# Asynchronous Partial Gaussian Approximation Detection Algorithm for Uplink-Grouped MIMO-SCMA System
## 3 Asynchronous Detection Algorithm
### Asynchronous Log-MPA Method
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Scheme** & **Complexity (Normalized)** & **Bit Error Rate (30 dB)** \\ \hline Log-MPA & Perfect & 0.2122 & \(2.1713\times 10^{-2}\) \\ SP-MPA & Perfect & 0.2097 & \(2.0167\times 10^{-5}\) \\ PM-MPA & Perfect & 0.0644 & \(6.6250\times 10^{-2}\) \\ SP-MPA(II) & Imperfect & 0.2401 & \(4.5256\times 10^{-2}\) \\ SP-MPA & Imperfect & 1.0000 & \(1.8750\times 10^{-5}\) \\ PGA-MPA & Imperfect & 0.7803 & \(2.1056\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Complexity and bit error rate in different algorithms. Figure 20: Normalized complexities of different algorithms. ## 6 Conclusions

In this paper, an asynchronous grouped MIMO-SCMA system model is presented and its related detection algorithms are studied. First, with a perfect case in one group, the SP-MPA is proposed to utilize the information of previous detection and reduce the bit error rate of the system. Secondly, to compensate the imperfect synchronization in one group, the PGA-MPA is proposed to approximate the interference on parts of the resource blocks, which balances the complexity and correct ability, achieving a better detecting result. However, only four transmit antennas are considered in this paper due to the complexity problem. The cases with more antennas should be studied further. Conceptualization and methodology, X.W., N.Z. and J.H. ; software and validation, X.W., N.Z. ; writing\(-\)original draft preparation, X.W. ; writing\(-\)review and editing, X.W. ; supervision and project administration, J.H. All authors have read and agreed to the published version of the manuscript. This research was funded by National Natural Science Foundation of China, grant number 62071319. Not applicable. The authors declare no conflict of interest. ## References

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