frequency-domain bistatic sar processing for spaceborne ......refereeing of this contribution was...

Frequency-DomainBistatic SAR Processingfor Spaceborne/AirborneConfiguration

ROBERT WANG, Member, IEEEOTMAR LOFFELD, Senior Member, IEEEHOLGER NIESSTEFAN KNEDLIK, Member, IEEEQURAT UL-ANN, Member, IEEEAMAYA MEDRANO-ORTIZUniversity of SiegenGermany

JOACHIM H. G. ENDER, Senior Member, IEEEFraunhofer FHRGermany

This paper focuses on the bistatic synthetic apertureradar (BiSAR) signal processing in the spaceborne/airborneconfiguration. Due to the extreme differences in platformvelocities and slant ranges, the airborne system operates in theinverse sliding spotlight mode, while the spaceborne systemworks in the sliding spotlight mode to achieve a tradeoffbetween the azimuth scene size and azimuth resolution. Sucha mode is generally called double sliding spotlight mode. Inthis configuration, the echoed signal has two characteristics.Firstly, both transmitter and receiver have very short syntheticaperture times. Secondly, the airborne platform operates withwide squint difference, while the spaceborne platform works inthe small squint case. According to these two features, we usedifferent Taylor expansions to address the slant range historiesof transmitter and receiver. Based on the presented model, atwo-dimensional space-variant bistatic point target referencespectrum (BPTRS) is derived. Furthermore, we linearizethe BPTRS to derive the transfer function of the basebandscene. From the transfer function, the signal features of thespaceborne/airborne configuration become very clear. Using thetransfer function, the two-dimensional inverse scaled Fouriertransform (ISFT) is used to focus the bistatic signal in thespaceborne/airborne configuration.

Manuscript received January 18, 2008; revised August 10, 2008 andFebruary 8, 2009; released for publication March 19, 2009.

IEEE Log No. T-AES/46/3/937975.

Refereeing of this contribution was handled by P. Lombardo.

This work is part of the joint DFG (German Science Foundation)research initiative Bistatic Exploration (PAK 59) of ZESS andFraunhofer FHR, individually funded under Grant “Lo 455/7-1.”

Authors’ address: R. Wang, O. Loffeld, H. Nies, S. Knedlik,Q. Ul-Ann, and A. Medrano-Ortiz, Paul-Bonatz-Strasse9-11, University of Siegen, Siegen 57076, Germany, E-mail:([email protected]); J. H. G. Ender, Fraunhofer Institute forHigh Frequency Physics and Radar Techniques (Fraunhofer FHR)53343 Wachtberg, Germany.

0018-9251/10/$26.00 c° 2010 IEEE

I. INTRODUCTION

Bistatic synthetic aperture radar (BiSAR)configurations can generally be grouped into twocategories: azimuth-invariant, where the baselinebetween transmitter and receiver is constant, andazimuth-variant ones, where the baseline is variant(also known as the general case [1]). Recently, aspecial azimuth-variant configuration referred to asthe spaceborne/airborne case became an active areaof research [2—8]. The intended hybrid experimentwill not only demonstrate the feasibility of theazimuth-variant bistatic configuration [4] but willalso offer an excellent opportunity to develop andvalidate new BiSAR processing algorithms andimaging techniques, especially for the azimuth-variantcase. Moreover, this configuration also bringsadditional benefits with respect to monostatic SARsystems like increased reliability and flexibilityof future SAR missions, reduced vulnerabilityfor military applications, reduced cost using anexisting radar satellite, and capacity of forward- orbackward-looking SAR imaging [3, 4, 6].The focusing of BiSAR data is addressed in a

steadily growing number of publications [10—20].Based on an approximate spectrum (Loffeld's bistaticformula (LBF) [9]), the two-dimensional inversescaled Fourier transform (ISFT) [10] and chirpscaling algorithm [11] are applied to focus theBiSAR data. Furthermore, the bistatic compensationmotion model and approach are presented for theazimuth-invariant bistatic configurations in [11].For the spaceborne/airborne configuration, however,the original LBF shows a limitation, and recentlyis extended to the general bistatic configurationssuch as high squint, wide swath, and unparallelflight trajectories [12]. The wave-number domainalgorithm (WDA) to process BiSAR data is describedin [13, 14]. In [15], a preprocessing techniqueknown as dip move out (DMO) is used to transformthe azimuth-invariant bistatic configuration to themonostatic one; a method for the azimuth-variantconfiguration is developed in [16]. In [17], a modifiedrange Doppler algorithm is proposed to space-surface(spaceborne/airborne) BiSAR data. In particular,based on an analytical bistatic point target referencespectrum (BPTRS) [18], the nonlinear chirp scalingalgorithm (NLCS) and range-Doppler algorithm(RDA) has been applied to process BiSAR data in theazimuth-variant and azimuth-invariant configurations,respectively [19, 20].In the spaceborne/airborne configuration, the

velocity of the overlapping antenna footprint alongthe ground is much greater than that of the airborneplatform, but much less than the velocity of thespaceborne platform. Therefore, the antenna of theairborne platform needs to be steered with a higherazimuth scan angle than the antenna of the spaceborne

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 46, NO. 3 JULY 2010 1329

platform to increase the width of the overlappingscene. And thus, for the spaceborne platform, theinstantaneous satellite-to-target slant range is almostequal to the slant range at its zero Doppler time.However, for the airborne platform, the instantaneousantenna-to-target range approximates to the slantrange at the beam center time. Based on this fact, weexpand the slant range histories of the spaceborne andairborne platforms around the zero Doppler time andthe beam center time, respectively, in a second-orderTaylor series. Finally, combining the two quadraticfunctions and applying the principle of stationaryphase yields BPTRS [21, 22].After we obtain the BPTRS, we express it in

terms of the receiver-referenced coordinates. Inaddition, a two-dimensional linearization operationis performed to derive the transfer function of thebaseband scene (TFBS). From TFBS, we can clearlyunderstand the features of the bistatic signal in thespaceborne/airborne configuration. Additional tothe well-known range scaling (range cell migration(RCM)), we discover an additional azimuth scaling.The azimuth scaling phenomenon is an intrinsicfeature of BiSAR in the azimuth-variant configuration.Based on the proposed TFBS, we apply the ISFT andthe matched filtering to correct the two-dimensionalscaling and cancel the range and azimuth modulationsin the frequency domain. The processing performed inthe frequency domain would offer the computationalbenefit compared with the back projection algorithm(BPA); the BPA scales with complexity O(N3) whereN2 is the number of pixels in the image [23], whereasthis proposed approach achieves a complexity ofO(N2).This paper is organized as follows. In Section II,

we start with the geometry and signal model ofspaceborne/airborne configuration and derive the pointtarget reference spectrum (PTRS). Subsequently, wederive the transfer function of the baseband scenein Section III. Section IV describes the focusingmethod. Some simulations to verify the approach areperformed in Section V. Finally, in Section VI, someconclusions are reported.

II. GEOMETRY, SIGNAL MODEL, AND BPTRS

Here, we investigate the spaceborne/airborneconfiguration using TerraSAR-X as the illuminatorand the airborne SAR system, FGAN’s PAMIR, as thebistatic receiver [2—8].

