# LPI Radar Waveform Recognition Based on Deep Convolutional Neural Network Transfer Learning

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## Abstract

**:**

## 1. Introduction

## 2. System Overview

## 3. Signal Model and CWD Time-Frequency Analysis

#### 3.1. Signal Model

#### 3.2. Choi-Williams Distribution

#### 3.3. Comparison of Different Signal CWD Time-Frequency Images

## 4. CNN Model-Based Transfer Learning and Feature Extraction

#### 4.1. Inception-v3

#### 4.2. ResNet

#### 4.3. Inception-v3-SVM and ResNet-152-SVM Recognition Model

## 5. Simulation Experiment and Result Analysis

#### 5.1. Sample Creation

#### 5.2. Feasibility Experiment

#### 5.3. Identification Success Rate Experiment

#### 5.4. Robustness Experiment

#### 5.5. Experiment with Computation

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

LPI | Low probability of intercept |

CWD | Choi-Williams distribution |

SVM | Support Vector Machine |

PSK | Phase Shift Keying |

FSK | Frequency Shift Keying |

WVD | Wigner-Ville Distribution |

PWD | Pseudo-Wigner Distribution |

ENN | Elman neural network |

TFI | Time-frequency images |

CNN | Convolutional neural network |

ILSVRC | ImageNet Large Scale Visual Recognition Challenge |

ReLU | Rectified Linear Unit |

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**Figure 2.**8 types of LPI radar waveform CWD time-frequency diagram. In this figure, different waveform classes are shown. For BPSK, the number of Barker codes set 13. The Number change in the Costas codes signal set to 5. For the Frank signal, the samples per frequency steps M set 8. For the multi-time code T1–T4 signal, the number of basic waveform segments set 4, 5, 6, 5, respectively. Specific parameter settings are shown in Section 5, Table 2.

**Figure 4.**ResNet’s residual learning module. In this figure, ReLU is a commonly used activation function in neural networks.

**Figure 6.**2-D feature map with SNR of 8 dB. (

**a**) ResNet-152 2-D feature map; (

**b**) Inception-v3 2-D feature map.

**Figure 8.**LPI radar waveform recognition results under −4 dB SNR. (

**a**) ResNet-152-SVM confusion matrix; (

**b**) Inception-v3-SVM confusion matrix.

**Figure 9.**LPI radar waveform recognition accuracy under different training data. (

**a**) ResNet-152-SVM; (

**b**) Inception-v3-SVM.

Layer Name | Output Size | 50-Layer | 101-Layer | 152-Layer |
---|---|---|---|---|

conv1 | $112\times 112$ | $7\times 7$, 64, stride 2 | ||

conv2_x | $56\times 56$ | $3\times 3$, max pool, stride 2 | ||

$\left[\begin{array}{c}1\times 1,64\\ 3\times 3,64\\ 1\times 1,256\end{array}\right]\times 3$ | $\left[\begin{array}{c}1\times 1,64\\ 3\times 3,64\\ 1\times 1,256\end{array}\right]\times 3$ | $\left[\begin{array}{c}1\times 1,64\\ 3\times 3,64\\ 1\times 1,256\end{array}\right]\times 3$ | ||

conv3_x | $28\times 28$ | $\left[\begin{array}{c}1\times 1,128\\ 3\times 3,128\\ 1\times 1,512\end{array}\right]\times 4$ | $\left[\begin{array}{c}1\times 1,128\\ 3\times 3,128\\ 1\times 1,512\end{array}\right]\times 4$ | $\left[\begin{array}{c}1\times 1,128\\ 3\times 3,128\\ 1\times 1,512\end{array}\right]\times 4$ |

conv4_x | $14\times 14$ | $\left[\begin{array}{c}1\times 1,256\\ 3\times 3,256\\ 1\times 1,1024\end{array}\right]\times 6$ | $\left[\begin{array}{c}1\times 1,256\\ 3\times 3,256\\ 1\times 1,1024\end{array}\right]\times 23$ | $\left[\begin{array}{c}1\times 1,256\\ 3\times 3,256\\ 1\times 1,1024\end{array}\right]\times 36$ |

conv5_x | $7\times 7$ | $\left[\begin{array}{c}1\times 1,512\\ 3\times 3,512\\ 1\times 1,2048\end{array}\right]\times 3$ | $\left[\begin{array}{c}1\times 1,512\\ 3\times 3,512\\ 1\times 1,2048\end{array}\right]\times 3$ | $\left[\begin{array}{c}1\times 1,512\\ 3\times 3,512\\ 1\times 1,2048\end{array}\right]\times 3$ |

