Velocity Estimation of Moving Targets in SAR Imaging

A new scheme is presented for velocity estimation of movingtargets in synthetic aperture radar imaging. First, the moving targetis imaged using a range-Doppler algorithm, where clutter lock,range correction, and focus filtering are done automatically. Then,the parameters obtained in this algorithm are used to estimate thevelocity of the moving target. The Doppler centroid is used toestimate the radial velocity of the moving target, and the out-of-focuscoefficient is used to estimate the cross-range velocity of the movingtarget. The ambiguity of the Doppler centroid is resolved accordingto the range-migration coefficient and the out-of-focus coefficient.This scheme is accurate and computationally efficient.

I. INTRODUCTION

Velocity estimation of moving targets is a problem ofinterest in synthetic aperture radar (SAR) imaging. It canbe carried out using single-channel SAR ormultiple-channel SAR. In this paper, we only deal withsingle-channel SAR. In addition, we limit ourselves toairborne stripmap SAR, although our technique can beextended to other cases. Generally, the velocity of amoving target in the imaging plane is decomposed into aradial velocity and a cross-range velocity, and the twovelocities are estimated from the Doppler centroid and theDoppler rate, respectively.

The Doppler centroid can be estimated by thenominal-spectrum method, the energy-balancing method,the maximum-likelihood method, and the time-domainmethod [1, 2]. Because it is limited to the baseband, thisestimate may be ambiguous; that is, the true Dopplercentroid may be this estimate plus a multiple of the pulserepetition frequency (PRF). The ambiguity occurs whenthe radial velocity between the radar and the target is solarge that the absolute value of the Doppler centroidattains or exceeds half the PRF. In such cases, the estimateof the Doppler centroid cannot be directly used tocalculate the radial velocity of the moving target.

The potential ambiguity associated with the Dopplercentroid can be solved by finding an unambiguousDoppler centroid and calculating the ambiguity number.Because it is only used to calculate the ambiguity number,this unambiguous Doppler centroid does not have to be asaccurate as the estimate of the baseband Doppler centroid.Typical methods include the multiple-look method [3, 4],the wavelength-diversity method [5, 6], and thesharpest-projection method [7]. In the multiple-look

Manuscript received March 19, 2012; revised April 12, 2013; releasedfor publication July 12, 2013.

DOI. No. 10.1109/TAES.2014.120151.

Refereeing of this contribution was handled by S. Watts.

0018-9251/14/$26.00 C© 2014 IEEE

method, the range displacement between two looks is usedto estimate the unambiguous Doppler centroid. Thismethod may not work when the velocity of the movingtarget is so large that the two looks are seriously blurredand cannot be registered. In the wavelength-diversitymethod, the unambiguous Doppler centroid is estimatedfrom the skew of the two-dimensional spectrum. Thismethod is not robust if the target is embedded in strongground clutter. For the sharpest-projection method, whenthe unambiguous Doppler centroid is correctly estimated,the power of the signal in the range-Doppler domain hasthe sharpest projection on the range axis. This method iscomputationally expensive.

In this paper, a new scheme is presented for velocityestimation of moving targets in SAR imaging. In ourprevious work, we developed two automatic algorithms:one for focus filtering [8] and one for range correction [9].The two algorithms, together with an automatic algorithmfor clutter lock, can be used to image a moving target. Inthis paper, we further develop an algorithm to numericallyestimate the velocity of the moving target from theparameters obtained in these imaging processes. TheDoppler centroid is used to estimate the radial velocity ofthe moving target, and the out-of-focus coefficient is usedto estimate the cross-range velocity of the moving target.The range-migration coefficient and the out-of-focuscoefficient are used to resolve the ambiguity potentiallyassociated with the Doppler centroid. This scheme is bothaccurate and computationally efficient. A preliminarydescription of this work has been given in [10].

This paper is organized as follows. Section II describesautomatic imaging. Section III describes how to use theparameters obtained in automatic imaging to estimate thevelocity of the moving target. Two additional issues arediscussed in Section IV. Section V shows the results ofautomatic imaging and velocity estimation. Theconclusion is given in Section VI.

