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The standard interference functions introduced by Yates have been veryinfluential on the analysis and design of distributed power control laws. Whilepowerful and versatile, the framework has some drawbacks: the existence offixed-points has to be established separately, and no guarantees are given onthe rate of convergence of the iterates. This paper introduces contractiveinterference functions, a slight reformulation of the standard interferencefunctions that guarantees the existence and uniqueness of fixed-points alongwith linear convergence of iterates. We show that many power control laws fromthe literature are contractive and derive, sometimes for the first time,analytical convergence rate estimates for these algorithms. We also prove thatcontractive interference functions converge when executed totallyasynchronously and, under the assumption that the communication delay isbounded, derive an explicit bound on the convergence time penalty due toincreased delay. Finally, we demonstrate that although standard interferencefunctions are, in general, not contractive, they are all para-contractions withrespect to a certain metric. Similar results for two-sided scalableinterference functions are also derived.

Contractive Interference Functions and Rates of Convergence of Distributed Power Control Laws