Contractive interference functions and rates of convergence of distributed power control laws

Hamid Reza Feyzmahdavian*, Mikael Johansson, Themistoklis Charalambous

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

10 Citations (Scopus)


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 existence and uniqueness of fixed-points and geometric convergence rates. We show that many power control laws from the literature are contractive and derive, sometimes for the first time, convergence rate estimates for these algorithms. Finally, we show that although standard interference functions are not contractive, they are paracontractions with respect to a certain metric space. Extensions to two-sided scalable interference functions are also discussed.

Original languageEnglish
Title of host publication2012 IEEE International Conference on Communications, ICC 2012
Number of pages5
ISBN (Print)9781457720529
Publication statusPublished - 2012
MoE publication typeA4 Article in a conference publication
EventIEEE International Conference on Communications - Ottawa, Canada
Duration: 10 Jun 201215 Jun 2012


ConferenceIEEE International Conference on Communications
Abbreviated titleICC

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