# Clipping Noise Compensation with Neural Networks in OFDM Systems

^{*}

## Abstract

**:**

## 1. Introduction

^{−6}[6]. Here, we consider the simplest PAPR reduction technique, namely digital clipping, which is easily implemented in the transmitter. However, digital clipping causes the problems of in-band distortion and out-of-band leakage; therefore, a potent clipping compensation scheme at the receiver is needed to work with digital clipping to maintain the overall system performance [6,7,8].

## 2. Clipping Noise Compensation

## 3. Results

#### 3.1. Interpretation of NN Weight Matrices

#### 3.2. MSE and BER Performances

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The schematic of reconstructing clipped orthogonal frequency division multiplexing (OFDM) signals.

**Figure 2.**The weight matrices of the learned three-layer neural network. (

**a**) ${W}_{1}$. (

**b**) ${W}_{2}$. (

**c**) ${W}_{3}$.

**Figure 3.**(

**a**) DFT matrix, (

**b**) IDFT matrix, (

**c**) The learned DFT matrix (the central part of${\widehat{W}}_{2}{W}_{3}$), (

**d**) The learned IDFT matrix (${\widehat{W}}_{1}$ ).

**Figure 4.**The reordered weight matrices. (

**a**) ${\widehat{W}}_{1}$ (

**b**) ${\widehat{W}}_{2}$ (

**c**) ${\widehat{W}}_{2}{W}_{3}$.

**Figure 5.**Mean square error (MSE) versus Signal-to-Noise Ratio (SNR): (

**a**) clipped part, cr = 1.0 dB (

**b**) clipped part, cr = 1.3 dB (

**c**) unclipped part cr = 1.0 dB (

**d**) unclipped part, cr = 1.3 dB.

**Figure 6.**BER performance in AWGN and Rayleigh fading channels with different clipping ratios. In (

**a**,

**b**), dashed line: no clipping noise compensation; solid line: Neural Network (NN). In (

**c**,

**d**), dashed lines: CS; solid lines: NN.

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**MDPI and ACS Style**

Sang, T.-H.; Xu, Y.-C.
Clipping Noise Compensation with Neural Networks in OFDM Systems. *Signals* **2020**, *1*, 100-109.
https://doi.org/10.3390/signals1010005

**AMA Style**

Sang T-H, Xu Y-C.
Clipping Noise Compensation with Neural Networks in OFDM Systems. *Signals*. 2020; 1(1):100-109.
https://doi.org/10.3390/signals1010005

**Chicago/Turabian Style**

Sang, Tzu-Hsien, and You-Cheng Xu.
2020. "Clipping Noise Compensation with Neural Networks in OFDM Systems" *Signals* 1, no. 1: 100-109.
https://doi.org/10.3390/signals1010005