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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2024, Vol. 58 Issue (12): 2609-2618    DOI: 10.3785/j.issn.1008-973X.2024.12.020
    
GSM-OTFS signal detection algorithm based on belief propagation and expectation propagation
Wei ZHOU1,2(),Wenjing DOU1,2,Qianqian LI2,Rui XU2
1. School of Optoelectronic Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2. Chongqing Key Laboratory of Mobile Communications Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
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Abstract  

A signal detection algorithm adopting the hybrid belief propagation and expectation propagation (EP-BP) was proposed, by combining the orthogonal time frequency space (OTFS) technology and the generalized spatial modulation (GSM). The discrete probability distribution was projected into a multivariate complex Gaussian function, and the beliefs of the GSM transmission symbols were calculated via the iterative propagation of the mean vectors and the covariance matrices. A two-stage TS-EP-BP signal detection algorithm was designed to reduce the computational complexity. The activated antenna combination was determined via the EP-BP in the first stage, and in the second stage, the vector variable node (VN) in the factor graph was decomposed into multiple sub-VNs, and the invalid sub-VNs were cut out. Considering that the modulation symbols were independent to the activated antennas, the computation times of symbol belief were greatly reduced by the approximation of the univariate complex Gaussian distribution function. Bit error rates of different algorithms in different conditions were compared through simulation, and the results showed that, the proposed EP-BP and TS-EP-BP algorithms had better performance of bit error rate, especially, by the TS-EP-BP algorithm, a flexible performance-complexity tradeoff was striked by changing the maximum iteration times in the first stage.

Key words： orthogonal time frequency space      generalized spatial modulation      belief propagation      expectation propagation      signal detection     
Received: 09 October 2023      Published: 25 November 2024
CLC:  TN 929.5  
Fund:  国家自然科学基金资助项目（61701062）；重庆市基础与前沿研究计划资助项目（cstc2019jcyj-msxmX0079）.
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Wei ZHOU
Wenjing DOU
Qianqian LI
Rui XU
Cite this article:

Wei ZHOU,Wenjing DOU,Qianqian LI,Rui XU. GSM-OTFS signal detection algorithm based on belief propagation and expectation propagation. Journal of ZheJiang University (Engineering Science), 2024, 58(12): 2609-2618.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2024.12.020     OR     https://www.zjujournals.com/eng/Y2024/V58/I12/2609


基于置信度和期望传播的GSM-OTFS信号检测算法

结合正交时频空（OTFS）技术与广义空间调制（GSM），提出混合置信度（EP）和期望传播（BP）的EP-BP信号检测算法. 该算法将离散概率分布投影到多元复高斯分布函数中，通过均值向量和协方差矩阵的迭代传递计算出GSM发射符号置信度. 为了降低计算复杂度，设计了两阶段的TS-EP-BP信号检测算法：第1阶段通过EP-BP确定激活天线组合，第2阶段将因子图中的矢量变量节点（VN）分离为多个子VN，并剪除无效子VN. 考虑调制符号独立于激活天线，采用一元复高斯分布函数近似以大幅度减少符号置信度计算次数. 通过仿真对不同条件下不同算法的误码率进行对比，结果表明，所提EP-BP和TS-EP-BP算法具有较优的误码率性能，尤其TS-EP-BP算法可以通过改变第1阶段的最大迭代次数来灵活地平衡误码率性能和计算复杂度.


关键词： 正交时频空（OTFS）,  广义空间调制（GSM）,  置信传播,  期望传播,  信号检测 
Fig.1 Model diagram of GSM-OTFS system
Fig.2 EP-BP factor graph for GSM-OTFS system
Fig.3 TS-EP-BP factor graph for GSM-OTFS system
算法复数乘法次数
EP-BP$ TMN[12{N_{\text{r}}}{N_{\text{t}}}+8{N_{\text{t}}}+(2N_{\text{t}}^2+{N_{\text{t}}}+2){C_{\text{c}}}+{N_{\text{a}}}{({C_{\text{m}}})^{{N_{\text{a}}}}}] $
TS-
EP-BP		$ \begin{gathered} {T^{\text{b}}}MN[12{N_{\text{r}}}{N_{\text{t}}}+8{N_{\text{t}}}+(2N_{\text{t}}^2+{N_{\text{t}}}+2){C_{\text{c}}}+{N_{\text{a}}}{({C_{\text{m}}})^{{N_{\text{a}}}}}]+ \\ (T - {T^{\text{b}}})MN[(13{N_{\text{r}}}+8{C_{\text{m}}}+2){N_{\text{a}}}+3{N_{\text{t}}}] \\ \end{gathered} $
GAMP[14]$ \begin{gathered} {N_{\text{t}}}N(4N_{\text{t}}^2+8{N_{\text{t}}}+1)+MN[10N_{\text{t}}^2{2^Q} - {N_{\text{t}}}+10{N_{\text{t}}} - \\ 6N_{\text{t}}^2+26{N_{\text{r}}}{N_{\text{t}}}+4N_{\text{r}}^3+22N_{\text{r}}^2 - {N_{\text{r}}}+8N_{\text{r}}^2{N_{\text{t}}}+ \\ 16{N_{\text{r}}}N_{\text{t}}^2+3 \times {2^Q} - 1+8{N_{\text{t}}}(2M+2N - 1)] \\ \end{gathered} $
MP[21]$ {(MN)^2}(84{C_{\text{m}}}+20) - MN(75{C_{\text{m}}}+10) $
Tab.1 Algorithm complexity summary table
参数数值
载波频率/ GHz4
子载波间隔/ kHz15
子载波个数（$M$）16、32
时隙数（$N$）16、32
调制阶数4-QAM
终端移动速度/ (km·h?1)500
路径数9
调制脉冲矩形窗
信道估计理想估计
Tab.2 Simulation parameter table of GSM-OTFS system
Fig.4 Relationship between bit error rate performance and iteration times of EP-BP algorithm
Fig.5 Relationship between bit error rate performance and signal-to-noise ratio of EP-BP algorithm under different UE speeds
Fig.6 Relationship between bit error rate performance and signal-to-noise ratio of different algorithms when $M = N = 16$
Fig.7 Relationship between bit error rate performance and signal-to-noise ratio of different algorithms when$M = N = 32$
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