## 5 Simulation Results and Discussion
### EE Performance  
Figure 4 shows the EE performance of the different receivers with ADCs of different resolutions for \(K=20,N=30,d_{\text{max}}=100\) and a target \(\text{BER}_{0}=10^{-2}\). It is seen that LR-SIC achieves the highest EE in general. In such a scenario, the numbers of antennas and the UEs are comparable. LR-SIC and MMB-LR-SIC can significantly reduce the transmission power required as can be seen from Figure 2. A large portion of the total power is consumed by the transmitter. The nonlinear detectors can reduce the transmitted power requirement which outweighs the increased signal processing power. As the ADC resolution improves, the EE first improves and then degrades. This is because when the resolution is too low, the transmitted power required is high; while when the resolution becomes higher, the power consumption due to the ADCs is increased. It appears that ADCs of 5 to 7 bits are advantageous. In Figure 5, we increase the number of receiver antennas to \(N=60\), to consider a massive MIMO scenario. Interestingly, it is seen that in such a scenario the linear MMSE detector can be advantageous. This is because the transmission power required for achieving \(\text{BER}_{0}=10^{-2}\) becomes similar for different detectors but nonlinear detectors exhibit higher signal processing complexity, which translates into higher receiver power consumption and lower EE. Also it is noted that low-resolution ADCs are advantageous when the number of antennas is large as compared with high-resolution ADCs. However, it is noticed that the overall EE degrades as compared to Figure 3 when the receiver antenna is increased from \(N=20\) to \(N=60\). Figure 6 shows the EE when the size of the cell is increased to 400 m for the scenario in Figure 4. Compared to Figure 4, the EE degrades due to increase of the transmission power required as the propagation loss increases on average when the cell size is increased. The relative gains provided by  
Figure 3: BER versus the receiver SNR for \(K=20,N=60\). nonlinear LR-SIC receivers are larger in larger cells. This suggests that the nonlinear receivers may be preferred for transmissions over longer distance. Figure 7 demonstrates the circuit power and transmission power with different numbers of quantization bits, where \(d_{\max}=400\) m and \(\text{BER}_{0}=10^{-2}\), \(L_{\text{BS}}=75\) Gflops/W. The circuit power consumption includes \(\text{P}_{\text{ADC}}\). It is seen that when low-resolution ADCs are used, the transmission power dominates the overall power consumption; when the number of bits increases, the circuit power consumptions become more significant. This explains the EE change in Figure 6.  
Figure 8 has the same parameter as Figure 6 except BER\({}_{0}=10^{-3}\). Comparing Figures 6 and 8, nonlinear detectors are capable of supporting higher reliability with a higher energy efficiency, especially the LR-SIC, as compared to the MMSE detector. This is due to the relatively lower transmission power consumption for supporting a better BER. However, the advantages of nonlinear LR-SIC detector over the MMSE detector vanish when the number of BS antennas is increased. This is shown in Figure 9 where \(N=60\) antennas are used. Furthermore, increasing the number of antennas can improve the EE as compared with Figure 8. The above results also suggest that the maximum EE is typically achieved with ADCs of intermediate resolutions, which offers good tradeoff between in the increase of transmission power due to quantization errors and the increase of the power consumptions due to ADCs themselves. Figure 10 shows the EE with \(K=20,N=30,d_{\max}=400\) m, BER\({}_{0}=10^{-2}\) and the computational efficiency is improved to \(L_{\text{BS}}=500\) Gflops/W. Comparing this with Figure 8, the EE is increased and similar trends are observed for the performance of different detectors. Figure 8: Energy efficiency for \(K=20,N=30,d_{\max}=400\) m at \(\text{BER}_{0}=10^{-3}\), \(L_{\text{BS}}=75\) GFlops/W.