# Analysis of Hypersonic Platform-Borne SAR Imaging: A Physical Perspective

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- Based on the hypersonic platform-borne SAR signal propagation characteristics under plasma sheath, the hypersonic platform-borne SAR signal model is established. The transmission coefficient for SAR signal propagating through plasma sheath is computed by scatter matrix method. Furthermore, because the hypersonic platform-borne SAR signal propagates through the plasma sheath twice, the double transmission effect is coupled in the SAR signal model.
- By building a ground experiment system, SAR signal model under plasma sheath is verified experimentally. The plasma is produced by low-pressure glow discharge plasma generator. By comparing the theoretical and experimental results of time domain, frequency domain, and range compressed signal, the SAR signal model under plasma sheath is verified. From the theoretical and experimental results, it can be found that the plasma sheath will bring significant amplitude attenuation of SAR signal, which will cause the decrease of peak value of range compressed signal. This phenomenon is important and will significantly affect SAR imaging quality.
- The effect of attenuation characteristics caused by plasma sheath on SAR imaging is studied, and the key factors determining the SAR imaging quality are explored. The point target and the area targets imaging results under plasma sheath show that large attenuation will cause the focus depth decrease and even cause the target response to be submerged in the noise. In addition, by studying the key factors determining the SAR imaging quality under plasma sheath, it can be concluded that the severe degradation of SAR imaging appears at condition of high plasma sheath electron density and low SAR carrier frequency.

## 2. Model and Experiment

#### 2.1. Introduction of Hypersonic Platform-Borne SAR Imaging under Plasma Sheath

^{16}/m

^{3}to 1 × 10

^{19}/m

^{3}.

#### 2.2. Hypersonic Platform-Borne SAR Signal Model Coupling Plasma Sheath Effect

_{1}and c

_{2}represent the shape of the distribution of electron density vertically on the platform surface. Ne

_{peak}is the maximum density and z

_{peak}is the location of peak electron density. The plasma sheath can be approximately divided into a series of adjacent homogeneous thin plasma layers. The distribution of plasma sheath is shown in Figure 4.

_{r}is fast time, ${T}_{p}$ is the pulse width, ${f}_{c}$ is carrier frequency, and $\gamma $ is the frequency modulation rate. If without plasma sheath, after being reflected by the target P in the scene, the echo can be written as

_{0}are the platform velocity and minimum slant range, respectively. By applying the principle of stationary phase (POSP), the range compressed SAR signal without plasma sheath can be written as

_{m}is wave number, and reads

#### 2.3. Experimental Verification of the SAR Signal Model under Plasma Sheath

^{16}/m

^{3}whose plasma frequency is near the carrier frequency, and the purpose is to reproduce the situation in which serious attenuation happens when carrier frequency is close to plasma frequency. This situation is common due to a large varying range of plasma sheath electron density, and it deserves to be discussed in detail. This is reason why we chose the selected experimental parameters in this section.

^{16}/m

^{3}. As shown in Figure 13, the signal waveforms of theory and experiment in time domain are similar. It can be found that the SAR signal shows an upward trend in time domain. The frequency spectrum of signal after down conversion in Figure 14 also shows the same trend. The frequency spectrum in Figure 14 is normalized to a maximum value of amplitude of spectrum without plasma. This phenomenon is closely related to the transmission coefficient shown in Figure 16. As the transmission coefficient of the EM wave in high frequency is larger than that in low frequency, the transmission coefficient shows an upward trend. Based on Equation (10), the transmission coefficient $T\left({f}_{r}\right)$ of SAR signal is coupled into the SAR signal model under plasma sheath. Therefore, the envelope of SAR signal with plasma will also show an upward trend. The transmission coefficient $T({f}_{r})$ is key factor determining the signal characteristics. In order to further illustrate the correctness of signal model, the computing result of transmission coefficient $T({f}_{r})$ using scatter matrix method and FDTD method are compared in Figure 16, and their results are similar. Therefore, the signal model coupling transmission coefficient computed by scatter matrix method is credible based on theoretical and experiment results.

