Abstract
Here， we present our implementation of two-dimensional （2D） high-resolution inverse synthetic aperture radar （ISAR） imaging using a 0.22 THz stepped-frequency （SF） radar system. The system is suitable for both near- and far-field imaging with a synthesis bandwidth of 12 GHz. The radar can provide highly accurate range and cross-range results in the near field， and its ISAR image can reach centimeter-level resolution upon using a phase-compensated Back-Projection algorithm （BP algorithm）. These BP-realized results indicate that THz ISAR imaging can achieve both higher precision and finer resolution when compared to previously demonstrated range-doppler （RD） results with the same SFCW radar setup. To accelerate BP’s relatively slow image retrieval process， we employ accelerated platforms based on a graph-processing unit （GPU）. Such success should pave the way for further research on near-field high-resolution radar imaging especially at THz/sub-millimeter bands.
To date， THz/sub-millimeter waves have been pursued for a wide range of applications including communications， safety inspection， and high-resolution imaging. The Terahertz （THz） frequency band （0.1 to 10 THz） has become of high interest due to its remarkably wide bandwidth， which practically translates to fine spatial resolution and high performance imaging. The desirable performance features of the THz band are due to the technology’s use of wide bandwidth receivers and highly directional antenna
Experimental THz radar systems have been proposed and studied by many organizations over the past decad
Fig. 1 The progress of THz radar system （a） bandwidth， （b） resolution
图1 太赫兹雷达系统发展 （a）带宽，（b）分辨率
Typically， frequency-modulated continuous wave （FMCW） and stepped-frequency continuous wave （SFCW） signals are utilized in radar systems as indicated in Table I. These two waveforms have many merits and would cover various applications. Most of the current radar systems use FMCW signals， as these signals tend to achieve relatively higher transmitted power. However， this comes at a significantly higher cost of the radar system’s sampling devices， given that these systems operate in the THz frequency range and require stringent I and Q channel calibration. On the other hand， the SFCW signal consists of a series of pulses with linearly-increasing frequency. As a result， it is convenient to measure the phase and amplitude of each transmitted sub-pulse and use the inverse Fourier transform （IFFT） of these data to build a time domain profile. Furthermore， it is relatively simple to simultaneously synthesize large bandwidth and reduce A/D sampling rate challenge for SFCW signals. Here， we leverage and adapt these features of THz SFCW radar systems for high-resolution ISAR imaging.
Generally， there are two ways to generate THz signals： by converting microwave frequencies or by down-converting optical signals. For the first group， the THz systems under 350 GHz （low frequency-THz）， are based on up-conversion of microwave frequencies and features a relatively-high transmitting power advantage. Hence， they have great potential for remote sensing applications. Meanwhile， the second group， THz systems above 350 GHz （high frequency-THz）， often uses optical methods to generate their signals. When using optical methods， it is easier to acquire a wide bandwidth， but the transmitted power is relatively low. In our effort here， we up-convert microwave frequencies to achieve higher transmitted power levels to build a 0.22 THz SFCW ISAR imaging radar.
Previously in Ref. ［
Our SFCW THz ISAR imaging radar spans 214 GHz to 226 GHz. Hence， the 12 GHz synthetic bandwidth should theoretically lead to a 1.25 cm range resolution.
Fig. 2 The block diagram of the 0.22 THz radar system
图2 0.22 THz 雷达系统框图
As shown in
The 0.22 THz ISAR imaging experiment setup is shown in Figs. （3-4）. In
Fig. 3 Experimental model of 0.22 THz ISAR imaging
图3 0.22 THz逆合成孔径雷达成像系统模型
Fig. 4 Experimental scenario of 0.22 THz radar imaging
图4 0.22 THz雷达实验系统
The theoretical range resolution （Δδy） is related to the bandwidth of the radiated THz SFCW waveform and is estimated using
| cm , | （1） |
where c is the speed of light， N = 1024， is the frequency step size， MHz， and B is the synthetic bandwidth （ GHz）.
The resolution in azimuth （Δδx） depends on the accumulating rotatory angle of the turntable （Θ） in the whole imaging process， which is given by
| , | （2） |
where is the wavelength of the radar system， M is the number of bursts that the THz radar has transmitted in one scan （here， M =312）， and is the angle step of the turntable between successive bursts.
For high quality ISAR images， the range and azimuth resolutions should be approximately the same （）. Therefore， the accumulating angle in azimuth （Θ） theoretically should be 3.125° （rad）， based on a resolution of 1.25 cm. However， in our experiment， we used 4° instead to simplify the whole control process. Thus， the rotary step in the imaging process is 0.01° （rad）， which might cause a slight image distortion but has been neglected here. In this setup， too， the imaging range between the radar system and the center of the rotary turntable is R （R= 6.4 m）.
In the above experiment， the turntable takes approximately 20 seconds to complete one 2D scan. However， if you add the times for A/D sampling， signal pre-processing on-board， and the data transmission， it takes over 40 seconds to complete. Hence， THz ISAR imaging cannot realize real-time processing. The received data volume of each ISAR image is about 12 MB for a matrix of 1024×312 in size. The collected data are then processed by MATLAB using the BP algorithm on the host computer.
