S-modular games and power control in wireless networks

This note shows how centralized or distributed power control algorithms in wireless communications can be viewed as S-modular games coupled policy sets (coupling is due to the fact that the set of powers of a mobile that satisfy the signal-to-interference ratio constraints depends on powers used by other mobiles). This sheds a new light on convergence properties of existing synchronous and asynchronous algorithms, and allows us to establish new convergence results of power control algorithms. Furthermore, known properties of power control algorithms allow us to extend the theory of S-modular games and obtain conditions for the uniqueness of the equilibrium and convergence of best response algorithms independently of the initial state.