# A Deep Learning Approach for MIMO-NOMA Downlink Signal Detection
## 4 Simulation and Analyses
The allocation of the transmit power of the UEs at the BS is a crucial component of the conventional NOMA scheme, and has a substantial impact on the NOMA throughput with [PERSON]'s information theory. Several studies have provided optimal or suboptimal allocation methods. According to (5), the sum throughput of two UEs can be denoted as:  
\[R_{sum}(\alpha)=\log_{2}\frac{\left(1+\left(1-\alpha\right)\rho\left|h_{2} \right|^{2}\right)\left(1+\rho\left|h_{1}\right|^{2}\right)}{1+\left(1-\alpha \right)\rho\left|h_{1}\right|^{2}}, \tag{34}\]  
where \(\rho\) is the transmit SNR. \(h_{i}(i=1,2)\) is the channel gain, \(h_{1}<h_{2}\). The throughput can be shown to be a monotonically decreasing function of \(\alpha\) for \(\frac{dR_{sum}}{da}<0\), where \(\alpha\in[0,1]\). Figure 12 shows the throughput of the NOMA system with power allocation factor fixed at 0.6, 0.7, 0.8, and 0.9. The throughput increased as the transmit SNR increased. Moreover, the larger the power allocation factor was, the smaller the throughput. Usually, the throughput of different UEs should satisfy the quality of service (QoS) requirements, or the optimal power should be allocated according to the feedback of the channel state. Here, we considered the performance of the proposed methods from the perspective of reliability. Figure 13 shows the SER performance in MIMO-NOMA signal detection for different power allocation factors with BPSK modulation. The proposed DL-based methods achieved good SER performance compared with the SIC receiver in all cases of power allocation factors. Furthermore, a power allocation factor of 0.8 appeared to be closest to the optimal solution in terms of the minimum symbol error probability. Here, we considered some specific fixed power allocation factors on MIMO-NOMA signal detection. The optimal power allocation factors to minimize the SER performance and sum throughput for DL methods in cases of multiple users and clusters can be considered in our follow-up study. Figure 12: NOMA throughput with different \(\alpha\) values. The process of channel estimation and detection was finished at the training stage. By introducing the error into the channel at the testing stage, we explored how the proposed DL approach behaved when the estimated CSI deviated from the actual situation. The channel error model can be denoted as:  
\[\mathbf{H}=\mathbf{\hat{H}}+\beta\mathbf{\Omega}, \tag{35}\]  
where \(\mathbf{H}\) is the actual channel matrix impaired by error. \(\mathbf{\hat{H}}\) and \(\mathbf{\Omega}\) are the original Rayleigh channel matrix and the channel error matrix, respectively, and they are i.i.d. \(\beta\) is the error factor. Figure 14 shows the impact of channel estimation error on the DL-based approach. It can be seen that the SER deteriorated gradually with the increase of \(\beta\) from 0 to 0.1. Compared with the SIC method with perfect CSI, the DL approach still showed superiority when \(\beta\) was less than 0.08. This result explains that the performance suffered losses when deviations appeared between the estimated and actual CSI, though the performance of the DL-based approach could keep its predominance within a specified tolerance range. Figure 13: SER performance with different power allocation factors. Restricted by the performance of the CPU/GPU/RAM, the convergence of deep learning algorithms is often time consuming when addressing a large amount of data. Mini-batch gradient descent is a good way to shorten the training run-time to obtain the results efficiently. Here, different mini-batch sizes in the MIMO-NOMA-DL detection method were studied to provide a reference for related research. Figure 15 shows the loss values for three mini-batch sizes. The loss value for a mini-batch size of 1024 reached 0.32 at approximately 360 epochs. A mini-batch size of 1024 resulted in the fastest convergence but the worst loss value. By contrast, a mini-batch size of 102,400 produced the best loss performance but the longest run-time: the loss value tended towards stability at 0.015 at approximately 8000 epochs.