## 4 Interference-Aware Clipping Scheme
### SIR, SCR, and Effective SINR  
In the previous subsection, we showed how to determine \(\
u\) in LS-MU-MIMO-OFDM systems. In this subsection, we show the simulation results of signal-to-interference ratio (SIR) and signal-to-clipping distortion ratio (SCR) to show what level of \(\
u\) is appropriate in usual operating situations. Based on these, we present the SNR versus effective SINR. Figure 1 shows the SIR variation as the number of antennas/users increases. It is obvious that increasing the number of antennas guarantees a low IUI. We use \(N_{t}=10\) K, since it is the minimum required number of TX antennas to show an LS-MIMO channel hardening effect. In this case, the SIR is around 10 dB as shown in Figure 1. Even though this level of IUI is nothing to sneeze at, the LS-MIMO can increase the spectral efficiency significantly by transmitting dozens of streams coincidentally using an excessive amount of antennas. Figure 1: Signal-to-interference ratio as a function of \(N_{t}\) and \(U\). As increasing \(N_{t}\) or reducing \(U\), the signal-to-inference radio becomes higher. Now, let us check the SCR and EVM, which is shown in Figure 2. To measure the EVM, we use the following equation:  
\[EVM=\sqrt{\frac{\sum\limits_{n}{\left|{x_{t}(n)-\hat{x}_{t}(n)}\right|^{2}}}{ \sum\limits_{n}{\left|{x_{t}(n)}\right|^{2}}}}. \tag{27}\]  
If we see the case of Iter = 5 (5 iterations), which is reasonable for a real system, the range of \(\
u\) could be between 3 dB to 5 dB, remembering that the SIR is around 10 dB. Clipping without iteration causes a serious peak-regrowth, and this is not suitable for a real system. When we choose \(\
u\) = 3 dB, the SCR is already close to 10 dB, which is the same level as the SIR, and less than this would cause serious performance degradation. When we choose \(\
u\) = 5 dB, the SCR is around 20 dB, which is 10 dB higher than SIR. Choosing higher than 5 dB is not so meaningful since a lower \(\
u\) gives better EE. In the 3 GPP-LTE-(A) standard, there are EVM requirements for each modulation. Even though the LS-MIMO system would be used beyond an LTE-Advanced system, backward compatibility could be necessary. Since the worst case EVM requirement for 3 GPP-LTE-(A) is 17.5%, \(\
u\) should be higher than 4 dB to satisfy the 3 GPP LTE-(A) requirement. The visualized example of the interference and clipping noise level is shown in Figure 3. Higher clipping ratios result in less clipping distortion. However, using LS-MIMO with MF precoding, there always exists relatively high IUI, thus a relatively low clipping ratio can be successfully applied. In LS-MIMO, the level of interference can be easily detected due to the law of large numbers. As \(N_{t}\) increases, the interference level converges to a certain point. Figure 2: Signal-to-clipping distortion radio (SCR) and error vector magnitude (EVM) as increasing clipping ratio, \(\
u\). The dotted line indicates the case of no iteration, and the solid line indicates the case of Iter = 5. Now, we present an analysis of the effective SINR. Before showing the effective SINR, the clipping distortion noise should be investigated. We proposed a new normalized distortion power model in Equation (15), and we give a comparison of the simulation and analysis to show the validity of the proposed model in Figure 4.  
The red lines indicate the analytical results, and the blue lines indicate the results of simulation. In the case without oversampling, the analytical result exactly matches the results of simulation. However, this case is meaningless in a real situation. As the number of iterations increases, the clipping distortion power also increases. We use the adjustable factors in Table 3 for the analytical results. Table 3 shows the relationship between \(\eta\) and the number of iterations, Iter. Without oversampling, \(\eta=1\) and Equation (15) with this value is well-matched with the simulation result. However, with oversampling, \(\eta>1\), and \(\eta\) increases as the number of iterations increases.