II. AUTOMATIC IMAGING

Velocity estimation of the moving target is based on itsautomatic imaging (Fig. 1). SAR imaging can be carriedout by the range-Doppler algorithm [1], the chirp-scalingalgorithm [11] or the wavenumber-domain algorithm [12].The range-Doppler algorithm is used in our processing.First, signals from scatterers with different ranges areresolved using their different delays in fast time. Thematched-filter technique, the stretch technique, or thestep-chirp technique is usually used to improve rangeresolution. Then, signals from scatterers with differentazimuths are resolved using their different positions inslow time. Focus filtering is used to improve azimuthresolution. To obtain a right-located, fully focused image,clutter lock and range correction are required before focusfiltering. When a moving target is imaged, clutter lock,range correction, and focus filtering have to be carried outautomatically, i.e., based on the signal.

CORRESPONDENCE 1543

Fig. 1. Scheme for automatic imaging and velocity estimation.

A. Clutter Lock

To avoid shift and blurring of the image, the Dopplercentroid needs to be determined in the design of the focusfilter. This is called clutter lock. When the radar movesregularly and the target is stationary, the Doppler centroidcan be calculated from the imaging geometry. Otherwise,the Doppler centroid has to be estimated based on thesignal. Curlander and McDonough [1] and Bamler [2]summarize typical methods for the estimation of theDoppler centroid, such as the nominal-spectrum method,the energy-balancing method, the maximum likelihoodmethod, and the time-domain method. Here, the Dopplercentroid means the baseband Doppler centroid.

We adopt the nominal-spectrum method to implementclutter lock. In this method, the Doppler centroid is chosenas the Doppler frequency, where the correlation functionof the Doppler energy spectrum and its nominal form ismaximized.

B. Range Correction

The signals from the same scatterer are not situated atthe same range bin because of the variation of the rangebetween the radar and the scatterer. This is called rangemigration. To generate a fully focused image, before focusfiltering, range migration needs to be corrected so that thesignals from the same scatterer are situated at the samerange bin. This is called range correction. Usually, rangecorrection is carried out according to the relation betweenrange and Doppler frequency in the range-Doppler domain[1]. This relation can be obtained from the imaginggeometry if the radar moves regularly and the target isstationary. Otherwise, this relation has to be estimatedfrom the signal.

We developed a technique to automatically correctrange migration in SAR imaging [9]. The samples at aDoppler frequency constitute a Doppler slice in therange-Doppler domain. If the width of the swath is lessthan the range between the midswath and the flight path,range migration can be corrected by shifting the Dopplerslices. It is found that when there is no range migration,the Doppler slices have similar envelopes; that is, theenvelope of one Doppler slice roughly equals the envelopeof another Doppler slice multiplied by a constant. Thus,range migration can be corrected by shifting the Dopplerslices so that their envelopes are similar. This techniqueworks even if the radar moves irregularly or the target ismoving.

C. Focus Filtering

The focus filter improves azimuth resolution by pulsecompression. The design of the focus filter generallyassumes that the radar moves regularly and the target isstationary. When the radar moves irregularly or the targetis moving, the focus filter may not focus the signal welland the image may be blurred. In such a case, we have todesign the focus filter from the signal. This is calledautofocus. Typical methods include thesubaperture-correlation method [1], the time-frequencymethod [13], the phase-difference method [14], thephase-gradient method [15], and the sharpest-imagemethod [8, 16–19].

Attention is paid to the sharpest-image methodbecause of its good focus quality and robustness againstnoise. In this method, the phase response of the focus filteris designed so that the image is sharpest. The sharpness ofthe image is measured by contrast [16], entropy [17], oranother function [18]. The optimization is implemented bya parametric or nonparametric algorithm. In theparametric algorithms, the phase response of the focusfilter is derived by parametric modeling [8, 16]. In thenonparametric algorithms, the phase response of the focusfilter is found directly [18, 19]. We adopt a modifiedversion of the sharpest-image method in [8]. Thesharpness of the image is measured by entropy: A sharperimage has smaller entropy. The phase response of thefocus filter is modeled as a quadratic polynomial, and thecoefficient of this polynomial is adjusted to minimize theentropy of the image.

