# A Simple Joint Modulation Format Identification and OSNR Monitoring Scheme for IMDD OOFDM Transceivers Using K-Nearest Neighbor Algorithm

^{*}

## Abstract

**:**

## Featured Application

**This paper provides a feasible method for modulation format identification and OSNR monitoring. The application of KNN reduces complexity.**

## Abstract

^{2}, which is similar to that using an artificial neural network. Computational complexity assessment demonstrated that similar performance but less computing resource consumption can be achieved by using the proposed scheme rather than the artificial neural network-based scheme.

## 1. Introduction

^{2}, which is similar to what is achieved using an artificial neural network. Computational complexity assessment demonstrated that similar performance but less computing resource consumption can be achieved by using the proposed scheme rather than the artificial neural network (ANN)-based scheme. AMOOFDM without transceiver negotiations can also be achieved using the proposed scheme, showing its good potential for intelligent transceivers in elastic optical networks.

## 2. Operation Principle of Proposed KNN Based Scheme

- (a)
- If the number of points in an interval ≥256, the value of this interval will be set to 32.
- (b)
- If the number of points in an interval ≤32, the value of this interval will be set to 0.
- (c)
- If the number of points in an interval is between 32 and 256, the value of this interval will be set to an integer obtained by using the number divided by 8, which can be conveniently performed by a commercial processor in the future.

## 3. Experimental Verification and Discussions

^{−3}and power penalty is <0.5 dB for 4 different bit loading profiles. System performance with longer distance and higher signal rate will be studied in future works.

_{ep}is the number of samples in a training set and n

_{i}, n

_{hid}and n

_{o}are the number of neurons on the input, hidden and output layers, respectively. For KNN, N

_{TS}is the number of samples in a training set and n is the number of features. The identification accuracy results of both algorithms under the same condition are shown in Figure 10 and the identification accuracy is similar. MSE of OSNR monitoring for both algorithms when RoP is −11 dBm is listed in Table 3. The average MSE of KNN algorithm is 0.69 dB

^{2}, and that of the ANN algorithm is 0.71 dB

^{2}. In general, compared to the ANN, the KNN algorithm can effectively reduce multiplication operations. However, the KNN algorithm has similar performance to the ANN algorithms.

## 4. Conclusions

^{2}, which is similar to that using artificial neural network. Robustness and computational complexity of the proposed scheme are also experimentally assessed.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**The experimental setup of intensity modulation and direct detection (IMDD) orthogonal frequency division multiplexing (OFDM) system.

**Figure 3.**Subcarrier bit allocation profile for orthogonal frequency division multiplexing (OFDM) signals.

**Figure 4.**(

**a**) The constellations, (

**b**) AH (RoP = −11 dBm and −6 dBm) of mixed QAM modulation format from 4-QAM to 128-QAM.

**Figure 6.**The BER curves and identification accuracy for (

**a**) OBTB and (

**b**) 25 km SSMF configurations.

**Figure 7.**The identification accuracy under different residual phase rotation for (

**a**) OBTB and (

**b**) 25 km SSMF configurations. 4-QAM rotated constellation diagram for the additional phase rotation of π/32 at a specific RoP (−11 dBm) is embedded.

**Figure 8.**(

**a**) Estimated versus true OSNRs with different k values and (

**b**) MSE versus k values for 128 QAM (OBTB).

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

Modulation format | 128/64/32/16/4-QAM |

IFFT/FFT size | 64 points |

CP length | 16 points |

Bit rate | 4.28 Gb/s |

OFDM symbols per frame | 100 symbols |

SSMF length | 25 km |

DFB modulation bandwidth | 2 GHz |

DFB wavelength | 1550 nm |

PIN detector bandwidth | 12 GHz |

AWG sampling rate | 2 GS/s |

DSO sampling rate | 10 GS/s |

DSO/AWG resolution | 8 bit |

Training set sample size | 30 sample |

Data points per sample | 3000 points |

Algorithm | Multiplications | MFI | OSNR Monitoring |
---|---|---|---|

ANN | ${\mathrm{C}}_{\mathrm{train}}={\mathrm{N}}_{\mathrm{ep}}\left({\mathrm{n}}_{\mathrm{i}}{\mathrm{n}}_{\mathrm{hid}}+{\mathrm{n}}_{\mathrm{hid}}{\mathrm{n}}_{\mathrm{o}}\right)$${\mathrm{C}}_{\mathrm{predict}}={\mathrm{n}}_{\mathrm{i}}{\mathrm{n}}_{\mathrm{hid}}+{\mathrm{n}}_{\mathrm{hid}}{\mathrm{n}}_{\mathrm{o}}$${\mathrm{C}}_{\mathrm{ANN}}={\mathrm{C}}_{\mathrm{train}}+{\mathrm{C}}_{\mathrm{predict}}$ | ${\mathrm{C}}_{\mathrm{train}}=100\times \left(101\times 4+40\times 5\right)=424,000$${\mathrm{C}}_{\mathrm{test}}=101\times 40+40\times 5=4240$${\mathrm{C}}_{\mathrm{ANN}}=428,240$ | ${\mathrm{C}}_{\mathrm{train}}=100\times \left(101\times 40+40\right)=408,000$${\mathrm{C}}_{\mathrm{test}}=101\times 40+40=4080$${\mathrm{C}}_{\mathrm{ANN}}=412,080$ |

KNN | ${\mathrm{C}}_{\mathrm{KNN}}={\mathrm{C}}_{\mathrm{train}}+{\mathrm{C}}_{\mathrm{predict}}=2{\mathrm{C}}_{\mathrm{train}}=2{\mathrm{N}}_{\mathrm{TS}}\mathrm{n}$ | ${\mathrm{C}}_{\mathrm{KNN}}=2\times 30\times 101=6060$ | ${\mathrm{C}}_{\mathrm{KNN}}=2\times 30\times 101=6060$ |

MSE | 4-QAM | 16-QAM | 32-QAM | 64-QAM | 128-QAM |
---|---|---|---|---|---|

KNN(dB^{2}) | 0.66 | 1.3 | 0.77 | 0.3 | 0.42 |

ANN(dB^{2}) | 0.87 | 0.65 | 0.69 | 0.84 | 0.49 |

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**MDPI and ACS Style**

Zhang, Q.; Zhou, H.; Jiang, Y.; Cao, B.; Li, Y.; Song, Y.; Chen, J.; Zhang, J.; Wang, M. A Simple Joint Modulation Format Identification and OSNR Monitoring Scheme for IMDD OOFDM Transceivers Using K-Nearest Neighbor Algorithm. *Appl. Sci.* **2019**, *9*, 3892.
https://doi.org/10.3390/app9183892

**AMA Style**

Zhang Q, Zhou H, Jiang Y, Cao B, Li Y, Song Y, Chen J, Zhang J, Wang M. A Simple Joint Modulation Format Identification and OSNR Monitoring Scheme for IMDD OOFDM Transceivers Using K-Nearest Neighbor Algorithm. *Applied Sciences*. 2019; 9(18):3892.
https://doi.org/10.3390/app9183892

**Chicago/Turabian Style**

Zhang, Qianwu, Hai Zhou, Yuntong Jiang, Bingyao Cao, Yingchun Li, Yingxiong Song, Jian Chen, Junjie Zhang, and Min Wang. 2019. "A Simple Joint Modulation Format Identification and OSNR Monitoring Scheme for IMDD OOFDM Transceivers Using K-Nearest Neighbor Algorithm" *Applied Sciences* 9, no. 18: 3892.
https://doi.org/10.3390/app9183892