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Geodesical codebook design for precoded MIMO systems

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3 Author(s)
Schober, K. ; Helsinki Univ. of Technol., Helsinki, Finland ; Janis, P. ; Wichman, R.

We propose a numerical method for finding packings of multiple-input and multiple-output (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.

Published in:

Communications Letters, IEEE  (Volume:13 ,  Issue: 10 )