# A Hybrid PAPR Reduction Scheme in OFDM-IM Using Phase Rotation Factors and Dither Signals on Partial Sub-Carriers

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## Abstract

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## 1. Introduction

- This paper proposes a novel PAPR reduction method based on dither signals. The proposed method injects optimized constant amplitude signals on partial inactive sub-carriers. Comparisons show that utilizing partial idle sub-carriers can achieve better error performance than that of the conventional dither signal-based schemes.
- In order to solve the PAPR reduction performance degradation caused by the insufficient use of idle sub-carriers, the proposed PAPR reduction scheme introduces phase rotation operations. Simulation results show that compared with the conventional works, the proposed hybrid scheme can achieve better performance in terms of both PAPR and BER.
- This paper proposes an energy-based detection method in order to recover the transmitted signal. The proposed detection method is able to correctly detect the index of the transmitted phased rotation factor. Simulation results show that the decoding performance, which utilizes the proposed detection method is very close to the case where the side information is correctly received. Therefore, without sending side information, the spectral efficiency of OFDM-IM is higher than that of the previous works.

## 2. Preliminary Knowledge

#### 2.1. OFDM with Index Modulation

#### 2.2. PAPR

#### 2.3. The Conventional PAPR Reduction with Dither Signals

## 3. The Hybrid PAPR Reduction Scheme with Phase Rotation Factors and Dither Signals on Partial Subcarriers

#### 3.1. Interference Analysis

#### 3.2. The PAPR Reduction Scheme Utilizing Partial Idle Sub-Carriers Based on CSI

#### 3.3. The Proposed Hybrid PAPR Reduction Scheme

#### 3.4. Energy Efficiency of the Proposed Schemes

## 4. Simulation Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Transmitter structure of the scheme in [17].

**Figure 5.**A BER performance comparison among the original OFDM-IM, S.1 scheme, and the $Dither$ scheme [17].

**Figure 9.**The CCDF performance comparison among the proposed scheme, the SLM scheme, the PTS scheme, the $Dither$ scheme [17], the S.1 scheme, and the original OFDM-IM signal.

**Figure 10.**The BER performance comparison among the proposed schemes, the $Dither$ scheme [17], and the original OFDM-IM signal.

**Table 1.**A look-up table example between ${\mathbf{b}}_{u}$ and ${\chi}_{u}$ for $V=4$, $U=4$, and $\beta =0.5$.

${\mathbf{b}}_{1}$ | ${\chi}_{1}$ | $\{{I}_{1}^{c},{I}_{3}^{c}\}$ |

${\mathbf{b}}_{2}$ | ${\chi}_{2}$ | $\{{I}_{2}^{c},{I}_{4}^{c}\}$ |

${\mathbf{b}}_{3}$ | ${\chi}_{3}$ | $\{{I}_{1}^{c},{I}_{4}^{c}\}$ |

${\mathbf{b}}_{4}$ | ${\chi}_{4}$ | $\{{I}_{2}^{c},{I}_{3}^{c}\}$ |

${\mathbf{b}}_{1}=[1,1,1,1]$ | $\{{I}_{1}^{c},{I}_{3}^{c}\}=\{2,4\}$ | ${\mathbf{X}}^{1}=[X\left(0\right),{d}_{1}\left(0\right),0,{d}_{1}\left(1\right)]$ |

${\mathbf{b}}_{2}=[-1,-1,-1,-1]$ | $\{{I}_{2}^{c},{I}_{3}^{c}\}=\{3,4\}$ | ${\mathbf{X}}^{2}=[-X\left(0\right),0,{d}_{2}\left(1\right),{d}_{2}\left(1\right)]$ |

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**MDPI and ACS Style**

Zhang, S.-Y.; Zheng, H.
A Hybrid PAPR Reduction Scheme in OFDM-IM Using Phase Rotation Factors and Dither Signals on Partial Sub-Carriers. *Entropy* **2022**, *24*, 1335.
https://doi.org/10.3390/e24101335

**AMA Style**

Zhang S-Y, Zheng H.
A Hybrid PAPR Reduction Scheme in OFDM-IM Using Phase Rotation Factors and Dither Signals on Partial Sub-Carriers. *Entropy*. 2022; 24(10):1335.
https://doi.org/10.3390/e24101335

**Chicago/Turabian Style**

Zhang, Si-Yu, and Hui Zheng.
2022. "A Hybrid PAPR Reduction Scheme in OFDM-IM Using Phase Rotation Factors and Dither Signals on Partial Sub-Carriers" *Entropy* 24, no. 10: 1335.
https://doi.org/10.3390/e24101335