^{4}shown in Figure 12. The amplitude of signal waveform without plasma in time domain is about 3.5 shown in Figure 10. However, when plasma presents, the signal suffers from serious attenuation. The amplitude attenuation of transmission coefficient in bandwidth is more than −4 dB based on Figure 16. Therefore, the average amplitude of signal with plasma in time domain shown in Figure 13 is near 1.2 which is much smaller than the amplitude of signal without plasma. The spectrum with plasma sheath shown in Figure 14 also indicates an amplitude attenuation over −4 dB. As a result, after range compression, the peak value of range compressed signal with plasma sheath shown in Figure 15 decreases to 1 × 10

^{4}. Moreover, the plasma sheath will cause the additional phase shift for the SAR signal. However, the phase shift caused by the plasma sheath is relatively small, and it has little effect on range compression. The specific analysis is as follows. The theoretical phase shift within the bandwidth shown in Figure 17a is obtained by calculating the phase characteristics of transmission coefficient. The experiment phase characteristics within signal bandwidth are obtained by measuring phase shift of broadband signal propagating through plasma, and the result is shown in Figure 17b. It can be found that the phase varies about 45° within the bandwidth in the theoretical result and about 65° in the experiment result. The phase variation within the bandwidth is so small that it hardly causes the range dimension distortion.

## 3. Results and Discussion

^{17}/m

^{3}, 1 × 10

^{18}/m

^{3}, and 2 × 10

^{18}/m

^{3}, and the corresponding plasma frequencies are less than, equal to, or greater than the carrier frequency (10.5 GHz), respectively. For hypersonic platform-borne SAR whose carrier frequency is 10.5 GHz, it may encounter the condition that electron density is 1 × 10

^{17}/m

^{3}, 1 × 10

^{18}/m

^{3}, or 2 × 10

^{18}/m

^{3}due to large varying range of electron density under different flight conditions. The study of conditions below and above plasma frequency will make the research of SAR imaging under plasma sheath more comprehensive and closer to real flight condition.

#### 3.1. Point Target Response under Plasma Sheath

^{17}/m

^{3}, the plasma sheath has slight influence on the point target response shown in Figure 18a, and corresponding 1D results are not distorted by noise. However, when peak electron density increases to 1 × 10

^{18}/m

^{3}, the noise appears in the point target imaging result shown in Figure 18b, and amplitude of corresponding 1D results significantly decrease shown in Figure 20. Peak value of range and azimuth compressed result decrease and the energy of noise is close to the SAR signal energy, which lead to the abnormal main-lobe and side-lobe phenomenon. When the peak electron density of plasma sheath increases to the 2 × 10

^{18}/m

^{3}, the point target response result shown in Figure 18c is totally immersed in the noise, and the peak value cannot be distinguished from the noise. Due to significant attenuation, the energy of noise is far larger than the signal energy and this phenomenon occurs. For the further analysis, the transmission coefficients in bandwidth for Ne

_{peak}= 1 × 10

^{17}/m

^{3}, 1 × 10

^{18}/m

^{3}and 2 × 10

^{18}/m

^{3}are shown in Figure 22. For Ne

_{peak}= 1 × 10

^{17}/m

^{3}, the amplitude of transmission coefficient is around 0, which illustrates very small attenuation caused by plasma sheath. Therefore, the SNR of SAR signal with plasma sheath basically remains unchanged and SAR imaging quality is not influenced by plasma sheath. However, when the electron density is 1×10

^{18}/m

^{3}, the amplitude of transmission coefficient is around −16 dB, and SAR signal is serious attenuated. Compared with attenuated SAR signal, the energy of noise cannot be ignored. When the electron density is 2 × 10

^{18}/m

^{3}, the amplitude of transmission coefficient is around −46 dB and SAR signal is immersed in the noise, which will cause serious SAR image distortion. The result of transmission coefficient confirms the previous analysis.

