# An Improved GreenOFDM Scheme for PAPR Reduction
## 3 From SLM-OFDM to GreenOFDM
These reformulations allow us to predict the PAPR value for a given configuration (\(N\) and \(U\)) and at a given probability. Simulations were carried out for different values of \(N\) and \(U\) and for a fixed probability \(\text{CCDF}(\gamma)=10^{-3}\). Results are summarized in Figure 5 where the performance evolution with \(N\) are depicted at each subplot for a fixed value of \(U\). For all the schemes the marks represent the simulation results and the dashed lines correspond to the approximated expressions in (6) and (5). In all the cases, the value of \(\gamma\)[dB] is always lower for the proposed method as compared to the SLM-OFDM and the GreenOFDM. However, the difference with the original version of GreenOFDM reduces as \(U\) increases. It can also be noted that, for all the tested values of \(N\) and \(U\), the CCDF threshold \(\gamma\) obtained by simulation is very close to the one obtained from Equation (5). It means that the PAPR performance of the proposed technique is also well deterministically linked to the number of candidates and can be accurately predicted by the use of the Equations (4) and (5). Another way to interpret the results is in terms of the reduced number of IFFTs needed to attain the same PAPR performance. To facilitate the observation of this fact, Figure 6 regroups the different configurations with equivalent performance (PAPR threshold for CCDF of \(10^{-3}\)) for a number of subcarriers going from \(N=64\) to \(1024\). As expected, for all \(N\), the proposed method requires the smallest number of IFFTs, keeping always a reduction factor of 2 with respect to the initial GreenOFDM method. For example, to ensure that the PAPR stays under 8 dB (with a probability 1-\(10^{-3}\)), the required number of IFFTs is only 8 for the GreenOFDMv2 method, against \(8\times 2=16\) for the original GreenOFDM and \(8^{2}=64\) for the conventional SLM technique. Even for a large number of 1024 subcarriers, the GreenOFDMv2 technique maintains a quite reasonable complexity of 32 IFFTs contrary to SLM (\(32^{2}=1024\) expected IFFTs). So far we have limited the simulations to \(QPSK\)-modulated subcarriers. To improve this analysis, we have obtained the results depicted in Figure 7 for \(16-QAM\) (left side) and \(64-QAM\) (right side) modulated subcarriers. As it can be seen, with the same number of available

\[\text{CCDF}_{\text{SLM}}(\gamma)\approx\left(1-\left(1-\exp\left\{-\gamma \right\}\right)^{2.8N}\right)^{C_{\text{SLM}}} \tag{4}\]3 The value of \(\gamma\)[dB] to attain \(\text{CCDF}(\gamma)=10^{-3}\) for different values of \(U\) and \(N\) for OFDM, SLM-OFDM, GreenOFDM and GreenOFDMv2, obtained by simulation (marks) and approximated expressions (dashed lines). PAPR reductions are obtained for all the schemes but with the smallest required number of IFFTs for our proposed method. However, this time, the PAPR values for a CCDF of \(10^{-3}\) are slightly above the analytical expressions (represented by the dashed lines) and that for all the schemes. These discrepancies tends to vanish as \(N\) increases. The drawback that remains, as for all the SLM-based methods, is the need of a Side Information (SI) in order to correctly de-randomize the received data symbols on the receiver-side. \[\text{CCDF}_{\text{SLM}}(\gamma)\approx\left(1-\left(1-\exp\left\{-\gamma \right\}\right)^{2.8N}\right)^{C_{\text{SLM}}} \tag{4}\]4 The value of \(\gamma\)[dB] to attain \(\text{CCDF}(\gamma)=10^{-3}\) for different values of \(U\) and \(N\) for SLM-OFDM, GreenOFDM and GreenOFDMv2 obtained by simulation (marks). Approximated expressions in Equation (5) are also plotted in dashed lines for GreenOFDMv2. \[\text{CCDF}_{\text{SLM}}(\gamma)\approx\left(1-\left(1-\exp\left\{-\gamma \right\}\right)^{2.8N}\right)^{C_{\text{SLM}}} \tag{4}\]5 The value of \(\gamma\)[dB] to attain \(\text{CCDF}(\gamma)=10^{-3}\) for different values of \(U\) and \(N\) for SLM-OFDM, GreenOFDM and GreenOFDMv2 obtained by simulation (marks). Approximated expressions in Equation (5) are also plotted in dashed lines.