RECENT interest has arisen in processing bistatic synthetic

Transcription

1 4 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 46, NO., JANUARY 2008 Proessing of Azimuth-Invariant Bistati SAR Data Using the Range Doppler Algorithm Yew Lam Neo, Frank H. Wong, and Ian G. Cumming, Life Senior Member, IEEE Abstrat This paper disusses bistati syntheti aperture radar proessing omplex image rmation) using the Range Doppler Algorithm. The key step is to use an analytial rm of the signal spetrum derived by the method of series reversion. The spetrum is used r seondary range ompression SRC), range ell migration orretion, and azimuth ompression. The algorithm is able to us the azimuth-invariant bistati onfiguration where the transmitter and reeiver platrms are moving in parallel traks with idential veloities. Moreover, the algorithm is able to handle reasonably high squints and wide apertures beause SRC an be perrmed in the 2-D frequeny domain. Index Terms Bistati syntheti aperture radar SAR) proessing, range ell migration orretion RCMC), Range Doppler Algorithm RDA), seondary range ompression SRC), series reversion. I. INTRODUCTION RECENT interest has arisen in proessing bistati syntheti aperture radar SAR) data partly beause of two airborne experiments that have been perrmed in the last few years ], 2]. Bistati SAR range histories, unlike monostati ones, are azimuth variant in general as both the transmitter and the reeiver an assume different motion trajetories. Nevertheless, the bistati system an remain azimuth invariant by restriting the transmitter and reeiver platrm motions to llow parallel traks with idential veloities. In this ase, the baseline between the two platrms does not vary with time. This azimuth-invariant property is important to onventional monostati algorithms suh as the Range Doppler Algorithm RDA) ] 5] and Chirp Saling Algorithm CSA) 6], or any algorithm that takes advantage of blok proessing in the azimuth. This is beause the proessing effiieny is ahieved by taking advantage of the fat that point targets with the same range of losest approah ollapse to the same range history in the range Doppler domain. Perrming one range ell migration orretion RCMC) operation in this domain ahieves the orretion of a whole family of targets. Moreover, Manusript reeived April 2, Y. L. Neo is with DSO National Laboratories, Singapore nyewlam@dso.org.sg). F. H. Wong is with MaDonald Dettwiler and Assoiates, Rihmond, BC V6V 2J, Canada. I. G. Cumming is with the Department of Eletrial and Computer Engineering, University of British Columbia, Vanouver, BC V6T Z4, Canada. Color versions one or more of the figures in this paper are available online at Digital Objet Identifier 0.09/TGRS The baseline is the vetor onneting the two platrms. The azimuth invariant is equivalent to a fixed baseline. Eah beam an have different squint and inidene angles. The bistati angle is the angle β subtended by the baseline at the target see Fig. ). the range Doppler domain allows the azimuth ompression parameters to be onveniently hanged with range. The purpose of this paper is to examine whether the same advantages an be obtained in the bistati ase when the data are azimuth invariant. The proessing of monostati strip-map SAR data, whih are aquired with the platrm llowing a straight line flight path, is based on a hyperboli range equation. However, as the transmitter and reeiver ranges are independent in the bistati ase, a double hyperboli range equation results, whih leads to a double square root in the range equation. The sum of the two square roots is referred to as the flat-top hyperbola 7] 9]. As monostati SAR proessing algorithms assume the single) hyperboli range equation, they must be modified to handle bistati SAR data. For small baseline/range ratios, the range equation is nearly hyperboli, and onventional monostati algorithms an be used to us the data without signifiantly affeting the image quality. However, when the separation between the transmitter and the reeiver inreases, the bistati range equation diverges further from the hyperboli rm. Modifiations to monostati algorithms are neessary to allow them to us with this different geometry model. The main diffiulty in modifying monostati algorithms to handle the azimuth-invariant bistati onfiguration lies in finding an analytial solution r the 2-D target spetrum 8] the double square root funtion makes it hard to apply the priniple of stationary phase). Several algorithms have been developed to overome this diffiulty. Modified ω k algorithms were introdued in 0] and ]. These algorithms work in the 2-D frequeny domain 2-D FD) and make use of numerial methods to alulate the double square root phase term. Bamler and Boerner 2] proposed a using algorithm that replaes the analytial SAR transfer funtions with numerial equivalents. Their algorithm is able to handle the azimuth-invariant ase inluding squint. A preproessing tehnique derived from Dip and Move Out in the seismi literature ] is used to transrm the bistati data to a monostati equivalent 7]. The data an subsequently be used with any monostati algorithm. Loffeld et al. 9] derived an approximate bistati point target spetrum, and a few subsequent algorithms were developed based on this approah 4], 5]. In partiular, Rodríguez-Cassolá et al. 6] made use of this point target spetrum to develop a bistati RDA and a bistati CSA. While all these algorithms are able to handle azimuthinvariant ases, the bistati geometries that an be used by these algorithms are often limited by the auray of the point target spetrum. Reently, an aurate 2-D point target spetrum has been derived based on the reversion of a power series r the general bistati ase 7]. Our approah is to apply /$ IEEE

