Quantization on the Grassmann manifold: applications to precoded MIMO wireless systems

This paper studies the problem of quantization of a source that lives on the complex Grassmann manifold. The special structure of the Grassmann manifold and the distortion measures that are defined on it differentiates this problem from the traditional problem of vector quantization in Euclidean spaces. Assuming a uniform source distribution along with a distortion based on chordal distance, codebook design algorithms are mentioned and rate distortion tradeoffs are studied. The expected distortion for such a quantizer is approximately characterized. These results are then applied to the performance analysis of a multiple antenna wireless communication system.