An Application of Joint Spectral Radius in Power Control Problem for Wireless Communications

TL;DR

This paper applies the joint spectral radius concept to analyze the convergence conditions of power control algorithms in wireless communications, accounting for dynamic link gains.

Contribution

It introduces a novel application of joint spectral radius to establish convergence criteria for distributed power control and balancing algorithms under variable link gains.

Findings

Derived convergence conditions using joint spectral radius

Applicable to dynamic wireless link scenarios

Provides theoretical guarantees for power stability

Abstract

Resource management, including power control, is one of the most essential functionalities of any wireless telecommunication system. Various transmitter power-control methods have been developed to deliver a desired quality of service in wireless networks. We consider two of these methods: Distributed Power Control and Distributed Balancing Algorithm schemes. We use the concept of joint spectral radius to come up with conditions for convergence of the transmitted power in these two schemes when the gains on all the communications links are assumed to vary at each time-step.