# Clock Recovery Challenges in DSP-Based Coherent Single-Mode and Multi-Mode Optical Systems

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Clock Recovery in Coherent Optical Receivers

#### Feedback Timing Synchronization Method

## 3. Matrix Propagation Model for Optical Fibers

#### 3.1. Single-Mode Fibers without Coupling between Polarizations

#### 3.2. Single-Mode Fibers with Strong Coupling between Polarizations

#### 3.3. Multi-Mode and Multi-Core Fibers

#### 3.4. Time Skew between Polarizations and Modes

## 4. Clock Recovery Performance in Single-Mode Fibers

#### 4.1. Time Skew between Polarizations

#### 4.2. Polarization Mode Dispersion

## 5. Clock Recovery Performance in Multi-Mode Fibers

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CD | Chromatic dispersion |

CTA | Clock tone amplitude |

DGD | Differential group delay |

DSP | Digital signal processing |

IM-DD | Intensity modulation/direct detection |

FMF | Few mode fiber |

MCF | Multi-core fiber |

MD | Mode delay |

MDL | Mode-dependent loss |

MDM | Mode division multiplexing |

MIMO | Multiple-input multiple-output |

M-PSK | m-ary phase shift keying |

M-QAM | m-ary quadrature amplitude modulation |

NCO | Numeric controlled oscillator |

NRZ | Non-return-to-zero |

PDM | Polarization division multiplexing |

PDL | Polarization dependent loss |

PMD | Polarization mode dispersion |

PSK | Phase shift keying |

P+I | Proportional-plus-integral controller |

QPSK | Quadriphase shift keying |

SDM | Space-division multiplexing |

SMF | Single-mode fiber |

WDM | Wavelength division multiplexing |

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**Figure 2.**(

**a**) QPSK constellation, in red, with its intersymbol transitions, in black; (

**b**) In-phase component eye-diagram; (

**c**) Power eye-diagram; (

**d**) S-curve, in red, and all values ${e}_{Gardner}$ can assume in a QPSK signal, in black.

**Figure 4.**Normalized clock tone amplitude as function of rotation angle and transmitter-side inter-polarization time skew.

**Figure 8.**Normalized clock tone amplitude as a function of crosstalk between mode groups in a 1000 km transmission of a 3-mode FMF for different values of uncoupled group delay.

**Figure 9.**Normalized clock tone amplitude as a function of uncoupled group delay between mode groups in a 3-mode FMF for distinct transmission distances.

Parameter | Value |
---|---|

Modulation format | NRZ-QPSK |

Symbol rate | 32 GBd |

Rotation angle interval | $[0,90\xb0]$ |

Rotation angle step size | $1\xb0$ |

Transmitter time skew interval | $[0,31.125]$ ps |

Transmitter time skew step size | $778.125$ fs |

Receiver time skew | 0 |

Parameter | Value |
---|---|

Modulation format | NRZ-QPSK |

Symbol rate | 32 GBd |

Number of fiber sections | 10,000 |

Fiber length per section | 10 m |

Total fiber length | 100 km |

Rotation angle per section | uniform distribution $\sim [0,360\xb0)$ |

Uncoupled DGD interval | $[0.005,500]$ ps/km |

Uncoupled DGD step size | $25.89\%$ greater every iteration |

Transmitter time skew | 0 |

Receiver time skew | 0 |

Parameter | Value |
---|---|

Modulation format | NRZ-QPSK |

Symbol rate | 32 GBd |

Number of degrees of freedom | 6 |

Fiber length per section | 10 km |

Total fiber length (Figure 8) | 1000 km |

Total fiber length (Figure 9) | 100, 300, 500 and 1000 km |

Uncoupled group delay (Figure 8) | 0, 0.03, 0.3, 3 and 300 ps/km |

Uncoupled group delay interval (Figure 9) | $[0.001,1000]$ ps/km |

Rotation angle per section | zero-mean normal distribution |

Rotation angle variance interval | $[0,2000\xb0]$ |

Transmitter time skew | 0 |

Receiver time skew | 0 |

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**MDPI and ACS Style**

Diniz, J.C.M.; Da Ros, F.; Zibar, D.
Clock Recovery Challenges in DSP-Based Coherent Single-Mode and Multi-Mode Optical Systems. *Future Internet* **2018**, *10*, 59.
https://doi.org/10.3390/fi10070059

**AMA Style**

Diniz JCM, Da Ros F, Zibar D.
Clock Recovery Challenges in DSP-Based Coherent Single-Mode and Multi-Mode Optical Systems. *Future Internet*. 2018; 10(7):59.
https://doi.org/10.3390/fi10070059

**Chicago/Turabian Style**

Diniz, Júlio César Medeiros, Francesco Da Ros, and Darko Zibar.
2018. "Clock Recovery Challenges in DSP-Based Coherent Single-Mode and Multi-Mode Optical Systems" *Future Internet* 10, no. 7: 59.
https://doi.org/10.3390/fi10070059