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Multiple-Antenna Interference Channel with Receive Antenna Joint Processing and Real Interference Alignment
We consider a constant -user Gaussian interference channel with
antennas at each transmitter and antennas at each receiver, denoted as a
channel. Relying on a result on simultaneous Diophantine
approximation, a real interference alignment scheme with joint receive antenna
processing is developed. The scheme is used to provide new proofs for two
previously known results, namely 1) the total degrees of freedom (DoF) of a
channel is ; and 2) the total DoF of a channel is
at least . We also derive the DoF region of the channel,
and an inner bound on the DoF region of the channel
Degrees of Freedom of Wireless X Networks
We explore the degrees of freedom of user wireless networks,
i.e. networks of transmitters and receivers where every transmitter has
an independent message for every receiver. We derive a general outerbound on
the degrees of freedom \emph{region} of these networks. When all nodes have a
single antenna and all channel coefficients vary in time or frequency, we show
that the \emph{total} number of degrees of freedom of the network is equal
to per orthogonal time and frequency dimension.
Achievability is proved by constructing interference alignment schemes for
networks that can come arbitrarily close to the outerbound on degrees of
freedom. For the case where either M=2 or N=2 we find that the outerbound is
exactly achievable. While networks have significant degrees of freedom
benefits over interference networks when the number of users is small, our
results show that as the number of users increases, this advantage disappears.
Thus, for large , the user wireless network loses half the
degrees of freedom relative to the MIMO outerbound achievable
through full cooperation. Interestingly, when there are few transmitters
sending to many receivers () or many transmitters sending to few
receivers (), networks are able to approach the degrees
of freedom possible with full cooperation on the MIMO channel.
Similar to the interference channel, we also construct an example of a 2 user
channel with propagation delays where the outerbound on degrees of freedom
is achieved through interference alignment based on a simple TDMA strategy.Comment: 26 page
Secure Degrees of Freedom Regions of Multiple Access and Interference Channels: The Polytope Structure
The sum secure degrees of freedom (s.d.o.f.) of two fundamental multi-user
network structures, the K-user Gaussian multiple access (MAC) wiretap channel
and the K-user interference channel (IC) with secrecy constraints, have been
determined recently as K(K-1)/(K(K-1)+1) [1,2] and K(K-1)/(2K-1) [3,4],
respectively. In this paper, we determine the entire s.d.o.f. regions of these
two channel models. The converse for the MAC follows from a middle step in the
converse of [1,2]. The converse for the IC includes constraints both due to
secrecy as well as due to interference. Although the portion of the region
close to the optimum sum s.d.o.f. point is governed by the upper bounds due to
secrecy constraints, the other portions of the region are governed by the upper
bounds due to interference constraints. Different from the existing literature,
in order to fully understand the characterization of the s.d.o.f. region of the
IC, one has to study the 4-user case, i.e., the 2 or 3-user cases do not
illustrate the generality of the problem. In order to prove the achievability,
we use the polytope structure of the converse region. In both MAC and IC cases,
we develop explicit schemes that achieve the extreme points of the polytope
region given by the converse. Specifically, the extreme points of the MAC
region are achieved by an m-user MAC wiretap channel with (K-m) helpers, i.e.,
by setting (K-m) users' secure rates to zero and utilizing them as pure
(structured) cooperative jammers. The extreme points of the IC region are
achieved by a (K-m)-user IC with confidential messages, m helpers, and N
external eavesdroppers, for m>=1 and a finite N. A byproduct of our results in
this paper is that the sum s.d.o.f. is achieved only at one extreme point of
the s.d.o.f. region, which is the symmetric-rate extreme point, for both MAC
and IC channel models.Comment: Submitted to IEEE Transactions on Information Theory, April 201
Multiple-Antenna Interference Channels with Real Interference Alignment and Receive Antenna Joint Processing
In this paper, the degrees of freedom (DoF) regions of constant coefficient multiple antenna interference channels are investigated. First, we consider a K-user Gaussian interference channel with Mk antennas at transmitter k, 1≤k≤K, and Nj antennas at receiver j, 1≤j≤K, denoted as a (K,[Mk],[Nj]) channel. Relying on a result of simultaneous Diophantine approximation, a real interference alignment scheme with joint receive antenna processing is developed. The scheme is used to obtain an achievable DoF region. The proposed DoF region includes two previously known results as special cases, namely 1) the total DoF of a K-user interference channel with N antennas at each node, (K,[N],[N]) channel, is NK/2; and 2) the total DoF of a (K,[M],[N]) channel is at least KMN/(M+N). We next explore constant-coefficient interference networks with K transmitters and J receivers, all having N antennas. Each transmitter emits an independent message and each receiver requests an arbitrary subset of the messages. Employing the novel joint receive antenna processing, the DoF region for this set-up is obtained. We finally consider wireless X networks where each node is allowed to have an arbitrary number of antennas. It is shown that the joint receive antenna processing can be used to establish an achievable DoF region, which is larger than what is possible with antenna splitting. As a special case of the derived achievable DoF region for constant coefficient X network, the total DoF of wireless X networks with the same number of antennas at all nodes and with joint antenna processing is tight while the best inner bound based on antenna splitting cannot meet the outer bound. Finally, we obtain a DoF region outer bound based on the technique of transmitter grouping
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