Decentralized simultaneous energy and information transmission in multiple access channels

In this paper, the fundamental limits of decentralized simultaneous information and energy transmission in the two-user Gaussian multiple access channel (G-MAC) are fully characterized for the case in which a minimum energy transmission rate b is required for successful decoding. All the achievable and stable information-energy transmission rate tuples (R1, R2, B) are identified. R1 and R2 are in bits per channel use measured at the receiver and B is in energy units per channel use measured at an energy-harvester (EH). Stability is considered in the sense of an η-Nash equilibrium (NE), with η ≥ 0 arbitrarily small. The main result consists of the full characterization of the η-NE information-energy region, i.e., the set of information-energy rate triplets (R1, R2, B) that are achievable and stable in the G-MAC when: (a) both transmitters autonomously and independently tune their own transmit configurations seeking to maximize their own information transmission rates, R1 and R2 respectively; (b) both transmitters jointly guarantee an energy transmission rate B at the EH, such that B ≥ b. Therefore, any rate triplet outside the η-NE region is not stable as there always exists one transmitter able to increase by at least η bits per channel use its own information transmission rate by updating its own transmit configuration.