Wireless communications games in fixed and random environments

Zhengyuan Zhou, Nicholas Bambos

Abstract: Most of the work on power control in wireless communications has focused on the fixed deterministic (thermal) noise paradigm, which results in elegant distributed power control schemes with desired convergence properties. In this paper, we lift the deterministic noise assumption. Instead, we consider a generalized stochastic noise framework, akin to a random environment, which not only incorporates the intrinsic thermal noise at the receivers but also the effect of potential interferers that are extraneous to the communication links under consideration. Given this random environment framework, we develop a game-theoretic formulation where N links play a non-cooperative game, inducing a distributed power control scheme. We first examine the deterministic game and show the existence and uniqueness of the Nash equilibrium. We then study the stochastic behavior of the equilibrium under the random environment. The results indicate that the long-run behavior of the corresponding power control is “stable” (explained technically below), demonstrating its robustness and, hence, applicability.