# An Improved GreenOFDM Scheme for PAPR Reduction
## 3 From SLM-OFDM to GreenOFDM
Compared to the initial well known SLM technique, the improved GreenOFDM technique provides then definitively a drastic complexity reduction while keeping the same idea, requiring only the square-root of the number of IFFTs for a same PAPR reduction performance. Finally, approximate formula (mainly accurate for small constellation size such as QPSK or for high values of \(N\)) are provided to predict the PAPR performance of the proposed method as a function of the number of sub-carriers and the number of candidates, or alternatively to determine the number of required IFFTs for a given PAPR performance. This prediction is very useful not only to anticipate the complexity of the technique, but also to allow for the implementation of further complexity reduction methods dedicated to GreenOFDM proposed previously [28; 31] as has been discussed and shown in the paper. Further studies are needed to propose efficient blind methods adapted to the presented technique to recover the data on the receiver side without the need of implicit side-information. \[\text{CCDF}_{\text{SLM}}(\gamma)\approx\left(1-\left(1-\exp\left\{-\gamma \right\}\right)^{2.8N}\right)^{C_{\text{SLM}}} \tag{4}\]9 The Computational Complexity Reduction Factor (CCRF) between the GreenOFDM and SLM-OFDM as presented in [28] **(left-side)** and the CCRF between the proposed method and the conventional SLM-OFDM (right-side) with complexity reduction as a function of \(\gamma_{P_{i}}\)[dB] and \(N\). **Author Contributions:** [PERSON] and [PERSON] conceived the presented idea. [PERSON] performed the computer simulations, and wrote the main part of the paper helped by [PERSON] All the authors verified the methods, discussed the results, contributed and approved a first short version of the manuscript, accessible online since April 2020 [[[https://hal.archives-ouvertes.fr/hal-02548839/document](https://hal.archives-ouvertes.fr/hal-02548839/document)]([https://hal.archives-ouvertes.fr/hal-02548839/document](https://hal.archives-ouvertes.fr/hal-02548839/document))]. The 3 authors [PERSON], [PERSON], and [PERSON]-[PERSON] performed the extended final version of the manuscript. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Acknowledgments:** The authors would wish to acknowledge [PERSON] for the helpful comments and remarks on this work. **Conflicts of Interest:** The authors declare no conflict of interest. ## Abbreviations

The following abbreviations are used in this manuscript: \begin{tabular}{l l} CCDF & Complementary Cumulative Distribution Function \\ CCRF & Computational Complexity Reduction Factor \\ IAPR & Instantaneous-to-Average Power Ratio \\ IFFT & Inverse Fast Fourier Transform \\ OFDM & Orthogonal Frequency Division Multiplexing \\ PA & Power Amplifier \\ PAPR & Peak-to-Average Power Ratio \\ SLM & SeLected Mapping \\ \end{tabular} 

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