#### 3.2. Area Targets Response under Plasma Sheath

^{17}/m

^{3}, the real SAR image is hardly affected by the plasma sheath. Lakes, rivers, banks, and farmland are very clear. The quality of the image is good. However, as the peak electron density increases to 1 × 10

^{18}/m

^{3}, the imaging quality is severely degraded as shown in Figure 23b. The noise appears in the SAR image and lakes, rivers, banks, and farmland are not very clear. The imaging quality becomes worse compared with Figure 23a. When the peak electron density reaches 2 × 10

^{18}/m

^{3}, the imaging quality is the most serious shown in Figure 23c. All the lakes, rivers, banks, and farmland disappear, and only noise can be seen in the SAR image.

#### 3.3. The Factors Determining SAR Imaging Quality

^{16}/m

^{3}, 4 × 10

^{17}/m

^{3}, and the 1 × 10

^{18}/m

^{3}, respectively. The other parameters are shown in Table 2. The PSLR and ISLR of range compressed result varying with carrier frequency and electron density are shown in Figure 24. The value 0 in Figure 24a,b means that there is no obvious peak, which is the same as the result in Figure 21. For Ne

_{peak}= 4 × 10

^{16}/m

^{3}and Ne

_{peak}= 4 × 10

^{17}/m

^{3}at low carrier frequency, the PSLR and ISLR are 0 which is due to significant attenuation shown in Figure 24c. The target response is immersed in the noise under this circumstance. With the increase of the carrier frequency, the value of PSLR gradually approaches −13.22 dB which is the ideal PSLR value. The value of ISLR approaches −10.11 dB which is also the ideal ISLR value. It can be concluded that the effect of plasma sheath on SAR imaging will weaken with the increase of carrier frequency. In addition, the PSLR at Ne

