Stability and delay of zero-forcing SDMA with limited feedback

This paper addresses the stability and queueing delay of space-division multiple access (SDMA) systems with bursty traffic, where zero-forcing beamforming enables simultaneous transmissions 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 feedback of channel-direction information (CDI) and equal power allocation over scheduled queues, the stability region is proved to be a convex polytope having the derived vertices. A similar result is obtained for the case with perfect feedback of CDI and channel-quality information (CQI), where CQI allows scheduling and power control for enlarging the stability region. For any set of arrival rates in the stability 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. 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 effect of limited feedback on queueing delay is also quantified. CDI quantization errors are shown to multiply average queueing delay by a factor $M > 1$. For given $M\rightarrow 1$, the number of feedback bits per mobile is proved to be $O(-\log-{2}(1-1/M))$.Department of Applied Mathematic