  Limited feedback is a paradigm for the feedback of channel state information
in wireless systems. In multiple antenna wireless systems, limited feedback
usually entails quantizing a source that lives on the Grassmann manifold. Most
work on limited feedback beamforming considered single-shot quantization. In
wireless systems, however, the channel is temporally correlated, which can be
used to reduce feedback requirements. Unfortunately, conventional predictive
quantization does not incorporate the non-Euclidean structure of the Grassmann
manifold. In this paper, we propose a Grassmannian predictive coding algorithm
where the differential geometric structure of the Grassmann manifold is used to
formulate a predictive vector quantization encoder and decoder. We analyze the
quantization error and derive bounds on the distortion attained by the proposed
algorithm. We apply the algorithm to a multiuser multiple-input multiple-output
wireless system and show that it improves the achievable sum rate as the
temporal correlation of the channel increases.
