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In this paper, we propose a practical structured constellation fornon-coherent communication with a single transmit antenna over Rayleigh flatand block fading channel without instantaneous channel state information. Theconstellation symbols belong to the Grassmannian of lines and are defined up toa complex scaling. The constellation is generated by partitioning theGrassmannian of lines into a collection of bent hypercubes and defining amapping onto each of these bent hypercubes such that the resulting symbols areapproximately uniformly distributed on the Grassmannian. With a reasonablechoice of parameters, this so-called cube-split constellation has higherpacking efficiency, represented by the minimum distance, than the existingstructured constellations. Furthermore, exploiting the constellation structure,we propose low-complexity greedy symbol decoder and log-likelihood ratiocomputation, as well as an efficient way to associate it to a multilevel codewith multistage decoding. Numerical results show that the performance of thecube-split constellation is close to that of a numerically optimizedconstellation and better than other structured constellations. It alsooutperforms a coherent pilot-based scheme in terms of error probability andachievable data rate in the regime of short coherence time and largeconstellation size.

Cube-Split: A Structured Grassmannian Constellation for Non-Coherent SIMO Communications