# Volterra-Aided Neural Network Equalization for Channel Impairment Compensation in Visible Light Communication System

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## Abstract

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## 1. Introduction

- The structure information of the Volterra model is involved in the proposed DL equalizer to pre-emphasize the virgin data, which is favorable for the memory feature learning. Therefore, it can relax the learning pressure and reduce the structural complexity and training time.
- Based on the traditional model-solving procedure, the channel impairment compensation is formulated as a spatial memory pattern prediction problem, and the proposed DL model is ingeniously used to achieve the accurate prediction.
- Both the memory nonlinearity of the LED and the dispersive effect of the optical channel in a VLC system are simultaneously considered during the training stage.
- The proposed scheme can still provide an excellent BER performance under the mismatched conditions of training and testing, showing a good robustness.

## 2. System Nonlinearity

## 3. The Proposed Scheme

#### 3.1. Input Preprocessing Based on Volterra Feature

#### 3.2. Network Structure

#### 3.3. Complexity

#### 3.4. Training Strategy

## 4. Simulation Results

#### 4.1. Convergence Performance

#### 4.2. Nonlinearity Compensation

#### 4.3. Complexity

#### 4.4. Robustness Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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FLOPs ^{1} | Convergence Epochs | Time ^{2} | Accuracy | |
---|---|---|---|---|

Basic-LSTM | 89.9 M | 2735 | 0.015 s | −25.3 $\mathrm{dB}$ |

Basic-CNN | 2277.9 M | 3550 | 0.523 s | −26.8 $\mathrm{dB}$ |

The proposed | 755.6 M | 1750 | 0.268 s | −28.2 $\mathrm{dB}$ |

^{1}It is also related to the number of input signals.

^{2}The average time consumed for each training epoch.

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**MDPI and ACS Style**

Tian, D.; Miao, P.; Peng, H.; Yin, W.; Li, X.
Volterra-Aided Neural Network Equalization for Channel Impairment Compensation in Visible Light Communication System. *Photonics* **2022**, *9*, 845.
https://doi.org/10.3390/photonics9110845

**AMA Style**

Tian D, Miao P, Peng H, Yin W, Li X.
Volterra-Aided Neural Network Equalization for Channel Impairment Compensation in Visible Light Communication System. *Photonics*. 2022; 9(11):845.
https://doi.org/10.3390/photonics9110845

**Chicago/Turabian Style**

Tian, Daming, Pu Miao, Hui Peng, Weibang Yin, and Xiaorui Li.
2022. "Volterra-Aided Neural Network Equalization for Channel Impairment Compensation in Visible Light Communication System" *Photonics* 9, no. 11: 845.
https://doi.org/10.3390/photonics9110845