## 5 Results and Analysis
### Performance of DNN-Based Detector  
The DNN architecture consists of seven hidden layers, each with 100 neurons. The ReLU activation function is used for the hidden layers. The model was trained for 1000 epochs. The simulation results depicted in Figure 4 demonstrate that the DNN outper  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**SER**} & \multicolumn{3}{c}{**CT**} \\ \hline
**N** & **M** & **MLD** & **MMSE** & **ZF** & **MLD** & **MMSE** & **ZF** \\ \hline
2 & 2 & \(4.5\times 10^{-5}\) & 0.007245 & 0.00978 & 0.105489 & 0.00127795 & 0.00160855 \\ \hline
2 & 4 & \(5\times 10^{-6}\) & 0.000021 & 0.000022 & 0.0107284 & 0.00136752 & 0.00173983 \\ \hline
2 & 6 & \(1\times 10^{-5}\) & \(2.5\times 10^{-5}\) & \(2.5\times 10^{-5}\) & 0.114222 & 0.00154409 & 0.00198467 \\ \hline
2 & 8 & \(5\times 10^{-5}\) & \(5\times 10^{-6}\) & \(5\times 10^{-6}\) & 0.116254 & 0.00189622 & 0.0021896 \\ \hline
2 & 10 & \(8.5\times 10^{-5}\) & \(2.5\times 10^{-5}\) & \(2\times 10^{-5}\) & 0.132713 & 0.00255674 & 0.00321228 \\ \hline
2 & 12 & \(2\times 10^{-5}\) & \(1.5\times 10^{-5}\) & \(7\times 10^{-5}\) & 0.12416 & 0.0025504 & 0.00324025 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance comparison of MLD, MMSE, and ZF in a case with a different number of transmitters and receivers.  
Figure 3: Comparison of MLD, MMSE, and ZF in a case with a different number of transmitters and receivers.  
forms the traditional approaches (MMSE and MLD) and exhibits performance reasonably close to theirs. Additionally, the computational time of the DNN was compared to that of the conventional methods. The findings revealed that the DNN requires a longer processing time compared to MMSE and MLE.  
To further enhance the DNN's performance relative to MMSE and MLD, simulations were re-run with modified parameters. This involved fine-tuning the training procedure, optimizing hyperparameters, and exploring different network designs. The objective was to achieve a more significant performance gain compared to conventional techniques through optimization. The results for a specific simulation are presented in Figure 5, showcasing a DNN architecture with 10 hidden layers and 70 neurons per layer trained for 2000 epochs.  
The training state of the SISO-based DNN is depicted in Figure 6. Notably, the training process stopped at 1209 epochs, indicating that further training would not yield significant benefits. This suggests that the model achieved a good fit with the data and avoided over-fitting.  
Figure 4: Comparison of MLD and MMSE vs. DNN.  
Figure 5: Comparative analysis of MLD and MMSE vs. DNN.  
Before continuing the study to examine more complex MIMO systems, the values for the SISO system in Figure 6 were used as a benchmark to assess the DNN's performance in a more straightforward setting. This aids in comprehending the DNN model's basic capabilities and constraints. A baseline that demonstrates the efficacy and efficiency of the model in a simple situation may be established by comparing the DNN's performance in a SISO configuration. Establishing this baseline is essential for pinpointing the particular difficulties and small gains that arise throughout the MIMO system transition. SISO values provide the performance gains and computational complexity brought about via MIMO setups, offering a more understandable perspective.