Designing multidimensional constellations (MdCs) is an integral part of sparse code multiple access (SCMA). Since the optimal maximum a posteriori (MAP) receiver for SCMA is too complex in most applications, one highly popular technique is the near-optimal message passing algorithm (MPA), where its performance improves with increasing the signal-to-noise ratio (SNR) and the number of iterations. When the number of MPA iterations has to be limited (e.g., low-latency and/or low-complexity and/or energy-sensitive applications), the performance gap between MAP and MPA becomes significant, especially at low-to-medium SNRs. Inspired by the promising features of hypercubes when used along with bit-interleaved coded modulation, we construct novel MdCs which are based on a unitary rotation of a hypercube by a rotation angle that aims to achieve the minimum frame-error-rate (FER). By exploiting special properties of hypercubes, we fit a second-order rational polynomial to a few measured FER samples, and find a close-to-optimal rotation angle at each SNR and MPA iteration. Our proposed MdCs provide substantial performance gains (as much as 2 dB) in comparison to the best known SCMA MdCs in the literature, especially in low-to-medium SNR regions when the number of MPA iterations has to be low, and in the presence of 5G-compliant LDPC codes.

中文翻译：

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上行SCMA系统基于超立方体的SNR自适应多维星座设计

设计多维星座 (MdC) 是稀疏代码多址 (SCMA) 的组成部分。由于 SCMA 的最优最大后验 (MAP) 接收器在大多数应用中过于复杂，因此一种非常流行的技术是近最优消息传递算法 (MPA)，其性能随着信噪比 (SNR) 的增加而提高) 和迭代次数。当 MPA 迭代次数必须受到限制时（例如，低延迟和/或低复杂性和/或能量敏感的应用程序），MAP 和 MPA 之间的性能差距变得很大，尤其是在中低 SNR 时。受到超立方体与位交错编码调制一起使用时的有前途的特征的启发，我们构建了新的 MdC，它基于超立方体的单一旋转，旋转角度旨在实现最小帧错误率 (FER)。通过利用超立方体的特殊属性，我们将二阶有理多项式拟合到几个测量的 FER 样本中，并在每次 SNR 和 MPA 迭代中找到接近最佳的旋转角。与文献中最著名的 SCMA MdCs 相比，我们提出的 MdCs 提供了显着的性能提升（高达 2 dB），尤其是在 MPA 迭代次数必须很低的中低 SNR 区域中，并且存在5G 兼容的 LDPC 码。