A. Geometry Model

We start with a simple description of thedouble sliding imaging mode. For clarity, a generaltwo-dimensional geometry of spaceborne/airborneconfiguration is shown in Fig. 1. The spaceborne

platform trajectory is assumed to be a straight line andparallel to the airborne track.The sliding spotlight mode has been originally

presented in [24]. It is characterized by steering thebeam about a virtual point. In Fig. 1, the virtualrotation point of the spaceborne platform OT isbeneath the Earth’s surface and far away from thescene center O. During data acquisition time, thephase center of the transmitter antenna steadily pointsto the virtual point OT instead of O. The grade oftradeoff between scene extension and improvementof azimuth resolution is determined by the slidingfactor ®T that is given by ®T = vGT=vT = XGT=XT(see Fig. 1) [5, 6, 24, 25]. The parameters vGT andvT refer to the velocities of the antenna footprintand platform from transmitter, respectively; XGT andXT denote the distances covered by the trajectoriesof the platform and the antenna footprint from thetransmitter, respectively. From Fig. 1, it can be seenthat locating OT at infinity (®T = 1) or at the scenecenter (®T = 0), the strip-map or spotlight modes areobtained, respectively.The inverse sliding spotlight mode is a special

case of the sliding spotlight mode, where the virtualrotation point OR is located behind the platform inthe sky [5]. The factor of the corresponding slidingis defined by ®R = vGR=vR = XGR=XR (see Fig. 1).The parameters vGR and vR refer to the velocitiesof the antenna footprint and platform from receiver,respectively; XGR and XR denote the distances coveredby the trajectories of the platform and the antennafootprint from receiver, respectively.In this double sliding spotlight model, the azimuth

spectrum’s center frequency of a target depends onthe azimuth coordinate target [25]. The effect of thedependency on the SAR data processing is highlightedin Section IV.

B. Signal Model and BPTRS

After demodulation, the received signal from apoint target P (shown in Fig. 2) located at (s0R,r0R)is formulated as

g(s, t,s0R ,r0R)

= ¾(s0R ,r0R)rect

·t¡R(s)=c

¿

¸expf¡j¼Kr[t¡R(s)=c]2g

£ exp·¡j 2¼R(s)

¸

¸rect

·s¡ sRcTs

¸rect

·s0R ¡ scbL=vR

¸(1)

where s and t represent the slow- and fast-timevariables, respectively; Kr and ¿ are the chirp rateand pulse duration time of the transmitted signal,respectively; c is the speed of light and ¸ is theradar wavelength; Ts is the composite exposuretime; L is the width of the illuminated scene inazimuth given by 2r0R tanÁR +XR; r0R is the slant

1330 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 46, NO. 3 JULY 2010

Fig. 1. Two-dimensional geometry of spaceborne/airborne BiSAR in double sliding spotlight model.

range of receiver at the zero Doppler time s0R;(s0R,r0R) specifies the receiver-referenced coordinatesdefined as the coordinates of target space; ÁR isthe maximum steering angle of receiver (shown inFig. 1); scb is the azimuth scene center crossing timeof receiver; sRc is the beam center crossing time ofreceiver, and dependent on the target coordinates(s0R,r0R), i.e., expressed as sRc(s0R,r0R). In (1), thefirst rect[¢] accounts for the duration time of thetransmitted pulse; the second one represents thecomposite antenna pattern, which is approximatedas a uniform illumination over the ground; thelast one plays a key role in limiting the extensionof the illuminated area. R(s) is the sum of theone-way instantaneous slant range and is givenas

R(s) = RR(s) +RT(s) (2)

RR(s) =qr20R +(s¡ s0R)2v2R (3)

RT(s) =qr20T+(s¡ s0T)2v2T (4)

where s0T is the zero Doppler time of thetransmitter and r0T is the slant range oftransmitter at the zero Doppler time. Theyare also dependent on the target coordinates(s0R,r0R), i.e., expressed as s0T(s0R,r0R) andr0T(s0R,r0R).Performing the Fourier transform (FT) with

respect to the variable t, we can transform (1) into therange-frequency/azimuth-time domain.

g(s,f,s0R,r0R) = ¾(s0R,r0R)rect·f

Kr¿

¸exp

½j¼f2

Kr

¾£ exp[¡j'b(s,f)]rect

·s¡ sRcTs

¸£ rect

·s0R ¡ scbL=vR

¸(5)

WANG ET AL.: FREQUENCY-DOMAIN BISTATIC SAR PROCESSING FOR SPACEBORNE/AIRBORNE CONFIGURATION 1331

Fig. 2. Imaging geometry in spaceborne/airborne BiSAR configuration. X, Y, and Z represent along-track cross-track, and verticaldirections, respectively.

where

'b(s,f) =2¼(f+f0)R(s)

c(6)

represents the bistatic slant range history in therange-frequency/azimuth-time domain; f0 is the radarcarrier frequency; and f is the Fourier frequencyvariable for the fast-time variable t.From (3) and (4), it can be seen that a double

square root term is included in the phase of (6), whichmakes it difficult to apply the principle of stationaryto obtain the bistatic spectrum [18—19]. To circumventthe limitation of the double square root in (6), weexpand (3) and (4) around the beam center time andzero Doppler time, respectively,

RR(s) =qr20R +(s¡ s0R)2v2R ¼ rRc+

v2R(sRc¡ s0R)rRc

(s¡ sRc)

+12v2Rr

20R

r3Rc(s¡ sRc)2 (7)

RT(s) =qr20T +(s¡ s0T)2v2T ¼ r0T+

v2T(s¡ s0T)22r0T

(8)

where

rRc =qr20R + v

2R(sRc¡ s0R)2 (9)

refers to the receiver-to-target slant range at the beamcenter time, which is a function of the coordinates(s0R,r0R). The first approximation is justified by thesmall target exposure time. The second one is verified

by the fact that r0TÀ (s¡ s0T)vT, which implies asmall azimuth steering angle. Substituting (7)—(8) into(6) yields

'b(s,f)¼ 2¼f+f0c

·rRc+ r0T +

v2R(sRc¡ s0R)rRc

(s¡ sRc)

+12v2Rr

20R

r3Rc(s¡ sRc)2 +

v2T(s¡ s0T)22r0T

¸:

(10)

The approximation error included in (10) can beformulated as

'e(s,f)¼ 'eR(s,f) +'eT(s,f) (11)

where 'eR and 'eT are defined as the slant rangehistory approximation errors of receiver andtransmitter, respectively. They are the sums of thecubic and higher-order terms in the Taylor seriesexpansion. Because the cubic term is the mostdominant component, these truncated error termscan be approximately determined by the cubic term.However, the third-order term of RT(s) is equalto zero, and thus its error term is approximatelygiven by the quartic term, so that 'eR and 'eT areapproximately formulated as

'eR(s,f)¼¡2¼f+f0c

·r20Rv

4R(sRc¡ s0R)2r5Rc

(s¡ sRc)3¸(12)


Fig. 3. Range history error of receiver, denoted by (12).

Fig. 4. Range history error of transmitter, denoted by (13).

