# Modulation Signal Recognition of Underwater Acoustic Communication Based on Archimedes Optimization Algorithm and Random Forest

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Archimedes Optimization Algorithm

#### 2.1.1. Archimedes Principle

#### 2.1.2. Initialization

#### 2.1.3. Transfer Operator

#### 2.1.4. Object’s Acceleration

#### 2.1.5. Object’s Position

#### 2.2. Random Forest

#### 2.2.1. Determine the Number of DT

#### 2.2.2. Determine the Depth of the DT

#### 2.3. Overall Approach of this Study

## 3. Feature Parameter Extraction and Analysis

#### 3.1. Feature Parameters Based on Instantaneous Information

#### 3.1.1. Absolute Amplitude Standard Deviation ${\sigma}_{aa}$

#### 3.1.2. Absolute Frequency Standard Deviation ${\sigma}_{af}$

#### 3.1.3. Absolute Phase Standard Deviation ${\sigma}_{ap}$

#### 3.1.4. Direct Phase Standard Deviation ${\sigma}_{dp}$

#### 3.2. Feature Parameters Based on Higher-Order Cumulant

#### 3.3. Feature Parameters Based on a Spectral Line

^{6}Hz, the sampling frequency is 6 × 10

^{7}Hz, and the carrier frequencies corresponding to the bits are 8.5 × 10

^{6}Hz and 11.5 × 10

^{6}Hz; for 4FSK modulation signal, the bit rate is 2.5 × 10

^{6}Hz, the sampling frequency is 6 × 10

^{7}Hz, and the carrier frequencies corresponding to the bits are 5.5 × 10

^{6}Hz, 8.5 × 10

^{6}Hz, 11.5 × 10

^{6}Hz, and 14.5 × 10

^{6}Hz.

#### 3.4. Feature Parameters Based on Cyclic Spectrum

#### 3.5. Feature Parameters Based on Autocorrelation

^{6}Hz for the chip rate of the M sequence; 15 MHz for the carrier frequency; and 90 MHz for sampling. In Figure 6, which represents the second-order matrix of the autocorrelation function of the DSSS signal acquired through simulation, it is possible to see that there are clear periodic spectral peaks.

## 4. Simulation Results and Analysis

#### 4.1. Simulation Environment and Results

#### 4.2. Simulation Results under the BELLHOP Channel

#### 4.3. Comparison of Different Classifiers

## 5. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 8.**Recognition rate of seven modulation signals based on AOA–RF algorithm in AWGN environment.

**Figure 9.**Accuracy of each signal identification under 2.5 km transmission superposition model of BELLHOP channel.

**Figure 10.**Comparison of recognition performance of AOA–RF algorithm in different channel environments.

Modulation Pattern | ${\mathit{F}}_{1}$ | ${\mathit{F}}_{2}$ | ${\mathit{F}}_{3}$ | ${\mathit{F}}_{4}$ |
---|---|---|---|---|

2ASK | 1 | 1 | 2 | 32 |

4ASK | 1 | 1 | 1.36 | 27.52 |

2FSK | 0 | 0 | 1 | 16 |

4FSK | 0 | 0 | 1 | 16 |

2PSK | 1 | 1 | 2 | 32 |

4PSK | 1 | 0 | 1 | 16 |

Parameter Name | Numerical Value (First Group) | Numerical Value (Group 2) |
---|---|---|

Signal frequency | 10 khz | 10 khz |

Seawater depth | 345.78 m | 345.78 m |

Sound source depth | 100 m | 100 m |

Receiver depth | 120 m | 120 m |

Number of receivers in the horizontal direction | 50 | 50 |

Maximum transmission distance | 2.5 km | 5 km |

Seawater density (kg/m^{3}) | 1024 | 1024 |

Sound speed of seawater (m/s) | 1518 | 1518 |

Methods | Accuracy Recognition Rate in Different SNR Environments (%) | |||||
---|---|---|---|---|---|---|

−10 | −8 | −6 | −4 | −2 | 0 (dB) | |

RF | 24.57 | 29.57 | 43.29 | 63.14 | 78.14 | 93.04 |

Higher-order cumulant-RF | 36.48 | 64.63 | 84.33 | 94.25 | 98.92 | 99.64 |

Wavelet Transform | 56.00 | 64.63 | 84.33 | 94.25 | 98.92 | 99.64 |

Instantaneous feature-RF | 59.12 | 73.11 | 81.02 | 87.59 | 100 | 100 |

BPNN | 64.57 | 69.57 | 87.07 | 91.14 | 100 | 100 |

SVM | 71.09 | 84.06 | 95.10 | 100 | 100 | 100 |

AOA-RF | 76.50 | 85.21 | 96.23 | 99.71 | 100 | 100 |

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**MDPI and ACS Style**

Wang, M.; Zhu, Z.; Qian, G.
Modulation Signal Recognition of Underwater Acoustic Communication Based on Archimedes Optimization Algorithm and Random Forest. *Sensors* **2023**, *23*, 2764.
https://doi.org/10.3390/s23052764

**AMA Style**

Wang M, Zhu Z, Qian G.
Modulation Signal Recognition of Underwater Acoustic Communication Based on Archimedes Optimization Algorithm and Random Forest. *Sensors*. 2023; 23(5):2764.
https://doi.org/10.3390/s23052764

**Chicago/Turabian Style**

Wang, Maofa, Zhenjing Zhu, and Gaofeng Qian.
2023. "Modulation Signal Recognition of Underwater Acoustic Communication Based on Archimedes Optimization Algorithm and Random Forest" *Sensors* 23, no. 5: 2764.
https://doi.org/10.3390/s23052764