# An Improved Imaging Algorithm for Multi-Receiver SAS System with Wide-Bandwidth Signal

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## Abstract

**:**

## 1. Introduction

## 2. Imaging Geometry and PTRS

#### 2.1. Imaging Geometry

#### 2.2. PTRS

## 3. Error Discussion

#### 3.1. Signal Model Error

#### 3.2. PTRS Error

#### 3.3. Residual Quadratic Coupling Error

## 4. Imaging Algorithm

#### 4.1. Imagery

#### 4.2. Computation Load

_{r}sampling points in the cross-track dimension. N

_{a}sampling points are collected in the along-track dimension. $\rho $ represents the length of the interpolation kernel function, which is a sinc-function in this paper.

## 5. Experiment Results

#### 5.1. Simulations

#### 5.1.1. Results with Narrow-Bandwidth Case

#### 5.1.2. Results with Wide-Bandwidth Case

#### 5.2. Real Data Processing

#### 5.2.1. Results with the Narrow-Bandwidth Case

#### 5.2.2. Results with a Wide-Bandwidth Case

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Signal model error for the first transmitter/receiver pair when the system works with narrow-bandwidth. (

**a**) r = 40 m; (

**b**) r = 110 m; (

**c**) r = 180 m; (

**d**) r = 250 m.

**Figure 3.**Signal model error for the last transmitter/receiver pair when the system works with narrow-bandwidth. (

**a**) r = 40 m; (

**b**) r = 110 m; (

**c**) r = 180 m; (

**d**) r = 250 m.

**Figure 4.**Signal model error for the first transmitter/receiver pair when the system works with wide-bandwidth. (

**a**) r = 40 m; (

**b**) r = 110 m; (

**c**) r = 180 m; (

**d**) r = 250 m.

**Figure 5.**Signal model error for the last transmitter/receiver pair when the system works with wide-bandwidth. (

**a**) r = 40 m; (

**b**) r = 110 m; (

**c**) r = 180 m; (

**d**) r = 250 m.

**Figure 6.**PTRS error for the first transmitter/receiver pair when the system works with a narrow-bandwidth. (

**a**) r = 40 m; (

**b**) r = 110 m; (

**c**) r = 180 m; (

**d**) r = 250 m.

**Figure 7.**PTRS error for the last transmitter/receiver pair when the system works with a narrow-bandwidth. (

**a**) r = 40 m; (

**b**) r = 110 m; (

**c**) r = 180 m; (

**d**) r = 250 m.

**Figure 8.**PTRS error for the first transmitter/receiver pair when the system works with a wide-bandwidth. (

**a**) r = 40 m; (

**b**) r = 110 m; (

**c**) r = 180 m; (

**d**) r = 250 m.

**Figure 9.**PTRS error for the last transmitter/receiver pair when the system works with a wide-bandwidth. (

**a**) r = 40 m; (

**b**) r = 110 m; (

**c**) r = 180 m; (

**d**) r = 250 m.

**Figure 10.**Residual quadratic coupling error when the system works with a narrow-bandwidth signal. (

**a**) r = 40 m; (

**b**) r = 110 m; (

**c**) r = 180 m; (

**d**) r = 250 m.

**Figure 11.**Residual quadratic coupling error when the system works with a wide-bandwidth. (

**a**) r = 40 m; (

**b**) r = 110 m; (

**c**) r = 180 m; (

**d**) r = 250 m.

**Figure 14.**Imaging results with the case of a narrow-bandwidth signal. (

**a**) Traditional method; (

**b**) presented method; (

**c**) BP algorithm.

**Figure 16.**Imaging results with the case of a wide-bandwidth signal. (

**a**) Traditional method; (

**b**) presented method; (

**c**) BP algorithm.

**Figure 18.**Real data processing results with the case of a narrow-bandwidth signal. (

**a**) Traditional method; (

**b**) presented method; (

**c**) BP algorithm.

**Figure 19.**Cross-track slices of a target marked by a red circle in (

**a**). (

**a**) Global slices; (

**b**) close look.

**Figure 20.**Real data processing results with the case of a wide-bandwidth signal. (

**a**) Traditional method; (

**b**) presented method; (

**c**) BP algorithm.

**Figure 21.**Along-track slices of target marked by a red arrow in Figure 20a.

Parameter | Value | Unit |
---|---|---|

Platform velocity | 2 | m/s |

Pulse repetition interval | 0.35 | s |

Signal bandwidth | 20 | kHz |

Carrier frequency | 150 | kHz |

Receiver array length | 1.4 | m |

Receiver width | 0.04 | m |

Transmitter width | 0.08 | m |

Parameter | Value | Unit |
---|---|---|

Platform velocity | 2 | m/s |

Pulse repetition interval | 0.35 | s |

Signal bandwidth | 60 | kHz |

Carrier frequency | 150 | kHz |

Receiver array length | 1.4 | m |

Receiver width | 0.04 | m |

Transmitter width | 0.08 | m |

Operations | Data Size | Computation Load |
---|---|---|

Cross-track FT/IFT | ${N}_{r}$ | $\mathrm{O}(1.5{N}_{r}{\mathrm{log}}_{2}{N}_{r})$ |

