Stochastic characterization of the spectrum sharing game in ad-hoc networks

This work focuses on infrastructure-less ad hoc wireless networks where multiple transmitter/receiver pairs share the same radio resources (spectrum); transmitters have to choose how to split a total power budget across orthogonal spectrum bands with the goal to maximize their sum rate under cumulative interference from concurrent transmissions. We start off by introducing and characterizing the non-cooperative game among transmitter/receiver pairs when the network topology is deterministically given. The corresponding Nash equilibria are derived, highlighting their dependency on the topological parameters (distances between wireless nodes, propagation model, and background noise power). The analysis is then extended to the case of random network topologies drawn from a given spatial stochastic process. Tools of stochastic geometry are leveraged to derive a statistical characterization of the equilibria of the spectrum sharing game. Finally, a distributed algorithm is proposed to let the players of the spectrum sharing game converge to equilibria conditions. Numerical simulations show that the proposed algorithm drives the users to stable points that are close to the equilibria of the game requiring limited information exchange among nodes.