# Passive Bistatic Ground-Based Synthetic Aperture Radar: Concept, System, and Experiment Results

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## Abstract

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## 1. Introduction

## 2. System Overview

#### 2.1. PB-GB-SAR Concept

#### 2.2. Link Budget Analysis

_{1,1}, the power of the received reference signal from a single TV channel can be expressed as [38]

_{ref}denotes the gain of the reference antenna; λ = c/f

_{c}is the wavelength with c as the speed of light and f

_{c}as the carrier frequency.

_{1,2}is the distance between the TV satellite and the target, R

_{2}is the distance between the target and the surveillance antenna, G

_{surv}is the gain of the surveillance antenna (we note that, since only the feed-horn of the parabolic antenna without the reflector is used for the surveillance channel, as shown on the right of Figure 8, G

_{surv}is much smaller than G

_{ref}), and σ denotes the Radar Cross Section (RCS) of the target. Given the system noise temperature T

_{0}and the system noise bandwidth B

_{0}, the noise power can be written as [39]

_{0}is the Boltzmann constant.

_{int}is shown on the left of Figure 6. Due to the memory limitation of the used oscilloscope (only 1 Mpts deep memory is available for a data sampling rate of 10 GSamples/s); an integration time of 100 μs is used in this study. As we can see, to get an SNR higher than 0 dB after range compression, the minimal integration time should be ~236 μs, which cannot be obtained by the used oscilloscope in a single measurement (summing multiple measurements together is however possible). With a 100 μs coherent integration time, the SNR is still lower than 0 dB (−3.74 dB) and the target cannot be detected. Therefore, azimuth compression is further conducted. After both range and azimuth compression, the SNR of the SAR image is given by [44,45]

#### 2.3. LNB Synchronization

## 3. Signal Processing

#### 3.1. Signal Model

_{n}is the amplitude; h(t) is the impulse response of the root-raised-cosine (RRC) filter [47] with a duration of T

_{s}; ${f}_{c}^{n}$ is the carrier frequency; and ${\phi}_{i}^{n}$ is the phase of the i-th symbol. For QPSK modulation, ${\phi}_{i}^{n}$ equals to π/4, 3π/4, 5π/4, or 7π/4.

_{int}can be expressed as

_{ref}and A

_{surv}that are independent of the frequency, the received reference signal and surveillance signal from all the TV channels can be expressed as

_{0}(f) is the spectrum of all TV channels.

_{0}(f) in Equation (15), resulting in

_{s}(1 − α) can be extracted from each TV channel, i.e., only the flat spectrum can be used, to reduce the waveform influence of the used satellite digital TV signal (the amplitude-filtered spectrum), as indicated by Equation (9). However, this will also decrease the output SNR as the integration gain generated by the matched filtering is reduced. Therefore, in the concept-proof study stage, Equation (15) is used for the following process without considering the spectrum properties of the satellite digital TV signal.

#### 3.2. Imaging and Displacement Estimation

_{p}, y

_{p}), the range compression result obtained by combing N TV channels is given by

**F**is the Fourier-transform matrix.

_{int}/T

_{p}, with T

_{p}being the processing time. By doing so, the computational complexity can be reduced for the following imaging methods.

_{0}, y

_{0}) as

_{0}on the left of Figure 4.

_{0}is zero, i.e., the antenna moving direction should be parallel with the x axis. To this end, the reference antenna faced to the satellite is moved together with the surveillance antenna, as shown on the right of Figure 4.

_{p}= −L/2 + (p − 1)Δx is the p-th antenna position, which is only dependent on the moving step.

_{p}, y

_{ref}) denoting its p-th antenna position, based on the plane wave approximation and Taylor series expansion, it can be derived that

_{0}, as shown in Figure 13, where the simulation parameters are: y

_{T}= −36,000 km and x

_{p}is from −0.6 m to 0.6 m with a step of 5 mm. It can be seen that, with the considered local area imaging, the approximation error is always smaller than 0.15 mm (corresponding to a phase error of π/80). Therefore, the plane wave approximation is used for PB-GB-SAR imaging to simplify the imaging process, as, in such a case, the TV satellite position is not necessary to be known in advance.

_{0}, y

_{0}) can be estimated by BPA as

_{p}(

**f**) with the interpolation process or the type-II nonuniform FFT (NUFFT) [48] can be used. In this paper, the latter method is adopted, which can be expressed as

_{p}, we can get

_{1}(k

_{x}, k) can be approximated by

**Fx**and

**Fy**are the Fourier-transform matrices in the x and y directions, respectively.

## 4. Experiment Results

^{−12}). RMA requires only ~0.79 s (measured by the TIC and TOC instruction in MATLAB on a Core i5, 2.5 GHz, and 8 GB RAM PC), while, although the grid size has been reduced 8-fold (2 times in the x direction and 4 times in the y direction), BPA still needs ~8.54 s to get the SAR image, indicating the efficiency of RMA in such a case.

## 5. Discussions

#### 5.1. Artifact Suppression

**W**

_{SVA}(

**f**) in the frequency domain [37], the Fourier-transform of the n-th TV channel is given by

**F**

_{n}is the Fourier-transform matrix for the n-th TV channel. Then, by performing the inverse Fourier-transform, a band-unlimited signal can be obtained as

**W**

_{inv}(

**f**), which is the inverse Fourier-transform of the mainlobe of a sinc function in the time domain, the spectrum extrapolated signal can be obtained as [37]

#### 5.2. Improvement Directions

_{a}(a = 1, 2) is the two-way displacement estimated by the a-th surveillance antenna and θ

_{a}is equal to arctan [(x − ${x}_{0}^{a}$)/y] with ${x}_{0}^{a}$ being the center position of the a-th synthetic aperture.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Conventional ground-based synthetic aperture radar (GB-SAR) system: (

**left**) the imaging geometry and (

**right**) a real stepped-frequency continuous waveform (SFCW)-based GB-SAR system used for landslide monitoring [4].

**Figure 2.**Passive bistatic (PB)-GB-SAR with multiple receivers for 3D displacement vector estimation. Note the difference between the left and right subfigures with different numbers of reference and surveillance antennas. More configurations can be used for specific applications.

