## 3 MIMO System Model and the Implementation Steps of Channel Estimation
### Cost Function Computation  
The cost function evaluation is carried out in this developed channel estimation model in the MIMO system for estimating the coefficient of the channel in the wireless network by varying the number of iterations as given in Figure 4. From the analysis, it is seen that the cost function of the implemented RP-WHEVO-HSCN-based channel estimation model is 99.3%, 99%, 99.6% and 99.3% enhanced versus the HHO-HSCN, RSA-HSCN, WHO-HSCN, and EVO-HSCN models, correspondingly, at the iteration count of 20. From the cost function output, it is verified that the proposed RP-WHEVO-HSCN-based channel estimation model reduces the cost consequence to enlarge the effectiveness of the hybrid MIMO system. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Subcarrier count & 128 \\ Number of blocks in each channel realization & 1 \\ Modulation order & M = 4 \\ OFDM sample time & \(1\times 10^{-7}\) \\ Guard interval time & 16 \\ OFDM symbol time & \(128\times 1\times 10^{-7}\) \\ Location of the pilot in subcarrier & [20, 30, 40, 50, 60, 70....... 120] \\ Number of subcarriers that carry data & 12 \\ Channel trap count & 3 \\ Doppler in Hz & 0.1 \\ Number of columns in the dictionary & 128 \\ Channel SNR & 15 \\ Channel SNR for sweep & [5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29] \\ Iteration count & \(1\times 10^{2}\) \\ Inner loop length & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation Parameters of the Offered Channel Estimation in MIMO Systems. Figure 4: _Cont_. Performance Evaluation of the Suggested Channel Estimation Model in the MIMO System by Considering Various Techniques  
The error performance evaluation of the proposed channel estimation scheme for the MIMO system in wireless communication by varying SNR among different techniques is specified in Figure 5. The designed RP-WHEVO-HSCN-based channel estimation has a MAE that is 97.2% enhanced versus DNN, 97.3% enhanced versus SCMA, 97.32% enhanced versus LSTM, and 97.05% enhanced versus Autoencoder + LSTM at SNR 20. Thus, the MAE of the initiated RP-WHEVO-HSCN-based channel estimation model is reduced to improve the spectral efficiency of the serial cascaded-based channel assessment model. Figure 4: (**a–e**) Cost function analysis on the proposed serial cascaded deep learning-based channel estimation model in the MIMO system. Figure 5: _Cont._  
Performance Evaluation of Suggested Channel Estimation Model in MIMO System by Considering Different Optimizing Algorithms  
The error performance evaluation of a wireless proposed channel estimation scheme for the MIMO system using a serial cascaded Multiscale network is specified in Figure 6. The proposed RP-WHEVO-HSCN model-based channel estimation reduces the MPE, which is enhanced by 3.2% versus HHO-HSCN, 9.0% versus RSA-HSCN, and 14.23% versus HHO-HSCN. Figure 5: Performance assessment of the implemented serial cascaded deep learning-based channel estimation model in terms of **(a)** L1-Norms, **(b)** L2-Norms, **(c)** L-INF-NORM **(d)** MAE, **(e)** MASE, **(f)** MEP, **(g)** RMSE, and **(h)** SMAPE. EVO-HSCN at SNR 20. Thus, the proposed RP-WHEVO-HSCN-based channel coefficient estimation model reduces the MPE value to increase the coherences of the MIMO system to predict the coefficient at the transmitter side using SNR feedback signal information at the receiver side antenna. Figure 6: _Cont._  
Performance Analysis of the Implemented Channel Estimation Scheme for the MIMO System Model over Various Measures  
The performance evaluation of the executed channel estimation model for the MIMO system model among various measures is given in Figure 7. The delineated RP-WHEVO-HSCN-based channel estimation in the MIMO system improved its spectral efficiency by 18.6% versus HHO-HSCN, 21.3% versus RSA-HSCN, 24.9% versus WHO-HSCN, and 24.2% versus EVO-HSCN at the SNR 15. Thus, the error rate is reduced in the proposed model to improve the spectral efficiency of the hybrid MIMO system model.