An Improved Time-Frequency PhaseAdjustment Technique for ISAR

Mengmeng Zhu, Junfeng Wang and Xingzhao LiuDepartment of Electronic Engineering, Institute of Signal Processing

Shanghai Jiaotong UniversityShanghai, China

zmm7 65@hotmail.com, junfengwang@sjtu.edu.cn, xzhliu@sjtu.edu.cn

slices of time- frequency representation

Figure 1. The time-frequency representation and its slices

limitations, we develop an improved time-frequency method. Itestimates the translational Doppler frequency from thecorrelation of the envelopes of the time-frequencyrepresentation at adjacent times. Compared with the traditionaltime-frequency method, this technique can estimate thetranslational Doppler frequency more accurately. Moreover, wedevelop a preprocessing method to avoid the aliasing of thetime-frequency representation due to undersampling.

II. TRADITIONAL TIME-FREQUENCY METHOD

In the time-frequency method, the key to phase adjustmentis the estimatation of the translational Doppler frequency. Themore accurately the translational Doppler frequency isestimated, the better the focus quality of the image. The time­frequency method estimates the translational Dopplerfrequency from the time-frequency representation of aselected range bin, like the range bin close to the scatteringcentroid.

In the traditional time-frequency method, a time-frequencyrepresentation is taken of a selected range bin, and then thepeak of the slice of the time-frequency representation at eachinstant is detected (Figure. 1). The frequency of the peak of theslice at an instant can be regarded as the translational Dopplerfrequency at this instant. The translational Doppler phases canbe found by calculating the running sum of the translationalDoppler frequencies.

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I. INTRODUCTION

Inverse synthetic aperture radar (ISAR) utilizes theFourier transform to resolve the scatterers in azimuth. Beforetaking the Fourier transform, translation compensation is usedto remove the effect of the translation between the radar andthe target in range. Translation compensation consists of rangealignment, which aligns the signals from the same scatterer inrange, and phase adjustment, which removes the translationalDoppler phase.

Typical methods for phase adjustment include thedominant-scatterer method [1], the scattering-centroid method[2], the phase-gradient method [3], [4], the time-frequencymethod [5], the maximum-contrast method [6] and theminimum-entropy method [7]-[9]. These methods apply evenif no prior knowledge is available about the translation.

The time-frequency method is a promising phaseadjustment technique for ISAR. Usually, the time-frequencymethod estimates the translational Doppler frequency and thusthe translational Doppler phase by detecting the peaks of thetime-frequency representation at different times. Unfortunately,it has some defects, such as the sensitivity to noise and targetscintillation and the aliasing of the time-frequencyrepresentation due to undersampling. In order to remove these

Keywords-ISAR, phase adjustment, time-frequency method,envelope correlation, preprocessing.

Abstract-The time-frequency method is a promising phaseadjustment technique for inverse synthetic aperture radar(ISAR). Usually, the time-frequency method estimates thetranslational Doppler frequency and thus the translationalDoppler phase by detecting the peaks of the time-frequencyrepresentation at different times. Unfortunately, it has somedefects, such as the sensitivity to noise and target scintillation,and the aliasing of the time-frequency representation due toundersampling. In order to remove these limitations, we developan improved time-frequency method. It estimates thetranslational Doppler frequency from the envelope correlation ofthe instantaneous slices of the time-frequency representation.Compared with the traditional time-frequency method, thistechnique can estimate the translational Doppler frequency moreaccurately. Moreover, we develop a preprocessing method toavoid the aliasing of the time-frequency representation due toundersampling.

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III. IMPROVED TIME-FREQUENCY METHOD

A. Idea

As metioned in the introduction, there are still somelimitations to the traditional time-frequency method. In orderto remove these limitations, we develop an improved time­frequency method for phase adjustment in ISAR imaging.

The improved time-frequency method consists of threesteps. The first step is called phase preadjustment. In this step,the dominant-scatterer phase adjustment method [1] is appliedto the signals. Its purpose is to reduce the bandwidths of thesignals such that the Nyquist sampling rate can be met andthus the aliasing of the time-frequency representation can beavoided.