III. VELOCITY ESTIMATION

The parameters determined in automatic imaging areused to estimate the velocity of the moving target.

A. Signal From a Scatterer

The signal from a scatterer is written as

s(t) = σ exp

(−j 4πr

λ

), (1)

where t is slow time, σ is the scattering coefficient of thescatterer, r is the range of the scatterer to the radar, and λ

1544 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 50, NO. 2 APRIL 2014

Fig. 2. Geometry of SAR imaging in imaging plane.

is the carrier wavelength. Here, r is written as

r =√(y0 + vyt − Vyt

)2 + (x0 + vxt − Vxt)2. (2)

Equation (2) is derived according to the geometry of SARimaging in the imaging plane (Fig. 2). The y-axis isdirected along the radar boresight. The radar moves atvelocity Vx in the x-axis and velocity Vy in the y-axis, andit is situated at (0, 0) at t = 0. The scatterer moves atvelocity vx in the x-axis and velocity vy in the y-axis, and itis situated at (x0, y0) at t = 0. Let tc be the time when theradar boresight is directed to the scatterer, i.e.,

tc = x0

Vx − vx , (3)

and yc be the range of the scatterer to the radar at tc, i.e.,

yc = y0 + vytc − Vytc. (4)

Then, approximating r by its second-order Taylor series attc, we obtain

r = yc − (Vy − vy)

(t − tc) + (Vx − vx)2

2yc(t − tc)2 . (5)

The substitution of (5) into (1) yields

s(t) = σ exp

{− j 4π

λ

[yc − (Vy − vy)(t − tc

)+ (Vx − vx)2

2yc(t − tc)2

]}. (6)

B. Estimation of Radial Velocity

The instantaneous Doppler frequency of the scattereris defined as the derivative of the phase of s(t), i.e.,

� = 4π

λ

[(Vy − vy

)− (Vx − vx)2

yc(t − tc)

]. (7)

The Doppler centroid is found by letting t = tc in (7), i.e.,

�c = 4π

λ

(Vy − vy

). (8)

From (8), we obtain the radial velocity:

vy = Vy − λ

4π�c. (9)

Therefore, the radial velocity can be estimated from theDoppler centroid. Actually, (9) is written as

vy = Vy − λ

2MTkc, (10)

where M is the number of the Doppler samples, T is thepulse repetition period, and kc is the Doppler centroid withthe Doppler interval as the unit.

The Doppler centroid can be estimated by clutter lock.However, the Doppler centroid estimated by clutter locklies within the baseband. It may be ambiguous; that is, thetrue Doppler centroid may be this estimate plus a multipleof the PRF. This ambiguity occurs when the radialvelocity between the radar and the target is so large thatthe absolute value of the Doppler centroid attains orexceeds half the PRF. In such cases, the estimate of theDoppler centroid cannot be used to directly calculate theradial velocity. To solve the ambiguity of the Dopplercentroid, an unambiguous Doppler centroid should befound to calculate the ambiguity number. Thisunambiguous Doppler centroid does not have to be asaccurate as the Doppler centroid estimated by clutter lockbecause it is only used to calculate the ambiguity number.Hence, an accurate, unambiguous Doppler centroid can bedetermined by

kc = k0 +M × round

(kr − k0

M

), (11)

where k0 is the Doppler centroid estimated by clutter lock,kr is a rough but unambiguous Doppler centroid, andround (·) carries out the rounding operation to obtain theambiguity number. To solve the ambiguity of the Dopplercentroid, kr needs to be found as follows. From (7), weobtain

t − tc = − λyc

4π (Vx − vx)2 (�−�c) . (12)

The substitution of (12) into (5) yields

r = yc + λyc(Vy − vy)4π (Vx − vx)2 (�−�c)

+ λ2yc

32π2 (Vx − vx)2 (�−�c)2 . (13)

Equation (13) gives the relation of the range to theinstantaneous Doppler frequency. It is also takenapproximately as the relation of the range to the spectralDoppler frequency. So, in range correction, the shift madeto the Doppler slice in the range should be

r� = − λyc(Vy − vy)4π (Vx − vx)2 (�−�c)

− λ2yc

32π2 (Vx − vx)2 (�−�c)2 . (14)

