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

TL;DR

This paper fully characterizes the stable information and energy transmission rates in a decentralized K-user Gaussian multiple access channel with an energy harvester, considering autonomous transmitter behavior and energy rate constraints.

Contribution

It provides the first complete characterization of the $\\eta$-Nash equilibrium region for decentralized simultaneous information and energy transmission in the G-MAC.

Findings

The $\\eta$-NE region precisely describes achievable stable rate tuples.

Transmitters can independently optimize their configurations for maximum individual rates.

Energy rate constraints are incorporated into the stability analysis.

Abstract

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