# Performance Analysis of Rate Splitting in Massive MIMO Systems with Low Resolution ADCs/DACs
## 5 Simulation Results  
In this section, we present numerical results to evaluate the SE/EE performance of the massive MIMO system. All numerical results are obtained using MATLAB. Unless otherwise stated, we set the following parameters \(M=100\) and \(K=2\), respectively. Furthermore, we assume a coherence interval of \(\tau=200\) symbols with \(\tau_{p}=K\) for channel estimation. The pilot power is set as \(P_{p}=2\) dB. The transmit SNR is defined as SNR \(\triangleq P\). We assume that the users are randomly distributed in a cell of dimensions 500 m \(\times\) 500 m. The users are at least 35 m from the BS. The large scale fading coefficient is modeled as (2) and a standard deviation of 7 dB is set for \(z_{k}\). In all simulation results, the RS scheme is compared to the non-RS scheme, which is RZF linear precoding [12; 13; 14]. In Figure 4, we investigate the performance of the power allocation solution obtained in (26). We plot the power allocation factor, \(t\), against the bit resolution for different number of users (i.e., \(K=2\) and \(K=5\)). When the QN is very high i.e., \(b_{A}(b_{D})=1\), the RS scheme achieves the same SE as that of the non-RS scheme since all power is allocated to the private messages. As the bit resolution increases, the fraction of power allocated to the common message (i.e., 1-f) is increased. Hence, the rate gain of the RS scheme over the non-RS scheme can be realized. In addition, when the number of users increases from \(  
to \(K=5\), the SE increases for both schemes due to the spatial multiplexing gains. For the RS scheme, increasing the number of users decreases the power allocation to the common message in the high-SNR region. The rate gain reduces but the RS scheme still performs better than the non-RS scheme. Figure 4: Power Allocation versus bit resolution (\(M=100\), \(P_{p}=2\) dB, and \(\tau=200\)). Figure 5: SE versus transmit SNR for different number of users (**a**) Comparison of RS and non-RS schemes (**b**) Comparison of common and private messages (\(M=100\), \(\tau=200\), \(P_{p}=2\) dB, and \(b_{A}(b_{D})=3\)). Figure 6 depicts the SE versus the transmit SNR. For Figure 5(a), we fix the resolution of the DACs and vary the resolution of the ADCs. The effect of the low-resolution ADCs is captured only in the quality of channel estimates. This is reflected as the factor \(\alpha_{A}\) in (8). For the RS and non-RS schemes, the SE increases for increasing ADC quantization bits. The proposed RS scheme overcomes the effect of the multiuser interference and the SE increases at high-SNR. This is opposite to the non-RS scheme where the SE saturates at high-SNR due to multiuser interference. Furthermore, we observe the rate gain of the RS scheme over that of the non-RS scheme. For \(b_{A}=2\) and at 25 dB, the RS scheme shows a gain of about 2.5 bps/Hz (34% increase) over the non-RS scheme. For Figure 5(b), we fix the resolution of the ADCs and vary the resolution of the DACs. The effect of the low-resolution DACs is captured in the factor \(\alpha_{D}\) and the QN term \(\mathbf{h}_{k}^{H}\mathbf{R}_{\mathbf{n}0}\mathbf{h}_{k}\) in (16) and (17), respectively. For the same level of quantization, the performance of RS scheme with low-resolution DACs only (i.e., 2 bit to 1 bit) degrades faster and saturate at high SNR due to the combined effect of multiuser interference and the QN term. Therefore, low-resolution DACs have a more dominant effect on the SE performance than that of low-resolution ADCs. Next, Figure 7 illustrates the SE versus the transmit SNR for different bit resolution of ADCs/DACs. We assume equal ADC/DAC quantization bits in the evaluation. Whenthe QN is high (i.e., \(b_{A}(b_{D})=1\)), the RS scheme is unable to overcome the QN and multiuser interference of the low-resolution ADCs/DACs. Hence, the rate gain is negligible. As \(b_{A}(b_{D})\) increases, the RS scheme can still outperform the non-RS scheme under the effects of QN. The RS scheme with quantization achieves bigger SE compared to that of the conventional non-RS scheme with no quantization.