# Ambiguity Suppression Based on Joint Optimization for Multichannel Hybrid and ±π/4 Quad-Pol SAR Systems

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Multichannel Hybrid and $\pm \pi /4$ Quad-Pol SAR Systems

#### 2.1.1. Multichannel Quad-Pol SAR

#### 2.1.2. Sampling Frequency (PRF)

#### 2.2. Reconstruction Methods for Multichannel Quad-Pol SAR

#### 2.2.1. Conventional Matrix Inversion (MI) Method

#### 2.2.2. Joint Optimization to Suppress the Ambiguity (JOSA)

## 3. Results

- (1)
- AASR for different polarizations after reconstruction;
- (2)
- RASR for different polarizations after reconstruction;
- (3)
- Output signal-to-noise ratio (SNR) for different polarizations.

#### 3.1. Characterization of the Reconstruction and Performance

#### 3.1.1. Effects of Reconstruction on Azimuth Ambiguity

#### 3.1.2. Effects of Reconstruction on Range Ambiguity

#### 3.2. Numerical Simulation Results of Reconstruction Methods

#### 3.2.1. ASRs Performance of Single-Channel $\pm \pi /4$ Quad-Pol SAR System (System #1)

#### 3.2.2. ASRs Performance of Multichannel $\pm \pi /4$ Quad-Pol SAR System (Systems #2 & #3)

#### 3.2.3. Imaging Simulation Results

#### 3.3. Effects of Reconstruction on Noise

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AASR | Azimuth ambiguity-to-signal ratio |

JOSA | Joint optimization to suppress the ambiguity |

MI | Matrix inverse |

PRF | Pulse repetition frequency |

RASR | Range ambiguity-to-signal ratio |

SNR | Signal-to-noise ratio |

SAR | Synthetic aperture radar |

UDR | Ratio of undesired azimuth signal power and desired azimuth signal power |

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**Figure 2.**Spatial distribution of samples in azimuth direction from four transmit pulses separated by ${T}_{p}/2$ for a three-channel $\pm \pi /4$ quad-pol SAR systems. The circles represent equivalent phase centers separated by $d/2$.

**Figure 4.**Diagrams of systems #1, #2 and #3. Systems #1 and #2 have the same length of Rx antenna, while systems #2 and #3 have the same number of channels.

**Figure 5.**Configuration of systems #1, #2 and #3. Systems #1 and #2 have the same length of Rx antenna, while systems #2 and #3 have the same number of channels.

**Figure 6.**AASR and RASR performance of $\pm \pi /4$ quad-pol SAR system (system #1). (

**a**) AASR versus PRF; (

**b**) RASR (PRF = 3756 Hz) versus the ground range.

**Figure 7.**AASR and RASR performance of system #2 by MI method. (

**a**) the AASR versus PRF; (

**b**) the RASR (PRF = 3756 Hz) versus the ground range.

**Figure 8.**AASR and RASR performance of system #2 by JOSA method. (

**a**) the AASR versus PRF. (

**b**) the RASR (PRF = 3756 Hz) versus the ground range.

**Figure 9.**AASR and RASR performance of system #3 by MI method. (

**a**) the AASR versus PRF. (

**b**) the RASR (PRF = 3756 Hz) versus the ground range.

**Figure 10.**AASR and RASR performance of system #3 by JOSA method. (

**a**) the AASR versus PRF. (

**b**) the RASR (PRF = 3756 Hz) versus the ground range.

**Figure 11.**Multi-point imaging results of VH polarization with azimuth ambiguities considered (nine points). System parameters in Table 1 is applied. Amplitude of all the sub-figures is normalized in dB. (

**a**) Multi-point simulation result of VH polarization based on system #1 (single-channel $\pm \pi /4$ quad-pol SAR); (

**b**) points simulation result of VH polarization based on system #2 (multichannel $\pm \pi /4$ quad-pol SAR), reconstructed via the conventional MI method; (

**c**) points simulation result of VH polarization based on system #2 (multichannel $\pm \pi /4$ quad-pol SAR), reconstructed via the proposed JOSA method. Points marked with

**solid red rectangle**in (

**a**–

**c**) represent the desired targets, while the points in

**yellow dashed rectangle**represent the fake targets introduced by ambiguities. (

**d**–

**f**) give the up-sampled imaging results of the desired targets (points in the upper-left corner) in (

**a**–

**c**), respectively.

**Figure 12.**Multi-point imaging results of VV polarization with azimuth ambiguities considered (nine points). System parameters in Table 1 are applied. Amplitude of all the sub-figures is normalized in dB. (

