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Limited feedback is a paradigm for the feedback of channel state informationin wireless systems. In multiple antenna wireless systems, limited feedbackusually entails quantizing a source that lives on the Grassmann manifold. Mostwork on limited feedback beamforming considered single-shot quantization. Inwireless systems, however, the channel is temporally correlated, which can beused to reduce feedback requirements. Unfortunately, conventional predictivequantization does not incorporate the non-Euclidean structure of the Grassmannmanifold. In this paper, we propose a Grassmannian predictive coding algorithmwhere the differential geometric structure of the Grassmann manifold is used toformulate a predictive vector quantization encoder and decoder. We analyze thequantization error and derive bounds on the distortion attained by the proposedalgorithm. We apply the algorithm to a multiuser multiple-input multiple-outputwireless system and show that it improves the achievable sum rate as thetemporal correlation of the channel increases.

Grassmannian Predictive Coding for Limited Feedback in Multiple Antenna Wireless Systems