## 5 Numerical Results  
In this section, the spectral efficiency (SE), PAPR, and BER performance are analyzed with various CRs via computer simulations. We use the LS-MU-MIMO-OFDM system with \(N_{t}=400\), \(U=40\). Figure 6 shows the SE performance in terms of the SNR for various CRs, \(\
u\). For Figure 6, we use the equation below:  
\[R\approx\ \ \varepsilon\cdot\sum\limits_{k=1}^{K}E\left[\log_{2}\left(1+\gamma _{k}\right)\right]\, \tag{28}\]  
where \(\varepsilon=\left(\frac{T_{sl}-T_{p}}{T_{sl}}\right)\cdot\left(\frac{T_{s}}{T_ {s}}\right)\) is the scaling factor for the pilot overhead and guard interval [1]. As witnessed, a typical SINR of MF precoded LS-MIMO is around less than 10 dB, thus QPSK modulation is used. Even though MF precoded LS-MIMO has worse BER, it can achieve very high SE due to the multi-user characteristics. Forty UEs can receive the signal from 400 antennas coincidently. Thus, the SE per UE should be divided by 40 from Figure 6. When we use the clipping ratios, which are  
Figure 5: The effective SINR versus SNR (dB), when Iter = 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Iter = 2** & **Iter = 3** & **Iter = 4** & **Iter = 5** \\ \hline \(\eta\) & 1.5 & 2 & 2.3 & 2.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Adjustable factor, \(\eta\). in the ellipse \(\sharp 1\), there is little degradation in the SE performance. As shown in Figure 2 of the previous subsection, choosing \(\
u\) higher than 6 dB means SCR is much higher than 20 dB; thus, in this case, there is almost no performance degradation. The curves in the ellipse \(\sharp 2\) accompany a little bit of the SE performance degradation. However, it can definitely improve the PAPR performance. In particular, the case of \(\
u=5\) dB is included for both groups (ellipse \(\sharp 1\) and \(\sharp 2\)), and this case can be a very good alternative to improve the PAPR with little loss in the SE. The curves in the ellipse \(\sharp 3\) may not be the region of interest. Even if they can improve PAPR significantly, the SE performance degradation is quite severe, and this cannot be compensated by increasing the effective transmit power with a large number of antennas. When \(\
u=3\) dB, from Figure 2, the SCR becomes 10 dB, and it means that the clipping distortion is already almost the same level as the IUI. What we would like to say here is that there is a systematic logic in choosing the appropriate \(\
u\) (dB) in the proposed scheme. Figure 7 shows the BER performance based on various CR. Note that MF precoding with LS-MIMO is effective in a low SNR region. When we use the clipping ratios in the ellipse \(\sharp 1\), there is little BER performance degradation. As we can see from Figure 2 of the previous subsection, choosing \(\
u\) higher than 6 dB means SCR is higher than 20 dB. Thus, it obviously shows almost no performance degradation. The curves in the ellipse \(\sharp 2\) accompany a little degradation in the BER performance. However, it can definitely improve the PAPR performance. In particular, \(\
u=5\) dB is included in both groups (ellipse \(\sharp 1\) and \(\sharp 2\)), and it can be a very good alternative to improve the PAPR with little loss in the BER. The curves in the ellipse \(\sharp 3\) are not the region of interest. Even if they can improve PAPR significantly, the BER performance degradation is quite severe, and cannot be compensated by increasing the effective transmit power with a large number of antennas. When \(\
u=3\) dB, from Figure 2, the SCR becomes 10 dB, which means that the clipping distortion is already almost on the same level with the IUI. Thus, the logic of operation using the BER criterion is the same as using the SE criterion. Figure 6: SE performance (\(N_{t}=400\), U = 40) based on various CR, \(\
u\). The ellipse \(\sharp 1\) includes \(\
u=5,6,7,\infty\), the ellipse \(\sharp 2\) includes \(\
u=3,4,5\), the ellipse \(\sharp 3\) includes \(\
u=0,1,2\). Figure 8 shows PAPR performance for various \(\
u\).