# SNR-Based Receiver-Type Decision Using Deep Learning for Multiple-Input Multiple-Output Detection
## 4 Simulation Results  
In this section, we provide simulation results for a \(2\times 2\) and \(4\times 4\) MIMO system with \(4-\)QAM and \(16-\)QAM to evaluate the performance of the proposed receiver. The system parameters and DNN hyperparameters are summarized in Tables 1 and 2, respectively. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Number of transmit antennas, \(N_{T}\) & 2, 4 \\ \hline Number of receiver antennas, \(N_{R}\) & 2, 4 \\ \hline Modulation scheme & QAM \\ \hline Modulation order, \(M\) & 4, 16 \\ \hline Energy per symbol to noise spectral density ratio, & \\ \(\frac{E_{s}}{N_{0}}=\rho\) & 0, 4, 8, 12, 16, 20 dB \\ \hline \multirow{4}{*}{Threshold for receiver-type decision, \(\eta\)} & 0.8146, 0.6893, 0.4802, 0.2622, 0.1231, 0.0538 for \(2\times 2\), \(4-\)QAM \\  & 0.9600, 0.9444, 0.9133, 0.8243, 0.6249, 0.3883 for \(2\times 2\), \(16-\)QAM \\ \cline{1-1}  & 0.9339, 0.9209, 0.8864, 0.8196, 0.7324, 0.6424 for \(4\times 4\), \(4-\)QAM \\ \cline{1-1}  & 0.9370, 0.9573, 0.9914, 1.0970, 1.6050, 3.4955 for \(4\times 4\), \(16-\)QAM \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters for simulations. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Number of nodes of input, output layers, \(d_{0},d_{L+1}\) & 10, 2 for \(2\times 2\) \\  & 36, 4 for \(4\times 4\) \\ \hline Number of nodes of hidden layers, \(\{d_{1},\cdots,d_{L}\}\) & \(\{1024,1024,1024\}\) \\ \hline Learning rate & \(3\times 10^{-5}\) \\ \hline Number of epochs & 200 \\ \hline Batch size & 16 \\ \hline Optimizer & Adam \\ \hline \hline \end{tabular}
\end{table} 
Table 2: DNN hyperparameters for simulations. Figures 7-10 depict the probabilities of \(\hat{f}_{R}=1\), which means that the ZF receiver is used in the inference phase. It is shown that the probability in the low SNR region is much lower than that in the high SNR region. This implies that noise enhancement is critical, requiring more frequent use of the ML receiver in the low SNR region. In the high SNR region, on the other hand, increased use of the ZF receiver is feasible. Therefore, we can conclude that the proposed receiver accurately reflects the reduced effect of noise enhancement in the high SNR region, allowing for the correct selection of the receiver type. Comparing the \(2\times 2\) and \(4\times 4\) MIMO systems, we can notice that the probabilities of \(\hat{f}_{R}=1\) for the \(2\times 2\) MIMO system are higher than those of the \(4\times 4\) MIMO system. This is because the probability of the poorly conditioned channel of the \(4\times 4\) MIMO channel is relatively higher than that of the \(2\times 2\) MIMO channel. Taking into account that as the number of antennas increases, the ratio of the largest to the smallest singular values of the MIMO channel is also expected to increase, this result is reasonable. Figure 5: SER performances of \(4\times 4\) MIMO system with \(4-\)QAM. Figure 6: SER performances of \(4\times 4\) MIMO system with \(16-\)QAM. Figure 8: The probabilities of \(f_{R}=1\) in the inference phase for a \(2\times 2\) MIMO system with \(16-\)QAM. Figure 7: The probabilities of \(f_{R}=1\) in the inference phase for a \(2\times 2\) MIMO system with \(4-\)QAM. Figure 9: The probabilities of \(f_{R}=1\) in the inference phase for a \(4\times 4\) MIMO system with \(4-\)QAM. In Figures 11-14, for the metric of the number of candidate searches in the demodulation process of the proposed receiver, we define \(\zeta\) as follows:  
\[\zeta=\frac{C_{\text{proposed}}}{C_{ML}}. \tag{26}\]  
As already discussed, it is shown that \(\zeta\) decreases when the SNR increases. Moreover, compared to the ML receiver, the proposed receiver requires approximately 35%, 60%, 93%, and 75% computational complexity to achieve nearly identical error performance to the optimal ML receiver at 20 dB SNR, for the \(2\times 2\) and \(4\times 4\) MIMO systems with \(4-\)QAM and \(16-\)QAM, respectively.