## 4 Simulation Results
The three optimization methods, RMSProp, SGDm, and Adam, are discussed and compared in this part. Next, we will investigate how well the SGDm and RMSProp learning techniques performed in obtaining a more accurate DL peephole LSTM-based channel estimator. Figure 11: DL peephole LSTM-based estimator performance with 64, 8, and 4 pilots, respectively, and the Adam optimizer. Figure 10: Comparing SER performance with 4 pilots. Choosing the best approach for optimizing a particular scientific problem can be difficult. The learning process is not improved if the network remains at the local minimum during training due to an inaccurate optimization technique. DL peephole LSTM-based CE optimization requires a comparison of model-based and dataset-based optimizers. Figure 12 shows how the Adam model outperformed its competitors at 64 pilots. Figures 13 and 14 show how the RMSProp models outperformed the Adam and SGDm models at eight and four pilots, respectively. The same optimizer performed differently depending on how many pilots it had. As we can see in the end, the SGDm models performed the worst of all the cases. All parameters of the SGDm models had one learning rate. Figure 12: Comparison of SER performance with 64 pilots and various optimization algorithms for DL peephole LSTM-based CS estimators. Figure 13: Comparison of SER performance with 8 pilots and various optimization algorithms for DL peephole LSTM-based CS estimators. As can be seen in Figure 15, the additional optimization needs of the suggested DL peephole LSTM estimator and its robustness when used with constrained pilots. The proposed estimators can be used with lower pilots at low SNRs (0-4 dB)--consequently, the transmission rate increases. Tracking the DL training process is helpful, and the loss measurements help us evaluate training. As shown in Figures 16-18, the trained DL peephole LSTM-based CS estimators using the SGDm algorithm provided poor performance compared to the Adam and RMSProp optimization strategies. The loss of the Adam and RMSProp optimization methods can be seen in Figures 12-14. Figure 14: Comparison of SER performance with 4 pilots and various optimization techniques for DL peephole LSTM-based CS estimators. Figure 15: The proposed DL peephole LSTM-based estimator’s SER performance with various pilots using the best optimizer. Figure 19-21 show the comparison of the effects of the different pilots on peephole LSTM, LSTM, and GRU-based CSEs. In this part, the results from the previous subsection are compared with those of the LSTM and GRU-based CSEs. To evaluate the performance of the three estimators under identical channel conditions, pilots 4, 8, and 64 were used. In this simulation, the RMSProp optimizer was used. Figure 19 shows that for 64 pilots, the DL peephole LSTM-based estimator beat the rest of the studied CSEs over the entire SNR study range (0-20 dB). The performance of SNRs between 0 and 14 dB was identical to LSTM- and GRU-based CSEs. Figure 16: Comparison of loss functions using 64 pilots and various optimization techniques for DL peephole LSTM-based CSE training. Figure 8:0 Comparing the loss functions of 8 pilots and different optimization algorithms for DL peephole LSTM-based CSE training. The peephole LSTM and the LSTM performed better than the GRU for all SNR values. LSTM CSE outperformed peephole LSTM and GRU, as shown in Figure 8:1 At low SNRs, from 0 to 5 dB, the proposed CSE performed comparably well to the estimators of LSTM and GRU. The LSTM estimator was superior to the GRU estimator at all SNR values. Figures 19 and 20 demonstrate that the DL peephole LSTM-based estimator outperformed the GRU estimators when the number of pilots rose (8 and 64). In the case of using four pilots, Figure 21 shows that the peephole LSTM performed comparably to the LSTM and GRU estimators at SNRs between 0 and 9 dB. The GRU CSE outperformed the peephole LSTM and the LSTM in the remaining SNR test range (9-20 dB). Table 3 summarizes the accuracy percentages of the proposed and traditional estimators.