# Enabling Intelligent 6G Communications: A Scalable Deep Learning Framework for MIMO Detection
## 5 MIMONet: A DL-Based MIMO Detector
### MIMONet: Training and Testing
#### 5.2.3 Testing  
During testing, the trained network is used to predict the transmitted symbols \(\mathbf{\hat{s}}\) based on the received signal and channel matrix. The predicted symbols are compared with the true transmitted symbols to compute the SER. The SER is defined as the fraction of incorrectly detected symbols:  
\[\text{SER}=\frac{1}{N_{\text{Test}}}\sum_{i=1}^{N_{\text{Test}}}\mathbb{I}( \mathbf{\hat{s}}_{i}\
eq\mathbf{s}_{i}) \tag{29}\]  
where \(N_{\text{Test}}\) is the number of test samples, and \(\mathbb{I}\) is the indicator function, which is 1 if the symbol is incorrectly detected and 0 otherwise. In addition to SER, we also evaluate the BER, which measures the proportion of incorrectly detected bits across all transmitted symbols. After decoding the predicted symbols \(\mathbf{\hat{s}}\) into their corresponding bitstreams \(\mathbf{\hat{b}}\), BER is calculated as follows:  
\[\text{BER}=\frac{1}{N_{\text{bits}}}\sum_{i=1}^{N_{\text{bits}}}\mathbb{I} \Big{(}\mathbf{\hat{b}}_{i}\
eq\mathbf{b}_{i}\Big{)} \tag{30}\]  
where \(N_{\text{bits}}\) is the total number of transmitted bits. The inclusion of both SER and BER allows for a comprehensive evaluation of the detector's performance at both symbol and bit levels. To extract the final estimated transmitted signal \(\hat{s}\) based on the entire network model from start to end is derived through the following mathematical formulation:  
\[\mathbf{\hat{s}}=\text{argmax}\left(\mathbf{Y}_{4}\cdot\phi_{3}[\Psi_{3}\cdot \phi_{2}(\Psi_{2}\cdot\phi_{1}(\Psi_{1}\cdot\mathbf{X}+\beta_{1})+\beta_{2})+ \beta_{3}]+\beta_{4}\right) \tag{31}\]  
where \(\Psi_{i}\) represents the weight matrices at different layers, \(\beta_{i}\) represents the bias terms, \(\phi_{i}\) denotes the activation functions applied at each layer, and the argmax function selects the output with the highest probability corresponding to the transmitted signal. The training and testing procedure of the MIMONet MIMO detector is outlined in Algorithm 1, which presents the detailed steps involved in the process:```
Input:\(\mathbf{r}\), \(\mathbf{G}\) Output:\(\mathbf{\hat{s}}\) Data: Generate train and test data based on \(\mathbf{s},\mathbf{G},\mathbf{w}\) for\(i=1\)to\(m\)do  Calculate received signal \(\mathbf{r}^{(i)}\) using MIMO Equation  end for Extract features from \(\{\operatorname{Re}(\tilde{\mathbf{r}}),\operatorname{Im}(\tilde{\mathbf{r}}), \operatorname{Re}(\hat{\mathbf{G}}),\operatorname{Im}(\tilde{\mathbf{G}})\}\) for\(i=1\)to\(m\)do  Concatenate features for SNR index \(i\)  end for  Integrate MIMONet network model: \(\text{MIMONet}(\mathbf{r}^{(i)},\ \ \mathbf{G}^{(i)})\to\text{feature vector input}\) for\(i=1\)to\(m\)do  Estimate the transmitted signal \(\hat{\mathbf{s}}^{(i)}\) using \(\hat{\mathbf{s}}=\text{argmax}\left(\mathbf{\Psi}_{4}\cdot\phi_{3}[\mathbf{ \Psi}_{3}\cdot\phi_{2}(\mathbf{\Psi}_{2}\cdot\phi_{1}(\mathbf{\Psi}_{1}\cdot \mathbf{X}+\beta_{1})+\beta_{2})+\beta_{3}]+\beta_{4}\right)\)  Compute BER: \(BER^{(i)}=\frac{1}{N_{\text{bits}}}\sum_{j=1}^{N_{\text{bits}}}\mathbb{I}\Big{(} \hat{\mathbf{b}}_{j}\
eq\mathbf{b}_{j}\Big{)}\)  end for
```

**Algorithm 1**MIMONet: Deep learning-based MIMO detector

## 6 Simulation Setup and Results Discussion

To replicate the proposed method, a custom simulator based on MATLAB R2022b was developed. This simulator ran on a stand-alone Intel i9-10900K CPU @ 3.70 GHz with 128 GB RAM and included a 32 GB GPU for improved computational efficiency. Table 1 outlines the parameters used in the simulation setup. ### Results Discussion

To evaluate the effectiveness of the proposed DL-driven MIMONet detector, its performance is systematically benchmarked against both traditional MIMO detectors (MMSE,