Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 $D$ directly lead to an
$\mathcal{O}(1)$ capacity characterization of the form
$C(SNR)=D\log(1+SNR)+\mathcal{O}(1)$ 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.

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The categories of this paper are: nlin
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat