A Stochastic Stability Characterization of the Foschini-Miljanic Algorithm in Random Wireless Networks

Power control has been an important field in wireless communications with many applications. The well-known Foschini-Miljanic (FM) algorithm, which has greatly influenced the subsequent literature, is a simple and elegant distributed power control scheme that enjoys several desirable properties. However, the channel environment in the FM algorithm is assumed to be fixed and constant over time, an unrealistic assumption in most practical situations. In this paper, we lift this assumption and study the robustness of the FM algorithm by characterizing its stochastic stability in the presence of stochastic time- varying channel environments. We identify sufficient conditions that are both easily interpretable and efficiently verifiable, for ensuring such stochastic stability. We also present simulation examples to demonstrate the correctness and utility of our conditions.