Convergence time of power-control dynamics

Abstract

We study two (classes of) distributed algorithms for power control in a general model of wireless networks. There are n wireless communication requests or links that experience interference and noise. To be successful a link must satisfy an SINR constraint. The goal is to find a set of powers such that all links are successful simultaneously. A classic algorithm for this problem is the fixed-point iteration due to Foschini and Miljanic [8], for which we prove the first bounds on worst-case running times - after roughly O(n logn) rounds all SINR constraints are nearly satisfied. When we try to satisfy each constraint exactly, however, convergence time is infinite. For this case, we design a novel framework for power control using regret learning algorithms and iterative discretization. While the exact convergence times must rely on a variety of parameters, we show that roughly a polynomial number of rounds suffices to make every link successful during at least a constant fraction of all previous rounds. © 2011 Springer-Verlag.