Cube-Split: A Structured Grassmannian Constellation for Non-Coherent SIMO Communications
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In this paper, we propose a practical structured constellation for non-coherent communication with single transmit antenna over 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 grids and defining a mapping onto each of these bent grids 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 other structured constellations in the literature. Furthermore, exploiting the constellation structure, we design low-complexity greedy symbol decoder and low-complexity log-likelihood ratio computation. 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.
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