# Onboard Digital Beamformer with Multi-Frequency and Multi-Group Time Delays for High-Resolution Wide-Swath SAR

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## Abstract

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## 1. Introduction

## 2. Conventional Onboard DBF Processor and Analysis

## 3. Theories of Two Improved DBF Processors

#### 3.1. Improved DBF Processor with Multi-Group Time Delays

#### 3.2. Improved DBF Processor with Multi-Frequency Time Delays

#### 3.3. Major Drawbacks of Two Improved DBF Processors

## 4. Methodology of Proposed DBF Processor with Multi-Frequency and Multi-Group Time Delays

## 5. Results

#### 5.1. Simulation Experiments on Point Targets

#### 5.2. Simulation Experiments on Distributed Targets

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Simulation results processed by the conventional DBF processor. (

**a**) Real part of echoes with the selected reference slant range of 890 km. (

**b**) Real part of echoes with the optimized reference range of 875 km. (

**c**) Residual PEL in (

**a**,

**d**). Residual PEL in (

**a**,

**b**).

**Figure 5.**Simulation results processed by the DBF processor with the multi-group time delays. (

**a**) Real part of echoes handled by the improved DBF processor with two-group time delays. (

**b**) Real part of echoes handled by the improved DBF processor with four-group time delays. (

**c**) Residual PEL in (

**a**,

**d**). Residual PEL in (

**a**,

**b**).

**Figure 7.**Processing results of signals processed by the improved DBF processor with multi-frequency time delays. (

**a**) Real part of echoes with 3 sub-pulses. (

**b**) Real part of echoes with 7 sub-pulses. (

**c**) Residual PEL in (

**a**,

**d**). Residual PEL in (

**a**,

**b**).

**Figure 9.**Pulse compression results of the improved DBF processor with multi-frequency time delays (

**a**) Pulse compression results with amplitude errors between different frequency sub-bands. (

**b**) Pulse compression results with phase errors between different frequency sub-bands.

**Figure 10.**Processing diagram of the proposed DBF processor with multi-frequency and multi-group time delays.

**Figure 11.**Processing results of the proposed DBF processor. (

**a**) Real parts of the output signal handled by the proposed DBF processor. (

**b**) Residual PEL. (

**c**) Range compression result. (

**d**) Interpolations of compression results of the selected three point targets.

**Figure 12.**Processing results of the simulated distributed scene by the conventional DBF processor and the proposed DBF processor. (

**a**) Focused SAR image for echo simulation. (

**b**) Conventional DBF processor processing result. (

**c**) Proposed DBF processor processing result. (

**d**) Normalized average amplitude comparison.

Parameters | Symbol | Value |
---|---|---|

Radius of the earth | ${R}_{e}$ | 6371 km |

Orbit height | H | 750 km |

Look angle of antenna normal direction | $\beta $ | 30° |

Carrier frequency | ${f}_{c}$ | 9.6 GHz |

Number of channels in elevation | N | 12 |

Pulse duration | T | 30 us |

Subaperture spacing | d | 0.3 m |

Pulse bandwidth | ${B}_{r}$ | 1200 MHz |

Range sampling frequency | ${f}_{s}$ | 1440 MHz |

Method | Target 1 | Target 2 | Target 3 | Target 4 | Target 5 | Target 6 | Target 7 |
---|---|---|---|---|---|---|---|

Conventional DBF | −3.569 dB | −1.712 dB | −0.405 dB | 0 | −0.319 dB | −1.136 dB | −2.012 dB |

Conventional DBF after optimization | −2.562 dB | −0.799 dB | −0.029 dB | −0.023 dB | −1.028 dB | −2.125 dB | −3.128 dB |

DBF with two-group time delays | −0.431 dB | −0.455 dB | −0.851 dB | −0.392 dB | −0.002 dB | −0.216 dB | −0.806 dB |

DBF with four-group time delays | −0.005 dB | −0.091 dB | −0.183 dB | −0.002 dB | −0.254 dB | −0.021 dB | −0.115 dB |

DBF with 3 sub-bands | −1.982 dB | −1.152 dB | −0.479 dB | −0.148 dB | −0.009 dB | −0.027 dB | −0.162 dB |

DBF with 7 sub-bands | −0.558 dB | −0.289 dB | −0.127 dB | −0.035 dB | −0.002 dB | −0.007 dB | −0.043 dB |

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**MDPI and ACS Style**

Xu, W.; Yu, Q.; Fang, C.; Huang, P.; Tan, W.; Qi, Y.
Onboard Digital Beamformer with Multi-Frequency and Multi-Group Time Delays for High-Resolution Wide-Swath SAR. *Remote Sens.* **2021**, *13*, 4354.
https://doi.org/10.3390/rs13214354

**AMA Style**

Xu W, Yu Q, Fang C, Huang P, Tan W, Qi Y.
Onboard Digital Beamformer with Multi-Frequency and Multi-Group Time Delays for High-Resolution Wide-Swath SAR. *Remote Sensing*. 2021; 13(21):4354.
https://doi.org/10.3390/rs13214354

**Chicago/Turabian Style**

Xu, Wei, Qi Yu, Chonghua Fang, Pingping Huang, Weixian Tan, and Yaolong Qi.
2021. "Onboard Digital Beamformer with Multi-Frequency and Multi-Group Time Delays for High-Resolution Wide-Swath SAR" *Remote Sensing* 13, no. 21: 4354.
https://doi.org/10.3390/rs13214354