Resource allocation in fading multiple access wiretap channel via game theoretic learning

In this paper we consider a K-user fading multiple access wiretap channel, where each user wants to transmit a message confidentially. There is a passive eavesdropper (Eve) at the receiving end. We are interested in allocating rates and powers to the users fairly and reliably without the eavesdropper being able to decode the message. Initially we assume that each user knows only its own channel gain to the receiver and to the eavesdropper. When any user transmits a message, the receiver send an ACK if the message is decoded correctly and confidentially, else it sends a NACK. We use Multiplicative Weight no-regret algorithm to obtain a coarse correlated equilibrium. Next we maximize the weighted sum of utility of all the users and obtain Pareto optimal points. Since not all Pareto points are fair, we also obtain Nash Bargaining (NB) solutions which ensure certain fairness to all the users. In the next part of the paper we make more realistic assumption that each user knows only its own channel gain, and is ignorant of the channel gain to Eve (only its distribution is known). We use secrecy outage as the metric at the receiver to decide weather the message is correctly decoded or not. We obtain a coarse correlated equilibrium, a Pareto point and a Nash bargaining solution.