# A Novel Sidelobe Reduction Algorithm Based on Two-Dimensional Sidelobe Correction Using D-SVA for Squint SAR Images

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## Abstract

**:**

## 1. Introduction

## 2. Sidelobe Control Algorithms for SAR Images

#### 2.1. Traditional Linear Windowing

#### 2.2. Nonlinear Apodization (Windowing)

#### 2.3. Dual-Delta Factorization

#### 2.4. Iterative Adaptive Approach (IAA)

## 3. Non-Integer Nyquist SVA Algorithm

_{s}is the sampling frequency, f is the frequency whose support region is $\left[-\frac{{f}_{0}}{2},\frac{{f}_{0}}{2}\right],\hspace{1em}{f}_{0}$ is the signal bandwidth, a is a constraint parameter which guarantees the unit gain at the center of the aperture, and ω

_{1}is the parameter which can vary according to the weighting function.

- Calculate the value of g′(m) for ω
_{1}= 0 and ω_{1}= ω_{1_max}(the upper limit of Equation (9)). - If the two values of g′(m) are opposite in sign, the output equals to zero at pixel m.
- Otherwise, the output equals to the lowest magnitude.

## 4. Two-Dimensional Sidelobe Correction Using D-SVA for Squint SAR Images

#### 4.1. D-SVA for Non-Integer Nyquist Sampled Imagery

#### 4.1.1. Additional SVA Algorithm

- Calculate the value of g″(m) for ω′
_{1}= 0 and ω′_{1}= ω′_{1_max}(the upper limit of Equation (13)). - If the two values of g″(m) are opposite in sign, the output equals to zero at pixel m.
- Otherwise, the output equals to the lowest magnitude.

#### 4.1.2. D-SVA Algorithm

#### 4.2. Specturm Correction for Squint SAR Images

**α**as the range sidelobe correction angle between the original range sidelobe and the corrected range sidelobe, and the corresponding time delay in time domain as k

_{1}y:

_{2}x:

#### 4.3. Sidelobe Reduction for Squint SAR Images

- First, transform the squint SAR images E
_{0}into frequency domain and shift the center of the frequency spectrum to the data’s center. Then by applying an inverse IFT to the data in time domain, the new data E_{1}is recorded. - Range sidelobe correction

_{1}. According to the sidelobe directions of the strong scatterer, estimate the range sidelobe angle α

_{y}, so:

_{A}(·) and ift

_{A}(·) are the azimuth FT and azimuth IFT, respectively.

- 3.
- Azimuth sidelobe correction

_{2}. According to the sidelobe directions of the strong scatterer, estimate the azimuth sidelobe angle α

_{x}, so:

_{R}(·) and ift

_{R}(·) are the range FT and range IFT, respectively.

- 4.
- Use D-SVA to process the range and azimuth, obtaining E
_{4}. - 5.
- Use azimuth phase shift term to rotate the azimuth sidelobes for E
_{4}:$${E}_{5}=if{t}_{R}\left[f{t}_{R}({E}_{4})\cdot \mathrm{exp}\left\{j2\pi \cdot d{X}_{a}\cdot \eta \right\}\right]$$ - 6.
- Use range phase shift term to rotate the range sidelobes for E
_{5}:$${E}_{6}=if{t}_{A}\left[f{t}_{A}\left({E}_{5}\right)\cdot \mathrm{exp}\left\{j2\pi \cdot \xi \cdot d{Y}_{r}\right\}\right]$$ - 7.
- At each spatial location, select the minimum value between E
_{6}and E_{1}as output.

