# A CNN-MPSK Demodulation Architecture with Ultra-Light Weight and Low-Complexity for Communications
## 5 Conclusions  
This paper proposes a simplified and light-weight CNN-MPSK demodulation architecture based on deep learning technology. The proposed CNN-MPSK can be implemented without requiring the carrier synchronization and timing synchronization that make the system complex. Thus, the design complexity can be greatly reduced and the inverse \(\pi\) phenomenon is avoided. The simulation tests are conducted on BER performance of the proposed CNN structure for 4 PSK, 8 PSK and 16 PSK, respectively. We see that the proposed CNN-MPSK shows the similar performance to the coherent demodulation and the existing deep learning demodulations. More importantly, the CNN-MPSK structure has the advantage of greatly reduced computational complexity. As compared with the coherent demodulation, the computation complexity of the proposed architecture is reduced from \(\mathbf{O}(n^{2})\) to \(\mathbf{O}(n)\). Thus, the proposed architecture can be seen as an alternative scheme for low-complexity signal demodulation in communications.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type of** & **Multiplications** & **Additions** & **Complexity** \\
**Demodulation** & & & \\ \hline coherent & \(N(L_{p}+L_{f}+1)+\) & \(N(L_{p}-1)+N(L_{f}-1)+\) & \(\mathbf{O}(n^{2})\) \\  & \(L_{p}^{2}+L_{f}^{2}-(L_{p}+L_{f})\) & \((L_{p}-1)^{2}+(L_{f}-1)^{2}\) & \\ CNN-BPSK & \(3N+N/s\) & \(N+N/s\) & \(\mathbf{O}(n)\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The comparison of calculation between coherent and CNN demodulation.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type of Algorithms** & **Parameters** & **Multiplications** & **Additions** & \(\mathbf{-5}\)**dB** & \(\mathbf{0}\)**dB** & \(\mathbf{10}\)**dB** \\ \hline our CNN BPSK & 10 & 10 & 10 & 78.6\% & 92\% & 99.9\% \\ our CNN 4 PSK & 10 & 10 & 10 & 50.9\% & 70.8\% & 99.8\% \\ our CNN 8 PSK & 10 & 10 & 10 & 24\% & 40.9\% & 99\% \\ our CNN 16 PSK & 10 & 10 & 10 & 12\% & 21.8\% & 61.6\% \\ ResNet BPSK [7] & \(10^{5}\) & \(10^{7}\) & \(10^{7}\) & 50\% & 97\% & 99\% \\ ResNet 4 PSK [7] & \(10^{5}\) & \(10^{7}\) & \(10^{7}\) & 7\% & 70\% & 99\% \\ ResNet 8 PSK [7] & \(10^{5}\) & \(10^{7}\) & \(10^{7}\) & 7\% & 25\% & 99\% \\ ResNet 16 PSK [7] & \(10^{5}\) & \(10^{7}\) & \(10^{7}\) & 6\% & 40\% & 85\% \\ DBN BPSK [11] & \(10^{2}\) & \(10^{3}\) & \(10^{3}\) & 75\% & 97\% & 99\% \\ DBN 4 PSK [11] & \(10^{2}\) & \(10^{3}\) & \(10^{3}\) & 60\% & 80\% & 99\% \\ CNN based BPSK [11] & \(10^{5}\) & \(10^{6}\) & \(10^{6}\) & 61\% & 90\% & 99\% \\ CNN based 4 PSK [11] & \(10^{5}\) & \(10^{6}\) & \(10^{6}\) & 50\% & 75\% & 99\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: The comparison of the proposed algorithms and others.  
**Author Contributions:** Conceptualization, B.W. and Z.L.; methodology, B.W.; software, X.Z.; validation, B.W., Z.L. and X.Z.; formal analysis, Z.L.; investigation, Z.L.; resources, X.Z.; data curation, X.Z.; writing--original draft preparation, B.W.; writing--review and editing, Z.L.; visualization, X.Z.; supervision, X.Z.; project administration, B.W.; funding acquisition, Z.L. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by Science and Technology Research Program of Henan Province (No. 202102310530), Nsf of fuijan province (No. 2020J01301), and the key scientific research projects of colleges and universities in Henan Province (No. 21A520032, 21A520033).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Acknowledgments:** The authors would like to thank the reviewers for their thoughtful remarks and recommendations, which considerably enhanced the paper's presentation.  
**Conflicts of Interest:** The authors declare no conflict of interest.