CORRESPONDENCE 1545

Extending (14) to the fundamental interval anddiscretizing rΩ and Ω, we obtain

nk=

⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩−

2∑i=1

αi

[2

M(k − k0)

]i, 0 ≤ k < k0 + M

2

−2∑i=1

αi

[2

M(k − k0 −M)

]i, k0 + M

2≤ k < M

,

(15)

α1 = λyc(Vy − vy)4dT (Vx − vx)2 , (16)

α2 = λ2yc

32dT 2 (Vx − vx)2 , (17)

where k is the index of Ω, d is the sampling interval in therange, and nk is the shift made to the Doppler slice k andnormalized by d. α1 and α2 are called the range-migrationcoefficients and can be estimated in the automaticcorrection of range migration (Section II.B). The Fouriertransform of s(t) is approximately

S(�) = σ

√λyc

2(Vx − vx)2exp[

− j π4

− j 4π

λyc − j�tc

+j λyc

8π(Vx − vx)2(�−�c)2

]. (18)

Therefore, the phase response of the focus filter should be

φ(�) = − λyc

8π (Vx − vx)2 (�−�c)2 . (19)

Extending (19) to the fundamental interval anddiscretizing Ω, we obtain

ϕ(k) =

⎧⎪⎪⎪⎨⎪⎪⎪⎩−πβ

(k − k0

M

)2

, 0 ≤ k < k0 + M

2

−πβ(k − k0 −M

M

)2

, k0 + M

2≤ k < M

,

(20)

β = λyc

2T 2(Vx − vx)2, (21)

where ϕ(k) is the phase response of the focus filter with kas the independent variable. In (21), β, called theout-of-focus coefficient, can be estimated in autofocus(Section II.C). Dividing (16) by (21), we obtain

vy = Vy − 2d

T

α1

β. (22)

By substituting (22) into (10), an estimate of kc isobtained, i.e.,

kr = 4dM

λ

α1

β. (23)

Once kr is found, kc is calculated using (11). Here, kr isfound from α1 and β. It can also be found from α1 and α2

theoretically. This, however, is not a good method becausethe estimate of α2 may not be accurate enough.

C. Estimation of Cross-Range Velocity

From (21), we obtain the cross-range velocity:

vx = Vx − 1

T

√λyc

2β. (24)

Therefore, the cross-range velocity can be estimated fromthe out-of-focus coefficient.

IV. FURTHER DISCUSSION

A. Finer Imaging

A right-located, well-focused image can be generatedin the preceding automatic imaging. However, becausesome approximations are assumed, the image may still beunsatisfactory in particular applications. Once the velocityis estimated, the moving target can be reimaged using afiner algorithm. Taking the moving target as the frame ofreference for motion analysis, we can set up anotherimaging geometry. Then, a finer algorithm can be used toreimage the moving target.

B. Target Isolation

The aforementioned scheme for automatic imagingand velocity estimation applies to a single moving target.It may not work when there exists a stationary backgroundor other moving targets. In such a case, automatic imagingand velocity estimation can be carried out in the followingway [20, 21]. First, the stationary background and themoving targets are imaged with the assumption that theradar moves regularly and no target moves. Then, thecomplex image of each moving target is isolated from thestationary background and other moving targets. Finally,each moving target is reprocessed with the aforementionedscheme for automatic imaging and velocity estimation.

A moving target needs to be detected before it isisolated. However, in this paper, we mainly address theproblem of velocity estimation and assume that themoving target has been detected.

V. RESULTS

Several sets of simulated signals are used to evaluateour scheme. The platform moves at a radial velocity of1 m/s and a cross-range velocity of 250 m/s. The radar hasa pulse repetition period of 2 ms. The beam has an angleof 0.02 rad in azimuth. The pulses have a wavelength of3 cm and a bandwidth of 200 MHz. The samplingfrequency is 300 MHz, and 512 echoes with 256 rangebins each are recorded. When the slow time is 0, theplatform is situated at (0, 0) and the center of the target issituated at (0, 10 km).

