# Multi-User Joint Detection Using Bi-Directional Deep Neural Network Framework in NOMA-OFDM System
## 5 Simulation Results and Discussion
### Simulations Results  
To conduct the simulation performance, the proposed model is compared with different traditional CE and signal detection models and a one-dimensional CNN model. A confusion matrix simulation result is performed to observe the symbol classification robustness of the proposed model. Figure 6 shows the confusion matrix for symbol classification according to the number of labels during the testing process of the trained model. The  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Simulation tool & MATLAB Deep-learning toolboxTM \\ \hline Operating system & Windows 10 Pro \\ \hline OFDM subcarriers & 64 \\ \hline Pilot symbols & 64 \\ \hline Channel path & 20 \\ \hline Noise & AWGN \\ \hline Length of CP & 20 \\ \hline Channel fading & Rayleigh channel \\ \hline NOMA UEs & 2 \\ \hline Modulation type & QPSK \\ \hline Total number of packets & 50,000 \\ \hline Total model layers & 5 \\ \hline Epochs number & 100 \\ \hline Learning rate & 0.01 \\ \hline Minibatch size & 2000 \\ \hline Optimizer & ADAM \\ \hline \hline \end{tabular}
\end{table}
Table 1: The simulation parameters.  
symbol decoding and classification rate of the proposed model are very high in order of true class and predicted class, except for some minor missing classes.  
Figure 7 shows the simulation results of SER performances for \(UE_{1}\) and \(UE_{2}\). The output is taken by comparing the proposed network and the CNN model. The comparison of the proposed model and CNN is performed with the same simulation parameters. It can be seen that the SER performance of the CNN model is lower than the proposed Bi-LSTM model. The proposed detection network outperforms the CNN for both UE cases. In addition, with an increase in the SNR values, it can be seen that the SER performance is improved.  
Figure 6: The confusion matrix of the true and predicated class of the model.  
Figure 7: SER versus SNR performance of proposed Bi-LSTM model and CNN model.  
In Figure 8, the SER performances of the proposed network with the traditional LS method for \(UE_{1}\) and \(UE_{2}\) are well investigated. The comparison of the proposed model and conventional LS is performed using the SER and SNR curve. It is evident that the SER performance of the traditional methods is lower than the proposed BiLSTM model for both UEs with respect to the SNR values. The SER performance of the proposed Bi-LSTM model with traditional MMSE is shown in Figure 9. It is also shown that the SER performance of the proposed Bi-LSTM model is always higher than the MMSE method for both UEs.  
To investigate SER performance, the proposed model is compared with the ML method. Figure 10 shows the SER performance of the proposed model with the ML method. It is  
Figure 8: SER versus SNR performance of proposed Bi-LSTM model and LS method.  
Figure 9: SER versus SNR performance of proposed Bi-LSTM model and MMSE method.  
To observe the learning capability of the proposed model, the simulation results are performed in terms of testing accuracy and SNR (0-20) dB ranges of the last iteration of Monte Carlo simulations. The testing accuracy of the proposed Bi-LSTM and CNN model with different SNR values are shown in Figure 13. It is seen that the testing accuracy has a small amount of variation at the beginning of SNR. After that, the proposed Bi-LSTM model testing accuracy outperforms the CNN model during the measurement of the SER performance with SNR values. It is shown that the proposed model has the robustness of inference capability.  
Figure 12: SER versus SNR performance comparison for UE 2 of the proposed method against CNN, LS, MMSE, and ML.  
Figure 13: Testing accuracy performance of Bi-LSTM and CNN model.