Unifying view on min-max fairness and utility optimization in cellular networks

In this work, we are concerned with quality of service (QoS) control in wireless cellular networks utilizing linear receiver structures. We investigate the issues of fairness and operator utility efficiency. We disprove the common conjecture on contradiction between min-max fairness and utility optimality by characterizing the case in which both goals can be accomplished. Our analysis shows that such fair and utility efficient allocation of powers and prices is a saddle point of the utility optimization objective. This means that the min-max fair utility optimum, when existent, is the worst case one and indicates a trade-off between social goals and operator goals.