# LPI Radar Waveform Recognition Based on CNN and TPOT

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## Abstract

**:**

## 1. Introduction

## 2. CNN-TPOT Identification System Structure

## 3. Preprocessing

#### 3.1. Signal Model

#### 3.2. Choi–Williams Distribution

#### 3.3. Binary Image

- Get the probability of occurrence of each gray value that appears in the picture. For example, $PPix(0,i)$ stores the gray value of the ith pixel in the image, and $PPix(1,i)$ stores the probability that the ith gray value appears.
- Calculate the discrete function distribution $F\left(i\right)$ of the gray value.$$F\left(i\right)={\displaystyle \sum _{j=0}^{i}}PPix(0,j)\times PPix(1,j)$$
- Find the sum of the probabilities of the occurrence of the previous i kinds of gray values, $PSum\left(i\right)$.
- Obtain the gray average value AGray of the overall image, that is, sum the gray value of all the pixels in the image and then divide by the total number of pixels.
- Calculate the threshold weight $WValve\left(i\right)$ at different gray values.$$WValve\left(i\right)=\frac{AGray\times F\left(i\right)-PSum\left(i\right)}{\sqrt{F\left(i\right)\times (1-F(i\left)\right)}}$$
- Obtain the gray value corresponding to the i value of the maximum $WValve\left(i\right)$ as a global binarization threshold.

## 4. CNN Feature Extractor Design

#### 4.1. CNN Model

- The input image is a standardized CNN training data structure with a size of $32\times 32$. The detected LPI radar waveform is subjected to CWD time–frequency transform and image binarization. However, since the image size is too large to train the CNN network, we use image size conversion to $32\times 32$ size.
- The C1 layer is a convolutional layer with six feature maps. The size of the convolution kernel is $5\times 5$, thus each feature map has $(32-5+1)\times (32-5+1)$, i.e., $28\times 28$ Neurons. Each neuron is connected to a $5\times 5$ size region of the input layer.
- The S2 layer is a down sampling layer with six $14\times 14$ feature maps, and each neuron in each feature map is connected to a $2\times 2$ region in the feature map corresponding to the C1 layer.
- C3 is also a convolutional layer that uses a $5\times 5$ convolution kernel to process the S2 layer. The number of neurons that calculate the feature map of the C3 layer is $(14-5+1)\times (14-5+1)$, that is, $10\times 10$. C3 has 16 feature maps, each of which is composed of different combinations between the individual feature maps of the previous layer, as shown in Table 1.
- The S4 layer is a down sampling layer composed of 16 $5\times 5$ size feature maps, each of which is connected to a $2\times 2$ size region of the corresponding feature map in C3.
- The C5 layer is another convolutional layer. The same is used for a $5\times 5$ size convolution kernel. Each feature map has $(5-5+1)\times (5-5+1)$, i.e., $1\times 1$ neurons. Each unit is fully connected to the $5\times 5$ area of all 16 feature maps of S4. The C5 layer has 120 feature maps.
- The F6 fully connected layer has 84 feature maps, and each feature map has only one neuron connected to the C5 layer.
- The output layer is also a fully connected layer with a total of 12 nodes representing the 12 different LPI radar waveforms, respectively.

#### 4.2. Feature Extraction

## 5. TPOT Optimization Classifier

#### 5.1. Genetic Programming

- Replace mutation: The operational nodes in the individual process structure are randomly selected and replaced with new randomly generated process sequences.
- Insert mutation: A new randomly generated sequence of processes is inserted into the random location of the inserted individual.
- Remove mutation: A random culling sequence is performed on the processes of the deleted individual.

#### 5.2. Classifier Model Selection and Optimization

## 6. Simulation Experiment

#### 6.1. Create Sample

#### 6.2. CNN Feature Validity Experiment

#### 6.3. TPOT Optimized Classifier Performance Test

#### 6.4. Experiment Results with SNR

#### 6.5. Experiment with Robustness

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

LPI | low probability interception |

LFM | linear frequency modulation |

CNN | convolutional neural network |

TPOT | tree structure-based machine learning process optimization |

SNR | signal-to-noise ratio |

CWD | Choi–Williams distribution |

WVD | Wigner–Ville distribution |

ENN | Herman neural network |

PCA | principal components analysis |

GP | genetic programming |

SVM | support vector machine |

KNN | K-nearest neighbor method |

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**Figure 2.**The CWD transformation results for different LPI radar waveforms, namely LFM, BPSK, Frank, Costas code, P1–P4 code, and T1–T4 code. It can be seen that the time–frequency image distributions of different waveforms are different.

**Figure 3.**ITaking P1 encoding as an example, when the signal-to-noise ratio is 0 dB, by the signal pre-processing flow, after binarization, the noise is effectively suppressed.

**Figure 4.**Forty binary images are selected randomly from the train/test sets of SNR = 0 dB. All eight kinds of waveforms are included in the figure.

**Figure 5.**CNN structure diagram. [8]

**Table 1.**The CNN third layer feature map combination; for example, the 0th feature map is obtained by combining the zero-feature, one-feature and two-feature maps of the S2 layer.

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | X | X | X | X | X | X | X | X | X | X | ||||||

1 | X | X | X | X | X | X | X | X | X | X | X | |||||

2 | X | X | X | X | X | X | X | X | X | X | ||||||

3 | X | X | X | X | X | X | X | X | X | X | X | |||||

4 | X | X | X | X | X | X | X | X | X | X | ||||||

5 | X | X | X | X | X | X | X | X | X | X |

GP Parameter | Content |
---|---|

Population size | 100 |

Number of iterations | 10 |

Individual mutation rate | 90% |

Crossover rate | 5% |

Method of choosing | 10% elite reserve, 3 choice 2 bidding selection method, according to complexity 2 choose 1 |

Mutation | Replace, insert, delete, each type of mutation each accounted for 1/3 |

Repeated operation | 5 |

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

CPU | i5-8300H(Intel) |

GPU | NVIDIA GeForce GTX 1050 Ti |

Memory | 16 GB(DDR4 @2667 MHZ) |

MATLAB | R2018b |

Spyder | Python 3.5 |

**Table 4.**Simulation parameter list [9].

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 ${f}_{m}in$ | U(1/24,1/20) |

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

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

Frank&P1 | Carrier frequency ${f}_{c}$ | U(1/8,1/4) |

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

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

P2 | Carrier frequency ${f}_{c}$ | U(1/8,1/4) |

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

Samples of frequency stem M | 2 × [2, 4] | |

P3&P4 | Carrier frequency ${f}_{c}$ | U(1/8,1/4) |

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

Samples of frequency stem M | 2 × [16, 35] | |

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

Overall code duration T | [0.07, 0.1] |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Wan, J.; Yu, X.; Guo, Q.
LPI Radar Waveform Recognition Based on CNN and TPOT. *Symmetry* **2019**, *11*, 725.
https://doi.org/10.3390/sym11050725

**AMA Style**

Wan J, Yu X, Guo Q.
LPI Radar Waveform Recognition Based on CNN and TPOT. *Symmetry*. 2019; 11(5):725.
https://doi.org/10.3390/sym11050725

**Chicago/Turabian Style**

Wan, Jian, Xin Yu, and Qiang Guo.
2019. "LPI Radar Waveform Recognition Based on CNN and TPOT" *Symmetry* 11, no. 5: 725.
https://doi.org/10.3390/sym11050725