Table I shows the truths and the estimates of thevelocities for seven sets of signals. It can be seen that ourscheme has high accuracy. According to (8), when theradial velocity is −9, −6, −3, 6, or 9 m/s, the Dopplercentroid is 4000π /3, 2800π /3, 1600π /3, −2000π /3, or−3200π /3 rad/s. Because the absolute value of theDoppler centroid is larger than 500π rad/s, half the PRF,

1546 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 50, NO. 2 APRIL 2014

TABLE ITruths and Estimates of Velocities for Seven Sets of Signals (in Meters

per Second)

Radial Velocity Cross-Range Velocity

Truth Estimate Truth Estimate

−9 −9.00146 −9 −9.00594−6 −5.99854 −6 −5.93394−3 −2.99927 −3 −2.96872

0 0.00000 0 0.000003 2.99927 3 2.967166 5.99854 6 6.024989 9.00146 9 8.97199

TABLE IIEstimates of Velocities Under Different SNRs (Truths: 6 m/s)

Estimate of Radial Estimate of Cross-RangeSNR (dB) Velocity (m/s) Velocity (m/s)

20 5.99854 6.0249810 5.99854 6.02498

0 5.99121 6.02498−10 5.96558 6.02498−20 5.75317 5.92811

the Doppler centroid estimated by clutter lock isambiguous and is around 1000π /3, −200π /3, −1400π /3,1000π /3, or −200π /3 rad/s. If the ambiguity of theDoppler centroid were not solved, the estimate of theradial velocity would be around −1.5, 1.5, 4.5, −1.5, or1.5 m/s. However, as we see from Table I, the estimate ofthe radial velocity is around −9, −6, −3, 6, or 9 m/s. Thisindicates that our scheme is effective in solving theambiguity of the Doppler centroid.

The program is written in MinGW C on a DellPrecision T3400 workstation with a 3-GHz centralprocessing unit and 3 GB of memory. For the seven sets ofsignals, the computation times are 1.859, 1.781, 1.672,1.437, 1.703, 1.562, and 1.797 s. It can be seen that thisscheme is also computationally efficient. The times aremainly for the sharpest-image autofocus. In itsimplementation, the phase response of the focus filter isestimated from all range bins. If it is estimated from only apart of the range bins, the computational efficiency will befurther improved.

The estimates of the velocities under differentsignal-to-noise ratios (SNRs) are shown in Table II. Here,Gaussian noise with different intensities is added to thesignals when the radial velocity and the cross-rangevelocity are both 6 m/s. We can see that as the noiseincreases, the error increases. Nevertheless, the estimatesare accurate. This indicates that our scheme is robustagainst noise. Fig. 3 shows the image generated from thelast set of signals in Table II.

A set of real data, provided by the 38th Institute of theChina Electronic Technology Corporation, is also used toevaluate our scheme. The radar moves at a velocity of219 m/s and has a PRF of 1200 Hz. The pulses have awavelength of 3.158 cm and a bandwidth of 400 MHz.

Fig. 3. Image generated from last set of signals in Table II.

Fig. 4. Image of airport with moving car.

The sampling frequency is 480 MHz. The scene is anairport, where a car moves at a velocity of about 5 m/s.

Fig. 4 shows the image of the airport. The car isindicated in the image. It is blurred because of its motion.Using an interactive graphic user interface (implementedwith the function “roipoly” in the matrix laboratory, orMATLAB, computer language), the car is isolated and itscomplex image is converted into the signal (the signalresolved in the range and expressed in the range-Dopplerdomain). The signal is reprocessed with our scheme forautomatic imaging and velocity estimation. In the result,the estimates of the radial velocity and the cross-rangevelocity are −1.4664 and −4.9655 m/s, respectively.

The total velocity of the car can be estimated by

v =√[

vy

cos(θ)

]2

+ v2x, (25)

where θ is the depression angle of the radar sightline andvy/cos(θ) is the velocity of the car in ground range. Here,cos(θ) is estimated from yc and the height of the radar; it is0.9664. According to vy, vx, and cos(θ), the total velocityof the car can be estimated. It is 5.1922 m/s. This isconsistent the car moving at a velocity of about 5 m/s. Aswe see, this scheme works when the target hassignificantly larger intensity than the background. This istrue for most ships and some ground targets.