2 NEO et al.: PROCESSING OF AZIMUTH-INVARIANT BISTATIC SAR DATA 5 this spetral result in a modified RDA so that it an handle the azimuth-invariant ase with improved auray. Note that the onventional RDA does not normally do any proessing in the 2-D FD. Seondary range ompression SRC) is ommonly applied in the azimuth time domain as part of the range ompression operation 8]. This approximation limits the degree of squint and the extent of the aperture that an be aurately proessed. Fousing high squint and wide aperture ases is not a trivial task, as proessing is ompliated by the range/doppler oupling in the reeived data, whih degrades the using ability of the onventional RDA. The squint aperture ases that the RDA an aurately handle are onsiderably extended when SRC is perrmed in the 2-D FD, sine SRC takes on an inreasing amount of azimuth frequeny dependene as the squint or aperture inreases refer to SRC Option 2 in 9]). The 2-D FD operations ome at the expense omputing time and are therere avoided if possible. This paper begins with a brief desription of the bistati signal model and a derivation of its 2-D point target spetrum in Setion II, where an L-band example is given. The operations in the modified RDA are outlined in Setion III, and the important 2-D FD phase equations are derived. A C-band airborne radar simulation is used to demonstrate the auray of the algorithm in Setion IV. In Setion V, an effiient way to ombine the SRC with range ompression is developed r ertain squinted moderate aperture ases. II. 2-D SPECTRUM OF A BISTATIC SIGNAL The RDA developed in this paper is based on a 2-D spetrum of the referene point target that is derived in 7] and repeated here r onveniene as Sf τ,f η )=W r f τ )W az f η + +f τ ) k ) exp {jφf τ,f η )} ) where the phase funtion is given by + f τ φf τ,f η )= 2π +2π 4k 2 + f τ ) ) R en πf2 τ K r f η + + f τ ) k ) 2 2 k +2π 8k2 + f τ ) 2 f η + + f τ ) k ) ) +2π 9k 2 4k 2 k 4 64k2 5 + f τ ) f η + + f τ ) k ) 4 + 2) where K r is the FM rate of the range pulse, is the speed of light, and is the enter frequeny of the transmitted pulse. W r.) represents the spetral shape of the transmitted pulse, and W az.) represents the shape of the Doppler spetrum. f τ is the range frequeny, and f η is the azimuth frequeny. The definition of the bistati range at the aperture enter R en and the derivatives k, k 2, k, and k 4 ) of the expanded version of the range equation in azimuth time η are given in 7]. These derivatives are weakly range dependent. The auray of the spetrum is only limited by the number of terms used in the expansion of 2). For a higher resolution Fig.. Funtional blok diagram of the bistati RDA. or a wider aperture, we may need to inlude more phase terms to avoid signifiant degradation in the using algorithm. An example of the onvergene of the series is given in 7]. In 20], Eldhuset inverted a urth-order range equation to give an exat transfer funtion r a spaeborne monostati SAR. This method has been extended in 2] r an bistati azimuth-invariant spaeborne SAR. The method derived here is more general and an handle higher squints and wider apertures by adding more terms in the phase equation. The point target spetrum ) is entral to the bistati RDA that we disuss in this paper. In Setion III, we show how this point target spetrum an be used to proess the raw bistati SAR data r the azimuth-invariant ase. III. BISTATIC RDA The proessing steps of the bistati RDA are shown in Fig., where ur Fourier transrms FT) are used. They are the same as the RDA when SRC is applied in the 2-D FD exept that the new spetrum is used in the SRC, RCMC, and azimuth ompression operations. Note that range ompression and SRC are both phase multiplies and an be ombined r effiieny. RCMC is applied with an interpolator, and azimuth ompression is applied with a range-dependent phase multiply. A. Analytial Development The development of the bistati RDA begins with the 2-D spetrum 2) of the point target being onsidered. The first step is to replae the /f τ + ) terms in 2) with the llowing power series expansions: + f τ ) = f ) 2 τ + + ] ) + f τ ) 2 = 2 2f ) 2 τ + + ] 4) + f τ ) = f ) 2 τ +6 + ]. 5) These power series quikly onverge beause f τ in pratie. Substituting ) 5) into 2), an expliit rm of the

