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Contractive interference functions and rates of convergence of distributed power control laws
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
2012 (English)In: IEEE Transactions on Wireless Communications, ISSN 1536-1276, E-ISSN 1558-2248, Vol. 11, no 12, 4494-4502 p.Article in journal (Refereed) Published
Abstract [en]

The standard interference functions introduced by Yates have been very influential on the analysis and design of distributed power control laws. While powerful and versatile, the framework has some drawbacks: the existence of fixed-points has to be established separately, and no guarantees are given on the rate of convergence of the iterates. This paper introduces contractive interference functions, a slight reformulation of the standard interference functions that guarantees the existence and uniqueness of fixed-points along with linear convergence of iterates. We show that many power control laws from the literature are contractive and derive, sometimes for the first time, analytical convergence rate estimates for these algorithms. We also prove that contractive interference functions converge when executed totally asynchronously and, under the assumption that the communication delay is bounded, derive an explicit bound on the convergence time penalty due to increased delay. Finally, we demonstrate that although standard interference functions are, in general, not contractive, they are all para-contractions with respect to a certain metric. Similar results for two-sided scalable interference functions are also derived.

Place, publisher, year, edition, pages
IEEE Communications Society, 2012. Vol. 11, no 12, 4494-4502 p.
Keyword [en]
contraction mapping, Interference function, power control, wireless networks
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-107592DOI: 10.1109/TWC.2012.102512.120101ISI: 000312836900027Scopus ID: 2-s2.0-84871748823OAI: oai:DiVA.org:kth-107592DiVA: diva2:576794
Note

QC 20120116

Available from: 2012-12-13 Created: 2012-12-13 Last updated: 2017-12-06Bibliographically approved

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