Wei Wan, Yuanyuan Peng, John M Cioffi, Kalia T. Glover

Abstract: The multiple-user terminals in a satellite transponder’s communication channel compete for limited radio resources to meet their own data rate needs. Because inter-user interference limits on the satellite transponder’s performance, the transponder’s power-control system needs to coordinate all its users to reduce interference and maximizes overall performance of this channel. This paper studies Stackelberg competition among the asymmetrical users in a transponder’s channel, where some users called leader have priority to choose their power control strategy, but other users called followers have to optimize their power control strategy with given leader’s controls. A Stackelberg Differential Game (SDG) is set up to model the Stackelberg competition in a transponder’s communication channel. Each user’s utility function is a trade-off between transmission data rate and power consumption. The dynamics of the system is the changing of channel gain. The optimality condition of Stackelberg equilibrium of leaders and followers is a set of Differential Algebraic Equations (DAE) with an imbedded control strategies from its counterpart. In order to solve for Stackelberg equilibrium, an algorithm based on optimizing leaders’ and followers’ Hamiltonians iteratively is developed. The numerical solution of the SDG model provides the transponder’s power control system with each user’s power-control strategy at the Stackelberg equilibrium.

Keywords: Stackelberg Differential Game, Spectrum and Power Allocation, Energy-Efficiency, Satellite Communication

Date Published: September 30, 2024
DOI: 10.11159/jmids.2024.008

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