I. Introduction
While traditionally the goal of resource allocation algorithms has been to optimize some system performance measures such as achievable rate and bit error rate, recently, the growing concerns on sustainable growth, and the need to maximize battery life in mobile headsets garnered a great deal of interest for energy-efficient resource allocation algorithms that aim at optimizing the efficiency with which each Joule of energy drained from the battery is employed [1], [2]. The first and most widely used metric to mathematically express the energy efficiency (EE) of a given terminal has been the ratio between the throughput and the consumed power [3]–[7], and references therein. Another proposed metric uses the goodput in place of the throughput [8]. In all of the above works, as far as the computation of the consumed power is concerned, only the transmit power is considered, whereas the power that is dissipated in the electronic circuitry of each terminal to operate the device is neglected. More recently, this assumption has been relaxed, and several papers have begun to address this issue [9]–[13]. In [11], [13], a thorough analysis of the circuit power dissipated in wireless networks is provided. The results indicate that the consumed power in a mobile terminal is given by the sum of the transmit power plus a constant term independent of the transmit power, which models the circuit power needed to operate the terminal. In [12] a single user channel is considered. The optimization is carried out through transmit power control and the achievable rate is used at the numerator of the EE in place of the throughput. In [9], [10], interference channels (IC) are considered and a competitive scenario in which the users selfishly aim at individual EE maximization is considered. This conflict situation is modeled and analyzed using non-cooperative game theory [14], [15]. Indeed, game theory provides a natural mathematical framework to analyze the interactions between autonomous decision-makers with possibly conflicting interests.