  This paper considers multiaccess multiple-input multiple-output (MIMO)
systems with finite rate feedback. The goal is to understand how to efficiently
employ the given finite feedback resource to maximize the sum rate by
characterizing the performance analytically. Towards this, we propose a joint
quantization and feedback strategy: the base station selects the strongest
users, jointly quantizes their strongest eigen-channel vectors and broadcasts a
common feedback to all the users. This joint strategy is different from an
individual strategy, in which quantization and feedback are performed across
users independently, and it improves upon the individual strategy in the same
way that vector quantization improves upon scalar quantization. In our proposed
strategy, the effect of user selection is analyzed by extreme order statistics,
while the effect of joint quantization is quantified by what we term ``the
composite Grassmann manifold''. The achievable sum rate is then estimated by
random matrix theory. Due to its simple implementation and solid performance
analysis, the proposed scheme provides a benchmark for multiaccess MIMO systems
with finite rate feedback.
