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1 Geodesical Codebook Design for Precoded MIMO Systems

By K. Schober, P. Jänis and R. Wichman


Abstract—We propose a numerical method for finding packings of MIMO semi-unitary precoding matrices in Grassmannian manifolds with different metrics. The proposed expansion– compression algorithm (ECA) is practical, simple and produces efficient packings without the need for a sophisticated initialization. With chordal distance metric, the algorithm tends to converge into a degenerated point constellation, where two points contain identical as well as orthogonal columns and distance between them cannot increase further along geodesic. Therefore, we alternate between max-min and min-max clustering parts of ECA algorithm, where the latter prevents degenerated constellations. With Fubini-Study distance metric, the algorithm converges to best known packings without extra min-max processing. I

Year: 2011
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