# Focusing Bistatic Forward-Looking Synthetic Aperture Radar Based on an Improved Hyperbolic Range Model and a Modified Omega-K Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Geometry and Equivalent Slant Range Model

#### 2.1. Equivalent Slant Range Model

#### 2.2. Range Error Analysis

## 3. Imaging Algorithm

#### 3.1. Signal Model

#### 3.2. Modified Omega-K Imaging Algorithm

- (1)
- Performing range fast Fourier transform (FFT) on SAR data gets ${S}_{2}({f}_{r},\eta )$.
- (2)
- (3)
- Performing azimuth fast Fourier transform (FFT) on ${S}_{3}({f}_{r},\eta )$ gets ${S}_{7}({k}_{r},{k}_{x})$.
- (4)
- (5)
- (6)
- Performing Stolt interpolation on ${S}_{9}({k}_{r},{k}_{x})$ gets ${S}_{10}({k}_{r},{k}_{x})$.
- (7)
- Performing 2D-IFFT on ${S}_{10}({k}_{r},{k}_{x})$ gets output SAR focusing results.

## 4. Simulation Results

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Approximation error of the bistatic slant range. (

**a**) Approximation error of the traditional range model. (

**b**) Approximation error of the proposed range model.

**Figure 5.**Imaging results. (

**a**) Imaging results of the traditional hyperbolic omega-K algorithm. (

**b**) Imaging results of the proposed hyperbolic omega-K algorithm.

**Figure 6.**Imaging results. (

**a**) Imaging result of ${P}_{0}$ by the traditional algorithm. (

**b**) Imaging result of ${P}_{2}$ by the traditional algorithm. (

**c**) Imaging result of ${P}_{3}$ by the traditional algorithm. (

**d**) Imaging result of ${P}_{0}$ by the proposed algorithm. (

**e**) Imaging result of ${P}_{2}$ by the proposed algorithm. (

**f**) Imaging result of ${P}_{3}$ by the proposed algorithm.

**Figure 7.**Azimuth impulse response of ${P}_{3}$. (

**a**) Traditional hyperbolic omega-K algorithm. (

**b**) Proposed hyperbolic omega-K algorithm.

Parameters | Values | Parameters | Values |
---|---|---|---|

Carrier frequency | 9 GHz | Transmitter center slant range | 4300 m |

Pulse duration | 2 $\mathsf{\mu}\mathrm{s}$ | Transmitter squint angle | ${7}^{\circ}$ |

Bandwidth | 200 MHz | Receiver center slant range | 3600 m |

Sampling frequency | 300 MHz | Receiver forward-looking angle | ${33}^{\circ}$ |

Pulse repetition frequency | 1 kHz | Sensor speed | 200 m/s |

**Table 2.**Image quality parameters of ${P}_{3}$. PSLR, peak sidelobe ratio; ISLR, integrated sidelobe ratio.

Targets | PSLR (dB) | ISLR (dB) | ||
---|---|---|---|---|

Azimuth | Range | Azimuth | Range | |

Traditional omega-K algorithm | −1.705 | - | - | - |

Proposed omega-K algorithm | −12.87 | −13.33 | −8.86 | −9.9558 |

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## Share and Cite

**MDPI and ACS Style**

Wang, C.; Su, W.; Gu, H.; Yang, J.
Focusing Bistatic Forward-Looking Synthetic Aperture Radar Based on an Improved Hyperbolic Range Model and a Modified Omega-K Algorithm. *Sensors* **2019**, *19*, 3792.
https://doi.org/10.3390/s19173792

**AMA Style**

Wang C, Su W, Gu H, Yang J.
Focusing Bistatic Forward-Looking Synthetic Aperture Radar Based on an Improved Hyperbolic Range Model and a Modified Omega-K Algorithm. *Sensors*. 2019; 19(17):3792.
https://doi.org/10.3390/s19173792

**Chicago/Turabian Style**

Wang, Chenchen, Weimin Su, Hong Gu, and Jianchao Yang.
2019. "Focusing Bistatic Forward-Looking Synthetic Aperture Radar Based on an Improved Hyperbolic Range Model and a Modified Omega-K Algorithm" *Sensors* 19, no. 17: 3792.
https://doi.org/10.3390/s19173792