
This paper considers the quantization problem on the Grassmann manifold
\mathcal{G}_{n,p}, the set of all p-dimensional planes (through the origin) in
the n-dimensional Euclidean space. The chief result is a closed-form formula
for the volume of a metric ball in the Grassmann manifold when the radius is
sufficiently small. This volume formula holds for Grassmann manifolds with
arbitrary dimension n and p, while previous results pertained only to p=1, or a
fixed p with asymptotically large n. Based on this result, several quantization
bounds are derived for sphere packing and rate distortion tradeoff. We
establish asymptotically equivalent lower and upper bounds for the rate
distortion tradeoff. Since the upper bound is derived by constructing random
codes, this result implies that the random codes are asymptotically optimal.
The above results are also extended to the more general case, in which
\mathcal{G}_{n,q} is quantized through a code in \mathcal{G}_{n,p}, where p and
q are not necessarily the same. Finally, we discuss some applications of the
derived results to multi-antenna communication systems.Comment: 26 pages, 7 figures, submitted to IEEE Transactions on Information
Theory in Aug, 200
Degrees of Freedom of Certain Interference Alignment Schemes with Distributed CSIT
In this work, we consider the use of interference alignment (IA) in a MIMO
interference channel (IC) under the assumption that each transmitter (TX) has
access to channel state information (CSI) that generally differs from that
available to other TXs. This setting is referred to as distributed CSIT. In a
setting where CSI accuracy is controlled by a set of power exponents, we show
that in the static 3-user MIMO square IC, the number of degrees-of-freedom
(DoF) that can be achieved with distributed CSIT is at least equal to the DoF
achieved with the worst accuracy taken across the TXs and across the
interfering links. We conjecture further that this represents exactly the DoF
achieved. This result is in strong contrast with the centralized CSIT
configuration usually studied (where all the TXs share the same, possibly
imperfect, channel estimate) for which it was shown that the DoF achieved at
receiver (RX) i is solely limited by the quality of its own feedback. This
shows the critical impact of CSI discrepancies between the TXs, and highlights
the price paid by distributed precoding.Comment: This is an extended version of a conference submission which will be
presented at the IEEE conference SPAWC, Darmstadt, June 201
Multiuser Diversity for Secrecy Communications Using Opportunistic Jammer Selection -- Secure DoF and Jammer Scaling Law
In this paper, we propose opportunistic jammer selection in a wireless
security system for increasing the secure degrees of freedom (DoF) between a
transmitter and a legitimate receiver (say, Alice and Bob). There is a jammer
group consisting of jammers among which Bob selects jammers. The
selected jammers transmit independent and identically distributed Gaussian
signals to hinder the eavesdropper (Eve). Since the channels of Bob and Eve are
independent, we can select the jammers whose jamming channels are aligned at
Bob, but not at Eve. As a result, Eve cannot obtain any DoF unless it has more
than receive antennas, where is the number of jammer's transmit
antenna each, and hence can be regarded as defensible dimensions against
Eve. For the jamming signal alignment at Bob, we propose two opportunistic
jammer selection schemes and find the scaling law of the required number of
jammers for target secure DoF by a geometrical interpretation of the received
signals.Comment: Accepted with minor revisions, IEEE Trans. on Signal Processin