## 4 Methodology
### DNN Architecture and Training  
The structure of a DNN has a major effect on how well it finds signals in MIMO systems. A very important part of creating the DNN is choosing the number of nodes that will go in each layer. This part, therefore, requires more detail about the rules that are used to decide how many nodes are in the secret layers.  
The complexity of MIMO signal detection, characterized by high-dimensional input data and the need to capture intricate relationships between transmitted and received signals, necessitates a sufficiently large number of nodes to ensure the DNN can learn and model these relationships effectively. The number of nodes in the input layer corresponds to the dimension of the input signal, determined by the number of antennas and the modulation scheme used. Hidden layers are designed to progressively extract higher-level features from the input signal, with a larger number of nodes in initial layers to capture complex patterns, gradually reducing in subsequent layers to refine the learned features.  
The number of nodes in the output layer is determined by the classification or regression task, such as the number of possible transmitted symbols in signal detection. The optimal number of nodes is often determined through empirical tuning and cross-validation, involving grid search over a range of values and evaluating performance using a validation set to identify the architecture that minimizes the SER. Computational resources available for training and deploying the DNN influence the choice of the number of nodes, requiring a trade-off between model complexity and computational efficiency to ensure feasible training times and real-time deployment. To avoid over-fitting, the number of nodes is kept in check, with techniques such as dropout regularization and early stopping employed to mitigate over-fitting, ensuring the model performs well with both training and unseen data.  
Table 2 summarizes the DNN architecture and training setup used in this context:  
This section has outlined the methodology employed to evaluate the performance of various data detection techniques for wireless communication systems. The following section delves into the results obtained by comparing conventional methods (MLD, MMSE, and ZF) with DNN-based detectors, the optimization of the activation function, and the findings from these evaluations, and it discusses their implications for data detection in MIMO communication systems.  
\begin{table}
\begin{tabular}{l l} \hline
**Aspect** & **Description** \\ \hline \hline \multicolumn{1}{l}{Learning rate} & 0.01 \\ \hline \multicolumn{1}{l}{Loss function} & \multicolumn{1}{l}{Mean squared error (MSE)} \\ \hline \multicolumn{1}{l}{Training epochs} & 1000 with early stopping \\ \hline \multicolumn{1}{l}{**Evaluation Metrics**} & \multicolumn{1}{l}{SER, SNR, computational Time} \\ \hline \end{tabular}
\end{table}
Table 1: _Cont._  
\begin{table}
\begin{tabular}{l l} \hline
**Aspect** & **Description** \\ \hline \multicolumn{1}{l}{Input layer} & \multicolumn{1}{l}{Corresponds to input signal dimension} \\ \hline \multicolumn{1}{l}{Hidden layer} & \multicolumn{1}{l}{Extract higher-level features, more nodes initially for complex patterns} \\ \hline \multicolumn{1}{l}{Output layer} & \multicolumn{1}{l}{
\begin{tabular}{l} Determined according to classification/regression task (e.g., transmitted \\ symbols) \\ \end{tabular} } \\ \hline \multicolumn{1}{l}{Number of nodes} & \multicolumn{1}{l}{Tuned empirically using cross-validation (grid search, validation set)} \\ \hline \multicolumn{1}{l}{Regularization} & \multicolumn{1}{l}{Techniques like dropout and early stopping to avoid overfitting} \\ \hline \end{tabular}
\end{table}
Table 2: Summary of DNN architecture and training setup.