Contractive Interference Functions and Rates of Convergence of Distributed Power Control Laws
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. The authors show that many power control laws from the literature are contractive and derive, sometimes for the first time, convergence rate estimates for these algorithms.