_{peak}= 4 × 10

^{16}/m

^{3}is −13.22 dB for all carrier frequencies while the PSLR at Ne

_{peak}= 1 × 10

^{18}/m

^{3}is 0 even when carrier frequency is 10 GHz which is a relatively large carrier frequency. We can also obtain that when the electron density is larger, the effect of plasma sheath on SAR imaging is more serious. This conclusion also confirms the result in Section 3.2.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Tang, S.; Guo, P.; Zhang, L.; So, H.C. Focusing Hypersonic Vehicle-Borne SAR Data Using Radius/Angle Algorithm. IEEE Trans. Geosci. Remote Sens.
**2019**, 58, 281–293. [Google Scholar] [CrossRef] - Xu, X.; Liao, G.; Yang, Z.; Wang, C. Moving-in-pulse duration model-based target integration method for HSV-borne high-resolution radar. Digit. Signal Process.
**2017**, 68, 31–43. [Google Scholar] [CrossRef] - Han, J.; Cao, Y.; Yeo, T.S.; Wang, F. Robust Clutter Suppression and Ground Moving Target Imaging Method for a Multichannel SAR with High-Squint Angle Mounted on Hypersonic Vehicle. Remote Sens.
**2021**, 13, 2051. [Google Scholar] [CrossRef] - Han, J.; Cao, Y.; Yeo, T.-S.; Wang, F.; Liu, S. A novel hypersonic vehicle-borne multichannel SAR-GMTI scheme based on adaptive sum and difference beams within eigenspace. Signal Process.
**2021**, 187, 108168. [Google Scholar] [CrossRef] - Wang, Y.; Cao, Y.; Peng, Z.; Su, H. Clutter suppression and GMTI for hypersonic vehicle borne SAR system with MIMO antenna. IET Signal Process.
**2017**, 11, 909–915. [Google Scholar] [CrossRef] - Stollery, J.L. Hypersonic flight. Nature
**1972**, 240, 133–135. [Google Scholar] [CrossRef] - Starkey, R.P. Hypersonic Vehicle Telemetry Blackout Analysis. J. Spacecr. Rocket.
**2015**, 52, 426–438. [Google Scholar] [CrossRef] - Chen, J.; Liang, B.; Yang, D.-G.; Zhao, D.-J.; Xing, M.; Sun, G.-C. Two-Step Accuracy Improvement of Motion Compensation for Airborne SAR with Ultrahigh Resolution and Wide Swath. IEEE Trans. Geosci. Remote Sens.
**2019**, 57, 7148–7160. [Google Scholar] [CrossRef] - Jin, G.; Dong, Z.; He, F.; Yu, A. Background-Free Ground Moving Target Imaging for Multi-PRF Airborne SAR. IEEE Trans. Geosci. Remote Sens.
**2019**, 57, 1949–1962. [Google Scholar] [CrossRef] - Wei, X.; Chong, J.; Zhao, Y.; Li, Y.; Yao, X. Airborne SAR Imaging Algorithm for Ocean Waves Based on Optimum Focus Setting. Remote Sens.
**2019**, 11, 564. [Google Scholar] [CrossRef] [Green Version] - Ding, Z.; Xiao, F.; Xie, Y.; Yu, W.; Yang, Z.; Chen, L.; Long, T. A Modified Fixed-Point Chirp Scaling Algorithm Based on Updating Phase Factors Regionally for Spaceborne SAR Real-Time Imaging. IEEE Trans. Geosci. Remote Sens.
**2018**, 56, 7436–7451. [Google Scholar] [CrossRef] - Tian, J.; Wu, Y.; Cai, Y.; Fan, H.; Yu, W. A Novel Mosaic Method for Spaceborne ScanSAR Images Based on Homography Matrix Compensation. Remote Sens.
**2021**, 13, 2866. [Google Scholar] [CrossRef] - Wang, Y.; Li, J.; Yang, J.; Sun, B. A Novel Spaceborne Sliding Spotlight Range Sweep Synthetic Aperture Radar: System and Imaging. Remote Sens.
**2017**, 9, 783. [Google Scholar] [CrossRef] [Green Version] - Chen, Z.; Zhou, Y.; Zhang, L.; Lin, C.; Huang, Y.; Tang, S. Ground Moving Target Imaging and Analysis for Near-Space Hypersonic Vehicle-Borne Synthetic Aperture Radar System with Squint Angle. Remote Sens.
**2018**, 10, 1966. [Google Scholar] [CrossRef] [Green Version] - Wang, Y.; Cao, Y.; Wang, S.; Su, H. Clutter suppression and ground moving target imaging approach for hypersonic vehicle borne multichannel radar based on two-step focusing method. Digit. Signal Process.
**2019**, 85, 62–76. [Google Scholar] [CrossRef] - Rybak, J.P.; Churchill, R.J. Progress in Reentry Communications. IEEE Trans. Aerosp. Electron. Syst.
