The standard interference functions introduced by Yates have been very influential on the analysis and design of distributed power control laws. While powerful and versatile, the framework has some drawbacks: the existence of fixed-points has to be established separately, and no guarantees are given on the rate of convergence of the iterates. This work introduces contractive interference functions, a reformulation of the standard interference functions that guarantees the existence and uniqueness of fixed-points along with linear convergence of iterates. We show that many power control laws from the literature are contractive and derive, sometimes for the first time, analytical convergence rate estimates for these algorithms. We also prove that contractive interference functions converge when executed totally asynchronously and, under the assumption that the communication delay is bounded, derive an explicit bound on the convergence time penalty due to increased delay. In addition, we demonstrate that although standard interference functions are, in general, not contractive, they are all para-contractions with respect to a certain metric. Similar results for two-sided scalable interference functions are also derived. Finally, preliminary results for joint power and rate control are discussed.

About Themistoklis Charalambous

Themistoklis Charalambous received his B.A. and M.Eng. in Electrical and Information Sciences from Trinity College, Cambridge University. He completed his Ph.D. studies in the Control Laboratory of the Engineering Department, Cambridge University. Following his Ph.D., he joined the Human Robotics Group as a Research Associate at Imperial College London and worked as a Visiting Lecturer at the Department of Electrical and Computer Engineering, University of Cyprus. From January 2012 to March 2015 he worked in the Department of Automatic Control of the School of Electrical Engineering at the Royal Institute of Technology (KTH) as a Post-doctoral Researcher. Since April 2015 he has been working as a Post-doctoral Researcher at the Communication Group of the Department of Signals and Systems at Chalmers University of Technology. His research is interdisciplinary combining theory and applications from control theory, communications, network and distributed optimization and involves cooperative control, distributed decision making, and control to various resource allocation problems in complex and networked systems

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