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A satellite transponder’s communication channel is studied in this paper. The multiple terminal users in this channel compete for limited radio resources to satisfy their own data rate needs. Because inter-user interference limits the transponder’s performance, it is beneficial for the transponder’s power-control system to coordinate all users in its channel to reduce interference and to improve performance. By the special properties of channel gain in this type of channel, a non-cooperative Differential Game (DG) is set up to study the competition in a transponder’s channel. Each user’s utility is a trade-off between transmission data rate and power consumption. Nash Equilibrium (NE) is defined to be the solution of the DG model. The optimality condition of NE is derived to be a system of Differential Algebraic Equations (DAE). An algorithm based on minimizing all users’ Hamiltonian is developed to solve the DAE system. The numerical solution of the NE provides the transponder’s power control system with each user’s power-control strategy at the equilibrium. 

This paper studies a satellite transponder’s communication channel, in which there exist multiple-user terminals, who 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. A non-cooperative Differential Game (DG) is set up to model the users’ competition in a transponder’s communication channel. Each user’s utility function is a trade-off between transmission data rate and power consumption. Nash Equilibrium (NE) is defined to be the solution of the DG model. The optimality condition of NE is derived to be a set of Differential Algebraic Equations (DAE). An algorithm based on minimizing Hamiltonians is developed to solve the DAE system. The numerical solution of the DG model provides the transponder’s power control system with each user’s power-control strategy at the equilibrium.