# Efficient Deep Learning-Based Detection Scheme for MIMO Communication Systems
## 4 Results and Discussion  
This section describes the setup of the experiments carried out in this work. We present and discuss the results. Table 6 synthesizes the experiments. The first setup is a \(2\times 2\) MIMO system, which consists of two transmitter and two receiver antennas. The NN architecture for signal detection consists of \(L=1\) hidden layer with 100 hidden units. The second setup consists of a \(4\times 4\) MIMO system, with \(N_{t}=4\) and \(N_{r}=4\) respectively. Detection is achieved using an NN with \(L=2\) hidden layers, each containing 1000 neurons. The layers are fully connected for both cases. During the training phase, for all designed DL detectors, the learning rate selected is \(\alpha=0.01\), the Xavier method is used to initialize the weights, and the NRMSE (defined in Equation (6)) is the loss function. The experiments are conducted in MATLAB, Julia, and Octave frameworks on a workstation with 128 RAM GB, Intel Xeon Gold 5220R 24 cores @2.20 GHz, and Ubuntu 22.04 LTS operative system. The first architecture for MIMO \(2\times 2\) is trained with \(N_{e}=2000\) epochs and for the \(4\times 4\) two-layer NN, the number of epochs is increased to \(N_{e}=50,\!000\). The symbols used for the training dataset are modulated with 4-QAM. The channel samples follow a Rayleigh distribution, where perfect CSI at the receiver is assumed and the received samples are equalized. For simulations, an SNR level of 3 dB is selected. Figure 2 shows the NMSE loss curves obtained during the training phase for the MIMO configurations \(2\times 2\) and \(4\times 4\). In both cases, the training and test subsets present a close decay among epochs. Since there is no huge gap between the train and test datasets' NMSE curves, overfitting is not present among all models. It can be observed that OH labeling curves have the best BER performance since NMSE decays faster than the other approaches. The DSE strategy model shows the worst performance. For the \(4\times 4\) MIMO configuration, the NMSE cannot be reduced as in the \(2\times 2\) configuration between epochs. In the last \begin{table}
\begin{tabular}{c c c} \hline \hline
**MIMO** & **Hidden** & **Number of** \\
**Configuration** & **Layers** & **Neurons** \\ \hline \(2\times 2:N_{t}=2\), \(N_{r}=2\) & 1 & 100 \\ \(4\times 4:N_{t}=4\), \(N_{r}=4\) & 2 & 1000 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: MIMO setup for the conducted experiments. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Symbol** & **Bit Label** \\  & **Transmitted** & **Mapping** \\ \(\mathbf{a_{1}}\) & \(\mathbf{a_{2}}\) & **Mapping** \\ \hline \(s_{1}\) & \(s_{1}\) & \(1\,0\,0\,0\,1\,0\,0\,0\) \\ \(s_{1}\) & \(s_{2}\) & \(1\,0\,0\,0\,0\,1\,0\,0\) \\ \(s_{1}\) & \  
training epochs, the NMSE curve presents oscillations rather than decay. The OHA strategy for labeling in the MIMO DL detector is an intermediate option for both cases. Figure 3 shows a comparison of the BER performance for the \(2\times 2\) MIMO DL schemes. The OH encoding scheme presents the closest performance to the optimal ML detector at every level of SNR. The OHA shows performance with 0.5 dB of distance compared to the optimal ML detector. Finally, the DSE shows a distance of almost 2 dB compared with the reference scheme for a \(\text{BER}=10^{-4}\). Figure 4 shows the BER performance of the systems for the \(4\times 4\) MIMO configuration. Since the number of antennas increases the dimensionality, the number of neurons and layers also increases, compared to the MIMO \(2\times 2\) configuration. The behavior of the BER performance curves is similar to the \(2\times 2\) configuration. The OH encoding presents the closest distance to the optimal ML detector, with 0.5 dB approximately. The next closest BER curve is the OHA, which now presents a gap of almost 1 dB compared to the ML detector. Finally, the DSE scheme presents the furthest curve to ML performance, with a difference of almost 2 dB at \(\text{BER}=10^{-4}\).