## 5. Simulation Results and Analysis

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Sun, Z.C.; Wu, J.J.; Li, Z.Y.; Huang, Y.L.; Yang, J.Y. Highly Squint SAR Data Focusing Based on Keystone Transform and Azimuth Extended Nonlinear Chirp Scaling. IEEE Trans. Geosci. Remote Sens. Lett.
**2015**, 12, 145–149. [Google Scholar] - An, D.X.; Huang, X.T.; Jin, T.; Zhou, Z.M. Extended Nonlinear Chirp Scaling Algorithm for High-Resolution Squint SAR Data Focusing. IEEE Trans. Geosci. Remote Sens.
**2012**, 50, 3595–3609. [Google Scholar] [CrossRef] - Stankwitz, H.C.; Dallaire, R.J.; Fienup, J.R. Nonlinear apodization for sidelobe control in SAR imagery. IEEE Trans. Aerosp. Electron. Syst.
**1995**, 31, 267–279. [Google Scholar] [CrossRef] - Smith, B.H. Generalization of Spatially Variant Apodization to Noninteger Nyquist Sampling Rates. IEEE Trans. Image Process.
**2000**, 9, 1088–1093. [Google Scholar] [CrossRef] [PubMed] - Castillo-Rubio, C.; Llorente-Romano, S.; Burgos-García, M. Robust SVA method for every sampling rate condition. IEEE Trans. Aerosp. Electron. Syst.
**2007**, 43, 571–580. [Google Scholar] [CrossRef] - Ni, C.; Wang, Y.F.; Xu, X.H.; Zhou, C.Y.; Cui, P.F. A SAR sidelobe suppression algorithm based on modified spatially variant apodization. Sci. China Technol. Sci.
**2010**, 53, 2542–2551. [Google Scholar] [CrossRef] - Xiong, T.; Wang, S.; Hou, B.; Wang, Y. A resample-based SVA algorithm for sidelobe reduction of SAR/ISAR imagery with noninteger Nyquist sampling rate. IEEE Trans. Geosci. Remote Sens.
**2015**, 53, 1016–1027. [Google Scholar] [CrossRef] - Shi, J.; Liu, Y.; Zhang, X.L.; Ling, F. A Novel SAR Sidelobe Suppression Method via Dual-Delta Factorization. IEEE Trans. Geosci. Remote Sens. Lett.
**2015**, 12, 1576–1580. [Google Scholar] - Castillo-Rubio, C.; Llorente-Romano, S.; Burgos-García, M. Spatially variant apodization for squint synthetic aperture radar images. IEEE Trans. Image Process.
**2007**, 16, 2023–2027. [Google Scholar] [CrossRef] [PubMed] - DeGraaf, S.R. Sidelobe Reduction via Adaptive FIR Filtering in SAR Imagery. IEEE Trans. Image Process.
**1994**, 3, 292–301. [Google Scholar] [CrossRef] [PubMed] - Sok-Son, J.; Thomas, G.; Flores, B.C. Range-Doppler Radar Imaging and Motion Compensation; Artech House: Norwood, MA, USA, 2001; pp. 218–230. [Google Scholar]
- Stankwitz, H.C.; Kosek, M.R. Sparse Aperture Fill for SAR Using Super-SVA. In Proceedings of the 1966 IEEE National Radar Conference, Ann Arbor, MI, USA, 13–16 May 1996; pp. 70–75. [Google Scholar]
- Ni, C.; Wang, Y.F.; Xu, X.H.; Zhou, C.Y.; Cui, P.F. A Super-Resolution Algorithm for Synthetic Aperture Radar Based on Modified Spatially Variant apodization. Sci. China Technol. Sci.
**2011**, 54, 355–364. [Google Scholar] [CrossRef] - Lim, B.G.; Woo, J.C.; Kim, Y.S. Noniterative Super-Resolution Technique Combining SVA with Modified Geometric Mean Filter. IEEE Trans. Geosci. Remote Sens. Lett.
**2010**, 7, 713–717. [Google Scholar] [CrossRef] - Wang, J.K.; Wang, P.B. Sidelobe Suppression Algorithm for SAR Imaging Based on Iterative Adaptive Approach. In Proceedings of the 2015 IEEE 5th Asia-Pacific Conference on Synthetic Aperture Radar, Marina Bay Sands, Singapore, 1–4 September 2015; pp. 443–446. [Google Scholar]
- Long, T.; Li, Y.; Ding, Z.; Liu, L. Interpolation method for geometric correction in highly squint synthetic aperture radar. IET Radar Sonar Navig.
**2012**, 6, 620–626. [Google Scholar] [CrossRef]