**Figure 3.**Communication satellite (N-SAT-110) digital TV signal: (

**left**) spatial coverage with different EIRPs [42] and (

**right**) spectrum of the real-sampled data.

**Figure 4.**The imaging geometry of PB-GB-SAR: (

**left**) the general geometry without the requirement of the antenna moving direction and (

**right**) the simplified geometry with plane wave approximation.

**Figure 5.**The designed PB-GB-SAR system, where the low noise block (LNB) oscillator controller is used to synchronize the phase and frequency of two LNBs, which will be detailed in Section 2.3.

**Figure 6.**The SNRs of (

**left**) the range compression result versus the integration time and (

**right**) the SAR image versus the synthetic aperture length.

**Figure 7.**Target SNRs versus different RCSs and target–receiver distances. With the current PB-GB-SAR system, we have focused on the targets within a 100 m range.

**Figure 8.**LNB synchronization setup: (

**left**) clock distribution circuit with three sets of in-phase and phase-opposition signal outputs feeding the phase locked loop (PLL) inputs of LNBs and (

**right**) the modified feed-horn of a 45-cm parabolic antenna receiving the in-phase and phase-opposition signals.

**Figure 9.**Diagram of the clock distribution circuit. Note that only one of “LO” or “Pierce oscillator” is needed. When an external LO is available, it can be used to provide more stable and precise results. In this study, the Pierce oscillator is used.

**Figure 10.**(

**left**) Time delay measurement setup and (

**right**) estimation result. The coherent integration time of each measurement is 10 μs, while, due to the delay caused by the data transmission from the oscilloscope to the PC, the measurement period is ~0.18 s. Therefore, for 5000 measurements, ~15 min is needed.

**Figure 12.**Using the stability of the peak amplitudes of reference signal autocorrelation function to determine the antenna moving direction: (

**left**) experiment setup and (

**right**) calculation results.

**Figure 13.**Approximation error for targets at different positions. The right subfigure is for the targets with y

_{0}= 100.

**Figure 14.**PB-GB-SAR imaging of a metallic plate: The plate angle is tuned to make its reflection maximal and the antenna moving direction is adjusted to be parallel with the wavefront of the TV signal.

**Figure 15.**Normalized focused SAR images of the metallic plate obtained by (

**left**) BPA and (

**right**) RMA.

**Figure 17.**PB-GB-SAR imaging of natural and man-made targets: The green solid line indicates a fence, the dotted rectangle indicates a light pole, the yellow ellipse includes a tree and a small house, and the red dotted line indicates some bicycles.

**Figure 18.**SAR image of natural and man-made targets: The right subfigure is the zoomed version of the left subfigure with specific focuses on the fence, light pole, tree, and house.

**Figure 19.**SAR image overlaid with the aerial view provided by Google maps. Note that the two strong targets at about 60 m and 65 m are located at a parking lot.

**Figure 20.**(

**Left**) SAR image of the metallic plate obtained by RMA after frequency gap filling and (

**right**) comparison between the results with and without gaps filling in the y direction.

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

TV signal power | EIRP | 55 | dBW |

Reference antenna gain | G_{ref} | 34 | dB |

Speed of light | c | 3 × 10^{8} | m/s |

Carrier frequency | f_{c} | 12.51 | GHz |

Wavelength | λ | 24 | mm |

Direct path | R_{1,1} | 36,000 | km |

Surveillance antenna gain | G_{surv} | 15 | dB |

Target RCS | σ | 10 | m^{2} |

Satellite-target distance | R_{1,2} | 36,000.1 | km |

Target–receiver distance | R_{2} | 100 | m |

Noise temperature | T_{0} | 290 | K |

Noise bandwidth | B_{0} | 34.5 | MHz |

Boltzmann constant | k_{0} | 1.38 × 10^{−23} | J/K |

Number of TV channels | N | 12 | 1 |

Path loss of Ku band | Lr | 2 | dB |

Synthetic aperture length | L | TBD | m |

Antenna moving step | Δx | 5 | mm |

Coherent integration time | T_{int} | TBD | μs |

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**MDPI and ACS Style**

Feng, W.; Friedt, J.-M.; Nico, G.; Wang, S.; Martin, G.; Sato, M. Passive Bistatic Ground-Based Synthetic Aperture Radar: Concept, System, and Experiment Results. *Remote Sens.* **2019**, *11*, 1753.
https://doi.org/10.3390/rs11151753

**AMA Style**

Feng W, Friedt J-M, Nico G, Wang S, Martin G, Sato M. Passive Bistatic Ground-Based Synthetic Aperture Radar: Concept, System, and Experiment Results. *Remote Sensing*. 2019; 11(15):1753.
https://doi.org/10.3390/rs11151753

**Chicago/Turabian Style**

Feng, Weike, Jean-Michel Friedt, Giovanni Nico, Suyun Wang, Gilles Martin, and Motoyuki Sato. 2019. "Passive Bistatic Ground-Based Synthetic Aperture Radar: Concept, System, and Experiment Results" *Remote Sensing* 11, no. 15: 1753.
https://doi.org/10.3390/rs11151753