## 4 Simulation Results  
This section discusses the DL peephole LSTM-based CS estimator proposed for OFDM 5G and beyond networks. Then, the suggested estimator is compared with the LSTM and GRU-based CS estimators. The proposed estimator, LSTM and GRU were trained on simulated datasets and their symbol error rates (SERs) compared to the conventional LS and MMSE CSE estimators under different signal-to-noise ratios (SNRs). The training dataset for a subcarrier was collected. The transmitter transmitted data and pilot symbols in each OFDM packet. Multiplexing the pilot series data symbols, there were 10,000 OFDM packets generated, with 80% at training and 20% at validation. The proposed estimator, LSTM, and GRU CSEs all follow the estimator settings and training options in Table 1. On the other hand, Table 2 shows the OFDM channel parameters. In addition, in the actual simulations, the proposed estimator, the LSTM, and the GRU were trained with ADAM, RMSProp, SGDm, and optimization algorithms to investigate their performance under these learning approaches. Figures 8-11 illustrate the effects of the number of pilots by comparing the proposed estimator with the LS and MMSE estimators. Using a variety of pilots of 4, 8, and 64 and assuming identical channel conditions and the Adam optimizer, the performance of the peephole LSTM-based CSE, LS, and MMSE estimators was evaluated. \begin{table}
\begin{tabular}{l l} \hline
**Parameter** & **Value** \\ \hline Input data size & 256 \\ \hline Layer hidden units & 16 \\ \hline Fully connected layer size & 4 \\ \hline Loss function & Crossentropyex \\ \hline Mini batch size & 1000 \\ \hline Number of epochs & 100 \\ \hline Optimization algorithm & RMSProp, Adam and SGDm \\ \hline Training data size & 8000—OFDM frame \\ \hline Validation & 2000—OFDM frame \\ \hline Testing data size & 10,000—OFDM frame \\ \hline \end{tabular}
\end{table} 
Table 1: Channel state estimators’ structure and training parameters. \begin{table}
\begin{tabular}{l l} \hline
**Parameter** & **Value** \\ \hline Modulation mode & Quadrature phase-shift keying \\ \hline Carrier frequency & 2.6 GHz \\ \hline No. of paths & 24 \\ \hline Cyclic prefix length & 16 \\ \hline No. of subcarriers & 64 \\ \hline No. of pilots & 4, 8, and 64 \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters for the OFDM system’s channels. Figure 8 indicates that the suggested estimator is superior to the LS estimator at SNRs from 0 to 18 dB and achieves identical results to the MMSE estimator at SNRs from 0 to 10. The proposed CSE strongly competes with the MMSE CSE at low SNRs. The MMSE estimator achieved better results than the LS estimator at all SNR values. The MMSE method incorporates Gaussian noise and employs second-order channel statistics to estimate performance. Figures 9 and 10 indicate that the DL peephole LSTM-based estimator was superior to the LS and traditional MMSE estimators with fewer pilots. As shown in Figure 9, using eight pilots led to a degradation of the estimators LS and MMSE, while Figure 10 shows that LS and MMSE became useless at 0 dB when only four pilots were used. On the other hand, the proposed estimator can further decrease its SER when the SNR increases. This proves that the DL peephole LSTM-based CSE was not affected by the few pilots available for CE. Figure 8: Comparing SER performance with 64 pilots. Figure 9: Comparing SER performance with 8 Pilots. As seen in Figures 8-10, the LS estimator performed the worst because it did not use primary channel data in the estimating method. Nevertheless, the MMSE estimator performed better using second-order channel statistics during the estimation process, especially when many pilots were available. Figure 11 shows how the suggested estimator performed for pilot numbers 4, 8, and 64. At 64 pilots, the DL peephole LSTM channel estimator outperformed all others. Thus, more pilots improved the suggested estimator's performance. Figures 12-18 show the effects of the different optimization algorithms on system performance.