Optimal rate control policies for proportional fairness in wireless networks

In this paper we consider a K transmitter and K receiver single-hop wireless network. We obtain a rate control policy that provides proportional fair rate allocation to the transmitters when the outcome of a transmission depends on the signal to interference plus noise ratio (SINR) at the corresponding receiver. The policy selects at any time slot one action from a set of actions that are described through two different schemes; the probability of selecting each action is optimized to achieve proportional fairness. The two schemes we consider are to either activate only a single transmitter at any given time slot or to allow all transmitters to transmit simultaneously. Although we demonstrate our approach by considering rates given by the Shannon formula, as well as rates obtained through a combination of phase shift keying (PSK) modulation with symbol rate control, our results are more general and are valid under any rate function that relates the maximum achievable rate to its required SINR.