Convergence Time of Power-Control Dynamics

We study convergence of distributed protocols for power control in a non-cooperative wireless transmission scenario. There are n wireless communication requests or links that experience interference and noise. To be successful a link must satisfy an SINR constraint. Each link is a rational selfish agent that strives to be successful with the least power that is required. A classic approach to this problem is the fixed-point iteration due to Foschini and Miljanic , for which we prove the first bounds on worst-case convergence times - after roughly O(n log n) rounds all SINR constraints are nearly satisfied. When agents try to satisfy each constraint exactly, however, links might not be successful at all. 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.