**1971**, AES-7, 879–894. [Google Scholar] [CrossRef] - Shao, C.; Nie, L.; Chen, W. Analysis of weakly ionized ablation plasma flows for a hypersonic vehicle. Aerosp. Sci. Technol.
**2016**, 51, 151–161. [Google Scholar] [CrossRef] - Xie, K.; Yang, M.; Bai, B.; Li, X.; Zhou, H.; Guo, L. Re-entry communication through a plasma sheath using standing wave detection and adaptive data rate control. J. Appl. Phys.
**2016**, 119, 023301. [Google Scholar] [CrossRef] - Li, L.; Wei, B.; Yang, Q.; Yang, X.; Ge, D. High-Order SO-DGTD Simulation of Radio Wave Propagation Through Inhomogeneous Weakly Ionized Dusty Plasma Sheath. IEEE Antennas Wirel. Propag. Lett.
**2017**, 16, 2078–2081. [Google Scholar] [CrossRef] - Song, L.; Li, X.; Bai, B.; Liu, Y. Effects of Plasma Sheath on the Signal Detection of Narrowband Receiver. IEEE Trans. Plasma Sci.
**2018**, 47, 251–258. [Google Scholar] [CrossRef] - Yao, B.; Li, X.; Shi, L.; Liu, Y.; Lei, F.; Zhu, C. Plasma sheath: An equivalent nonlinear mirror between electron density and transmitted electromagnetic signal. Phys. Plasmas
**2017**, 24, 102104. [Google Scholar] [CrossRef] - Yao, B.; Li, X.; Shi, L.; Liu, Y.; Zhu, C. A Geometric-Stochastic Integrated Channel Model for Hypersonic Vehicle: A Physical Perspective. IEEE Trans. Veh. Technol.
**2019**, 68, 4328–4341. [Google Scholar] [CrossRef] - Zhang, Y.; Liu, Y.; Li, X. A 2-D FDTD Model for Analysis of Plane Wave Propagation Through the Reentry Plasma Sheath. IEEE Trans. Antennas Propag.
**2017**, 65, 5940–5948. [Google Scholar] [CrossRef] - Bai, B.; Li, X.; Liu, Y.; Xu, J.; Shi, L.; Xie, K. Effects of Reentry Plasma Sheath on the Polarization Properties of Obliquely Incident EM Waves. IEEE Trans. Plasma Sci.
**2014**, 42, 3365–3372. [Google Scholar] [CrossRef] - Liu, Z.; Bao, W.; Li, X.; Liu, D.; Bai, B. Effects of Pressure Variation on Polarization Properties of Obliquely Incident RF Waves in Re-Entry Plasma Sheath. IEEE Trans. Plasma Sci.
**2015**, 43, 3147–3154. [Google Scholar] [CrossRef] - Liu, H.; Liu, Y.; Yang, M.; Li, X. A Joint Demodulation and Estimation Algorithm for Plasma Sheath Channel: Extract Principal Curves with Deep Learning. IEEE Wirel. Commun. Lett.
**2019**, 9, 433–437. [Google Scholar] [CrossRef] - Yang, M.; Li, X.; Wang, D.; Liu, Y.; He, P. Propagation of phase modulation signals in time-varying plasma. AIP Adv.
**2016**, 6, 055110. [Google Scholar] [CrossRef] [Green Version] - Chen, X.-Y.; Li, K.-X.; Liu, Y.-Y.; Zhou, Y.-G.; Li, X.-P. Study of the influence of time-varying plasma sheath on radar echo signal. IEEE Trans. Plasma Sci.
**2017**, 45, 3166–3176. [Google Scholar] [CrossRef] - Ding, Y.; Bai, B.; Gao, H.; Liu, Y.; Li, X.; Zhao, M. Method of Detecting a Target Enveloped by a Plasma Sheath Based on Doppler Frequency Compensation. IEEE Trans. Plasma Sci.
**2020**, 48, 4103–4111. [Google Scholar] [CrossRef] - Bian, Z.; Li, J.; Guo, L. Simulation and Feature Extraction of the Dynamic Electromagnetic Scattering of a Hypersonic Vehicle Covered with Plasma Sheath. Remote Sens.
**2020**, 12, 2740. [Google Scholar] [CrossRef] - Ren, Y.; Guo, L.; Chen, W.; Liu, S. Analysis of the electromagnetic scattering characteristics in two-dimensional time-varying and spatially non-uniform plasma sheath. Phys. Plasmas
**2019**, 24, 093515. [Google Scholar] [CrossRef] - Sha, Y.-X.; Zhang, H.-L.; Guo, X.; Xia, M.-Y. Analyses of Electromagnetic Properties of a Hypersonic Object with Plasma Sheath. IEEE Trans. Antennas Propag.
**2019**, 67, 2470–2481. [Google Scholar] [CrossRef] - Zheng, B.; Jiangting, L.; Lixin, G.; Xi, L. Range Profile Analysis of Hypersonic Vehicles Covered by Inhomogeneous Plasma Sheath Using Physical Optics. IEEE Trans. Plasma Sci.
**2019**, 47, 4961–4970. [Google Scholar] [CrossRef]

