Distributed Power Control for One-to-Many Transmissions in Gaussian Interference Channels

In this paper, we extend the distributed power control problem for one-to-one transmissions in Gaussian interference channels to one-to-many transmission scenarios. We assume a user-centric wireless network where the end users play the roles of decision makers. We formulate the power control problem as a noncooperative game. New challenges arise due to the coupling issues among power strategy spaces of distributed end users, which make standard Nash equilibrium based noncooperative game approach inapplicable. Indeed, our problem turns out to be a generalized Nash equilibrium problem (GNEP). Resorting to variational inequality theory, we show several fundamental properties of the GNEP. Then we propose a penalty-based distributed algorithm IP(2)JA, which possesses favorable properties for practical implementation. Numerical results are provided to verify our arguments and proposed algorithm.