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.

中文翻译：

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立方体分裂：用于非相干 SIMO 通信的结构化格拉斯曼星座

在本文中，我们提出了一种实用的结构化星座，用于在瑞利平坦和块衰落信道上使用单个发射天线进行非相干通信，无需瞬时信道状态信息。星座符号属于格拉斯曼线，并被定义为复杂的缩放比例。星座是通过将格拉斯曼线划分为一组弯曲超立方体并定义到这些弯曲超立方体中的每一个的映射来生成的，从而生成的符号在格拉斯曼线上近似均匀分布。通过合理选择参数，这种所谓的立方体分裂星座比现有的结构星座具有更高的填充效率，以最小距离表示。此外，利用星座结构，我们提出了低复杂度贪婪符号解码器和对数似然比计算，以及一种将其与多级解码的多级代码相关联的有效方法。数值结果表明，立方体分割星座的性能接近于数值优化的星座，优于其他结构化星座。在短相干时间和大星座尺寸的情况下，它在错误概率和可实现的数据速率方面也优于基于相干导频的方案。