**a**) Multi-point simulation result of VV polarization based on system #1 (single-channel $\pm \pi /4$ quad-pol SAR); (

**b**) points simulation result of VV polarization based on system #2 (multichannel $\pm \pi /4$ quad-pol SAR), reconstructed via the conventional MI method; (

**c**) points simulation result of VV polarization based on system #2 (multichannel $\pm \pi /4$ quad-pol SAR), reconstructed via the proposed JOSA method. Points marked with

**red solid rectangle**in (

**a**–

**c**) represent the desired targets, while the points in

**yellow dashed rectangle**represent the fake targets induced by ambiguities. (

**d**–

**f**) give the up-sampled imaging results of the desired targets (points in the upper-left corner) in (

**a**–

**c**), respectively.

**Figure 13.**SNR performance curves of system #2 after reconstruction (

**a**) via conventional MI method; (

**b**) via the proposed JOSA method.

**Figure 14.**SNR performance curves of system #3 after reconstruction (

**a**) via conventional MI method; (

**b**) via the proposed JOSA method.

Parameters | System #1 | System #2 | System #3 |
---|---|---|---|

Radar frequency | 5.4 GHz (C-band) | ||

Orbit height | 628 km | ||

Radar velocity | 7600 m/s | ||

Minimum ground range | 334 km | ||

Maximum ground range | 370 km | ||

Tilt angle | ${31.5}^{\circ}$ | ||

Antenna type | Planar | ||

Antenna height | 2.1 m | ||

Tx antenna length | 8 m | 8 m | 8 m |

Rx antenna total length | 8 m | 8 m | 16 m |

Number of Rx channels | 1 | 2 | 2 |

Length of sub-antenna | – | 4 m | 8 m |

Antenna spacing | – | 4 m | 8 m |

Doppler bandwidth | 673 Hz | 838 Hz | 673 Hz |

Backscatter model | Ulaby and Dobson, shrubs |

Systems | System #1 | System #2 | System #3 | ||
---|---|---|---|---|---|

Methods | Combination | MI | JOSA | MI | JOSA |

HV | $-5.42$ dB | $31.22$ dB | $-25.74$ dB | $-10.01$ dB | $-12.51$ dB |

HH | $-23.51$ dB | $12.14$ dB | $-25.89$ dB | $-27.16$ dB | $-27.33$ dB |

VH | $-6.59$ dB | $29.98$ dB | $-25.77$ dB | $-11.24$ dB | $-13.70$ dB |

VV | $-22.48$ dB | $13.38$ dB | $-25.89$ dB | $-26.33$ dB | $-26.62$ dB |

Systems | System #1 | System #2 | System #3 | ||
---|---|---|---|---|---|

Methods | Combination | MI | JOSA | MI | JOSA |

HV | $-2.33$ dB | $16.16$ dB | $-20.44$ dB | $-7.7$ dB | $-14$ dB |

HH | $-20.49$ dB | $-2.9$ dB | $-23.11$ dB | $-26.26$ dB | $-28.15$ dB |

VH | $-3.57$ dB | $14.92$ dB | $-20.97$ dB | $-8.95$ dB | $-15.17$ dB |

VV | $-19.46$ dB | $-1.66$ dB | $-23.11$ dB | $-25.14$ dB | $-27.45$ dB |

Systems | System #1 | System #2 | |
---|---|---|---|

Methods | Combination | MI | JOSA |

VH | $-19.39$ dB | $17.88$ dB | $-50.26$ dB |

VV | $-38.49$ dB | $-1.24$ dB | $-68.98$ dB |

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**MDPI and ACS Style**

Zhao, P.; Deng, Y.; Wang, W.; Zhang, Y.; Wang, R.
Ambiguity Suppression Based on Joint Optimization for Multichannel Hybrid and ±*π*/4 Quad-Pol SAR Systems. *Remote Sens.* **2021**, *13*, 1907.
https://doi.org/10.3390/rs13101907

**AMA Style**

Zhao P, Deng Y, Wang W, Zhang Y, Wang R.
Ambiguity Suppression Based on Joint Optimization for Multichannel Hybrid and ±*π*/4 Quad-Pol SAR Systems. *Remote Sensing*. 2021; 13(10):1907.
https://doi.org/10.3390/rs13101907

**Chicago/Turabian Style**

Zhao, Pengfei, Yunkai Deng, Wei Wang, Yongwei Zhang, and Robert Wang.
2021. "Ambiguity Suppression Based on Joint Optimization for Multichannel Hybrid and ±*π*/4 Quad-Pol SAR Systems" *Remote Sensing* 13, no. 10: 1907.
https://doi.org/10.3390/rs13101907