Spatial spectrum access game

Abstract

A key feature of wireless communications is the spatial reuse of wireless resources. However, such a spatial aspect is relatively less understood for the purpose of designing efficient spectrum sharing mechanisms. In this chapter, we propose a framework of spatial spectrum access games, where we model fairly general spatial interference relationships among users as directed interference graphs. We show that a pure Nash equilibrium exists for the two classes of games: (1) any spatial spectrum access games on directed acyclic graphs and (2) any games satisfying the congestion property on directed trees and directed forests. We identify the graphical structures under which the spatial spectrum access games have pure Nash equilibria and further show that under mild conditions, the spatial spectrum access games with random backoff and Aloha channel contention mechanisms on undirected graphs are potential games and have pure Nash equilibria as well. We also quantify the price of anarchy of the general spatial spectrum access game. We then propose a distributed learning algorithm, which only utilizes users' local observations to adaptively adjust the spectrum access strategies. We show that the distributed learning algorithm can converge to an approximate mixed strategy Nash equilibrium for any spatial spectrum access games. We further generalize the spatial spectrum access game framework to accommodate the physical interference model. Numerical results demonstrate that the distributed learning algorithm achieves significant performance improvement over the benchmark algorithms.