**Figure 6.**Outline of plasma generator used in experiment. (

**a**) Photo of plasma generator. (

**b**) Schematic diagram of plasma generator.

**Figure 10.**The signal in time domain without plasma sheath: (

**a**) experimental result, (

**b**) theoretical result.

**Figure 11.**Signal frequency spectrum without plasma sheath: (

**a**) experimental result, (

**b**) theoretical result.

**Figure 12.**Range compressed signal without plasma sheath: (

**a**) experimental result, (

**b**) theoretical result.

**Figure 14.**Signal frequency spectrum with plasma sheath: (

**a**) experimental result, (

**b**) theoretical result.

**Figure 15.**Range compressed result with plasma sheath: (

**a**) experimental result, (

**b**) theoretical result.

**Figure 17.**Signal phase shift characteristics caused by plasma within signal bandwidth: (

**a**) theoretical result, (

**b**) experimental result.

**Figure 18.**Point target imaging result with plasma sheath. (

**a**) Ne

_{peak}= 1 × 10

^{17}/m

^{3}, (

**b**) Ne

_{peak}= 1 × 10

^{18}/m

^{3}, (

**c**) Ne

_{peak}= 2 × 10

^{18}/m

^{3}.

**Figure 19.**1D result when Ne

_{peak}= 1 × 10

^{17}/m

^{3}: (

**a**) range dimension, (

**b**) azimuth dimension.

**Figure 20.**1D result when Ne

_{peak}= 1 × 10

^{18}/m

^{3}: (

**a**) range dimension, (

**b**) azimuth dimension.

**Figure 21.**1D result when Ne

_{peak}= 2 × 10

^{18}/m

^{3}: (

**a**) range dimension, (

**b**) azimuth dimension.

**Figure 23.**Area targets response: (

**a**) Ne

_{peak}= 1 × 10

^{17}/m

^{3}, (

**b**) Ne

_{peak}= 1 × 10

^{18}/m

^{3}, (

**c**) Ne

_{peak}= 2 × 10

^{18}/m

^{3}.

**Figure 24.**(

**a**) PSLR varying with carrier frequency and electron density. (

**b**) ISLR varying with carrier frequency and electron density. (

**c**) Transmission coefficient varying with carrier frequency and electron density.

**Figure 25.**(

**a**) PSLR varying with collision frequency and carrier frequency. (

**b**) ISLR varying with collision frequency and carrier frequency. (

**c**) Transmission coefficient varying with collision frequency and carrier frequency.

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

Pulse width | 40 μs |

Bandwidth | 120 MHz |

Carrier frequency | 10.5 GHz |

PRF | 7460 Hz |

Platform velocity | 7000 m/s |

Elevation angle | 35° |

Collision frequency | 4 GHz |

SNR | 15 dB |

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

Pulse width | 40 μs |

Bandwidth | 120 MHz |

PRF | 7460 Hz |

Platform velocity | 7000 m/s |

Elevation angle | 30° |

Collision frequency | 4 GHz |

SNR | 10 dB |

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

Pulse width | 40 μs |

Bandwidth | 120 MHz |

PRF | 7460 Hz |

Platform velocity | 7000 m/s |

Elevation angle | 30° |

Peak electron density | 5 × 1017/m^{3} |

SNR | 10 dB |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Song, L.; Bai, B.; Li, X.; Niu, G.; Liu, Y.; Zhao, L.; Zhou, H.
Analysis of Hypersonic Platform-Borne SAR Imaging: A Physical Perspective. *Remote Sens.* **2021**, *13*, 4943.
https://doi.org/10.3390/rs13234943

**AMA Style**

Song L, Bai B, Li X, Niu G, Liu Y, Zhao L, Zhou H.
Analysis of Hypersonic Platform-Borne SAR Imaging: A Physical Perspective. *Remote Sensing*. 2021; 13(23):4943.
https://doi.org/10.3390/rs13234943

**Chicago/Turabian Style**

Song, Lihao, Bowen Bai, Xiaoping Li, Gezhao Niu, Yanming Liu, Liang Zhao, and Hui Zhou.
2021. "Analysis of Hypersonic Platform-Borne SAR Imaging: A Physical Perspective" *Remote Sensing* 13, no. 23: 4943.
https://doi.org/10.3390/rs13234943