## 7 Conclusions  
A neural network-based channel efficiency estimation scheme was developed to estimate the channel coefficient in the wireless network. The proposed system was developed to predict the channel coefficient of the MIMO system at the transmitter side antenna by utilizing the SNR feedback information to reduce the error rate. The serial cascade-forward network provides a nonlinear relationship between input and output antennas without changing the linear relationship between the antennas. The coefficient of the system was  
\begin{table}
\begin{tabular}{c c} \hline
**Proposed Model** & **Computation Complexity** \\ \hline RP-WHEVO & \(O[MaxIter*N_{pop}+1]\) \\ \hline \end{tabular}
\end{table}
Table 6: Computation complexity analysis of the implemented channel estimation scheme against various Algorithms.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Performance Measures** & **SNR-5** & **SNR-10** & **SNR-15** & **SNR-20** & **SNR-25** \\ \hline COA & 0.040793 & 0.046796 & 0.056003 & 0.067714 & 0.075696 \\ AVOA & 0.048505 & 0.05445 & 0.056944 & 0.073091 & 0.077741 \\ GMO & 0.03517 & 0.043669 & 0.044523 & 0.046719 & 0.050763 \\ EBOA & 0.00513 & 0.01252 & 0.020719 & 0.025459 & 0.04144 \\ RP-WHEVO-HSCN & 0.076509 & 0.077266 & 0.081016 & 0.0889 & 0.093545 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Analysis of the Performance of the Offered Channel Estimation Model Regarding Diverse SNR Rates Against Various Algorithms.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Performance Measures** & **J-HBF-DLLPA** & **PSS-PARAFAC** & **OE-HHO** & **RP-WHEVO-HSCN** \\ \hline MEP & 28.656 & 28.565 & 29.745 & 27.20 \\ SMAPE & 0.41345 & 0.40576 & 0.60989 & 39.994 \\ MASE & 0.27905 & 0.27474 & 0.28635 & 97.987 \\ MAE & 0.42201 & 0.41657 & 0.43106 & 27.22 \\ RMSE & 697.63 & 686.85 & 715.86 & 41.121 \\ L1-NORM & 21.101 & 20.828 & 21.553 & 67.999 \\ L2-NORM & 0.94369 & 0.94369 & 0.94838 & 20.561 \\ L-INF-NORM & 28.656 & 28.565 & 29.745 & 95.307 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Validation of the Performance Offered by the Proposed Channel Estimation Model Against Recent Approaches.  
predicted by utilizing an autoencoder and LSTM network. The parameters in this network were optimized using the RP-WHEVO algorithm to achieve an improved channel coefficient in the system by decreasing the model intricacy. The results from this system were evaluated by comparing the performances of the implemented channel estimation scheme against various heuristic algorithms and different channel estimation techniques. From the experimental outcomes, it was seen that the effective achievable rate of estimating the channel coefficient by the executed channel estimation scheme in the MIMO system was improved by 15% versus HHO-HSCN, 66.3% versus RSA-HSCN, 42.8% versus the WHO-HSCN algorithm, and 23.4% versus EVO-HSCN at an SNR value of 25. Thus, the initiated RP-WHEVO-HSCN-based channel estimation offered a higher spectral effectiveness rate in estimating the channel than several other conventional techniques. In the future, the non-coherent systems [42] based on the DPSK scheme will be surely included in our proposed algorithm to show effective performance.  
All authors contributed equally to the conceptualization, formal analysis, investigation, methodology, and writing and editing of the original draft. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2023R125), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.  
Not Applicable.  
Data Availability Statement: Data are contained within the article.  
The authors declare no conflict of interest.