Resource Allocation in a MAC with and without security via Game Theoretic Learning

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 -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.