CORRESPONDENCE 1547

VI. CONCLUSION

In SAR imaging, the velocity of moving targets can beeffectively estimated using the scheme presented in thispaper. First, the moving target is imaged using arange-Doppler algorithm, where clutter lock, rangecorrection, and focus filtering are done automatically.Then, the parameters obtained in this algorithm are used toestimate the velocity of the moving target. The Dopplercentroid is used to estimate the radial velocity of themoving target, and the out-of-focus coefficient is used toestimate the cross-range velocity of the moving target. Theambiguity of the Doppler centroid is resolved according tothe range-migration coefficient and the out-of-focuscoefficient. This scheme is accurate and computationallyefficient.

Further research is needed on velocity estimation whenthe moving target is embedded in strong ground clutter. Inaddition, it is assumed in our scheme that the targettranslates with a constant velocity. Further research is alsoneeded on motion estimation when the target translateswith a variable velocity or rotates. When the target isstationary, the velocity estimated in this scheme reflectsthe velocity error of the platform. This is useful in thenavigation of aircraft and spacecraft.

ACKNOWLEDGMENT

This work is supported by the National NaturalScience Foundation of China (No. 61072150), theNational High-Technology Research and DevelopmentProgram of China (No. 200812Z108), and the NationalBasic Research Program of China (No. 2010CB731904).

JUNFENG WANG,XINGZHAO LIUShanghai Jiaotong UniversityDepartment of Electronic

Engineering800 Dongchuan RoadShanghai, 200240, ChinaE-mail:

(junfengwang@sjtu.edu.cn)

REFERENCES

[1] Curlander, J. C., and McDonough, R. N.Synthetic Aperture Radar: Systems and Signal Processing.New York, NY: John Wiley & Sons, 1991.

[2] Bamler, R.Doppler frequency estimation and the Cramer-Rao bound.IEEE Transactions on Geoscience and Remote Sensing, 29, 3(May 1991), 385–390.

[3] Cumming, I. G., Kavanagh, P. F., and Ito, M. R.Resolving the Doppler ambiguity for spaceborne syntheticaperture radar. In Proceedings of the IEEE InternationalGeoscience and Remote Sensing Symposium, Zurich,Switzerland, 1986, 1639–1643.

[4] Cumming, I. G., and Wong, F. H.Digital Processing of Synthetic Aperture Radar Data:

Algorithms and Implementation. Norwood, MA, USA: ArtechHouse, 2005.

[5] Bamler, R., and Runge, H.PRF-Ambiguity resolving by wavelength diversity.IEEE Transactions on Geoscience and Remote Sensing, 29, 6(Nov. 1991), 997–1003.

[6] Marques, P., and Dias, J.Velocity estimation of fast moving targets using a single SARsensor.IEEE Transactions on Aerospace and Electronic Systems, 41,1 (Jan. 2005), 75–89.

[7] Li, G., Xia, X., Xu, J., and Peng, Y.A velocity estimation algorithm of moving targets using singleantenna SAR.IEEE Transactions on Aerospace and Electronic Systems, 45,3 (July 2009), 1052–1062.

[8] Wang, J., and Liu, X.SAR minimum-entropy autofocus using an adaptive-orderpolynomial model.IEEE Geoscience and Remote Sensing Letters, 3,4 (Oct. 2006), 512–516.

[9] Wang, J., and Liu, X.Automatic correction of range migration in SAR imaging.IEEE Geoscience and Remote Sensing Letters, 7,2 (Apr. 2010), 256–260.

[10] Wang, J., and Liu, X.Velocity estimation of moving targets using SAR.In Proceedings of the IEEE International Geoscience andRemote Sensing Symposium, Vancouver, Canada, 2011,340–343.

[11] Raney, R. K., Runge, H., Bamler, R., Cumming, I. G., and Wong,F. H.Precision SAR processing using chirp scaling.IEEE Transactions on Geoscience and Remote Sensing, 32, 4(July 1994), 786–799.

[12] Bamler, R.A comparison of range-Doppler and wavedomain SARfocusing algorithms.IEEE Transactions on Geoscience and Remote Sensing, 30, 4(July 1992), 706–713.

