# PAPR Reduction in UFMC for 5G Cellular Systems
## 4 Numerical Results and Discussions
### Discussions  
So far in the previous subsections, we show the improvements that have been added to the UFMC system, owing to the proposed Dcomp-SLM. This includes a reduction in PAPR while maintaining the BER and OOB emission performance. This enhances the potential utilization of UFMC systems in 5G communication networks. In addition, in this section, comparisons between the proposed Dcomp-SLM, E-SLM [20], P-SLM [37], FTS [34], and LC-PTS [35] approaches are conducted based on the BER, CCDF-PAPR, OOB, and computational complexity. The various parameters that are used in the simulations are summarized in Table 2. In this table and for fair comparisons, we consider those methods that can be classified within the same family of the probabilistic techniques. Consequently, the table clearly shows that the Dcomp-SLM approach outperforms other compared approaches in terms of PAPR reduction ability, BER, and PSD. For instance, at \(10^{-3}\) CCDF-PAPR, the Dcomp-SLM based UFMC system can provide PAPR of 8.2 dB, whereas the P-SLM, E-SLM, and LC-PTS approaches provide PAPR of approximately 8.4 dB, 8.6 dB, and 8.8 dB, respectively. Besides, the proposed Dcomp-SLM can achieve this PAPR reduction with a remarkable lower complexity. Precisely, the Dcomp-SLM is implemented with \(U=6\) phase vectors, while the P-SLM and E-SLM methods were implemented with \(U=16\) phase vectors. Additionally, the LC-PTS technique introduces an extra sub-division parameter \(K\) for the \(V\) IFFT copies which is equivalent to \(VK\) phase vectors, hence more complexity. On the other side, though the PTS approach in [34] provides 7 dB PAPR reduction, owing to the transmitted frame of length \(N=256\) subcarriers and phase vectors of \(U=16\), it requires 18.3 dB SNR to reach \(10^{-3}\) BER which is 4.3 dB higher than our proposed approach (i.e., \(E_{b}/N_{0}=14\) dB). Finally, as mentioned before, in this paper we consider the main source of the computational complexity, which is owing to the operation of the IFFT system. Accordingly, the fundamental complexity of the IDFT was considered as a reference for comparisons between the different techniques. Based on that, the proposed Dcomp-SLM, P-SLM, and E-SLM schemes were implemented, almost, at the same computational complexity as conventional SLM techniques. While the method of LC-PTS introduced an extra complexity over the others because of the sub-division factor \(K\). However, the PTS approach of [34] shows the lowest complexity when comparing to all other schemes, which operates the IFFT system at complexity of \((B+U+1)\frac{N}{2}\log_{2}N\) multiplications and \((B+U+1)N\log_{2}N\) additions. Figure 9: The power spectral density (PSD) of OFDM, UFMC, and the proposed Dcomp-SLM UFMC. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & & & & & & \\ \cline{3-8}  & **Technique [Ref. ]** & **Simulation Parameters** & **PARR (dB)** & **SNR (dB)** & **PSD (dB)** & **Computational Complexity** \\  & & **CCPD = 10\({}^{-3}\)** & **BER = 10\({}^{-3}\)** & **at 1 st SLL (OOB)** & **Multiplication** & **Addition** \\ \hline \multirow{4}{*}{SLM} & \multirow{4}{*}{Dcomp-SLM (proposed)} & \(U=6\), \(N=512\), & \multirow{4}{*}{8.2} & \multirow{4}{*}{14 for AWCN and 30 for Rayleigh channels} & \multirow{4}{*}{-95} & \(\frac{BN(U+1)}{2}\text{log}_{2}N\) & \(BN(U+1)\text{log}_{2}N\) \\  & & & 16-QAM & & & & \\ \cline{2-8}  & \multirow{2}{*}{P-SLM [20]} & \(U=16\), \(N=512\), & \multirow{2}{*}{8.4} & \multirow{2}{*}{min. BER = 7\(\times 10^{-2}\) for Rayleigh channel} & \multirow{2}{*}{-93} & \(\frac{BN(U+1)}{2}\text{log}_{2}N\) & \(BN(U\text{log}_{2}N\) \\  & & & 16-QAM & & & & \\ \cline{2-8}  & \multirow{2}{*}{E-SLM [57]} & \(U=16\), \(N=512\), & \multirow{2}{*}{8.6} & \multirow{2}{*}{min.