## 5 Results and Analysis
### MIMO-Based DNN Signal Detection Model  
A MIMO-based DNN signal detection model was developed in MATLAB. This involved constructing a neural network tailored to data identification within MIMO communication systems. The process encompassed selecting activation functions, creating loss functions and optimization techniques, and defining the architecture, including the number of layers and neurons. The model was trained on labeled data, and its performance was evaluated using validation and test sets. Regularization techniques and monitoring tools, such as early stopping and learning rate adjustments, were employed to ensure the model's robustness and generalization capabilities.  
The DNN architecture for the MIMO-based model adopted a specific configuration throughout the experiments. Each layer consisted of a set number of neurons, and the overall architecture comprised a defined number of hidden layers. The training dataset (XTrain) contained one million data samples, while the testing dataset (XTest) included one hundred thousand samples. During training, the model underwent a specified number of epochs, with each epoch representing a complete pass through the training dataset. This iterative process allows the DNN to learn and refine its internal parameters to capture complex relationships within the data. These simulation parameters collectively define the neural network's architecture and training regime, aiming to achieve optimal performance in data detection tasks specific to MIMO systems.  
To find the best setup for MIMO signal recognition in this study, different DNN models were tested. At first, the DNN model was made with seven hidden layers, each layer having  
Figure 6: SISO-based DNN training state.  
100 neurons. This was done to find a good mix between model complexity and computer speed. More testing led to a better design with 10 hidden layers, 70 neurons per layer, and training for 2000 epochs. This architecture showed major improvements in SER while still having reasonable computing requirements. Eventually, the chosen DNN design had three hidden layers with 300, 200, and 100 neurons each. This achieved the best balance of performance and processing efficiency, as shown with the lower SER at different SNRs (see Figure 7).  
The selection process for the number of nodes and layers was guided by the criteria mentioned above, ensuring that the DNN model was well suited for the complexity of MIMO signal detection tasks.  
The initial MIMO-based DNN configuration consisted of 10 hidden layers, each containing 80 neurons. The model was trained over 2000 epochs using a dataset of 10,000 samples from both the training and testing sets. However, as shown in Figure 8, this configuration did not yield significant improvements in the DNN's performance, as evidenced by the increasing SER values across all SNRs.  
Subsequent experiments explored the impact of modifying the DNN architecture and dataset size. As illustrated in Figure 7, increasing the training dataset size to 500,000 samples with a network architecture of three hidden layers containing 300, 200, and 100 neurons per layer, respectively, resulted in a noticeable improvement in the DNN's performance. This is reflected in the lower SER values observed across all SNR levels.  
Figure 8: MIMO-based DNN system showing dataset of 80 neurons per layer  
Figure 7: MIMO-cased DNN showing dataset of [300, 200, 100] neurons per layer.  
Further experimentation with a larger dataset of one million samples while the same three-layer architecture was maintained with 300, 200, and 100 neurons per layer consistently led to improved results, as shown in Figure 9. This observation solidified the chosen architecture and dataset size for subsequent evaluations.