VFM waveforms, composed of two chirp signals with the opposite slopes, can also achieve high range resolution with wide bandwidth via intrapulse frequency modulation. In this paper, a framework for inverse synthetic aperture radar (ISAR) imaging of moving targets with VFM waveforms is investigated, where the range compression of the received signals is achieved by the dualchannel dechirping and the azimuth compression is done via the traditional Fourier transform (FT). The two corresponding reconstructed temporary highresolution range profiles (HRRPs) from the double channels are synthesized for the HRRPs of the target, in which one is flipped from left to right and added to the other. Then the final HRRPs are arranged into a twodimensional (2D) array and the azimuth compression is done via FT to achieve the ISAR imaging after the motion compensation. Simulated trials, adopting the scattering center modeling of the Yak42 plane, are used to validate the correctness of the analyses and the finally wellfocused images greatly support the effectiveness of VFM waveforms in ISAR imaging.
Inverse synthetic aperture radar (ISAR) is a powerful tool in many civilian and military fields such as air traffic control, harbor and river traffic surveillance, and remote sensing of satellites, benefiting from the superiorities such as robust performance under allweather conditions, highresolution images, and long detection range [
VFM signal, possessing a “thumbtack” ambiguity function as mentioned in [
Due to the special characteristics of the VFM waveforms, a dualchannel dechirping algorithm is proposed to recover the HRRPs of moving targets in this paper. The main idea of dualchannel dechirping of wideband VFM waveforms is that two temporary HRRPs are reconstructed from the two independent channels with dechirping processing and one is flipped from left to right and added to the other to synthesize the final HRRPs. Then the rearranged 2D matrix of synthesized HRRPs is utilized to form the ISAR image after motion compensation.
This paper is organized as follows. The pulse compression via dualchannel dechirping is discussed in detail in Section
The signal model of wideband VFM waveforms and the corresponding pulse compression of moving targets via dualchannel dechirping are devoted in this section.
Assume that the complex VFM waveform in zero intermediate frequency form is composed of two chirp signals with the opposite slopes as shown in Figure
Sketch map of VFM waveforms in timefrequency plane.
After the upconversion, we have the transmitted VFM waveform as follows:
The geometry of ISAR imaging is shown in Figure
Geometry of ISAR imaging.
The reference signals of the two channels can be expressed, respectively, as
The timedomain compressed signals of the two channels after dechirping are given as follows:
The first exponentials of
It can be seen that the two temporary HRRPs form the dualchannel dechirping being with the same amplitude but symmetrical about zero in the frequency domain.
After the two temporary HRRPs are achieved, the second temporary HRRPs
Without loss of generality, let the reference range
Thus, the Doppler frequency of scattering center
The flow chart of HRRPs reconstruction after the RVP of each channel is removed and ISAR image formation with wideband VFM waveforms via dualchannel dechirping are shown in Figure
Flow chart of ISAR imaging with wideband VFM waveforms.
To analyze the performance of the proposed HRRPs reconstruction and ISAR image formation via the dualchannel dechirping technique, two aspects should be counted: the reconstructed HRRPs and the ultimate ISAR image after azimuth compression. We simulate radar echoes of moving targets with simple and complex shapes (Yak42 model) to validate the effect of wideband VFM waveforms in the applications of highresolution ISAR imaging. The carrier frequency and the signal bandwidth of the VFM waveforms are
The simulation parameters.
Carrier frequency 

10 GHz 
Bandwidth 

300 MHz 
Pulse width 

100 
PRI 

1 KHz 
The modeling of the simples target is shown in Figure
Modeling of the simple target.
Scatterer distribution in
Backscattering coefficients of scatterers
In high SNR scenarios (SNR = 20 dB), the two recovered HRRPs of the dualchannel dechirping are shown in Figures
HRRPs reconstruction (SNR = 20 dB).
Recovered HRRPs (channel 1)
Recovered HRRPs (channel 2)
Recovered HRRPs of channel 2 (flipped)
Finally synthesized HRRPs
The finally synthesized HRRPs shown in Figure
Gaussian distributed complex noise with four groups of SNRs, 5 dB, 0 dB, −5 dB, and −10 dB, are adopted here to illuminate the effect of the HRRPs reconstruction algorithm in a more realistic scenario.
The synthesized HRRPs are shown in Figure
HRRPs reconstruction with various SNRs.
To demonstrate the effect of wideband VFM waveforms in ISAR imaging, 256 pulses with a time duration
Model of Yak42 plane with 330 scatterers.
The 256 pulses are referred to the reconstructed 256 HRRPs which can be rearranged into a 2D matrix to achieve the ISAR image after standard motion compensation. Comparing the 256 HRRPs of channel 1 shown in Figure
ISAR image formation of the Yak42 plane model (SNR = 20 dB).
256 HRRPs from channel 1
256 HRRPs from channel 2
256 finally reconstructed HRRPs
Ultimate ISAR image
Similar to Section
ISAR image formation of the Yak42 plane model with various SNRs.
SNR = 5 dB
SNR = 0 dB
In a high SNR case, for example,
Based on the characteristics of wideband VFM waveforms, both of the MF and the dechirping algorithms can be applied on the HRRPs reconstruction. The novelty of this paper is that it proposed and validated the effect of wideband VFM waveforms in the application of HRRPs reconstruction and ISAR imaging of moving targets. Via dualchannel dechirping, the finally synthesized HRRPs from the two independent channels were robust and in accordance with the real HRRPs and the final ISAR image formation was also focused under high SNR conditions. Under various SNRs, the recovered HRRPs of wideband VFM waveforms were also addressed which reveals that the reconstructed HRRPs were robust when SNR is no less than −10 dB.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
The authors would like to thank Dr. Lei Zhang for providing the modeling data of Yak42. This work was supported by the National Natural Science Foundation of China under Grant 61571451.