Abstract
In this paper, we study a K-user fading multiple access channel (F-MAC), with and without an eavesdropper (Eve). In the system without Eve, we assume that each user knows only its own channel gain and is completely ignorant about the other users’ channel state. The legitimate receiver sends a short acknowledgement message Acknowledge (ACK) if the message is correctly decoded and a No Acknowledge (NACK) if the message is not correctly decoded. Under these assumptions, we use game theoretic learning setup to make transmitters learn about the power allocation under each state. We use multiplicative weight no-regret algorithm to achieve an ε-coarse correlated equilibrium. We also consider the case where a user can receive other users’ ACK/NACK messages. Now, we can maximize a weighted sum utility and achieve Pareto optimal points. We also obtain Nash bargaining solutions, which are Pareto points that are fairer to the transmitting users. Fairness among users is quantified using Jain’s index.With Eve, we first assume each user knows only its own channel gain to the receiver as well as to Eve. The receiver decides whether to send an ACK or a NACK to the transmitting user based on the secrecy-rate condition. We use the above developed algorithms to get the equilibrium points. Next, we study the case where each user knows only the distribution of the channel state of Eve. Finally, we also consider the system where the users do not know even the distribution of the Eve’s channel.
Highlights
A multiple access channel (MAC) is a basic building block in wireless networks [1]
All users can learn about the utility of each other at time t. We show that this information can be used to get a socially optimal Pareto point which generally provides a better performance than a coarse correlated equilibrium (CCE)
We find the Bayesian equilibrium (BE) for the case when each user knows the distribution of all the channel gains to Eve, as done in [8] for fading multiple access channel (F-MAC) without security constraints
Summary
A multiple access channel (MAC) is a basic building block in wireless networks [1]. it models the uplink in a wireless cellular system. In an orthogonal multiple access channel, the authors in [9] have used evolutionary game theory to obtain a power allocation scheme, while assuming that each user knows the channel gain of all users via feedback. In [11], the authors consider a more general setup wherein they consider a discrete memoryless multiple access channel where the transmitting users receive a noisy version of each others’ conversation, and they do not trust each other In this scenario, the authors have obtained an achievable secrecy-rate region and some outer bounds. In [17], the authors have studied a fading MAC-WT with full Channel State Information (CSI) of Eve and when each user knows the channel state of all the users to the receiver but is ignorant of the instantaneous value of channel state to the eavesdropper (only its distribution is known). In the rest of the paper, we develop algorithms to compute equilibrium points for this game
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