Survey of Multi-user Detection Algorithms for Sparse Code Multiple Access System
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摘要: 稀疏码多址接入(SCMA)是一种非正交多址接入技术，具备高频谱效率和大连接特性。多用户检测是SCMA系统的关键问题，而如何降低检测算法的复杂度成为多址接入领域的研究热点。该文从影响算法复杂度的不同因素入手，分类综述了现有多用户检测算法并对几种典型算法进行了原理剖析和性能对比。同时，指出了SCMA多用户检测算法的改进思路。最后总结并探讨了SCMA检测算法未来的发展趋势和面临的挑战。Abstract: Sparse Code Multiple Access (SCMA) is a non-orthogonal multiple access scheme with high spectrum efficiency and massive connectivity. Multi-user detection is a key issue of SCMA system and how to reduce the complexity of detection algorithms has become a research hotspot in the field of multiple access. This paper reviews the existing multi-user detection algorithms from different factors that affect the complexity of the algorithms. Furthermore, the principle and performance of several typical multi-user detection algorithms are introduced and compared. In addition, the improved ideas of multi-user detection algorithms for SCMA system are pointed out in this paper. Finally, the future development trend and challenges of SCMA detection algorithms are summarized and discussed.
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表 1 LOG-MPA算法与各类算法加法复杂度对比分析
算法 加法 LOG-MPA $TK{d_r}{M^{{d_r}}}(2{d_r} + 1) + TK{d_r}(3{M^{{d_r}}} - M) + TJ{d_v}M({d_v} - 2) + JM({d_v} - 1)$ DT-MPA $\begin{gathered} K{d_r}{M^{ {d_r} } }(2{d_r} + 1) + K{d_r}(3{M^{ {d_r} } } - M) + J{d_v}M({d_v} - 2) + JM({d_v} - 1) + J(3M - 3) \\ + \sum\limits_{t = 1}^{T - 1} {\sum\limits_{k = 1}^K { {d_r}\prod\limits_{i = 1}^{ {d_r} } { {m_c}[t,{\xi _k}(i)](2{d_r} + 1) + } \sum\limits_{t = 1}^{T - 1} {\sum\limits_{k = 1}^K {(3{d_r}{m_c}[t,{\xi _k}(i)] - \sum\limits_{i = 1}^{ {d_r} } { {m_c}[t,{\xi _k}(i)]} )} } } } \\ + \sum\limits_{t = 1}^{T - 1} {\sum\limits_{j = 1}^J { {d_v}{m_c}[t,j]} } ({d_v} - 2) + \sum\limits_{t = 1}^{T - 1} {\sum\limits_{j = 1}^J { {m_c}[t,j]} } ({d_v} - 1) + \sum\limits_{t = 1}^{T - 1} {\sum\limits_{j = 1}^J {(3{m_c}[t,j]} } - 3) \\ \end{gathered}$ ISS-MPA ${T'}K{d_r}{M^{{d_r}}}(2{d_r} + 1) + {T'}K{d_r}(3{M^{{d_r}}} - M) + {T'}J{d_v}M({d_v} - 2) + JM({d_v} - 1)$ ES-MPA $TK{d_r}(M + 3{d_r} - 2{d_s} - 5) + TK{d_r}{M^{{d_s} + 1}}(2{d_s} + 5) + TJ{d_v}M({d_v} - 2) + JM({d_v} - 1)$ SD-MPA $T{d_r}\displaystyle\sum\limits_{k = 1}^K {|\phi (k)} |(2{d_r} + 1) + T{d_r}\left(3\displaystyle\sum\limits_{k = 1}^K {|\phi (k)} | - KM\right) + TJ{d_v}M({d_v} - 2) + JM({d_v} - 1)$ DFG-MPA $\begin{gathered} \sum\limits_{t = 1}^T {|{{\boldsymbol{B}}_s}(t)} |{M^{{d_r}}}(2{d_r} + 1) + \sum\limits_{t = 1}^T {|{{\boldsymbol{B}}_s}(t)|} (3{M^{{d_r}}} - M) + \sum\limits_{t = 1}^T {|{{\boldsymbol{B}}_s}(t)} |(2M - 1) - T \\ + TJ{d_v}M({d_v} - 2) + JM({d_v} - 1) \\ \end{gathered} $ 
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表 2 LOG-MPA算法与各类算法乘法复杂度对比分析
算法 乘法 LOG-MPA $ TK{d}_{r}{M}^{{d}_{r}}({d}_{r}+2)+TK{d}_{r}({M}^{{d}_{r}}+M)$ DT-MPA $\begin{array}{l}K{d}_{r}{M}^{ {d}_{r} }({d}_{r}+2)+K{d}_{r}({M}^{ {d}_{r} }+M)+{\displaystyle\sum\limits_{t=1}^{T-1}{\displaystyle\sum\limits_{k=1}^{K}{d}_{r}{\displaystyle \prod _{i=1}^{ {d}_{r} }{m}_{c}[t,{\xi }_{k}(i)]({d}_{r}+2})} }\\ +{\displaystyle\sum\limits_{t=1}^{T-1}{\displaystyle\sum\limits_{k=1}^{K}\left({d}_{r}{\displaystyle \prod _{i=1}^{ {d}_{r} }{m}_{c}[t,{\xi }_{k}(i)]+{\displaystyle\sum\limits_{i=1}^{ {d}_{r} }{m}_{c}[t,{\xi }_{k}(i)]} }\right)} }\end{array}$ ISS-MPA $ {T}'K{d}_{r}{M}^{{d}_{r}}({d}_{r}+2)+{T}'K{d}_{r}({M}^{{d}_{r}}+M)$ ES-MPA $TK{d_r}(4M + 2{d_r} - 2{d_s}) + TK{d_r}{M^{{d_s} + 1}}({d_s} + 3) + TK{d_r}({M^{{d_s} + 1}} + M)$ SD-MPA $T{d}_{r}{\displaystyle\sum\limits_{k=1}^{K}|\varphi (k)}|({d}_{r}+2)+T{d}_{r}\left({\displaystyle\sum\limits_{k=1}^{K}|\varphi (k)}|+KM\right)$ DFG-MPA $ {\displaystyle\sum\limits_{t=1}^{T}|{\boldsymbol{B}}_{s}(t)}|{M}^{{d}_{r}}({d}_{r}+2)+{\displaystyle\sum\limits_{t=1}^{T}|{\boldsymbol{B}}_{s}(t)}|({M}^{{d}_{r}}+M)+{\displaystyle\sum\limits_{t=1}^{T}|{\boldsymbol{B}}_{s}(t)}|(2M+1)$ 注：${T'}$为ISS-MPA的迭代次数；${m_c}[t,{\xi _k}(i)]$为第$t$次迭代中，与资源$k$连接的第$i$用户的码本大小；${m_c}[t,j]$为第$t$次迭代中，第$j$个用户的码本大小；$\phi (k)$为资源节点$k$上给定半径范围内的叠加星座点；${{\boldsymbol{B}}_s}(t)$第$t$次迭代时的实线分支集。
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表 3 仿真参数
参数 值 信道条件 瑞利衰落信道 蒙特卡罗次数 107 $J$ 6 $K$ 4 ${d_r}$ 3 ${d_v}$ 2 $\lambda $ 150% $G$ 3 $\tau $ 10 $r$ 3$\delta $或4$\delta $ 注：$\delta $为噪声的标准差。
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