Geodesical Codebook Design for Precoded MIMO Systems
Karol Schober, Pekka Jänis, Risto Wichman · IEEE Communications Letters · 2009
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 betweenmax-minandmin-maxclustering parts ofECAalgorithm, where the latter prevents degenerated constellations. With Fubini-Study distance metric, the algorithm converges to best known packings without extramin-maxprocessing.