A game-theoretic framework for interference avoidance

Various iterative algorithms for interference avoidance (IA) in networks with co-located receivers, suitable for distributed implementation, have been proposed in the literature. In this paper, the IA problem is cast in a game-theoretic framework and is formulated as a potential game. This formulation accommodates previously proposed algorithms and, in addition, gives us a framework that enables the design of new distributed and convergent algorithms for IA including algorithms with nonidentical utility functions for the users. Two new convergence results for potential games are then derived. The first result establishes the convergence of a class of potential games to the global solution while following best response iterations and when noise is added. The second result establishes the convergence of potential games to the Nash equilibria of the game while following random better response iterations. The first result combined with the potential game formulation allows us to show that for a large class of network scenarios, arbitrarily small noise assures the convergence of best response IA algorithms, including the eigeniterations, to an arbitrarily small neighborhood of the globally optimal signature sequence set. The second result enables the design of reduced feedback mechanisms for IA that converge to desirable solutions.