Feedback Enhances Simultaneous Wireless Information and Energy Transmission in Multiple Access Channels

In this paper, the fundamental limits of simultaneous information and energy transmission in the two-user Gaussian multiple access channel with feedback (G-MAC-F) and without feedback (G-MAC) are fully characterized. More specifically, all the achievable information and energy transmission rates (in bits per channel use and energy-units per channel use, respectively) are identified. Furthermore, the fundamental limits on the individual and sum-rates given a minimum-energy rate ensured at an energy harvester are also characterized. In the case without feedback, an achievability scheme based on power-splitting and successive interference cancellation is shown to be optimal. Alternatively, in the G-MAC-F case, a simple yet optimal achievability scheme based on power-splitting and Ozarow's capacity achieving scheme is presented. Finally, the energy transmission enhancement induced by the use of feedback is quantified. Feedback can at most double the energy transmission rate at high SNRs when the information transmission sum-rate is kept fixed at the sum-capacity of the G-MAC, but it has no effect at very low SNRs.