Stability of zero-forcing SDMA with limited feedback

This paper addresses the stability of a multi-antenna space division multiple access (SDMA) system that uses zero-forcing beamforming to support packet data services for a small number of mobiles. Define the stability region as the set of packet arrival rates for which finite queue lengths are feasible in the steady state. Consider perfect feedback of channel state information (CSI) and equal power allocation over the scheduled queues. The stability region is proved to be a convex polytope with the derived vertices. For any set of arrival rates in this region, multiuser queues are shown to be stabilized by the joint queue-and-beamforming control policy that maximizes the departure-rate-weighted sum of queue lengths. For quantized CSI feedback (limited feedback), the reduced stability region is proved to be inner bounded by the perfect-CSI counterpart multiplied by a factor close to one. This bound is achieved by scaling the number of feedback bits per mobile logarithmically with the inverse of the above factor.