[13] Barbarossa, S., and Farina, A.A novel procedure for detecting and focusing moving objectswith SAR based on the Wigner-Ville distribution.In Proceedings of the IEEE International Radar Conference,Arlington, VA, USA, 1990, 44–50.

[14] Niho, Y. G.Phase difference auto focusing for synthetic aperture radarimaging, U.S. Patent 4 999 635, 1991.

[15] Eichel, P. H., Ghiglia, D. C., and Jakowatz, C. V.Speckle processing method for synthetic aperture radar phasecorrection.Optics Letters, 14, 1 (Jan. 1989), 1–5.

[16] Herland, E. A.Seasat SAR Processing at the Norwegian defense researchestablishment. In Proceedings of the EARSeL-ESASymposium, Voss, Norway, 1981, 247–253.

[17] Bocker, R. P., Henderson, T. B., Jones, S. A., and Frieden, B. R.A new inverse synthetic aperture radar algorithm fortranslational motion compensation.Proceedings of the SPIE, 1569 (1991), 298–310.

[18] Fienup, J. R., and Miller, J. J.Aberration correction by maximizing generalized sharpnessmetrics.Journal of Optical Society of America A, 20, 4 (Apr. 2003),609–620.

[19] Wang, J., Liu, X., and Zhou, Z.Minimum-entropy phase adjustment for ISAR.IEE Proceedings: Radar, Sonar and Navigation, 151, 4 (Aug.2004), 203–209.

1548 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 50, NO. 2 APRIL 2014

[20] Soumekh, M.Reconnaissance with ultra wideband UHF synthetic apertureradar.IEEE Signal Processing Magazine, 12, 4 (July 1995), 21–40.

[21] Perry, R. P., DiPietro, R. C., and Fante, R. L.SAR imaging of moving targets.IEEE Transactions on Aerospace and Electronic Systems, 35,1 (Jan. 1999), 188–200.

Binary Codes for Multirange-Resolution Radarand Pulse-Compression Properties

We propose new binary codes with various bandwidths formultirange-resolution radar. These spectrums do not have deepvalleys over a wide frequency range. A mismatched filter, whichconsists of a matched filter and a least-error energy-shaping filter, isapplied for the pulse compression. It is demonstrated that thepulse-compression loss of the proposed codes is very small comparedwith the loss of conventional binary codes, even though the proposedcodes are compressed to a very narrow pulse width by expansion ofthe bandwidth.

I. INTRODUCTION

Many researchers have studied pulse-compressioncodes for matched filters (MFs) and have found codes withsmall range sidelobes [1–3]. This is because these MFscan maximize detectability in white Gaussian noise. Suchconventional radar systems generally have a fixedradar-range resolution regardless of detection range, whichis approximately given by the reciprocal of the frequencybandwidth of the transmitting signal. It is desirable that therange resolution be improved as the distance between theradar and a target becomes shorter, because we might feelthreatened as unknown targets become close. We proposeda method for multirange resolution that translates the highsignal-to-noise ratio (SNR) of a target at a closer distanceto better range resolutions with little sacrifice of themaximum detection range [4]. Mismatched filters (MMF)are then applied to multirange-resolution radar becausethis can change the output pulse width. However, the filterwould generate a large pulse-compression loss if the MMFtried to compress a simple pulse or a conventional code toa pulse width smaller than the reciprocal of the bandwidthof the input signals [4, 5]. Shinriki et al. have proposed areceiving system of multirange resolutions using plainbinary codes [6].

In this paper, we propose new binary codes withvarious bandwidths for multirange-resolution radar. Wethen choose codes whose spectrums do not have the deepvalley over the wide frequency range. A MMF, whichconsists of an MF and a least-error energy-shaping filter, isapplied for the pulse compression. It is demonstrated thatthe pulse-compression losses have very small values, bychoosing codes without the deep spectrum valley over thewide frequency range, compared with those ofconventional codes. We also indicate that the length of the

Manuscript received October 12, 2012; revised April 11, 2013, June 30,2013; released for publication July 12, 2013.

DOI. No. 10.1109/TAES.2014.120643.

Refereeing of this contribution was handled by S. Blunt.

0018-9251/14/$26.00 C© 2014 IEEE

CORRESPONDENCE 1549