Energy-Aware Competitive Power Control in Relay-Assisted Interference Wireless Networks

Competitive power control for energy efficiency maximization in wireless interference networks is addressed, for the scenarios in which the users´ SINR can be expressed as either (a) γ = (αp)/(φp + ω), or (b) γ = (αp + βp²)/(φp + ω), with p the user´s transmit power. The considered SINR expressions naturally arise in relay-assisted systems. The energy efficiency is measured in bit/Joule and is defined as the ratio of a proper function of the SINR, divided by the consumed power. Unlike most previous related works, in the definition of the consumed power, not only the transmit power, but also the circuit power needed to operate the devices is accounted for. A non-cooperative game theoretic approach is employed and distributed power control algorithms are proposed. For both SINR expressions (a) and (b), it is shown that the competitive power allocation problem always admits a Nash equilibrium. Moreover, for the SINR (a), the equilibrium is also shown to be unique and the best-response dynamic is guaranteed to converge to such unique equilibrium. For the two-user case, the efficient computation of the Pareto frontier of the considered game is addressed, and, for benchmarking purposes, a social optimum solution with fairness constraint is derived.