Multi-user spatial modulation (SM) assisted by sparse code multiple access (SCMA) has been recently proposed to provide uplink high spectral efficiency transmission. The message passing algorithm (MPA) is employed to detect the transmitted signals, which suffers from high complexity. This paper proposes three low-complexity algorithms for the first time to the SM-SCMA. The first algorithm is referred to as successive user detection (SUD), while the second algorithm is the modified version of SUD, namely modified SUD (MSUD). Then, for the first time, the tree-search of the SM-SCMA is constructed. Based on that tree-search, another variant of the sphere decoder (SD) is proposed for the SM-SCMA, referred to as fixed-complexity SD (FCSD). SUD provides a benchmark for decoding complexity at the expense of bit-error-rate (BER) performance. Further, MSUD slightly increases the complexity of SUD with a significant improvement in BER performance. Finally, FCSD provides a near-optimum BER with a considerable reduction of the complexity compared to the MPA decoder and also supports parallel hardware implementation. The proposed algorithms provide flexible design choices for practical implementation based on system design demands. The complexity analysis and Monte-Carlo simulations of the BER are provided for the proposed algorithms.

中文翻译：

---

用于空间调制的上行稀疏码多址复杂度降低

最近提出了由稀疏码多址 (SCMA) 辅助的多用户空间调制 (SM) 以提供上行链路高频谱效率传输。消息传递算法（MPA）用于检测传输的信号，其复杂度高。本文首次向SM-SCMA提出了三种低复杂度的算法。第一种算法称为连续用户检测（SUD），而第二种算法是SUD的修改版本，即修改的SUD（MSUD）。然后，首次构建了 SM-SCMA 的树搜索。基于该树搜索，为 SM-SCMA 提出了球体解码器 (SD) 的另一种变体，称为固定复杂度 SD (FCSD)。SUD 以误码率 (BER) 性能为代价为解码复杂性提供了基准。更多，MSUD 略微增加了 SUD 的复杂性，同时显着提高了 BER 性能。最后，与 MPA 解码器相比，FCSD 提供了近乎最佳的 BER，同时大大降低了复杂性，并且还支持并行硬件实现。所提出的算法为基于系统设计需求的实际实现提供了灵活的设计选择。为所提出的算法提供了BER的复杂度分析和蒙特卡罗模拟。所提出的算法为基于系统设计需求的实际实现提供了灵活的设计选择。为所提出的算法提供了BER的复杂度分析和蒙特卡罗模拟。所提出的算法为基于系统设计需求的实际实现提供了灵活的设计选择。为所提出的算法提供了BER的复杂度分析和蒙特卡罗模拟。