## 3 Performance Analysis of the PSI Technique
### Signal Spectrum Leakage  
As important as it is to analyse a PAPR performance, it should be always considered that by modifying the signal, additional distortion is not added. Here the spectra of the signal with and without PSI technique are compared, and any leakage is carefully measured. This indicates how well the signal is behaving with respect to allocated bandwidth frequency. Figure 12a represents the spectrum of an LTE signal with a bandwidth of 20 Mhz, and as it is seen there is a slight different between the processed signal and original signal (indicated by red spectrum and blue spectrum in Figures 12 and 13); however, this amount of leakage is normal due to the process of shrinking, and the smoothing algorithm keeps this slight different within acceptable range, as it does not interfere with adjacent channels. However, it should be noted that in case of 5G signals, considering carrier aggregation of for example 20 aggregation process, this leakage should be further tested. Here, the leakage behaviour, as well as PAPR reduction performance are mathematically modeled in order to have good estimation for signals with high bandwidth, and/or carrier aggregation. The PAPR reduction value is formulated as \(PAPR_{reduction}=-35~{}SR^{4}+53~{}SR^{3}-25~{}SR^{2}+4.7~{}SR+2.9\). Here, a simulation is performed to understand this effect more clearly. The leakage is also measured for variety of values of \(SR\), and it should be noted that in both cases, the re-sampled signal is re-sampled in order to match, The analysis results are presented in Figure 14a,b. As it is observable from Figure 14a, the leakage is reduced by increasing the value of \(SR\). The behaviour is reasonable, as a value of \(SR\) shows the amount of shrinking process. The optimum of value observed from other results (\(SR_{opt}\)) is sufficient in terms of PAPR reduction, EVM performance, and this leakage. Here, an analysis is presented that explains how PSI technique can be equally used for different types of LTE signal, as described in Table 5. A parameter known as number of resource block (NRB) [30] is varied and the spectrum is compared. The NRB indicates how many blocks of \(180 KHz\) is occupied by the signal \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of CFR Technique** & **Number of Required Multiplications** & **Number of Required Bits** \\
**Length of the FFT (\(K=1024\))** & **(\(n_{mult}\))** & **(\(n_{bit}\))** \\ \hline Clipping and Filtering (CF) & \(\geq\)\(10^{6}\) & \(\geq\)\(10^{3}\) \\ Two Step Peak Clipping (TPC) [14] & \(\geq\)\(2\times 10^{6}\) & \(\geq\)\(10^{3}\) \\ DSI-SLM technique [20] & 47810 & 1024 \\ DSI-PTS technique [41] & 67,112,615 & 1024 \\ Conventional SLM(C-SLM) technique [36] & 95,620 & 1024 \\ Peak Shrinking and Interpolation (PSI) & 1440 & 80 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Computational complexity comparison. structure. The spectrum results in Figures 12a and 13a are captured, when the original and also processed signals are both re-sampled with re-sampling factor of two. It can be observed that the leakage caused does not reach the next harmony and it is acceptable. Figures 12b and 14b shows the spectrum results when NRB values of 5, and 15 are employed, and the  
Figure 14: (**a**) Leakage behaviour versus SR. (**b**) PAPR reduction versus SR, and mathematical modelling. Figure 12: (**a**) Signal spectrum before and after PSI technique, when NRB = 100 [24]. (**b**) Signal spectrum before and after PSI technique for LTE when NRB = 6. Figure 13: (**a**) Signal spectrum SR = 0.7, NRB = 25 and re-sampling Factor = 2. (**b**) Signal spectrum when SR = 0.7 and NRB = 25.  
signal is not re-sampled. It should be noted that these tests are performed when \(NS=16\), \(SR=0.9\), and \(RP=10\). Table 5, shows the structure of LTE standard and the PAPR reduction that can be achieved by applying the PSI technique on different settings.