The second step is the estimation of the translationalDoppler frequency. This is the key step of the algorithm. Wedevelop a new method to estimate the translational Dopplerfrequency more accurately. In this method, a time-frequencyrepresentation is taken of a selected range bin. The envelopesof the slices of the time-frequency representation at differentinstants are similar (Figure. 1). The translational Dopplerfrequency can be estimated from the envelope correlation ofthe instantaneous slices of the time-frequency representationat adjacent instants. When the envelope correlation of twoadjacent slices is a maximum, the frequency shift is actuallythe difference between the two corresponding translationalDoppler frequencies. Therefore, if the translational Dopplerfrequency at the initial instant is given, the translationalDoppler frequency at any other instant can be estimated.

The third step is phase adjustment. The translationalDoppler phase can be found by calculating the running sum ofthe translational Doppler frequencies. This phase is thenremoved from the signal.

IV. RESULTS

The field data of a Boeing-727 aircraft [10], provided byProf. B. D. Steinberg of the University of Pennsylvania, areused to evaluate our method. The aircraft was 2.7 km awayfrom the radar and flew at a speed of 147 mls. The radartransmitted short pulses at a wavelength of 3.123 em and awidth of 7 ns, and the echoes were sampled at an interval of5ns. The pulse repetition frequency was 400Hz. 512 echoeswere recorded. The 512 echoes are divided into four equalsegments, and each segment is processed individually. In allthe imaging processes, range alignment is carried out by theglobal method [11]. In both the traditional time-frequencymethod and the improved time-frequency method, the time­frequency representation is taken by the STFT.

Figure 2 shows the images obtained by the improved time­frequency method without preadjustment. Undersamplingcauses the aliasing of the time-frequency representation andthus the failure of the imaging. Figure 3 shows the imagesobtained by the dominant scatterer method. The images areacceptable. This shows that after the dominant scatterermethod is used for phase adjustment, the bandwidths of thesignals have been reduced such that the Nyquist sampling rateis satisfied. Figure 4 shows the images obtained by theimproved time-frequency method with the preadjustmentbased on the dominant-scatterer method. As we see, its focusquality is superior to that of Figs. 3. This shows that theimproved time-frequency method is effective.

Figure 5 shows the images obtained by the traditionaltime- frequency method with the preadjustment based on thedominant scatterer method. As we see, the focus quality ofFigure 5 is inferior to that of Figure 4. This shows that the

improved time-frequency method has a better performancethan the traditional time-frequency method.

B. Details

The envelop correlation of the slices at two adjacent instants,t and t+T, is defined as

R(l1f,t) == IIX(t,f)1 x IX(t +T,f + I1f)l, (1)f

where t is time, f is frequency, T is the sampling interval intime, ~f is the frequency shift, and X(t,f) is the time-frequencyrepresentation. When R(~f, t) is a maximum, ~f is optimal. Ifthe translational Doppler frequency is f at t, and the estimatedfrequency shift is ~f, then the translational Doppler frequencywill be f+~f at t+T. Therefore, if the translational Dopplerfrequency at the initial instant is given, the translationalDoppler frequency at any other instant can be estimated. Thetranslational Doppler frequency at the initial instant can beinitialized as any value, usually O.

The translational Doppler phase can be found bycalculating the running sum of the translational Dopplerfrequencies, i.e.

Figure 2. Images obtained by the improved time-frequency method withoutpreadjustment

Echoes 12~9~-2~5_6 ~-,

Echoes 385-512

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Echoes 1-128 Echoes 129-256 Echoes 257-384 Echoes 385-512

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Echoes 257-384 Echoes 385-512 Figure 5. Images obtained by the traditional time-frequency method withpreadjustment

(3)

The focus quality of an image can be measured by itsentropy [9]. The smaller the entropy is, the better the focusquality. The entropy of an image is defined as

E[lg(k,ntJ = ~I Ig(k,nt In S 2'

k=O n=O S Ig(k, n)1where

Figure 3. Images obtained by the dominant Scatterer method M-IN-I

S = 2:2:lg(k,n)12

• (4)k=O n=O

g(k,n) is the complex image, and k, n are the indices ofDoppler frequencies and range bins, respectively. Table Igives the entropies of the images in Figs 3, 4 and 5. Thisshows quantitatively that the improved time-frequency methodhas a better performance than the traditional time-frequencymethod.

