Decentralized Simultaneous Information and Energy Transmission in K-User\n Multiple Access Channels

In this paper, the fundamental limits of decentralized simultaneous\ninformation and energy transmission in the $K$-user Gaussian multiple access\nchannel (G-MAC), with an arbitrary $K \\geqslant 2$ and one non-colocated energy\nharvester (EH), are fully characterized.\n The objective of the transmitters is twofold. First, they aim to reliably\ncommunicate their message indices to the receiver; and second, to harvest\nenergy at the EH at a rate not less than a minimum rate requirement $b$. The\ninformation rates $R_1,\\dots,R_K$, in bits per channel use, are measured at the\nreceiver and the energy rate $B$ is measured at an EH.\n Stability is considered in the sense of an $\\eta$-Nash equilibrium\n($\\eta$-NE), with $\\eta > 0$.\n The main result is a full characterization of the $\\eta$-NE\ninformation-energy region, i.e., the set of information-energy rate tuples\n$(R_1,\\dots,R_K,B)$ that are achievable and stable in the G-MAC when:\n $(a)$ all the transmitters autonomously and independently tune their own\ntransmit configurations seeking to maximize their own information transmission\nrates $R_1,\\dots, R_K$; and\n $(b)$ all the transmitters jointly guarantee an energy transmission rate $B$\nat the EH, such that $B \\geqslant b$.\n Therefore, any rate tuple outside the $\\eta$-NE region is not stable as there\nalways exists at least one transmitter able to increase by at least $\\eta$ bits\nper channel use its own information transmission rate by updating its own\ntransmit configuration.\n