# Deep Neural Network Equalization for Optical Short Reach Communication

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## Abstract

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## 1. Introduction

## 2. Principles of Nonlinear Equalizer

#### 2.1. General Volterra Equalizer

#### 2.2. Memory Polynomial Volterra Equalizer

#### 2.3. Deep Neural Network Equalizer

- $\underline{s}=[{s}_{1},...,{s}_{M}]$ denotes the input signal,
- $\tilde{\underline{s}}=[{\tilde{s}}_{1},...,{\tilde{s}}_{A}]$ denotes the equalized signal,
- ${\mathit{W}}^{\left[l\right]}$ denotes a weight matrix (including the bias) between the $(l-1)$-th layer to the l-th layer,
- ${a}_{i}^{\left[l\right]}$ denotes the output of the i-th neuron in the l-th layer,
- ${z}_{i}^{\left[l\right]}$ denotes the summed up input to the i-th neuron in the l-th layer,
- The activation function ${\sigma}_{i}^{\left[l\right]}$ is the relation between ${z}_{i}^{\left[l\right]}$ and ${a}_{i}^{\left[l\right]}$ of the i-th neuron in the l-th layer,

## 3. Experimental Verification and Discussion

#### 3.1. Measurement Setup

#### 3.2. Measurement Results over an Optical Channel with 600 Gb/s/$\lambda $

#### 3.2.1. General and Memory Polynomial (MP-) Volterra nonlinear Equalizer (VNLE)

#### 3.2.2. Deep Neural Network Equalizer

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**L-layers feed-forward deep neural networks (DNN) with M nodes in the input layer, H nodes in the hidden layers and A nodes in the output layer.

**Figure 4.**Back-to-back offline measurement setup including Tx and Rx digital signal processing (DSP) with different methods to compute the L-values.

**Figure 5.**Back to back 600 Gb/s (+15% FEC) measurements of different modulations without nonlinear equalizers (NLE).

**Figure 12.**Optical Back-to-Back 660 Gb/s/λ postFEC BER measurements results applying different Volterra and deep neural network architectures.

Number | Architecture | Design | Multipliers |
---|---|---|---|

1 | joint I&Q | $10\left|20\right|30\left|40\right|2$ | (10 ∗ 20 + 20 ∗ 30 + 30 ∗ 40 + 40 ∗ 2) ∗ 2 = 4160 |

2 | Independent I&Q | $5\left|20\right|30\left|40\right|1$ | (5 ∗ 20 + 20 ∗ 30 + 30 ∗ 40 + 40 ∗ 1) ∗ 2 ∗ 2 = 7760 |

3 | Independent I&Q | $5\left|20\right|20|1$ | (5 ∗ 20 + 20 ∗ 20 + 20 ∗ 1) ∗ 2 ∗ 2 = 2080 |

4 | Independent I&Q | $5\left|10\right|10\left|10\right|1$ | (5 ∗ 10 + 10 ∗ 10 + 10 ∗ 10 + 10 ∗ 1) ∗ 2 ∗ 2 = 1040 |

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## Share and Cite

**MDPI and ACS Style**

Schaedler, M.; Bluemm, C.; Kuschnerov, M.; Pittalà, F.; Calabrò, S.; Pachnicke, S. Deep Neural Network Equalization for Optical Short Reach Communication. *Appl. Sci.* **2019**, *9*, 4675.
https://doi.org/10.3390/app9214675

**AMA Style**

Schaedler M, Bluemm C, Kuschnerov M, Pittalà F, Calabrò S, Pachnicke S. Deep Neural Network Equalization for Optical Short Reach Communication. *Applied Sciences*. 2019; 9(21):4675.
https://doi.org/10.3390/app9214675

**Chicago/Turabian Style**

Schaedler, Maximilian, Christian Bluemm, Maxim Kuschnerov, Fabio Pittalà, Stefano Calabrò, and Stephan Pachnicke. 2019. "Deep Neural Network Equalization for Optical Short Reach Communication" *Applied Sciences* 9, no. 21: 4675.
https://doi.org/10.3390/app9214675