# Efficient Deep Learning-Based Detection Scheme for MIMO Communication Systems
## 3 Proposed DL-Based Detection Scheme  
Figure 1 illustrates the proposed MIMO signal detection scheme based on DL. Throughout the training stage, three labeling encoding strategies are introduced to facilitate accurate signal detection. In the first stage, the information bits are assigned to the \(M\)-QAM symbols \(\mathbf{s}\). Then, a serial-to-parallel converter sends each symbol to a transmission antenna \(a_{k}\), with \(k=\{1,2,\cdots,N_{t}\}\). Each symbol is multiplied by a channel impulse response \(h_{ij}\in\mathbf{H}\) arriving at any reception antenna, where the AWGN is added. The symbols received \(r_{j}\in\mathbf{r}\), with \(j=\{1,2,\cdots,N_{r}\}\) are divided into their real and imaginary parts \(\mathfrak{R}(r_{j})\) and \(\mathfrak{I}(r_{j})\), respectively; therefore, the input training data contain \(N_{F}=4\) features. Algorithm 1 describes the general procedure of the proposed MIMO DL detection scheme. First, we take the real and imaginary parts of each received symbol \(\mathbf{r}\) as the input data. Then, we select a strategy to generate the matrix \(\mathbf{y}\) to label each entry row of the data array \(\mathbf{X}\). During the training stage, we perform the forward pass calculation of \(\mathbf{x}_{\ell+1}\) over several epochs. The values of the weights and biases array \(\mathbf{W}_{\ell}\) and \(\mathbf{b}_{\ell}\) are optimized when  
Figure 1: Proposed DL-based detection scheme for MIMO communication systems. performing the SGD method from the calculation of its gradients \(\
abla\mathbf{W}_{\ell},\
abla\mathbf{b}_{\ell}\), respectively. For the monitoring and evaluation of the training loop, we calculate the LMSE loss function \(\mathcal{L}(\mathbf{y},\hat{\mathbf{y}})\). Once the weights and biases arrays have been optimized (the training phase loop has ended), we perform _forward pass_ again to estimate the received symbol \(\hat{\mathbf{r}}\). Now, it is possible to obtain the BER using the designed model. ```
0:\(\mathbf{s},N_{t},N_{r},L,N_{e},\mathbf{W}_{\ell},\mathbf{b}_{\ell},\sigma( \cdot),\alpha\) Output:\(\hat{\mathbf{r}},\mathcal{L}(\mathbf{y},\hat{\mathbf{y}})\)  Symbol reception: \(\mathbf{r}=\mathbf{H}\mathbf{s}+\mathbf{n}\)  Generate input data \(\mathbf{X}:\{\Re(r_{j}),\Im(r_{j})\}\ \forall j=1,\cdots,N_{r}\)  Generate \(\mathbf{y}\) labels vector by selecting any label encoding method \(\mathbf{x}_{0}=\mathbf{X}\) \(\triangleright\) Start of training phase \(\mathbf{x}_{t+1}=\sigma(\mathbf{W}_{t}\mathbf{x}_{t}+\mathbf{b}_{\ell})\ \forall\ell=0,\cdots,L\)  Calculate gradients: \(\
abla\mathbf{W}_{\ell},\
abla\mathbf{b}_{\ell}\) \(\mathbf{W}_{\ell}:=\mathbf{W}_{\ell}-\alpha\cdot\
abla\mathbf{W}_{\ell}\) \(\triangleright\) SGD optimization \(\mathbf{b}_{\ell}:=\mathbf{b}_{\ell}-\alpha\cdot\
abla\mathbf{b}_{\ell}\) \(\hat{\mathbf{y}}=\mathbf{x}_{L}\)  Calculate RMSE loss: \(\mathcal{L}(\mathbf{y},\hat{\mathbf{y}})\) endfor \(\hat{\mathbf{r}}=\sigma(\mathbf{W}_{\ell}\mathbf{x}_{\ell}+\mathbf{b}_{\ell})\ \forall\ell=0,\cdots,L\) \(\triangleright\) Received symbol estimation
```  
**Algorithm 1** Proposed DL-based detector. From the revised DL-based frameworks in literature, it can be seen that the information and data processing of the received symbols \(\mathbf{r}\) cannot be extended to extract more learning parameters. Therefore, in this framework, our main approach is to explore different ways of labeling the predicted class vector \(\mathbf{y}\). This is actually how to assign values to the classifier that identify the M-QAM symbol and antenna labels to feed the DL-based detector. The procedure is described in Figure 1 as label encoding, which is executed only during the training phase. We analyze the following three labeling strategies. * One-hot (OH) encoding of the \(M^{N_{t}}\) combinations in transmission [29]. * Direct symbol encoding (DSE) (\(\log_{2}(M)\times N_{t}\) different encoding labels). * One-hot encoding per antenna (OHA) for the possible \(M\) symbols (\(M\times N_{t}\) labels).