## 3 Performance Analysis of the PSI Technique
### Analysing the Error Vector Magnitude (EVM)
This reduction is same as the reduction for \(K=4096\), however the point is that by doubling the value of \(K\), the length of IFFT is doubled, and it is directly related to number of carrier aggregations or in other words, the bandwidth in 5G signal. This consistent performance makes PSI a reliable and adaptive technique for high bandwidth applications as seen in LTE-Advanced, and 5G signals. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Length of the IFFT (K)** & **Scenario 1** & **Scenario 2** & **Scenario 3** & **Scenario 4** & **Scenario 5** & **Scenario 6** \\ \hline
512 & 0.1652\% & 0.1652\% & 0.2035\% & **0.2405**\% & 0.2192\% & 0.1857\% \\
1024 & 0.0756\% & 0.0756\% & 0.0932\% & 0.1143\% & 0.1053\% & 0.0840\% \\
2048 & 0.0345\% & 0.0345\% & 0.0435\% & 0.0542\% & 0.0486\% & 0.0381\% \\
4096 & 0.0142\% & 0.0169\% & 0.0189\% & 0.0237\% & 0.0162\% & 0.0156\% \\
8192 & 0.0064\% & 0.0083\% & 0.0077\% & 0.0105\% & 0.0079\% & **0.0070\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Maximum measured error vector magnitude (EVM) (\(EVM_{max}\)) for PSI algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Length of IFFT (K)** & **Original Signal without CFR** & **After PSI** & **Amount of Reduction (dB)** \\ \hline
1024 & 12 dB & 7.3 dB & 4.7 dB \\
2048 & 12.4 dB & 7.7 dB & 4.7 dB \\
4096 & 12.7 dB & 8.3 dB & 4.4 dB \\
8192 & 12.9 dB & 8.5 dB & 4.4 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 3: PAPR reduction performance for different length of IFFT at 0.0001 CCDF. An analysis is provided in order to demonstrate value of \(NS\) can effect the PAPR reduction performance. It is seen in Figure 9a that increasing the value of \(NS\) does not necessarily improve the PAPR reduction performance; here, 16 was the value used for \(NS\). Figure 9b shows how PAPR reduction performance is improved by increasing the value of \(RP\). However, it should be noted that the computational complexity is also affected by incremented \(RP\). It was observed that choosing \(RP=10\) is sufficient to satisfy the rule of thumb minimum 4 dB PAPR reduction performance. When \(RP=10\), it means that 10 iterations for the loop presented in Figure 11, are performed to search for peaks and shrink them. This is by means of employing a search for maximum power points. It should be noted that if threshold enforcement is employed instead of search for maximum point, the loop is replaced with iterative shrinking process, which in fact has same effect in terms of computational complexity. It is in Table 2 that changing \(NS\), \(RP\), and \(SR\) has a marginal effect on EVM. As observed from results in Figure 10, the SR value plays an important role for PAPR reduction performance. Therefore, furthermore in Section 3.4, the mathematical relationship between PAPR reduction, and the value of SR is modeled as seen in Figure 14.  
It can be observed from the plot, and measurements, that when SR is selected about 0.6 and 0.7, the PAPR reduction achieves its optimum performance, which is 3.45 dB for this particular scenario. This simplifies the implementation of PSI as the \(SR_{rev. }\) has also same value of 0.7; therefore, it can be  
Figure 8: **(a)** Signal power before and after PSI technique [24]. **(b)** CCDF probability of PAPR before and after PSI technique for \(K=1024\), to \(K=8192\)[24]. Figure 9: **(a)** PAPR reduction performance variation with \(NS\)[24]; **(b)** PAPR reduction performance variation with \(RP\)[24]. excluded. It should be noted that this analysis was performed in CCDF of \(10^{-1}\), and for full CCDF analysis, the reduction at CCDF of \(10^{-4}\) was considered, which can be seen in Figure 8b.