Providing Quadratic Convergence of Decentralized Power Control in Wireless Networks—The Method of Min-Max Functions

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper addresses the problem of power control in wireless networks with elastic traffic and no central network controller, such as ad hoc networks or hybrid mesh networks. We propose a novel power allocation iteration, prove its local quadratic convergence, and design a feedback/handshake scheme for a distributed implementation of the iteration. The combined feature of quadratic convergence and amenability to decentralized realization makes the algorithm suitable for efficient online application and incorporation in multihop policies. To the best of our knowledge, a similarly fast convergence and decentralization are not offered by any known power control algorithm. The proposed power control concept is designed and analyzed using the powerful framework of convex-concave functions and min-max functions. </para>