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

Abstract : 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.
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Submitted on : Thursday, December 9, 2021 - 9:55:29 AM
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Ngo Khac-Hoang, Alexis Decurninge, Maxime Guillaud, Yang Sheng. Cube-Split: A Structured Grassmannian Constellation for Non-Coherent SIMO Communications. IEEE Transactions on Wireless Communications, Institute of Electrical and Electronics Engineers, 2020, 19 (3), pp.1948-1964. ⟨10.1109/twc.2019.2959781⟩. ⟨hal-02556938⟩



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