'eT(s,f)¼¡2¼f+f0c

·v4T(s¡ s0T)4

8r30T

¸: (13)

Examining (7) and (8), it can be seen that thevalidity of our quadratic model is limited by themaximum slant range history errors expressed by (12)and (13). The phase errors in the range-frequencyand azimuth-time domain are shown in Figs. 3and 4.The simulation parameters for Figs. 3 and 4 are

listed in Table I. In this simulation, we assume that thescene center crossing time of the receiver is the zeroazimuth time, i.e., scb = 0. The simulated target of PT9is located at (4 s, 6666.21 m), shown in Fig. 6. FromFigs. 3 and 4, we can see that both j'eR(s,f)j ¿ ¼=8and j'eT(s,f)j ¿ ¼=8 are satisfied. Using these twoinequalities, the constraints for the quadratic modelsof receiver and transmitter can be expressed as,respectively,

Ts¿·

cr5Rc2(f+f0)r

30Rv

3R tanÁR

¸1=3(14)

vT(s¡ s0T)¿·

cr30T2(f+f0)

¸1=4: (15)

Then, an azimuth Fourier is performed totransform the signal into the two-dimensionalfrequency domain.

G(fa,f,s0R,r0R)

=Zg(s,f,s0R,r0R)exp(¡j2¼fas)ds

= ¾(s0R,r0R)rect·f

Kr¿

¸exp

½j¼f2

Kr

¾£ rect

·s0R ¡ scbL=vR

¸Zexpf¡j['b(s,f)+2¼fas]g

£ rect·s¡ sRcTs

¸ds (16)

where fa is the Fourier variable for the slow-timevariable s. To evaluate (16) using the principle ofstationary phase, we must determine the bistatic pointof stationary phase. The phase function of (16) isgiven by

ª (fa,f,s) = 'b(s,f) +2¼fas: (17)

Letting the first derivative of (17) go to zero, weobtain

@

@s[ª (fa,f,s)] =

@'b(s,f)@s

+2¼fa = 0: (18)

Solving (18) for the stationary point sp yields

sp =v2Rr

20Rr0TsRc+ v

2Tr3Rcs0T ¡

r3Rcr0Tc

f +f0fa¡ v2R(sRc¡ s0R)r2Rcr0T

[v2Rr0Tr20R + r

3Rcv

2T]

:

(19)

Substituting (19) for s in the integral of (16) gives1

G(fa,f,s0R ,r0R) = ¾(s0R ,r0R)rect

·f

Kr¿

¸exp

μj¼f2

Kr

¶£ exp[¡jª (fa,f,s0R ,r0R)]rect

·fa¡fDcBa

¸£ rect

·s0R ¡ scbL=vR

¸(20)

where ª (fa,f,s0R,r0R) is BPTRS and given as

ª(fa,f,s0R,r0R)¼ ©1(f,s0R,r0R)+©2(fa,f,s0R,r0R)+©3(fa,f,s0R,r0R) +©4(fa,f,s0R,r0R)

+©5(fa,f,s0R,r0R) (21)

©1(f,s0R,r0R) = 2¼f+f0c

(rRc+ r0T) (22)

1The inessential magnitude and phase terms are ignored.


©2(fa,f,s0R,r0R) = 2¼(f+f0)v

2R(sRc¡ s0R)c

24v2Tr2Rc(s0T¡ sRc)¡ cr2Rcr0Tf+f0

fa¡ v2R(sRc¡ s0R)rRcr0T(v2Rr0Tr

20R + r

3Rcv

2T)

35 (23)

©3(fa,f,s0R,r0R) = ¼(f+f0)v

2Rr20R

cr3Rc

24v2Tr3Rc(s0T¡ sRc)¡ cr3Rcr0T

f+f0fa¡ v2R(sRc¡ s0R)r2Rcr0T

(v2Rr0Tr20R + r

3Rcv

2T)

352 (24)

©4(fa,f,s0R,r0R) = ¼(f+f0)v

2Tr0T

c

24v2Rr20R(sRc¡ s0T)¡ v2R(sRc¡ s0R)r2Rc¡ cr3Rc

f+f0fa

[v2Rr0Tr20R + r

3Rcv

2T]

352 (25)

©5(fa,f,s0R,r0R) = 2¼fa

"v2Rr

20Rr0TsRc+ v

2Tr3Rcs0T¡ r3Rcr0T cfa

f+f0¡ v2R(sRc¡ s0R)r2Rcr0T

[v2Rr0Tr20R + r

3Rcv

2T]

#: (26)

In (20), the last two rectangular functions showthe width and location of the point target azimuthspectrum. They are given as

fDc =v2T¸r0T

s0T+v2R¸rRc

s0R ¡μv2R¸rRc

+v2T¸r0T

¶sRc

(27)

Ba = Ts

μv2r r

20R

¸r3Rc+v2T¸r0T

¶: (28)

Examination of (27) and (28) suggests that bothDoppler center and bandwidth are two-dimensionallyspace dependent. The dependency is caused by thebeam steering of both antennas. The implicationof this space-variant feature on the BiSAR dataprocessing is discussed in Section IV.

III. TWO-DIMENSIONAL LINEARIZATION OF BPTRSAND TRANSFER FUNCTION OF THE BASEBANDSCENE

Because the transfer function of the scene is thesum of reflected signals from all the point targets, itcan be expressed as [10]

H(fa,f) =Z Z

G(fa,f,s0R,r0R)ds0Rdr0R: (29)

However, the phase term ª (fa,f,s0R,r0R) ofG(fa,f,s0R,r0R) is not linearly dependent on thevariables r0R and s0R. To obtain the transfer functionof the scene, ª(fa,f,s0R,r0R) needs to be expressed asa linear function of the coordinate variables r0R ands0R in the target space.

A. Linearization of BPTRS

To formulate ª(fa,f,s0R,r0R) as a linearfunction of the coordinate variables r0R and s0R, atwo-dimensional linearization operation is performedin (s0R = 0,r0R = Rm) (refer to the Appendix). The

linear expression of BPTRS ªL(fa,f,s0R,r0R) is givenas

ªL(fa,f,s0R,r0R)¼ ©0(fa,f) +2¼©R(fa,f)(r0R ¡Rm)+2¼©A(fa,f)s0R (30)

©0(fa,f) =ª (fa,f,0,Rm) (31)

©R(fa,f) =@ª (fa,f,s0R,r0R)

2¼@r0R

¯s0R=0,r0R=Rm

(32)

©A(fa,f) =@ª (fa,f,s0R,r0R)

2¼@s0R

¯s0R=0,r0R=Rm

(33)

where Rm is the closest range from the scene centerto the ideal trajectory of receiver. ©0(fa,f) representsthe space-invariant component; ©R(fa,f)(r0R ¡Rm) and©A(fa,f)s0R are the range-variant and azimuth-variantcomponents, respectively, and they denote thespace-variant characteristic of the BiSAR signal in thespaceborne/airborne configuration.To further show the signal characteristics of

BiSAR in the spaceborne/airborne case, we expand©R(fa,f) and ©A(fa,f) in the first-order Taylor seriesin terms of f and fa, respectively,

©R(fa,f)¼ ERV(fa) +ERVF(fa)f (34)

©A(fa,f)¼ EAV(f) +EAVFfa: (35)

