## 6 Conclusions  
In this study, we investigate the BER performance of our hybrid DL (HDL) model combining a 1D-CNN and Bi-LSTM under imperfect channel conditions. By preprocessing the channel vector and received signal based on domain-specific knowledge, the HDL model effectively recovers transmitted data bits. Our evaluation included a thorough analysis of various batch sizes, learning rates, optimizers, and equalizers, finding that the HDL model achieves optimal results with the Adam optimizer and ZF equalizer. Although our proposed model demonstrates effective performance at positive training SNR values, its performance is comparatively lower at negative training SNR values, which led us to exclude such values during training. Our comparative results reveal that the HDL model outperforms GD, ML, DeepIM, CNN, and LSTM-IM detectors, demonstrating its robustness compared to both traditional and conventional models. Additionally, we explored the performance of our HDL detector across different modulation orders and data configurations, confirming that the best performance is achieved with QPSK modulation and the \((4,1,4)\) data setup. These promising results highlight the advantages of HDL, suggesting that it can provide valuable contributions towards further integration of DL within advanced IM systems. Furthermore, to substantiate the resilience of the proposed HDL-based OFDM-IM system, we evaluated it in terms of both throughput and SE. Our findings should inspire continued research on ways to leverage DL techniques in next-generation communication systems. Figure 13: Throughput and SE of the proposed HDL-based OFDM-IM system: (**a**) throughput performance and (**b**) SE performance. **Author Contributions:** Conceptualization, M.A.A. and M.H.R. ; methodology, M.A.A., R.T. and M.A.S.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. **Funding:** This work was supported in part by an Institute of Information and Communications Technology Planning and Evaluation (IITP) grant funded by the Korean Government (Ministry of Science and ICT (MSIT), South Korea); in part under the Metaverse Support Program to Nurture the Best Talents, 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, Korea) under the ITRC (Information Technology Research Center) support program (IITP-2024-RS-2024-00437494) supervised by the IITP (Institute for Information and Communications Technology Planning and Evaluation). **Data Availability Statement:** The data will be made available by the authors upon request. **Conflicts of Interest:** The authors declare no conflicts of interest. The following abbreviations are used in this manuscript: