Geometric analysis of distributed power control and Möbius MAC design

This paper presents a geometric analysis of the convergence condition for the FoschiniMiljanic power control algorithm. The Möbius transform is exploited for the first time to analyze the convergence conditions of the power control algorithm. A novel MAC scheme based on the Möbius transform is proposed for the link scheduling problem and proven to improve spatial reuse by scheduling links in pairs if possible. The peak power constraint of wireless networks is analyzed theoretically, and applications to random networks are explored in detail. Observations from the analysis of peak power constraints are also applied to the design of the MAC scheme to improve the convergence speed and system performance. Applications to cognitive networks and heterogeneous networks are discussed. Copyright c © 2010 John Wiley & Sons, Ltd.