Grassmann-based signal design for non coherent reception

We propose, in this paper, the construction of noncoherent spherical constellations, both uncoded and coded, by mapping a T-1 dimensional constellation carved from Z[i]^T-1 onto the unit T dimensional sphere. The chosen mapping corresponds to the parametrization of the Grassmann manifold G_T,1 where T is the code-length. The advantage of the spherical codes that we propose here is that the GLRT detector can be slightly simplified. The coding and decoding principles are derived from Galliou et al. (2002).