Simplified decoding for some non-coherent codes over the Grassmannian

We consider multiple-antenna non-coherent communications over Rayleigh flat fading channels and single-antenna non-coherent systems with unknown channel phase. For both systems, we propose some sub-optimal simplified decodings for the class of unitary space-time codes obtained via the exponential map (I. Kammoun and J.-C. Belfiore, Nov. 2003). To this aim, we use the geometrical interpretation of these codes as sets of points over the Grassmann manifold G_TM. We compare these codes with other propositions in the literature, for which a simplified decoder exists.