# Radar Maneuvering Target Detection Based on Product Scale Zoom Discrete Chirp Fourier Transform

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## Abstract

**:**

## 1. Introduction

## 2. Signal Model and Problem Formulation

## 3. Description of the Proposed Method

#### 3.1. MDCFT and Its Limitations

#### 3.2. Zoom DCFT

**Example**

**1.**

**Example**

**2.**

**Remark**

**1.**

#### 3.3. Scale ZDCFT

**Example**

**3.**

**Remark**

**2.**

#### 3.4. Product Operation and Coherent Integration

## 4. Analysis of the Proposed Method

#### 4.1. PSZDCFT for Multi-Targets

#### 4.2. Implementation of SZDCFT

#### 4.3. Computational Complexity

#### 4.4. Procedure of the Proposed Method

## 5. Numerical Results

#### 5.1. Coherent Integration for a Single Target

#### 5.2. Coherent Integration for Multi-Targets

#### 5.3. Detection Performance

#### 5.4. Parameter Estimation Performance

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Simulation results of Example 1. (

**a**) The result of MDCFT. (

**b**) The result of ZDCFT ($\alpha =4,\beta =1$).

**Figure 2.**Simulation results of Example 2. (

**a**) The correct result of ZDCFT ($\alpha =4,\beta =2$). (

**b**) The blurred result of ZDCFT ($\alpha =1,\beta =2$). (

**c**) The invalid result of ZDCFT ($\alpha =4,\beta =1$).

**Figure 3.**Simulation results of Example 3. (

**a**) The result of SZDCFT (${\psi}_{1}=1.01$). (

**b**) The result of SZDCFT (${\psi}_{2}=0.99$). (

**c**) The result of ZDCFT (${\psi}_{1}=1.01$). (

**d**) The result of ZDCFT (${\psi}_{2}=0.99$).

**Figure 7.**Coherent integration for a single target at SNR = 20 dB. (

**a**) The result of PC. (

**b**) The result of MDCFT at $f=-4$ MHz. (

**c**) The result of SZDCFT at $f=-4$ MHz. (

**d**) The result of SZDCFT at $f=4$ MHz. (

**e**) The result of PSZDCFT. (

**f**) The result of coherent integration.

**Figure 8.**The role of product operation in a low SNR environment (

**a**) The result of PC. (

**b**) The result of SZDCFT at $f=0$ MHz. (

**c**) The result of PSZDCFT. (

**d**) The result of coherent integration.

**Figure 9.**Coherent integration for multi-targets. (

**a**) The result of PC. (

**b**) The result of SZDCFT at $f=-4$ MHz. (

**c**) The result of SZDCFT at $f=4$ MHz. (

**d**) The result of PSZDCFT. (

**e**) The result of coherent integration for target A. (

**f**) The result of coherent integration for target B. (

**g**) The result of coherent integration for target C.

**Figure 11.**The results of parameter estimation for the proposed method and GRFT at SNR = −12 dB. (

**a**) The result of of parameter estimation for the proposed method. (

**b**) The result of of parameter estimation for GRFT.

**Figure 12.**Parameter estimation performance of different methods. (

**a**) RMSE of velocity estimation. (

**b**) RMSE of acceleration estimation.

Methods | Computational Complexity |
---|---|

GRFT | $O\left({N}_{v}{N}_{a}MN\right)$ |

RLVD | $O\left(3N{N}_{v}{N}_{a}{M}^{2}lo{g}_{2}M\right)$ |

ACCF | $O\left(MN(2lo{g}_{2}N+lo{g}_{2}M)\right)$ |

PC-TRT | $O\left({N}_{v}MNlo{g}_{2}\left(MN\right)\right)$ |

FAF-LVD | $O(3{M}^{2}lo{g}_{2}M+MN(7lo{g}_{2}M+2lo{g}_{2}N))$ |

Proposed | $O\left(N{M}^{2}(2+3lo{g}_{2}M)\right)$ |

Carrier frequency, ${\mathit{f}}_{\mathit{c}}$ | 1 GHz |

Bandwidth, B | 10 MHz |

Sample frequency, ${f}_{s}$ | 20 MHz |

Pulse repetition frequency, $PRF$ | 500 Hz |

Pulse duration, ${T}_{p}$ | 20 $\mathsf{\mu}$s |

Number of pulses, M | 1000 |

Motion Parameters | Target A | Target B | Target C |
---|---|---|---|

Initial range cell number | 451st | 476st | 501st |

Radial velocity | 120 m/s | −108 m/s | 117 m/s |

Radial acceleration | 45 m/${\mathrm{s}}^{2}$ | −30 m/${\mathrm{s}}^{2}$ | 42 m/${\mathrm{s}}^{2}$ |

SNR (after PC) | 20 dB | 20 dB | 20 dB |

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## Share and Cite

**MDPI and ACS Style**

Xia, L.; Gao, H.; Liang, L.; Lu, T.; Feng, B. Radar Maneuvering Target Detection Based on Product Scale Zoom Discrete Chirp Fourier Transform. *Remote Sens.* **2023**, *15*, 1792.
https://doi.org/10.3390/rs15071792

**AMA Style**

Xia L, Gao H, Liang L, Lu T, Feng B. Radar Maneuvering Target Detection Based on Product Scale Zoom Discrete Chirp Fourier Transform. *Remote Sensing*. 2023; 15(7):1792.
https://doi.org/10.3390/rs15071792

**Chicago/Turabian Style**

Xia, Lang, Huotao Gao, Lizheng Liang, Taoming Lu, and Boning Feng. 2023. "Radar Maneuvering Target Detection Based on Product Scale Zoom Discrete Chirp Fourier Transform" *Remote Sensing* 15, no. 7: 1792.
https://doi.org/10.3390/rs15071792