  This paper addresses the stability and queueing delay of Space Division
Multiple Access (SDMA) systems with bursty traffic, where zero-forcing
beamforming enables simultaneous transmission to multiple mobiles. Computing
beamforming vectors relies on quantized channel state information (CSI)
feedback (limited feedback) from mobiles. Define the stability region for SDMA
as the set of multiuser packet-arrival rates for which the steady-state queue
lengths are finite. Given perfect CSI feedback and equal power allocation over
scheduled queues, the stability region is proved to be a convex polytope having
the derived vertices. For any set of arrival rates in the stability region,
multiuser queues are shown to be stabilized by a joint queue-and-beamforming
control policy that maximizes the departure-rate-weighted sum of queue lengths.
The stability region for limited feedback is found to be the perfect-CSI region
multiplied by one minus a small factor. The required number of feedback bits
per mobile is proved to scale logarithmically with the inverse of the above
factor as well as linearly with the number of transmit antennas minus one. The
effects of limited feedback on queueing delay are also quantified. For Poisson
arrival processes, CSI quantization errors are shown to multiply average
queueing delay by a factor larger than one. This factor can be controlled by
adjusting the number of feedback bits per mobile following the derived
relationship. For general arrival processes, CSI errors are found to increase
Kingman's bound on the tail probability of the instantaneous delay by one plus
a small factor. The required number of feedback bits per mobile is shown to
scale logarithmically with this factor.
