On Orthogonal Space-Time Block Codes and Packings on the Grassmann Manifold

We show that orthogonal space-time block codes may be identified with packings on the Grassmann manifold. We describe a general criterion for packings on the Grassmann manifold that yield coherent space-time constellations with the same code properties that make orthogonal space-time block codes so favorable. As an example, we point out that the rate 3/4 orthogonal space-time block code motivates a packing on the Grassmann manifold that allows for a simplified maximum likelihood detection rule using the newly introduced framework. As a side product, this packing defines a non coherent space-time constellation that may be regarded as a generalization of certain existing non coherent space-time codes.