Propagation of Chaos in Power Control Games for Energy-Efficient Wireless Networks

The question of energy management is a major engineering challenge in any wireless communication system that is constrained by finite battery resources. In this article we address the problem of transmit power control in a multi-user wireless network with a single base station and random time-varying channels transmitting in parallel and interfering between each other. We suggest a stochastic particle system for studying the game of control; specifically, the channels are modelled as purely discontinuous Markov processes with known characteristics. The signal to interference plus noise ratio (SINR) determines the interactions among particles. Dimensionality reduction of the multi-objective optimization problem relies on chaos propagation, i.e., on the fact that the independence of particles persists in time as and when their number becomes large. And then we solve the optimal control problem for one representative of the particle system. Here we develop a martingale approach for an alternative open-loop optimal control instead of the feedback one since the latter is not computationally feasible.