A unified fairness framework in multi-antenna multi-user channels

In a multi-antenna broadcast channel, the access point (AP) has several alternatives for distributing the scarce resources among the users. When realistic conditions are taken into account, it is not clear which is the best suited option for the AP, since there exist a trade-off between the global performance and the individual needs. In this paper, we derive an analytical framework to study fairness in a multi-antenna multi-user channel, which is useful in practical situations. Since fairness indexes in the literature usually reflect relative performance among users, we borrow ideas from portfolio selection and propose a mean versus standard deviation analysis that allows us to select a certain technique under practical conditions. We particularize this framework for a multi-antenna AP communicating simultaneously with several single-antenna terminals, and give closed-form expressions for the mean versus standard deviation trade-off for zero forcing beamforming, dirty paper encoding, and the cooperative bound, under the assumption of a uniform power allocation among the active users. This framework can be extended to analyze other types of multi-user communications.