John Wiley & Sons
In this paper, the authors present a geometric analysis of the convergence condition for the Foschini-Miljanic power control algorithm. The Mobius transform is exploited for the first time to analyze the convergence conditions of the power control algorithm. A novel MAC scheme based on the Mobius 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.