Impact of Selfish Power Control on the Stability in Wireless Networks

Power control can help to reduce energy consumption in wireless networks, while the selfish power control of a link may affect the performance of the neighbors. This paper studies the impact of selfish power control on the stability in wireless networks where each link is under a throughput requirement. Employing the modulation scheme non-coherent frequency shift keying (NFSK), we prove that there is an optimal reception rate and a corresponding optimal transmission strategy to minimize the energy consumption for a link with fixed channel condition, and further present a transmission strategy selection algorithm for links with varying channel condition. A round-based repeated non-cooperative game is proposed, assuming that there is only one link which can adjust its transmission strategy in each unit time and the link always adopts the self-optimal strategy myopically. It is observed that this game cannot converge in some cases, since links are motivated to move transmission power from high interference durations to low interference ones. To bring the game into a steady state, a penalty function is introduced and the performance of various penalty functions is investigated. Simulation results show that heavier penalty leads to faster convergence, but has no effect on the energy consumption of the steady state.