It is worth emphasizing that EAVF is independentof the range frequency variable f due to theapproximations in (7) and (8).For easy description of the baseband spectrum in

the next section, herein we introduce a substitution ofa range variable r = r0R ¡Rm in (30). The parameterr denotes the zero-offset receiver-to-target rangevariable. Furthermore, we define (s0R,r) as thecoordinates of image space; that is, the image space(s0R,r) uses the scene center range in target space(s0R,r0R) as zero reference slant range. Therefore,using the substitutions of r = r0R ¡Rm and (34)—(35)


in (30) yields the linearized BPTRS as

ªL(fa,f,s0R,r)¼ ©0(fa,f) +2¼[ERV(fa)+ERVF(fa)f]r+2¼[EAV(f)+EAVFfa]s0R: (36)

B. Derivation of TFBS

In reality, we would like to focus the target tothe relative range position with respect to the scenecenter (i.e., image space or baseband slant rangedomain) rather than to the real position. A simpleway of doing this is to transform the raw data intothe baseband slant-range domain before focusing thetarget. According to the shifting theorem of FT, toshift the sampling starting time by a constant timetm to the right, the spectrum can be multiplied by anexponential with exp(¡j2¼ftm). Here, the shiftedtime tm is defined as tm = (Rm+RmT)=c, where RmTrepresents the slant range of the closest approach fromthe transmitter to the scene center.In the image space, the backscattering coefficient

of point target becomes ¾(s0R,r). Substituting (36) for(21) into (20) gives

G(fa,f,s0R,r) = ¾(s0R,r)rect·f

Kr¿

¸expμj¼f2

Kr

¶£ exp[¡jªL(fa,f,s0R,r)]

£ rect·fa¡fDcBa

¸rect

·s0R ¡ scbL=vR

¸:

(37)Using (37) in (29) yields TFBS as

H(fa,f) = rect

·f

Kr¿

¸exp

μj¼f2

Kr

¶expf¡j[©0(fa,f)]g

£Z Z

¾(s0R ,r)rect

·fa¡fDcBa

¸rect

·s0R ¡ scbL=vR

¸£ expf¡j2¼[ERV(fa)+ERVF(fa)f]rg£ expf¡j2¼[EAV(f) +EAVFfa]s0Rgds0Rdr

=G0(fa,f)¾[EAV(f) +EAVFfa,ERV(fa) +ERVF(fa)f]

(38)where

G0(fa,f) = rect·f

Kr¿

¸expμj¼f2

Kr

¶exp[¡j©0(fa,f)]:

(39)The first term G0(fa,f) represents the

two-dimensional space-invariant component. It isresponsible for the range- and azimuth-invariant RCM,range compression, secondary range compression(SRC) [23], azimuth scaling, and azimuth modulation.EAVF is an azimuth scaling factor, which is an

intrinsic feature of a BiSAR signal in the generalcase configuration. EAVF accounts for the relativeazimuth position of a point target with respect to thereference point. EAV(f) is the target position shift with

Fig. 5. Diagram block of BiSAR processing forspaceborne/airborne configuration.

respect to the range, expressing a azimuth-variantRCM. The azimuth-variant RCM is a residual partwith respect to the azimuth-invariant component thatis involved in ©0(fa,f). Generally, it is negligible [26].However, if the maximum steering angles of receiverand transmitter ÁR and ÁT are increased to obtain awider section of the illuminated scene, we can keepit within half of a range resolution cell using azimuthblocking. Therefore, (38) can be rewritten as

H(fa,f) =G0(fa,f)¾[EAVFfa,ERV(fa) +ERVF(fa)f]:

(40)

ERVF(fa) is a range frequency scaling factor. It exhibitsthe dependence of the range cell migration on theDoppler frequency in the two-dimensional frequencydomain. And thus, it is also called the migration factorin the two-dimensional frequency domain [26]. Thepurpose of the range cell migration correction is toremove the dependency, i.e., ERVF(fa) = 1. ERV(fa) isa pure Doppler term and denotes the range-variantDoppler modulation. They show the range-variantcharacteristic of BPTRS and are well known in themonostatic SAR processing [26].

IV. PROCESSING APPROACH

BiSAR data focusing can be interpreted as thetask of obtaining the backscattering coefficient¾ in the image space (s0R,r) by correcting thetwo-dimensional scaling and canceling the rangeand azimuth modulations [8]. In this paper, ISFTand matched filtering are applied to correct thescaling and cancel the modulation in both directions.In addition, it is worth emphasizing that chirpscaling transformation [26, 28] can also be appliedto interpolation, freely correcting the scalingphenomenon based on the presented TFBS. Thepresented functional diagram block of BiSARprocessing for the spaceborne/airborne configurationis shown in Fig. 5.


The implementation shown in Fig. 5 consists ofthe following five steps:

1) Transformation of the raw data into thetwo-dimensional frequency domain.2) Reference function multiplication (RFM).

It is carried out to transform the raw data into thebaseband by using a phase factor exp(¡j2¼ftm),removing the space-invariant phase, and compressingthe range signal. Thus, the RFM filter can beexpressed as

HRFM(fa,f) = exp½¡j2¼Rm+RmT

cf

¾£G¤0(fa,f):

(41)

After RFM filtering, the remaining bistatic signal isexpressed as

H1(fa,f) = ¾[EAVFfa,ERV(fa) +ERVF(fa)f]: (42)

3) ISFT along the range frequency to correct therange-variant RCM and transform the data to therange-Doppler domain. It is formulated as [8, 25]

H2(fa,r) =

ZH1(fa,f)expfj2¼rERVF(fa)fgd[ERVF(fa)f]:

(43)In (43), f is the frequency variable with respectto the fast-time variable t, but the output variableis r. To facilitate the fast Fourier transform (FFT),the frequency variable fr with respect to the rangevariable r needs to be converted by multiplying f by afactor of (1+p22)=c. Therefore, (43) can be rewrittenas

H2(fa,r) =ZH1(fa,f)exp

½j2¼r

·cERVF(fa)(1+p22)

¸fr

¾£ d

·cERVF(fa)(1+p22)

fr

¸= ¾(EAVFfa,r)£ exp[¡j2¼rERV(fa)] (44)

where p22 is defined in the Appendix, andcERVF(fa)=(1+p22) represents the range curvaturefactor in the range-Doppler domain.4) Range-variant matched filtering to remove the

azimuth modulation. The filter is given as

H3(fa,r) =H2(fa,r)£Ha(fa,r) = ¾(EAVFfa,r)(45)

where the filter Ha(fa,r) is defined as Ha(fa,r) =exp[j2¼rERV(fa)].5) Another ISFT to correct the azimuth scaling

factor. The azimuth scaling transformation is given as

H4(s0R,r) =ZH3(fa,f)exp(j2¼EAVFfas0R)d(EAVFfa)

= ¾(s0R,r): (46)

Examination of (41)—(46) suggests that all thesteps can be carried out via matrix multiplications

and FFTs, which maintain the advantages of the highprecision and efficiency in the overall processingprocedure.From (27), it can be seen that the Doppler centroid

is range- and azimuth-dependent. The azimuthdependency implies that the point targets locatedin the same slant range position have a differentDoppler centroid. Because the overall azimuth rawsignal bandwidth is obtained as the superpositionof all the individual point target contributions [25],the maximum range for the azimuth frequencyvariable is obtained by enforcing conditions foroverlapping of the following two rectangularwindows rect[(fa¡fDc)=Ba]rect[(s0R ¡ scb)=L=vR].The range for the azimuth frequency can beexpressed as

jfaj ·Ba2=Ba2+¢Ba2

(47)

where Ba indicates the bandwidth of the overall sceneinstead of the bandwidth of a single point target; ¢Barepresents an additional extension compared to theDoppler bandwidth of a single target and is given by

¢Ba =XGRvGR

·v2T¸r0T

L

XGT®T +

v2R¸rRc

L

XGR®R +

μv2R¸rRc

+v2T¸r0T

¶¸:

(48)

From (47), we can see that TFBS has a higherbandwidth compared with a single point target so thata higher pulse repetition frequency (PRF) is requiredto properly sample the azimuth signal. If the PRFprovided by the radar system is not high enoughto correctly sample the azimuth signal during theraw data acquisition, the azimuth spectrum will bealiased. The aliasing azimuth spectrum will affect theprocessing efficiency and precision [29].Therefore, for a practical radar system, the method

to reduce limitation of PRF has to be regarded. Thislimitation can be overcome by the three methodsproposed in [29—31].

