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Crystallization in large wireless networks
Authors
Veniamin I. Morgenshtern and Helmut BölcskeiReference
IEEE Transactions on Information Theory, Vol. 53, No. 10, pp. 3319-3349, Oct. 2007
DOI: 10.1109/TIT.2007.904789
[BibTeX, LaTeX, and HTML Reference] Abstract
We analyze fading interference relay networks
where M single-antenna source-destination terminal pairs
communicate concurrently and in the same frequency band
through a set of K single-antenna relays using half-duplex
two-hop relaying. Assuming that the relays have channel
state information (CSI), it is shown that in the large-M limit,
provided K grows fast enough as a function of M, the network
"decouples" in the sense that the individual source-destination
terminal pair capacities are strictly positive. The corresponding
required rate of growth of K as a function of M is found to be
sufficient to also make the individual source-destination fading
links converge to nonfading links. We say that the network
"crystallizes" as it breaks up into a set of effectively isolated
"wires in the air". A large-deviations analysis is performed to
characterize the "crystallization" rate, i.e., the rate (as a function
of M,K) at which the decoupled links converge to nonfading
links. In the course of this analysis, we develop a new technique
for characterizing the large-deviations behavior of certain sums
of dependent random variables. For the case of no CSI at the
relay level, assuming amplify-and-forward relaying, we compute
the per source-destination terminal pair capacity for M,K->\infty,
with K/M->\beta fixed, using tools from large random matrix
theory.Keywords
Amplify-and-forward, capacity scaling, crystallization, distributed orthogonalization, interference relay network, large-deviations theory, large random matrices, large wireless networks
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