Cross-track FT/IFT | ${N}_{a}\times {N}_{r}$ | $\mathrm{O}(1.5{N}_{a}\cdot {N}_{r}{\mathrm{log}}_{2}{N}_{r})$ |

Along-track FT/IFT | ${N}_{a}\times {N}_{r}$ | $\mathrm{O}(1.5{N}_{a}\cdot {N}_{r}{\mathrm{log}}_{2}{N}_{a})$ |

Multiplication | ${N}_{a}\times {N}_{r}$ | $\mathrm{O}({N}_{a}\cdot {N}_{r})$ |

Sinc-based interpolation | $\rho $ | $\mathrm{O}(2\rho -1)$ |

Operations | Presented Method | Traditional Method | BP Algorithm |
---|---|---|---|

Cross-track FT/IFT | 2M + 1 + N | 2M + 2 | 2 |

Along-track FT/IFT | M + 1 | M + 1 | 0 |

Multiplication | 3M + N + 1 | 3M + 1 | N_{a} × N_{r} |

Interpolation | M + 1 | M + 1 | ${N}_{a}^{2}\times {N}_{r}$ |

Method | PLSR (dB) | ISLR (dB) | Target |
---|---|---|---|

Traditional method | −14.47 | −8.04 | T1 |

Presented method | −14.66 | −8.17 | |

BP algorithm | −14.81 | −8.27 | |

Traditional method | −14.47 | −8.79 | T2 |

Presented method | −14.52 | −8.88 | |

BP algorithm | −14.64 | −8.90 | |

Traditional method | −14.70 | −9.76 | T3 |

Presented method | −14.75 | −9.81 | |

BP algorithm | −14.87 | −9.88 |

Method | Resolution (m) | PLSR (dB) | ISLR (dB) | Target |
---|---|---|---|---|

Traditional method | 0.05 | −13.31 | −5.26 | T1 |

Presented method | 0.04 | −15.65 | −8.96 | |

BP algorithm | 0.04 | −15.85 | −8.97 | |

Traditional method | 0.05 | −13.82 | −6.86 | T2 |

Presented method | 0.04 | −15.61 | −9.61 | |

BP algorithm | 0.04 | −15.66 | −9.65 | |

Traditional method | 0.04 | −16.18 | −10.62 | T3 |

Presented method | 0.04 | −15.79 | −10.83 | |

BP algorithm | 0.04 | −15.83 | −10.91 |

Parameter | Value | Unit |
---|---|---|

Platform velocity | 2.5 | m/s |

Pulse repetition interval | 0.32 | s |

Signal bandwidth | 20 | kHz |

Carrier frequency | 150 | kHz |

Receiver array length | 1.2 | m |

Receiver element width | 0.04 | m |

Transmitter width | 0.08 | m |

Parameter | Value | Unit |
---|---|---|

Platform velocity | 2 | m/s |

Pulse repetition interval | 0.06 | s |

Signal bandwidth | 7 | kHz |

Carrier frequency | 12 | kHz |

Receiver array length | 0.24 | m |

Receiver element width | 0.08 | m |

Transmitter width | 0.08 | m |

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**MDPI and ACS Style**

Zhang, X.; Yang, P.
An Improved Imaging Algorithm for Multi-Receiver SAS System with Wide-Bandwidth Signal. *Remote Sens.* **2021**, *13*, 5008.
https://doi.org/10.3390/rs13245008

**AMA Style**

Zhang X, Yang P.
An Improved Imaging Algorithm for Multi-Receiver SAS System with Wide-Bandwidth Signal. *Remote Sensing*. 2021; 13(24):5008.
https://doi.org/10.3390/rs13245008

**Chicago/Turabian Style**

Zhang, Xuebo, and Peixuan Yang.
2021. "An Improved Imaging Algorithm for Multi-Receiver SAS System with Wide-Bandwidth Signal" *Remote Sensing* 13, no. 24: 5008.
https://doi.org/10.3390/rs13245008