A Stochastic Game Formulation of Energy-Efficient Power Control: Equilibrium Utilities and Practical Strategies

TL;DR

This paper models energy-efficient power control in multi-access channels as a stochastic game, characterizing equilibrium utilities and showing practical strategies with limited channel information.

Contribution

It introduces a stochastic game framework for power control, deriving equilibrium utilities with partial CSI and revealing the role of time-sharing solutions.

Findings

Equilibrium utility region characterized for energy-efficient power control.

Time-sharing solutions are part of the equilibrium strategies.

Practical strategies can be implemented with individual CSI.

Abstract

Frequency non-selective time-selective multiple access channels in which transmitters can freely choose their power control policy are considered. The individual objective of the transmitters is to maximize their averaged energy-efficiency. For this purpose, a transmitter has to choose a power control policy that is, a sequence of power levels adapted to the channel variations. This problem can be formulated as a stochastic game with discounting for which there exists a theorem characterizing all the equilibrium utilities (equilibrium utility region). As in its general formulation, this theorem relies on global channel state information (CSI), it is shown that some points of the utility region can be reached with individual CSI. Interestingly, time-sharing based solutions, which are usually considered for centralized policies, appear to be part of the equilibrium solutions. This analysis is illustrated by numerical results providing further insights to the problem under investigation.