V. PROCESSING EXAMPLE

In this section, we carry out a simulationexperiment, using the airborne SAR systemparameters, FHR’s PAMIR [32], and satelliteparameters of TerraSAR-X listed in Table I. Thesimulated scene consists of nine point targets, whichare located on the vertices of a 3£ 3 matrix, shown inFig. 6.In this simulation, the maxima of the Doppler

spectrum shift and Doppler bandwidth are¡1468:11 Hz and 672.43 Hz, respectively. So, for thesimulated scene, the excursion for azimuth frequencysatisfies jfaj · 1804:3 Hz. Thus, a PRF of 4000 Hzcan properly sample the simulated signal.For the ongoing simulation, we assume a

rectangular shape of the windows in both directions.


TABLE ISpaceborne/Airborne SAR System Parameters

PAMIR TerraSAR-X

Carrier frequency 9.65 GHzRange bandwidth 150 MHzRange sampling rate 180 MHzPRF 4000 Hz

Velocity 100 m/s 7600 m/sAltitude 3 km 514 kmDepression angle 30± 50±

Scan angle §10:656± §0:75±Beam width 2± 0:33±Sliding factor 8.9018 0.2851

Overlapping time of footprints 2.86 s

Fig. 6. Simulated scene with nine point targets.

The processing procedure shown in Fig. 5 is used.To quantify the precision of the presented processingmethod, the impulse response width (IRW), peaksidelobe ratio (PSLR), and integrated sidelobe ratio(ISLR) are used as quality criteria. For conveniencein comparison, the Doppler bandwidth and measuredquality parameters of the nine compressed pointtargets are listed in Table II.In Table II, Range PSLR and ISLR have a

deviation of less than 0.1 dB with respect to thetheoretical values of ¡13:26 dB and ¡9:72 dB,respectively. The azimuth PSLR agrees well withthe theoretical value. However, the measured azimuthISLR has a deviation of less than 1 dB compared withthe theoretical value. The range resolutions of the ninepoints agree nicely with the theoretical value of 1 m.

TABLE IIQuality Parameters of Range and Azimuth Impulse Response Functions

Range Azimuth

IRW (cell) PSLR (dB) ISLR (dB) Bandwidth (Hz) IRW (cell) PSLR (dB) ISLR (dB)

PT1 1.198 ¡13:18 ¡9:79 660.84 6.016 ¡13:23 ¡10:64PT2 1.198 ¡13:11 ¡9:74 657.49 6.064 ¡13:23 ¡10:22PT3 1.198 ¡13:18 ¡9:76 659.84 6.068 ¡13:14 ¡10:18PT4 1.198 ¡13:19 ¡9:78 667.35 5.996 ¡13:15 ¡9:88PT5 1.198 ¡13:18 ¡9:70 664.83 6.012 ¡13:26 ¡9:78PT6 1.198 ¡13:18 ¡9:78 666.97 5.976 ¡13:23 ¡9:86PT7 1.198 ¡13:19 ¡9:75 672.58 5.932 ¡13:27 ¡10:23PT8 1.198 ¡13:18 ¡9:78 670.62 5.960 ¡13:23 ¡10:09PT9 1.198 ¡13:17 ¡9:78 670.56 5.948 ¡13:21 ¡10:68

Fig. 7. (a) Focused scene before azimuth scaling correction.(b) Focused scene after azimuth scaling correction.

The measured azimuth resolutions have a maximumbroadening of 0.6% in comparison with the theoreticalvalues. The processing result of the simulated scene isshown in Fig. 7.Fig. 7(a) shows the result before the azimuth

scaling correction. From Fig. 7(a), it can be seenthat the azimuth relative positions of targets to thereference point (PT5) is compressed. The correctedresult is shown in Fig. 7(b). In this paper, we onlyshow the image with a correction of 14% to thereal position in Fig. 7(b). Comparing Fig. 7(a)and Fig. 7(b) shows that the azimuth scaling isconsiderably severe in this extreme configuration.In order to further demonstrate the performance

of the presented method, four point targets awayfrom the center (i.e., PT1, PT3, PT7, and PT9) areexamined in more detail in Fig. 8(a)—(d). From Fig. 8,we can also see that the four point targets are focusedwell.


Fig. 8. Two-dimensional impulse responses of (a) PT1, (b) PT3,(c) PT7, and (d) PPT9.

VI. CONCLUSIONS

In this paper, an approximated BPTRS is derivedfor the BiSAR signal in a spaceborne/airborneconfiguration based on the two quadraticapproximations. With the derived BPTRS, we presenta transfer function using the linearization operation.

The transfer function clearly demonstrates therange- and azimuth-variant characteristics of BiSARsignal and facilitates the application of the monostaticprocessing algorithms. The range-variant feature iswell known for the monostatic SAR processing. Inthis paper, we deal with the range-variant feature withISFT in the same way as it is dealt with in monostaticSAR processing. Although we only describe and testthe processing procedure of ISFT, other monostaticSAR processing algorithms (e.g., CSA, RDA, andOmega-K algorithm) can also be applied to handlethe range-variant feature. The azimuth-variant scalingfactor is inherent for the azimuth-variant bistaticconfiguration. The azimuth scaling phenomenonis quite significant in the spaceborne/airborneconfiguration. Generally, interpolation and chirpscaling can be used to correct it.The presented processing approach can

also be applied to focus other azimuth-variantbistatic configurations (e.g., airborne/airborne,spaceborne/spaceborne) where only the proposedBPTRS (i.e., (21)) needs to be replaced by anotheraccurate spectrum (e.g., spectra presented in [12] and[18]).