**Figure 2.**Impulse response for Squint SAR images (40°). (

**a**) Original image; (

**b**) SVA processed image.

**Figure 6.**The squint SAR images (

**a**) Squint angle 40° SAR image; (

**b**)Range sidelobes corrected; (

**c**)Range and azimuth sidelobes corrected; (

**d**~

**f**) are the 2-D spectrum images for (

**a**~

**c**), respectively.

**Figure 11.**Range profiles for the nine points. (

**a11**~

**a33**) are the nine points’ range profiles, respectively.

**Figure 12.**Azimuth profiles for the nine points. (

**a11**~

**a33**) are the nine points’ azimuth profiles, respectively.

**Figure 13.**Sidelobe reduction results of squint SAR image (

**a**) Processed result by using the method of References [9]; (

**b**) Processed result by using the proposed method.

**Figure 14.**Range and azimuth profiles comparison between the two methods (

**a**) Range profiles; (

**b**) Azimuth profiles.

**Figure 15.**The unprocessed and processed squint SAR images (

**a**) Unprocessed image; (

**b**) Processed image by using our proposed method.

Parameters | Value | Units |
---|---|---|

Wavelength | 0.05657 | m |

Pulse bandwidth | 100 | MHz |

Sampling rate | 120 | MHz |

Velocity | 250 | m/s |

Pulse duration | 1 | $\mu s$ |

Pulse repetition frequency | 500 | Hz |

Squint angle | 40 | deg |

Synthetic aperture time | 2.5136 | sec |

Central slant range | 22.057 | Km |

Performance Index | Traditional SVA | Proposed Framework | |
---|---|---|---|

a11 | Range PSLR | −15.38 dB | −33.13 dB |

Azimuth PSLR | −14.42 dB | −30.63 dB | |

a12 | Range PSLR | −14.73 dB | −30.64 dB |

Azimuth PSLR | −14.67 dB | −30.51 dB | |

a13 | Range PSLR | −14.95 dB | −39.42 dB |

Azimuth PSLR | −14.54 dB | −30.88 dB | |

a21 | Range PSLR | −15.36 dB | −33.36 dB |

Azimuth PSLR | −14.42 dB | −30.64 dB | |

a22 | Range PSLR | −14.72 dB | −30.80 dB |

Azimuth PSLR | −14.63 dB | −30.44 dB | |

a23 | Range PSLR | −15.04 dB | −39.62 dB |

Azimuth PSLR | −14.59 dB | 30.43 dB | |

a31 | Range PSLR | −15.33 dB | −33.58 dB |

Azimuth PSLR | −14.43 dB | −30.84 dB | |

a32 | Range PSLR | −14.75 dB | −30.85 dB |

Azimuth PSLR | −14.61 dB | −30.26 dB | |

a33 | Range PSLR | −15.07 dB | −41.15 dB |

Azimuth PSLR | −14.59 dB | −30.34 dB |

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**MDPI and ACS Style**

Liu, M.; Li, Z.; Liu, L. A Novel Sidelobe Reduction Algorithm Based on Two-Dimensional Sidelobe Correction Using D-SVA for Squint SAR Images. *Sensors* **2018**, *18*, 783.
https://doi.org/10.3390/s18030783

**AMA Style**

Liu M, Li Z, Liu L. A Novel Sidelobe Reduction Algorithm Based on Two-Dimensional Sidelobe Correction Using D-SVA for Squint SAR Images. *Sensors*. 2018; 18(3):783.
https://doi.org/10.3390/s18030783

**Chicago/Turabian Style**

Liu, Min, Zhou Li, and Lu Liu. 2018. "A Novel Sidelobe Reduction Algorithm Based on Two-Dimensional Sidelobe Correction Using D-SVA for Squint SAR Images" *Sensors* 18, no. 3: 783.
https://doi.org/10.3390/s18030783