I. Introduction
Energy efficiency (EE) is one of the eight key figures of merit identified by the international telecommunication union (ITU) for shaping the next generation of communication systems [1]; as such, EE has recently received a surge of interests from the research community [2]–[4], as well as network vendors and operators who perceive EE as an enabler for sustainable communication (both from an economical and environmental perspectives). Equally, relay-based cooperative communication, which is also well-documented [5] –[7], has proved to be very effective for improving the spectral efficiency (SE) or/and the coverage of cellular networks [7], as well as reducing the cost of network deployment [8]. More recently, relays have also been used for improving the EE [9]– [12]. As a result, relay-based cooperative communication is an integral part of the existing wireless communication standards [13]; it is also foreseen to play a major role for enabling device-to-device communication in the near future [1] .