APPENDIX. TWO-DIMENSIONAL LINEARIZATION

ª (fa,f,s0R,r0R) nonlinearly depends on fourspace position variables (s0T, sRc, r0T, rRc) besidesthe coordinates of target space r0R and s0R. Thesefour variables are functions of target coordinates. Tolinearize ª (fa,f,s0R,r0R) in the target space, we firstpresent the coefficients of the partial derivatives ofs0T(s0R,r0R), sRc(s0R,r0R), r0T(s0R,r0R), and rRc(s0R,r0R)in the coordinates (s0R = 0,r0R = Rm) as

s0T(0,Rm) = Rmp1,@s0T(s0R,r0R)

@r0R

¯s0R=0,r0R=Rm

= p12,

@s0T(s0R,r0R)@s0R

¯s0R=0,r0R=Rm

= p13

r0T(0,Rm) = Rmp2,@r0T(s0R,r0R)

@r0R

¯s0R=0,r0R=Rm

= p22,

@r0T(s0R,r0R)@s0R

¯s0R=0,r0R=Rm

= p23

(49)

sRc(0,Rm) = Rmp3,@sRc(s0R,r0R)

@r0R

¯s0R=0,r0R=Rm

= p32,

@sRc(s0R,r0R)@s0R

¯s0R=0,r0R=Rm

= p33

rRc(0,Rm) = Rmp4,@rRc(s0R,r0R)

@r0R

¯s0R=0,r0R=Rm

= p42,

@rRc(s0R,r0R)@s0R

¯s0R=0,r0R=Rm

= p43:


Using (49), we directly linearize ª(fa,f,s0R,r0R) in(s0R = 0,r0R = Rm) of target space, i.e., (30). Herein,using (34)—(35) in (30), it is rewritten as

ªL(fa,f,s0R,r0R)¼ ©0(fa,f) +2¼[ERV(fa)+ERVF(fa)f](r0R ¡Rm)+2¼[EAV(f)+EAVFfa]s0R: (50)

The space-invariant term ©0(fa,f) is expressed as

©0(fa,f) =©1(f,0,Rm)+©2(fa,f,0,Rm) +©3(fa,f,0,Rm) +©4(fa,f,0,Rm) +©5(fa,f,0,Rm) (51)

where

©1(f,0,Rm) = 2¼f+f0c

Rm[p4 +p2]

©2(fa,f,0,Rm) = 2¼v2R(f+f0)p3Rm

c

26664v2Tp

24(p1¡p3)¡

cp24p2f+f0

fa¡ v2Rp3p4p2(v2Rp2 +p

34v2T)

37775

©3(fa,f,0,Rm) = ¼(f+f0)v

2RRm

cp34

26664v2Tp

34(p1¡p3)¡

cp34p2f+f0

fa¡ v2Rp2p3p24(v2Rp2 +p

34v2T)

377752

©4(fa,f,0,Rm) = ¼f+f0c

v2TRmp2

26664v2R(p3¡p1)¡ v2Rp3p24¡

cp34f+f0

fa

(v2Rp2 +p34v2T)

377752

©5(fa,f,0,Rm) = 2¼faRm

2664v2Rp2p3 + v

2Tp

34p1¡p34p2

cfaf+f0

¡ v2Rp3p24p2(v2Rp2 +p

24v2T)

3775 :

(52)

The range-variant azimuth modulation term ERV(fa) isexpressed as

ERV(fa) =G10 + (G210 +G220 +G230) + (G310 +G320 +G330) + (G410 +G420 +G430) + (G510 +G520 +G30) (53)

G10 =Rm¸

"1+ v2Rp3p32p1+ v2Rp

23

+p22

#

G210 =2v2Rv

2TRm¸

p42p4p3(p1¡p3)[v2Rp2 +p

34v2T]

+v2Rv

2TRmp

24

¸

£½p3(p12¡p32) +p32(p1¡p3)

[v2Rp2 +p34v2T]

¡ p3(p1¡p3)[v2Rp2 +p

34v2T]2[v2Rp22 +2v

2Rp2 +3p42p

24v2T]

¾

G220 =¡v4RRm¸

½[p42p2p

23 +p4p22p

23 + 2p32p4p2p3]

[v2Rp2 +p34v2T]

¡ p4p2p23[v

2Rp22 +2v

2Rp2 +3p42p

24v2T]

[v2Rp2 +p34v2T]2

¾

G230 =¡v2RRm½[p22p3p

24 +2p42p4p2p3 +p32p

24p2]

[v2Rp2 +p34v2T]

¡ p24p2p3[v

2Rp22 +2v

2Rp2 +3p42p

24v2T]

[v2Rp2 +p34v2T]2

¾fa

(54)


where

G310 =v2RRm(2p4 +p42)

2¸[v2Tp4(p1¡p3)¡ v2Rp2p3]2

[v2Rp2 +p34v2T]2

¡ v2RRmp4¸

½[v2Tp4(p1¡p3)¡ v2Rp3p2]2

[v2Rp22 +2v2Rp2 +3p42p

24v2T]

(v2Rp2 +p34v2T)3

¡ [v2Tp4(p1¡p3)¡ v2Rp3p2][v2T(p42(p1¡p3)+p4(p12¡p32))¡ v2R(p3p22 +p2p32)](v2Rp2 +p

34v2T)2

¾

G320 =¡v2RRmfa(2p24p2 +2p42p4p2 +p24p22)[v2Tp4(p1¡p3)¡ v2Rp2p3]

[v2Rp2 +p34v2T]2

(55)

¡ v2RRmfap24p2½v2T[p42(p1¡p3) +p4(p12¡p32)]¡ v2R(p3p22 +p2p32)

[v2Rp2 +p34v2T]2

¡ 2[v2Tp4(p1¡p3)¡ v2Rp3p2][v2Rp22 +2v2Rp2 +3p42p24v2T][v2Rp2 +p

34v2T]3

¾

G330 =¸v2RRmf

2a

2

·(3p42p

24p22 +2p

34p22 +2p2p22p

34)

[v2Rp2 +p34v2T]2

¡ 2p22p34(v

2Rp22 +2v

2Rp2 +3p42p

24v2T)

[v2Rp2 +p34v2T]3

¸

G410 =Rmv

2Tv4Rp22

2¸[p3¡p1¡p24p3]2[v2Rp2 +p

34v2T]2

¡ Rmv2Tv4Rp2

¸

[p3¡p1¡p24p3]2[v2Rp2 +p

34v2T]3

[v2Rp22 +2v2Rp2 +3p42p

24v2T]

+Rmv

2Tv4Rp2

¸

½[p3¡p1¡p24p3][v2Rp2 +p

34v2T]2

[(p32¡p12) +2(p3¡p1)¡ 2p42p4p3¡p32p24]¾

G420 =¡Rmfav2Tv2R(p22p34 +3p42p24p2)[(p3¡p1)¡p3p24][v2Rp2 +p

34v2T]2

+

(56)

¡Rmfav2Tv2Rp2p34½[2(p3¡p1)+ (p32¡p12)¡ 2p42p4p3¡p32p24]

[v2Rp2 +p34v2T]2

¡2 [(p3¡p1)¡p3p24]

[v2Rp2 +p34v2T]3[v2Rp22 +2v

2Rp2 + 3p42p

24v2T]

¾G430 =

f2a v2T¸Rm2

½[p22p

64 +6p42p2p

54]

[v2Rp2 +p34v2T]2

¡ 2p2p64[v

2Rp22 + 2v

2Rp2 +3p42p

24v2T]

[v2Rp2 +p34v2T]3

¾

G510 = faRm

½v2R[p22p3 +p32p2 +2p2p3] + v

2T[p12p

34 + 3p42p

24p1]

[v2Rp2 +p34v2T]

¡ [v2Rp2p3 + v

2Tp1p

34]

[v2Rp2 +p34v2T]2

[v2Rp22 +2v2Rp2 + 3p42p

24v2T]

¾(57)

G520 =¡fav2RRm½p22p3p

24 +2p4p42p2p3 +p32p2p

24

[v2Rp2 +p34v2T]

¡ p2p3p24[v

2Rp22 + 2v

2Rp2 +3p42p

24v2T]