$1\times 1$ | average pool, 1000-d fc, SoftMax | |||

FLOPs | $3.8\times {10}^{9}$ | $7.6\times {10}^{9}$ | $11.3\times {10}^{9}$ |

**Table 2.**Simulation parameter list [19].

Radar Waveform | Simulation Parameter | Ranges |
---|---|---|

– | Sampling frequency ${f}_{s}$ | 1 (${f}_{s}=8000$ HZ) |

BPSK | Barker codes ${N}_{c}$ | $\{7,11,13\}$ |

Carrier frequency ${f}_{c}$ | U$(1/8,1/4)$ | |

Cycles per phase code $cpp$ | $[1,5]$ | |

Number of code periods $np$ | $[100,300]$ | |

LFM | Number of samples N | $[500,1024]$ |

Bandwidth $\Delta f$ | U$(1/16,1/8)$ | |

Initial frequency ${f}_{0}$ | U$(1/16,1/8)$ | |

Costas | Fundamental frequency ${f}_{min}$ | U$(1/24,1/20)$ |

Number change ${N}_{c}$ | $[3,6]$ | |

Number of samples N | $[512,1024]$ | |

Frank | Carrier frequency ${f}_{c}$ | U$(1/8,1/4)$ |

Cycles per phase code $cpp$ | $[1,5]$ | |

Samples of frequency stem M | $[4,8]$ | |

T1–T4 | Number of segments k | $[4,6]$ |

Overall code duration T | $[0.07,0.1]$ |

Item | Model/Version |
---|---|

CPU | i5-8300H (Intel) |

GPU | NVIDIA GeForce GTX 1050 Ti |

Memory | 16 GB (DDR4@2667 MHZ) |

Spyder | Python3.5 |

SNR (dB) | $-6$ | 0 | 8 |
---|---|---|---|

BPSK | 43.54/141.87/51.32 | 43.43/140.17/51.20 | 43.27/139.25/50.88 |

Costas | 43.26/142.35/54.88 | 42.97/141.05/54.01 | 42.62/140.16/53.34 |

LFM | 42.79/142.72/55.60 | 42.42/141.09/54.98 | 42.19/139.86/54.78 |

Frank | 43.03/145.47/56.34 | 42.76/144.77/56.29 | 42.53/143.28/55.79 |

T1 | 42.68/143.94/58.63 | 42.48/142.86/58.42 | 42.28/141.34/57.68 |

T2 | 43.74/141.31/56.75 | 43.41/139.69/55.80 | 43.14/138.29/55.37 |

T3 | 43.17/140.82/58.83 | 42.89/139.38/58.11 | 42.29/138.04/57.51 |

T4 | 42.98/144.37/54.90 | 42.82/142.97/54.23 | 42.53/141.02/53.90 |

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**MDPI and ACS Style**

Guo, Q.; Yu, X.; Ruan, G.
LPI Radar Waveform Recognition Based on Deep Convolutional Neural Network Transfer Learning. *Symmetry* **2019**, *11*, 540.
https://doi.org/10.3390/sym11040540

**AMA Style**

Guo Q, Yu X, Ruan G.
LPI Radar Waveform Recognition Based on Deep Convolutional Neural Network Transfer Learning. *Symmetry*. 2019; 11(4):540.
https://doi.org/10.3390/sym11040540

**Chicago/Turabian Style**

Guo, Qiang, Xin Yu, and Guoqing Ruan.
2019. "LPI Radar Waveform Recognition Based on Deep Convolutional Neural Network Transfer Learning" *Symmetry* 11, no. 4: 540.
https://doi.org/10.3390/sym11040540