# A Reduction of Peak-to-Average Power Ratio Based Faster-Than-Nyquist Quadrature Signals for Satellite Communication

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## Abstract

**:**

## 1. Introduction

## 2. Optimization Problem with Constraint on PAPR

#### 2.1. Optimization Problem-Solving Method

#### 2.2. Results of Optimization Problem Solving

## 3. Simulation Model

## 4. Simulation Modeling Results

#### 4.1. Occupied Frequency Band and PAPR of Oscillations

#### 4.2. BER Performance in AWGN Channel

#### 4.3. BER Performance in Rayleigh-Fading Channel

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Results of the optimization problem for ${T}_{s}$ = 4T with the constraint on the PAPR for the packet length ${N}_{p}=5$.

**Figure 5.**Results of the optimization problem solving for ${T}_{s}=4T$ with the constraint on PAPR for the packet length ${N}_{p}=8$.

**Figure 6.**Results of the optimization problem solving for ${T}_{s}$ = 8T with the constraint on PAPR for the packet length ${N}_{p}=5$.

**Figure 7.**Results of the optimization problem solving for ${T}_{s}$ = 8T with the constraint on PAPR for the packet length ${N}_{p}=8$.

**Figure 8.**The shape of normalized signal sequence with OQPSK for: (

**a**) ${T}_{s}$ = 4T; and (

**b**) ${T}_{s}$ = 8T.

**Figure 9.**Optimal FTN signal packet with OQPSK: (

**a**) ${T}_{s}$ = 4T, ${N}_{p}=5$, $\Delta $maxPAPR = 3 dB; and (

**b**) ${T}_{s}$ = 8T, ${N}_{p}=8$, $\Delta $maxPAPR = 3 dB.

**Figure 10.**Dependence of the PAPR value on $\Delta $maxPAPR for pulse duraton of ${T}_{s}$ = 4T: (

**a**) ${N}_{p}=5$; and (

**b**) ${N}_{p}=8$.

**Figure 11.**Dependence of the PAPR value on $\Delta $maxPAPR for pulse duraton of ${T}_{s}$ = 8T: (

**a**) ${N}_{p}=5$; and (

**b**) ${N}_{p}=8$.

**Figure 14.**Occupied frequency band dependence on $\Delta $maxPAPR for pulse duration of ${N}_{p}=8$: (

**a**) ${T}_{s}$ = 4T; and (

**b**) ${T}_{s}$ = 8T.

**Figure 16.**BER performance of the optimal FTN signals with QPSK in the AWGN channel and pulse duration of: (

**a**) ${T}_{s}=4T$; and (

**b**) ${T}_{s}=8T$.

**Figure 17.**BER performance of optimal FTN signals with OQPSK in AWGN channel and pulse duration of: (

**a**) ${T}_{s}$ = 4T; and (

**b**) ${T}_{s}$ = 8T.

**Figure 18.**BER performance of optimal FTN signals in frequency-flat Rayleigh channel: (

**a**) QPSK; and (

**b**) OQPSK.

$\mathit{\Delta}{\mathit{F}}_{99\%},\phantom{\rule{4pt}{0ex}}1/\mathit{T}$ | ||
---|---|---|

$\Delta $maxPAPR, dB | ${\mathbf{T}}_{\mathbf{s}}=\mathbf{4}\mathbf{T}$ | ${\mathbf{T}}_{\mathbf{s}}=\mathbf{8}\mathbf{T}$ |

0 | 1.12 | 0.99 |

1 | 1.18 | 1.06 |

2 | 1.27 | 1.17 |

3 | - | 1.22 |

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**MDPI and ACS Style**

Makarov, S.B.; Liu, M.; Ovsyannikova, A.S.; Zavjalov, S.V.; Lavrenyuk, I.; Xue, W.; Xu, Y.
A Reduction of Peak-to-Average Power Ratio Based Faster-Than-Nyquist Quadrature Signals for Satellite Communication. *Symmetry* **2021**, *13*, 346.
https://doi.org/10.3390/sym13020346

**AMA Style**

Makarov SB, Liu M, Ovsyannikova AS, Zavjalov SV, Lavrenyuk I, Xue W, Xu Y.
A Reduction of Peak-to-Average Power Ratio Based Faster-Than-Nyquist Quadrature Signals for Satellite Communication. *Symmetry*. 2021; 13(2):346.
https://doi.org/10.3390/sym13020346

**Chicago/Turabian Style**

Makarov, Sergey B., Mingxin Liu, Anna S. Ovsyannikova, Sergey V. Zavjalov, ILya Lavrenyuk, Wei Xue, and Yidong Xu.
2021. "A Reduction of Peak-to-Average Power Ratio Based Faster-Than-Nyquist Quadrature Signals for Satellite Communication" *Symmetry* 13, no. 2: 346.
https://doi.org/10.3390/sym13020346