[v2Rp2 +p34v2T]2

¾

G530 =¡Rmf2a ¸½p22p

34 + 3p42p2p

24

[v2Rp2 +p34v2T]

¡ p2p34[v

2Rp22 +2v

2Rp2 +3p42p

24v2T]

[v2Rp2 +p34v2T]2

¾:

The range scaling factor ERVF(fa) is expressed as

ERVF(fa) =G10 +G210 +G220 +G310 +G330 +G410 +G430 +G530

f0: (58)

The azimuth-variant RCM EAV(f) is expressed as

EAV(f) =H10 +H210 +H220 +H310 +H410 (59)


where

H10 =f+f0c

Rm

"v2Rp3(p33¡ 1)p

1+ v2Rp23

+p23

#

H210 = 2f+f0c

v2Rv2TRmp4

½p43p3(p1¡p3)(v2Rp2 +p

34v2T)+p4

·p3(p13¡p33) + (p33¡ 1)(p1¡p3)

(v2Rp2 +p34v2T)

¡ p3(p1¡p3)(v2Rp2 +p

34v2T)2(v2Rp23 +3p43p

24v2T)

¸¾(60)

H220 =¡f+f0c

v4RRm

½[p43p2p

23 +p4p23p

23 +2p4p3p2(p33¡ 1)]

[v2Rp2 +p34v2T]

¡ p4p2p23[v

2Rp23 + 3p43p

24v2T]

[v2Rp2 +p34v2T]2

¾

H310 =f+f02c

v2RRm

½p43[v2Tp4(p1¡p3)¡ v2Rp2p3]2

[v2Rp2 +p34v2T]2

¡ 2p4[v2Tp4(p1¡p3)¡ v2Rp2p3]2

[v2Rp2 +p34v2T]3

(v2Rp23 +3p43p24v2T)

¾+(f+f0)c

v2RRmp4

½[v2Tp4(p1¡p3)¡ v2r p2p3][v2T(p43(p1¡p3)+p4(p13¡p33))¡ v2r (p3p23 +p2(p33¡ 1))]

[v2r p2 +p34v2T]2

¾

H410 =(f+f0)2c

Rmv2Tv4R

½p23[p3¡p1¡p24p3]2[v2Rp2 +p

34v2T]2

¡ 4p2[p3¡p1¡p24p3]2[v2Rp2 +p

34v2T]3

[v2Rp23 +3p43p24v2T]

¾(61)

+f+f0c

Rmv2Tv4Rp2

½[p3¡p1¡p24p3][(p33¡p13)¡ 2p43p2(p3¡p1)¡p24(p33¡ 1)]

[v2Rp2 +p34v2T]2

¾:

The azimuth scaling factor EAVF(f) is expressed as

EAVF =H231 +H321 +H421 +H511 +H521 (62)

where

H231 =¡v2RRm½[p23p3p

24 + 2p43p4p3p2 + (p33¡ 1)p24p2]

[v2Rp2 +p34v2T]

¡ p24p2p3[v

2Rp23 +3p43p

24v2T]

[v2Rp2 +p34v2T]2

¾

H321 =¡v2RRm½(2p43p4p2 +p23p

24)[v2Tp4(p1¡p3)¡ v2Rp3p2]

[v2Rp2 +p34v2T]2

¡ 2p24p2[v2Tp4(p1¡p3)¡ v2Rp2p3]

[v2Rp2 +p34v2T]3

[v2Rp23 +3p43p24v2T]

¾¡ v2RRmp24p2

½[v2Tp43(p1¡p3) + v2Tp4(p13¡p33)¡ v2Rp23p3¡ v2Rp2(p33¡ 1)]

[v2Rp2 +p34v2T]2

¾

H421 =¡Rmv2Tv2R(p23p34 +3p43p24p2)[(p3¡p1)¡p3p24][v2Rp2 +p

34v2T]2

¡Rmv2Tv2Rp2p34½[(p33¡p13)¡p24(p33¡ 1)¡ 2p3p43p4]

[v2Rp2 +p34v2T]2

¡ 2 [(p3¡p1)¡p3p24]

[v2Rp2 +p34v2T]3[v2Rp23 +3p43p

24v2T]

¾

H511 = Rm

½v2R(p23p3 +p33p2) + v

2T(p13p

34 + 3p43p

24p1)

[v2Rp2 +p34v2T]

¡ (v2Rp2p3 + v

2Tp1p

34)

[v2Rp2 +p34v2T]2

[v2Rp23 +3p43p24v2T]

¾

H521 =¡v2RRm½p23p3p

24 + 2p43p4p3p2 +p2p

24(p33¡ 1)

[v2Rp2 +p34v2T]

¡ p2p3p24[v

2Rp23 +3p43p

24v2T]

[v2Rp2 +p34v2T]2

¾:

(63)

ACKNOWLEDGMENT

The authors are grateful for the excellent and veryeffective cooperation between ZESS and FraunhoferFHR, which is seen as a key item of their work.

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[23] Desai, M. D. and Jenkins, W. K.Convolution back projection image reconstruction forspotlight mode synthetic aperture radar.IEEE Transactions on Image Processing, 1, 4 (Oct. 1992),505—517.

[24] Belcherand, D. P. and Baker, C. J.High resolution processing of hybrid strip-map/spotlightmode SAR.IEE Proceedings of Radar, Sonar and Navigation, 143, 6(Dec. 1996), 366—374.

[25] Lanari, R., Zoffoli, Sansosti, S. Fomaro, E., Serafino, G.,and Serafino, F.New approach for hybrid strip-map/spotlight SAR datafocusing.IEE Proceedings of Radio, Sonar and Navigation, 148, 6(Dec. 2001), 363—372.

[26] Cumming, I. G. and Wong, F. H.Digital Processing of Synthetic Aperture Radar DataAlgorithms and Implementation.Norwood, MA: Artech House, 2005.

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

[28] Loffeld, O., Schneider, F., and Rein, A.Focusing SAR images by inverse scaled Fouriertransform.In Proceedings of the ICSP, vol. 2, Las Palmas, Spain,1998, 630—632.

[29] Lanari, R., Tesauro, M., Sansosti, E., and Fornaro, G.Spotlight SAR data focusing based on a two-stepprocessing approach.IEEE Transactions on Geoscience and Remote Sensing, 39,9 (Sept. 2001), 1993—2004.

[30] Soumekh, M.Synthetic Aperture Radar Signal Processing with MATLABAlgorithms.Hoboken, NJ: Wiley-Interscience, 1999.


[31] Mittermayer, J., Moreira, A., and Loffeld, O.Spotlight SAR data processing using the frequencyscaling algorithm.IEEE Transactions on Geoscience and Remote Sensing, 37(Sept. 1999), 2198—2214.

Robert Wang (M’07) received the B.S. degree in control engineering from theUniversity of Henan, Kaifeng, China, in 2002, and the Dr. Eng. degree from theGraduate University of Chinese Academy of Sciences, Beijing, China, in 2007.In 2007, he joined the Center for Sensorsystems (ZESS), the University

of Siegen, Siegen, Germany. He is currently working at the hybrid bistaticexperiments. He was also involved in some SAR projects for the FraunhoferInstitute for High Frequency Physics and Radar Techniques (FHR). His currentresearch interests include monostatic and bistatic SAR signal processing, bistaticinterferometric, airborne SAR motion compensation, FMCW SAR system andmillimeter-wave SAR system.Dr. Wang has contributed to invited sessions on bistatic SAR at EUSAR

2008 conference. He is the author of a tutorial entitled “Results and Progressesof Advanced Bistatic SAR Experiments” presented at the European RadarConference 2009, and the coauthor of a tutorial entitled “Progress in Bistatic SARConcepts & Algorithms” presented at EUSAR 2008.

