25,661 research outputs found
Interference Alignment and the Degrees of Freedom for the K User Interference Channel
While the best known outerbound for the K user interference channel states
that there cannot be more than K/2 degrees of freedom, it has been conjectured
that in general the constant interference channel with any number of users has
only one degree of freedom. In this paper, we explore the spatial degrees of
freedom per orthogonal time and frequency dimension for the K user wireless
interference channel where the channel coefficients take distinct values across
frequency slots but are fixed in time. We answer five closely related
questions. First, we show that K/2 degrees of freedom can be achieved by
channel design, i.e. if the nodes are allowed to choose the best constant,
finite and nonzero channel coefficient values. Second, we show that if channel
coefficients can not be controlled by the nodes but are selected by nature,
i.e., randomly drawn from a continuous distribution, the total number of
spatial degrees of freedom for the K user interference channel is almost surely
K/2 per orthogonal time and frequency dimension. Thus, only half the spatial
degrees of freedom are lost due to distributed processing of transmitted and
received signals on the interference channel. Third, we show that interference
alignment and zero forcing suffice to achieve all the degrees of freedom in all
cases. Fourth, we show that the degrees of freedom directly lead to an
capacity characterization of the form
for the multiple access channel, the
broadcast channel, the 2 user interference channel, the 2 user MIMO X channel
and the 3 user interference channel with M>1 antennas at each node. Fifth, we
characterize the degree of freedom benefits from cognitive sharing of messages
on the 3 user interference channel.Comment: 30 pages. Revision extends the 3 user proof to K user
Interference alignment for the MIMO interference channel
We study vector space interference alignment for the MIMO interference
channel with no time or frequency diversity, and no symbol extensions. We prove
both necessary and sufficient conditions for alignment. In particular, we
characterize the feasibility of alignment for the symmetric three-user channel
where all users transmit along d dimensions, all transmitters have M antennas
and all receivers have N antennas, as well as feasibility of alignment for the
fully symmetric (M=N) channel with an arbitrary number of users.
An implication of our results is that the total degrees of freedom available
in a K-user interference channel, using only spatial diversity from the
multiple antennas, is at most 2. This is in sharp contrast to the K/2 degrees
of freedom shown to be possible by Cadambe and Jafar with arbitrarily large
time or frequency diversity.
Moving beyond the question of feasibility, we additionally discuss
computation of the number of solutions using Schubert calculus in cases where
there are a finite number of solutions.Comment: 16 pages, 7 figures, final submitted versio
Time Interference Alignment via Delay Offset for Long Delay Networks
The potential of Time Interference Alignment is investigated in this work, with particular reference to the attainable degrees of freedom. The K-user interference channel is considered, in which transmitters and receivers are placed randomly in a Euclidean space. A model for long delay networks is introduced and the degrees of freedom for different cases (with and without transmitter delay coordination) are evaluated. It is shown how time interference alignment can provide more dof than TDMA when the transmitters jointly coordinate their transmission delay and the number of pairs is K >=5. Closed form expressions are derived for several cases of interest which provide insight and useful predictions. This work is concluded with an investigation of the achievable degrees of freedom for multi-satellite networks, where it is shown that the results obtained under several assumptions do predict accurately the dof in a real setting
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