3,290 research outputs found
On the Capacity of the Finite Field Counterparts of Wireless Interference Networks
This work explores how degrees of freedom (DoF) results from wireless
networks can be translated into capacity results for their finite field
counterparts that arise in network coding applications. The main insight is
that scalar (SISO) finite field channels over are analogous
to n x n vector (MIMO) channels in the wireless setting, but with an important
distinction -- there is additional structure due to finite field arithmetic
which enforces commutativity of matrix multiplication and limits the channel
diversity to n, making these channels similar to diagonal channels in the
wireless setting. Within the limits imposed by the channel structure, the DoF
optimal precoding solutions for wireless networks can be translated into
capacity optimal solutions for their finite field counterparts. This is shown
through the study of the 2-user X channel and the 3-user interference channel.
Besides bringing the insights from wireless networks into network coding
applications, the study of finite field networks over also
touches upon important open problems in wireless networks (finite SNR, finite
diversity scenarios) through interesting parallels between p and SNR, and n and
diversity.Comment: Full version of paper accepted for presentation at ISIT 201
MIMO Interference Alignment Over Correlated Channels with Imperfect CSI
Interference alignment (IA), given uncorrelated channel components and
perfect channel state information, obtains the maximum degrees of freedom in an
interference channel. Little is known, however, about how the sum rate of IA
behaves at finite transmit power, with imperfect channel state information, or
antenna correlation. This paper provides an approximate closed-form
signal-to-interference-plus-noise-ratio (SINR) expression for IA over
multiple-input-multiple-output (MIMO) channels with imperfect channel state
information and transmit antenna correlation. Assuming linear processing at the
transmitters and zero-forcing receivers, random matrix theory tools are
utilized to derive an approximation for the post-processing SINR distribution
of each stream for each user. Perfect channel knowledge and i.i.d. channel
coefficients constitute special cases. This SINR distribution not only allows
easy calculation of useful performance metrics like sum rate and symbol error
rate, but also permits a realistic comparison of IA with other transmission
techniques. More specifically, IA is compared with spatial multiplexing and
beamforming and it is shown that IA may not be optimal for some performance
criteria.Comment: 21 pages, 7 figures, submitted to IEEE Transactions on Signal
Processin
Degrees of Freedom of Two-Hop Wireless Networks: "Everyone Gets the Entire Cake"
We show that fully connected two-hop wireless networks with K sources, K
relays and K destinations have K degrees of freedom both in the case of
time-varying channel coefficients and in the case of constant channel
coefficients (in which case the result holds for almost all values of constant
channel coefficients). Our main contribution is a new achievability scheme
which we call Aligned Network Diagonalization. This scheme allows the data
streams transmitted by the sources to undergo a diagonal linear transformation
from the sources to the destinations, thus being received free of interference
by their intended destination. In addition, we extend our scheme to multi-hop
networks with fully connected hops, and multi-hop networks with MIMO nodes, for
which the degrees of freedom are also fully characterized.Comment: Presented at the 2012 Allerton Conference. Submitted to IEEE
Transactions on Information Theor
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