Otmar Loffeld (M’05–SM’06) received the Diploma degree in electricalengineering from the Technical University of Aachen in 1982, the Eng. Dr.degree and the ‘habilitation’ in the field of digital signal processing andestimation theory in 1986 and 1989, respectively, both from the University ofSiegen.In 1991 he was appointed as Professor of Digital Signal Processing and

Estimation Theory at the University of Siegen. Since then he has given lectureson general communication theory, digital signal processing, stochastic modelsand estimation theory and synthetic aperture radar. In 1995 he became amember of the Center for Sensorsystems (ZESS) which is a central scientificresearch establishment at the University of Siegen. Since 2005 he has been thechairman of that center. In 1999 he became principal investigator (PI) on baselineestimation for the X-Band part of the shuttle radar topography mission (SRTM)where ZESS contributed to DLR’s baseline calibration algorithms. He is PI forinterferometric techniques in the German TerraSAR-X mission, and together withProfessor Ender from FGAN, he is one the PI’s for a bistatic spaceborne airborneexperiment, where TerraSAR-X serves as the bistatic illuminator while FGAN’sPAMIR system mounted on a Transall airplane is used as a bistatic receiver.In 2002 he founded the International Postgraduate Programme (IPP) “Multi

Sensorics,” and based on that programme, he established the NRW ResearchSchool on Multi Modal Sensor Systems for Environmental Exploration andSafety (MOSES) at the University of Siegen as an upgrade of excellence in2008. He is the speaker and coordinator of both doctoral degree programmes,hosted by ZESS. Furthermore he is the university’s scientific coordinator for“Multidimensional and Imaging Systems.”His current research interests comprise multi-sensor data fusion, Kalman

filtering techniques for data fusion, optimal filtering and process identification,SAR processing and simulation, SAR-interferometry, phase unwrapping, andbaseline estimation. A recent field of interest is bistatic SAR processing.Professor Loffeld is a member of the ITG/VDE and Senior Member of the

IEEE/GRSS. He received the scientific research award of Northrhine-Westphalia(“Bennigsen-Foerder Preis”) for his work on applying Kalman filters to phaseestimation problems such as Doppler centroid estimation in SAR, phase andfrequency demodulation. He is author of two textbooks on estimation theory.

[32] Brenner, A. R. and Ender, J. H. G.Demonstration of advanced reconnaissance techniqueswith the airborne SAR/GMTI sensor PAMIR.IEE Proceedings of Radar, Sonar and Navigation, 153, 2(Apr. 2006), 152—162.


Holger Nies received the Diploma degree in electrical engineering in 1999 andthe Dr. Eng. degree in 2006, both from the University of Siegen, Germany.Since 1999 he has been a member of the Center for Sensorsystems (ZESS) at

the University of Siegen and a lecturer in the Department of Signal Processingand Communication Theory. He worked in the project sector “Optimal SignalProcessing, Remote Sensing–SAR” of ZESS since 1999. He was also involvedin some project work for Daimler AG (Stuttgart, Germany) in the field of enginemodeling and optimization. Currently he is working in the area of interferometrictechniques in the German TerraSAR-X mission. His current research interestsinclude bistatic SAR processing, SAR interferometry, and distributed data fusion.

Stefan Knedlik (M’04) received the Diploma degree in electrical engineering andthe Dr.Eng. degree from the University of Siegen, Siegen, Germany, in 1998 and2003, respectively.Since 1998, he has been a member of the Center for Sensorsystems (ZESS),

University of Siegen, and since 2003 he has also been a researcher/assistantprofessor (C1) at the Institute of Signal Processing and Communication Theoryin the Department of Electrical Engineering and Computer Science. He isalso Executive Director of two international postgraduate programs, the IPPMulti Sensorics and the Research School on Multi Modal Sensor Systems forEnvironmental Exploration and Safety (MOSES). A few years ago he foundeda research group on navigation. His current research interests include GNSSbased navigation, inertial navigation, sensor data fusion, and signal processingin synthetic aperture radar interferometry.

Qurat-Ul-Ann (M’08) received the M.Sc. and M.Phil. degrees in electronics fromQuaid-i-Azam University, Islamabad, in 2001 and 2004, respectively.She is currently pursuing a Ph.D. degree in electrical engineering from

the University of Siegen. Her research interests include radar, antenna theory,estimation theory, signal processing, and synthetic aperture radar processing.

Amaya Medrano Ortiz received the Diploma degree in electrical engineeringfrom the Universidad Alfonso X el Sabio, Madrid, Spain, in 2003.Since 2004, she has been working toward the Ph.D. degree at the Center for

Sensorsystems (ZESS), University of Siegen, Siegen, Germany as a member ofthe IPP Multi Sensorics. She worked at Agilent Technologies as an associatedstudent in the calibration laboratory. Her current research interests are in the areasof bistatic SAR processing and simulation and parameter estimation.


Joachim H. G. Ender (M’02–SM’06) received the Diploma degree inmathematics and physics from the Westphalian Wilhelm University ofMunster, Germany in 1975 and the Ph.D. degree in electrical engineering fromRuhr-University Bochum, Germany.In 1976 he was with the Research Establishment of Applied Science (FGAN),

Wachtberg, Germany. Since 1992 he has been giving annual lectures on radarsignal processing at the Ruhr-University Bochum, which conferred the titleHonorary Professor upon him in 2002. He also gives lectures on radar techniquesat the Rhineish-Westphalian Technical-University, Aachen, Germany and theUniversity of Siegen, Germany. In 1999, he was the head of the ElectronicsDepartment, Research Institute for High Frequency Physics and Radar Techniques(FHR), FGAN, where he initiated and supervised research activities for variousaspects of phased array and imaging radars, including the design and operation ofexperimental SAR systems, such as AER-II and PAMIR. Since 2003, he has beenthe Director of FHR, and he was elected Vice Chairman of the FGAN in August2007. He is Executive Board Member of the German Institute of Navigationas well as Member-at-large of North Atlantic Treaty Organization Sensorsand Electronics Technology research panel. He further acts as Review BoardMember of the German Research Foundation and as a Review Board Memberof the Leibniz Society. His current research interests are very high resolutionSAR imaging, 3D-SAR, MIMO-SAR, multibaseline and wideband processingtechniques for across-track SAR interferometry, ground-moving target indicationwith air and space-based radar including multistatic satellite constellations, inverseSAR for moving target imaging and bistatic SAR processing.He has authored and coauthored numerous papers in various international

journals and conferences. Dr. Ender, jointly with colleagues, received the GermanSociety for Information Technology Paper Prize Award of the Association ofGerman Electrical Engineers in 1992 and the IEEE Transactions on Geoscienceand Remote Sensing Best paper award in 2006. In 1996, he was one of thefounding members of the biannual “European Conference on Synthetic ApertureRadar.”


frequency-domain bistatic sar processing for spaceborne ......refereeing of this contribution was...

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