  In this paper, we propose a practical structured constellation for
non-coherent communication with a single transmit antenna over Rayleigh flat
and block fading channel without instantaneous channel state information. The
constellation symbols belong to the Grassmannian of lines and are defined up to
a complex scaling. The constellation is generated by partitioning the
Grassmannian of lines into a collection of bent hypercubes and defining a
mapping onto each of these bent hypercubes such that the resulting symbols are
approximately uniformly distributed on the Grassmannian. With a reasonable
choice of parameters, this so-called cube-split constellation has higher
packing efficiency, represented by the minimum distance, than the existing
structured constellations. Furthermore, exploiting the constellation structure,
we propose low-complexity greedy symbol decoder and log-likelihood ratio
computation, as well as an efficient way to associate it to a multilevel code
with multistage decoding. Numerical results show that the performance of the
cube-split constellation is close to that of a numerically optimized
constellation and better than other structured constellations. It also
outperforms a coherent pilot-based scheme in terms of error probability and
achievable data rate in the regime of short coherence time and large
constellation size.
