# Deep Learning-Assisted Index Estimator for Generalized LED Index Modulation OFDM in Visible Light Communication

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## Abstract

**:**

## 1. Introduction

- An IE-based DNN (IE-DNN) is introduced into the GLIM (multiple-input multiple-output) MIMO-VLC demodulator;
- Only a single IE-DNN module without the need to change the transmitter and the signal demodulation part in the receiver structure;
- Three different structures of the IE-DNN are proposed and compared to demonstrate that the CNN-based estimator delivers the best performance;
- In comparison with conventional detectors, a remarkable active LED index estimation accuracy significantly improves the BER performance at acceptable complexity costs.

## 2. GLIM System Model

## 3. Structure and Operation of DL-Based Index Estimator

#### 3.1. Proposed DL-Based Index Estimator

#### 3.1.1. LFC-DNN

#### 3.1.2. SFC-DNN

#### 3.1.3. CNN

#### 3.2. Sample Generation

#### 3.3. Training Specification

#### 3.4. Complexity Analysis

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AWGN | Additive white Gaussian noise |

CL | Convolution layers |

CNN | Convolutional neural network |

DNN | Deep neural network |

FCL | Fully connected layers |

MIMO | Multiple-input multiple-output |

LED | Light emitting diode |

GLIM | Generalized LED index modulation optical orthogonal frequency-division multiplexing |

PD | Photo detector |

MAP | Maximum a posteriori |

ZF | Zero-forcing |

VLC | Visible light communication |

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**Figure 2.**IE-DNN-assisted active LED IE structures for GLIM-MIMO system: (

**a**) LFC-DNN, (

**b**) SFC-DNN, (

**c**) CNN.

**Table 1.**Complexity cost of matrix-vector operations [28].

Expression | Description | Multiplications | Summations | Total Flops |
---|---|---|---|---|

$\alpha \mathbf{a}$ | Vector Scaling | N | N | |

$\alpha \mathbf{A}$ | Matrix Scaling | $MN$ | $MN$ | |

Ab | Matrix-Vector Prod. | $MN$ | $M(N-1)$ | $2MN-M$ |

AB | Matrix-Matrix Prod. | $MNL$ | $ML(N-1)$ | $2MNL-ML$ |

AD | Matrix-Diagonal Prod. | $MN$ | $MN$ | |

${\mathbf{a}}^{H}\mathbf{b}$ | Inner Prod. | N | $N-1$ | $2N-1$ |

${\mathbf{ac}}^{H}$ | Outer Prod. | $MN$ | $MN$ | |

${\mathbf{A}}^{H}\mathbf{A}$ | Gram | $\frac{MN(N+1)}{2}$ | $\frac{N(M-1)(N+1)}{2}$ | $M{N}^{2}+N\left(\right)open="("\; close=")">M-\frac{N}{2}$ |

${\parallel \mathbf{A}\parallel}^{2}$ | Euclidean norm | $MN$ | $MN-1$ | $2MN-1$ |

${\mathbf{Q}}^{-1}$ | Inverse of Pos. Definite | $\frac{{N}^{3}}{2}+\frac{3{N}^{2}}{2}$ | $\frac{{N}^{3}}{2}-\frac{{N}^{2}}{2}$ | ${N}^{3}+{N}^{2}+N$ Including N roots |

Detector | Numbers of Trainable Parameters | Estimation Time |
---|---|---|

(Case 1/Case 2) | (Case 1/Case 2) | |

LFC-DNN | 994/994 | 13 ms/44 ms |

SFC-DNN | 4736/9544 | 28 ms/78 ms |

CNN | 3096/6328 | 22 ms/67 ms |

MAP | -/- | 6 ms/23 ms |

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**MDPI and ACS Style**

Le-Tran, M.; Kim, S.
Deep Learning-Assisted Index Estimator for Generalized LED Index Modulation OFDM in Visible Light Communication. *Photonics* **2021**, *8*, 168.
https://doi.org/10.3390/photonics8050168

**AMA Style**

Le-Tran M, Kim S.
Deep Learning-Assisted Index Estimator for Generalized LED Index Modulation OFDM in Visible Light Communication. *Photonics*. 2021; 8(5):168.
https://doi.org/10.3390/photonics8050168

**Chicago/Turabian Style**

Le-Tran, Manh, and Sunghwan Kim.
2021. "Deep Learning-Assisted Index Estimator for Generalized LED Index Modulation OFDM in Visible Light Communication" *Photonics* 8, no. 5: 168.
https://doi.org/10.3390/photonics8050168