Distributed Utility-Based Power Control: Objectives and Algorithms

This paper deals with the problem of medium access control (MAC)-layer fair power control in a wireless mesh network with an established network topology. The notion of MAC-layer fairness is defined along similar lines as end-to-end fairness for elastic traffic, except that instead of end-to-end flows, MAC-layer flows are considered, being that one hop flows between neighboring nodes. In this paper, we identify a class of utility functions of link rates that allows for a convex problem formulation. The convexity property is a key prerequisite for implementing power control algorithms in practice. We present a novel distributed algorithmic solution to the power control problem based on gradient-projection methods, prove its global convergence, and provide sufficient conditions for a geometric convergence rate. The main novelty of our scheme lies in the use of the so-called adjoint network in such a way that each transmitter can estimate its current update direction from the received signal power. This mitigates the problem of global coordination of the transmitters when carrying out gradient-projection algorithms in distributed wireless networks. The price for this are possible estimation errors so that the proposed scheme is analyzed within the framework of stochastic approximation.