Back-projection is a space-domain algorithm that is applied to reconstruct SAR/ISAR images using radar echo signals. In this paper， the theoretical imaging model is based on two isolated scattering points that are illuminated by the 0.22 THz SFCW radar system as illustrated in
Fig. 5 THz radar imaging model
图5 太赫兹雷达成像模型
The antennas array illuminates the scene with an SFCW radar signal s（t）. If we assume that p is one of the scattering points and is located at a position in the planar Cartesian coordinates （x，y）， then let us denote the distance between the antenna and the target point p on the
as shown in
| (i=1, 2, 3…M) , | （3） |
where is the two-path propagation delay； as the signal travels from the transmitter to the target in the
| , | （4） |
assuming the target is located at
Thus， the received signal at the
| . | （5） |
This process is repeated until the turntable has been rotated sequentially and we have covered all required rotations steps.
Given that the imaging region is divided into a finite number of pixels in range and azimuth directions， the entire echo signals are back projected to the destination region， where the imaging reconstruction process using BP algorithm is conducted as illustrated in
Fig. 6 Image reconstruction process using BP algorithm
图6 利用BP算法的图像重建过程
The complex composite signal corresponding to the image of the pixel located at is given by
| . | （6） |
The above process is repeated until all the pixels of the region D （2 m×2 m here） are covered and recorded to reconstruct the whole ISAR image.
The BP algorithm， generally， coherently integrates the radar echo data over each position of the target to reconstruct the ISAR image. The BP algorithm is relatively accurate for ISAR imaging and can attain higher precision in both range and azimuth directions after phase compensation while providing fine resolution. The imaging process using BP algorithm is summarized as follows：
1） Utilize the recorded I-channel and Q-channel data to synthesize an N×M echo- matrix （
2） Provide a phase compensation for the echo matrix， where the process of the phase compensation is indicated in the following four steps：
a） Extract phase information in the range direction from the echo matrix using φ = arcta
b） Use linear fitting of the phase of the echo matrix in the range direction； given that the THz waveform is a stepped-frequency signal and the phase of the signal should vary linearly；
c） Calculate the phase difference between the fitted signal and the original echo matrix， then the correction phase δmn is obtained （m=1…M， n=1…N）；
d） Correct the echo matrix by multiplying each element of the original matrix by the corresponding phase factor exp （jδmn）；
3） Mesh the destination area into a square matrix according to the radar imaging area （2 m×2 m） and the theoretical range resolution of the 0.22 THz radar syste
4） Calculate the distances between the antenna and all the divided grids of the destination area and repeat for each rotation angle step. Then， back project the N×M echo matrix to the meshed grid according to the calculated distances and observation angles of the radar. The number of the angle steps in this experiment is 312. Thus， 312 projected matrices with a size of 401×401 are obtained in this imaging process.
5） Coherently accumulate the 312-stack of projected matrices to form the THz ISAR image.
A flow chart depicting the overall imaging process using BP algorithm is shown in
Fig. 7 The flow chart of BP algorithm
图7 BP算法流程图
The THz ISAR experiment was carried out in an antenna chamber （shown in Figs.
Fig. 8 A photograph of the 0.22 THz radar system
图8 0.22 THz雷达
Fig. 9 The corner reflectors are mounted on the turntable
图9 位于转台上的角反射器
As indicated in the flow chart in
We have run two experiments and implemented the BP algorithm on the imaging data for two cases； one for a single corner reflector （
Fig. 10 ISAR imaging result for a corner reflector
图10 单个角反射器的ISAR成像结果
Fig. 11 ISAR result after phase compensation （single corner reflector）
图11 单个角反射器相位补偿后的ISAR成像结果
From
While the results of the two reflectors before phase compensation in
Fig. 12 ISAR imaging result for two corner reflectors
图12 角反射器组的ISAR成像结果
Fig. 13 ISAR result after phase compensation （two corner reflectors）
图13 角反射器组相位补偿后的ISAR成像结果
As previously mentioned， the ISAR image reconstruction time is relatively long using i7 processor. However， this process can be significantly accelerated， as the imaging process of BP requires repeatedly back projecting the echo matrix to a 401×401 grid column by column. Specifically， parallel processing （using a GPU） can be used to accelerate the computation drastically here. In this experiment， we used NVIDIA GeForce RTX 2060 for THz ISAR image reconstruction. Subsequently， the imaging time has been reduced to only 50 seconds. The parameters of the utilized GPU are shown in
In order to obtain a high-resolution ISAR image in the near field， we utilized a phase-compensated BP algorithm to reconstruct the THz stepped-frequency ISAR images. Upon phase compensation， the image resolution improved and the breakpoints in the images have been eliminated as can be observed by comparing Figs
Fig. 14 ISAR result using RD algorithm
图14 利用RD算法的ISAR成像结果
THz ISAR images of corner reflectors have been developed using a 0.22 THz SFCW radar system placed on a turntable for 2D scan. The developed THz stepped-frequency radar has a synthesized 12 GHz bandwidth with a reduced hardware complexity. In this paper， a phase-compensated BP algorithm is implemented to reconstruct the THz ISAR images and centimeter-scale spatial accuracy has been achieved after phase compensation， representing an improvement over our previous results using the RD algorithm
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