Towards better understanding of medium access control for multiuser beamforming systems

The paper investigates a single-cell multiuser system with a linear antenna array at the base station. We consider both the downlink and the uplink. The quality of service (QoS) parameter of interest depends monotonically on the signal-to-interference+noise ratio (SINR) through a given QoS-SINR mapping. In the case of no power constraints, the set of all QoS parameter values that can be supported by the system is determined by the spectral radius of a certain nonnegative irreducible matrix. The paper´s main result shows that if the spectral radius is required to be a convex function of the QoS parameter values for an arbitrary link gain matrix, then the inverse of the QoS-SINR mapping must be log-convex, which is, in general, stronger than the convexity property. We show that the log-convexity requirement can be dropped in two special cases of link gain matrices. These results provide a theoretical framework for the design of medium access control strategies.