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Figure 4. Images obtained by the improved time-frequency method withpreadjustment

Echoes 385-512

Echoes 129-256

v. CONCLUSIONS

The following conclusions can be drawn from the aboveresults and analyses. (1) The preadjustment based on thedominant-scatterer method or another method can reduce thebandwidths of the signals such that the aliasing of the time­frequency representation due to undersampling can be avoidedand the time-frequency method becomes applicable. (2) Theimproved time-frequency method can estimate the translationalDoppler frequency more accurately than the traditional time­frequency method .

REFERENCES

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[2] M. J. Prickett and C. C. Chen, "Principle of Inverse Synthetic ApertureRadar (ISAR) Imaging," 1980 IEEE EASCON Record, Pages 340-345.

the entropies of the images Figure. 3 Figure. 4 Figure. 5in Figures 3, 4 and 5Echoes 1-128 6.8003 6.7312 6.7900Echoes129-256 6.8342 6.8254 7.5736Echoes 257-384 6.3498 5.9227 6.8825Echoes 385-512 6.5168 5.4721 6.7725

..: ..: : -..

Y,:~···.<·:: '.:":"'- ..:..... ':.

. .

.; -.:. ..

Echoes 1-128

Echoes 257-384

...~.

(. ,.

~i -:? ~.<~:

t :.. -:.:'~~.~;

.-!(..•• ~

~ '.. r :. . ~:: .

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[3]

[4]

[5]

[6]

[7]

P. H. Eichel, D. C. Ghiglia and C. V. Jakowatz, "Speckle ProcessingMethod for Synthetic Aperture Radar Phase Correction," OpticsLetters, Volume 14, Number 1, January 1989, Pages 1-5.D. E. Wahl, P. H. Eichel, D. C. Ghiglia and C. V. Jakowatz, "PhaseGradient Autofocus-A Robust Tool for High Resolution SAR PhaseCorrection," IEEE Transactions on Aerospace and Electronic Systems,Volume 30, Number 3, July 1994, Pages 827-835.S. Barbarossa and A. Farina, "A Novel Procedure for Detecting andFocusing Moving Objects with SAR Based on the Wigner-VilleDistribution," 1990 IEEE International Radar Conference, Pages 44­50.F. Berizzi and G. Cosini, "Auto focusing of Inverse Synthetic RadarImages Using Contrast Optimization," IEEE Transactions onAerospace and Electronic Systems, Volume 32, Number 3, July 1996,Pages 1191-1197.R. P. Boeker, T. B. Henderson, S. A. Jones and B. R. Frieden, "A NewInverse Synthetic Aperture Radar Algorithm for Translational Motion

Compensation," Proceedings ofSPIE, Volume 1569, 1991, Pages 298­310.

[8] X. Li, G. Liu and J. Ni, "Autofocusing of ISAR Images Based onEntropy Minimization," IEEE Transactions on Aerospace andElectronic Systems, Volume 35, Number 4, October 1999, Pages1240-1251.

[9] J. Wang, X. Liu and Z. Zhou, "Minimum-entropy phase adjustmentfor ISAR," lEE Proceedings of Radar, Sonar and Navigation, Volume151, Number 4, August 2004, Pages 203-209.

[10] B. D. Steinberg and H. M. Subbaram, "Microwave ImagingTechniques," John Wiley & Sons, 1991.

[11] J. Wang and D. Kasilingam, "Global Range Alignment for ISAR,"IEEE Transactions on Aerospace and Electronic Systems, Volume 39,Number 1, January 2003, Pages 351-357.

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