# Deep Learning-Enhanced Autoencoder for Multi-Carrier Wireless Systems
## 7 Conclusions  
We proposed a robust GRU-based MC-AE system that optimizes diversity and coding gains over fading channels in a data-driven manner. We evaluated the BLER under both perfect and imperfect CSI conditions, comparing the performance of our proposed model with traditional and DL-based MC systems. Additionally, we assessed the BER performance under perfect CSI conditions. For further analysis, we calculated the SE and EE across varying SNR levels. Our findings show that the model performs optimally with a learning rate of 0.001, but it is capable of learning efficiently at different learning rates. Training at moderate SNR values helps capture more relevant features, improving generalization. Our  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Model Name** & **Complexity per Sample (ms)** \\ \hline OFDM [9] & 0.032 \\ \hline S-OFDM [10] & 0.121 \\ \hline OFDM-IM [11] & 0.107 \\ \hline DNN-based MC-AE [32] & 0.028 \\ \hline Proposed MC-AE & 0.049 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Computational complexity comparison of the proposed GRU-based MC-AE system with other systems.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Training SNR (dB)** & **Complexity per Sample (ms)** \\ \hline
5 & 0.04995 \\ \hline
7 & 0.049 \\ \hline
10 & 0.0517 \\ \hline
15 & 0.05281 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Computational complexity of the proposed GRU-based MC-AE system evaluated for various training SNRs.  
proposed model exhibited superior performance with 1000 epochs and a batch size of 512, achieving optimal results when configured with (4,16) and trained at 7 dB SNR. The results demonstrate that MC-AE outperforms conventional baselines, including recent IM-based and S-OFDM-based schemes, in terms of performance improvements. It also achieves superior performance compared to other DL-based OFDM-IM and MC-AE systems under both perfect and imperfect CSI conditions. Moreover, the SE and EE performance highlights the system's robustness. Our study is primarily simulation-based, and we have not pursued practical implementation at this stage. However, in the future, the research community may consider the design of this experiment for practical implementation.  
Conceptualization, M.A.A. and M.H.R.; methodology, M.A.A., R.T. and M.A.S.; software, M.A.A., M.H.R. and M.-S.B.; validation, M.A.A. and M.A.S.S.; formal analysis, M.A.A., M.H.R., R.T. and M.-S.B.; investigation, M.A.A., M.H.R. and M.A.S.S.; resources, H.-K.S.; data curation, M.A.A. and R.T.; writing--original draft preparation, M.A.A.; writing--review and editing, M.A.A. and H.-K.S.; visualization, M.A.A. and M.-S.B.; supervision, H.-K.S.; project administration, H.-K.S.; funding acquisition, H.-K.S. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the Institute of Information and Communications Technology Planning and Evaluation (IITP) grant funded by the Korea Government [Ministry of Science and ICT (MSIT)], Republic of Korea, under the Metaverse Support Program to Nurture the Best Talents under Grant IITP-2024-RS-2023-00254529; in part by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education under Grant 2020R1A6A1A03038540; and in part by the MSIT (Ministry of Science and ICT), Republic of Korea, under the ITRC (Information Technology Research Center) support program (IITP-2024-RS-2024-00437191) supervised by the IITP (Institute for Information and Communications Technology Planning and Evaluation).  
The data will be made available by the authors upon request.  
The authors declare no conflicts of interest.