# Performance Analysis of Rate Splitting in Massive MIMO Systems with Low Resolution ADCs/DACs
## 5 Simulation Results
For example, the RS scheme for \(b_{A}(b_{D})=3\) outperforms the non-RS scheme with \(b_{A}(b_{D})=\infty\) by 22% in terms of the SE. In Figure 8, we show a 3D surface plot of the SE as a function of ADC and DAC quantization bits. We consider only the asymptotic results and compare the SE performance of the RS and non-RS schemes. For both schemes, the lowest SE is achieved when \(b_{A}(b_{D})=1\). In this case, the RS scheme offers no gain over the non-RS scheme. As the quantization bits of the ADCs and DACs increase, the rate gain of the RS scheme over the non-RS scheme becomes evident. The highest SE is achieved for high-resolution ADCs and DACs i.e., \(b_{A}(b_{D})=10\). From the figure, the low-resolution DACs play a more dominant role in determining the SE performance compared to that of the low-resolution ADCs. This is because the rate gain decreases more with the low-resolution DACs than that of the low-resolution ADCs. Hence, it is preferable to equip the massive MIMO system with low-resolution ADCs than low resolution DACs. Figure 8: 3D plot of SE versus ADC and DAC quantization bits (\(M=100\), \(K=2\), \(P_{p}=2\) dB, \(\text{SNR}=30\) dB, and \(\tau=200\)). Figure 7: SE versus transmit SNR for different ADCs/DACs (\(M=100\), \(K=2\), \(P_{p}=2\) dB, and \(\tau=200\)). Figure 9 plots the SE against the number of BS antennas. We investigate the impact of the BS antennas on the SE performance for different quantization bits. From the figure, the SE performance is improved for more BS antennas for both schemes. For higher quantization bits, the RS scheme shows better performance than that of the non-RS scheme and can achieve the same SE with a lower number of BS antennas. Compared to that of the non-RS scheme, the number of antennas needed to achieve an SE of \(7\)\(\mathrm{bps}/\mathrm{Hz}\) in the RS scheme reduces by about \(11\%\) when \(b_{A}(b_{D})=2\). For \(b_{A}(b_{D})=3\), number of antennas decreases by about \(27\%\). Compared to that of the non-RS scheme, the RS scheme can achieve the same SE with fewer quantization levels. From the figure, the RS scheme can achieve an SE of \(8\)\(\mathrm{bps}/\mathrm{Hz}\) for \(b_{A}(b_{D})=3\) and \(M=80\). On the other hand, the non-RS scheme achieves the same SE for a higher quantization level with an even larger number of antennas, i.e., \(b_{A}(b_{D})=\infty\) and \(M=95\). Therefore, the QN effect can be compensated by the proposed RS scheme instead of deploying more antennas. Figure 10 shows the SE performance versus the number of quantization bits. As shown in the figure, the RS scheme performs better than the non-RS scheme as the bit resolution of the ADCs/DACs increases. Furthermore, as the number of users increases, the power allocated to the common message decreases and the rate gain of the RS scheme is degraded. Therefore, the bit resolution of the ADCs/DACs needed for the RS scheme to outperform the non-RS scheme increases. For \(K=2\), the 2 bit resolution ADCs/DACs are required. This increases to 3 bits when \(K=5\) for the RS scheme to outperform the non-RS scheme. In Figure 11, we plot the SINR of the private message against the regularization parameter for different quantization bits. We check the accuracy of the derived optimal regularization parameter, \(\xi_{opt}\), obtained in (30). We observe that the derived solution is accurate since it maximizes the SINR. Moreover, the results confirm the observation in (29) and (30). As the quantization bit decreases, \(\rho\) in (29) decreases and the optimal regularization parameter is increased. For instance, the optimal regularization parameter increases from 0.0607 to 0.101 when the quantization bit decreases from \(b_{A}(b_{D})=3\) to \(b_{A}(b_{D})=2\). Figure 12 shows the SE performance of the RS scheme versus the transmit SNR. We investigate how the optimal regularization parameter, obtained by (30), can increase the SE. In this plot, we consider different level of quantization bits.