# A Deep Learning Approach for MIMO-NOMA Downlink Signal Detection
## 4 Simulation and Analyses
In the MIMO-NOMA-DL scheme, however, the received signal is sent to the DNN, and labels are chosen only for the UE2 sequence during the training step. Figure 9 shows the SER-SNR curve of the numerical simulation. Taking \(10^{-4}\) as the standard to measure performance gain, we can see that the proposed MIMO-NOMA-DL reached 12.6 dB, whereas the traditional scheme reached 16.2 dB--a \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Operating system & Windows 7 \\ Framework & TensorFlow \\ Programming language & Python 3.6/MATLAB \\ Channel & MIMO channel/AWGN \\ Fading & Rayleigh distribution \\ Number of UEs per cluster & 2 \\ Number of transmit antennas & 4 \\ Number of receive antennas & 4 \\ Modulation & PSK \\ Number of training samples & 409,600 \\ Total transmitted power per antenna & 1 W \\ Power allocation factor & 0.8 \\ Hidden layer & ReLU \\ Output later & Sigmoid \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter settings used in the simulation. ReLU: rectified linear unit. difference of approximately 3.6 dB. Notably, no preprocessing nor postprocessing was performed. Instead of the traditional complex signal processing for channel estimation and signal demodulation, we used powerful deep learning tools to perform accurate signal detection. That is, we used a computer to automatically search for the most rational schemes for channel estimation and signal demodulation to avoid complicated human designs, which is the main reason we achieved performance gains. As indicated previously, the MIMO-NOMA system adopts superposition coding in which signals from different UEs in a cluster are overlaid with the specific proportion of the power. Different modulation types can be used for diverse UE signals. Because power-field NOMA is a type of non-orthogonal technology, interference from other UEs--especially the type of their modulation--is a significant factor in determining the demodulation performance. Here, we simulated several groups of different types of modulation from the most common PSK modulation, and we assessed whether the NOMA-DL system had good performance in these situations. Table 2 shows three groups of simulation parameter settings, including the situation where both UEs had BPSK or quadrature phase shift keying (QPSK) modulation and where one UE used BPSK modulation while the other used QPSK. Considering that decoding the UE2 signal requires the UE1 signal to be decoded first according to the SIC method, we considered only the UE2 signal detection in the DL method due to its higher complexity. Figure 10 shows the modulated MIMO-NOMA signal constellation graph for all three cases. The initial phases of BPSK and QPSK were \(0^{\circ}\) and \(45^{\circ}\), respectively, and there were two UEs in a cluster. The allocation \begin{table}
\begin{tabular}{c c c} \hline \hline
**Modulation Scheme** & **UE1** & **UE2** \\ \hline
1 & BPSK & BPSK \\
2 & BPSK & QPSK \\
3 & QPSK & QPSK \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter settings used in the simulation. Figure 9: Performance comparison of MIMO-NOMA-DL and MIMO-NOMA-SIC. of the transmit signal power affects the Euclidean distance between constellation points and the error probability. Here, we were not concerned with the power distribution, and set the power allocation factor to 0.8 for simplicity. Figure 11 depicts the detection performance in these three cases. Clearly, the MIMO-NOMA signal detection based on the DL system had good performance. Besides case 1 mentioned above, nearly 3.5 dB performance gain was achieved in case 2, and the gain was 1 dB in case 3. These results indicate that both the characteristics of the wireless MIMO channel with Rayleigh fading and the signal demodulation with NOMA could be learned through the DNN. Figure 11: Performance comparison of MIMO-NOMA-DL and MIMO-NOMA-SIC. Figure 10: Constellation of UE signal superposition coding: (**a**) BPSK and BPSK, (**b**) BPSK and QPSK, and (**c**) QPSK and QPSK.