3 6 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 46, NO., JANUARY 2008 phase of the 2-D spetrum an be obtained. The phase term in 2) an be deomposed into the llowing omponents: φf τ,f η ) φ rg f τ )+φ az f η ) + φ rm f τ,f η )+φ sr f τ,f η )+φ res. 6) Eah of these phase terms an be interpreted as llows: The first phase term φ rg represents the range modulation as φ rg f τ )= πf2 τ K r. 7) This phase term is dependent only on f τ and thus an be separated from the other phase terms. Range ompression uses a phase multiply to remove this phase term. Alternatively, the data ould be range ompressed in the range frequeny azimuth time domain just after the range FT. This operation is the same as in the monostati ase as the bistati geometry has no diret effet on the pulse modulation. The seond phase term φ az represents the azimuth modulation. It is solely dependent on f η and will be removed by the azimuth-mathed filtering as { φ az f η ) 2π 2k f η + ] fη 2 4k 2 + k 8k2 kf 2 η + k f o + 9k2 4k 2 k 4 64k2 5 ] fη fη 4kf η + 6k2 fη 2 + 4k 2 2 fη + fη 4 ]}. 8) Beause of the signifiant range dependene of these terms, the azimuth ompression is applied in the range Doppler domain. The third phase term φ rm is linearly dependent on the range frequeny f τ and represents the range ell migration term as φ rm f τ,f η ) { 2πf τ R en + 4k 2 + k k 8k2 k 2 + 9k2 4k 2 k 4 k 4 64k2 5 k 2 ] 2 fη 2 fη 2 22 fη 6k2 f 2 o ] f 2 η 8k 2 4 fη 4 f o f η ]}. 9) Note that the terms inside the large braes represent the range ell migration RCM) displaement. As the k oeffiients depend on range, as does the R en term, this range displaement must be ompensated in the range Doppler domain. This is allowed sine there is no range frequeny dependene in these terms. The displaement is orreted using a range diretion interpolator, as in the monostati RDA. The urth phase term φ sr represents the range/azimuth oupling term as { ) 2 ) ] φ sr f τ,f η ) 2π fη 2 4k 2 + k ) ) 2 8k2 k ) ) ) 2 fη 2 + 6k 2 ) 2 ) ) ] 4 fη + 9k2 4k 2 k 4 64k2 5 ) ) 2 ) ) ) 2 +4k ) + 6 ) 2 0 ) 2 4 ) ) f 2 η ) ) f 4 η f η ]}. 0) This phase term is the remaining ontribution that depends on f η and f τ. This phase term beomes signifiant in higher squint, finer resolution, and longer wavelength ases. If unompensated, the range/azimuth oupling may ause signifiant degradation in the resolution, espeially in the range diretion. The SRC is used to remove this oupling term. SRC is applied in the 2-D FD domain, as the strongest dependenies exist in this domain. However, the SRC term is weakly range dependent, and 0) must be evaluated at a speifi range alled the referene range, whih is usually at the swath enter. While the SRC that orrets the phase at the sene enter is often suffiient r the whole sene, r wider range swaths, it may be neessary to segment the sene into range invariane regions whose width is seleted by the quadrati phase error allowed. The last phase term φ res represents a residual phase as { φ res 2π R en + ] k 2 4k 2 + k ] ]} k 8k2 + 9k2 4k 2 k 4 k 4 64k2 5. ) As this phase does not depend on the range frequeny or azimuth frequeny, it has no effet on the using proess. However, it does depend on the target range and should only be ignored if a magnitude image is the final produt. After removing the range modulation and range/azimuth oupling using the phase terms 7) and 0) in the 2-D FD,

4 NEO et al.: PROCESSING OF AZIMUTH-INVARIANT BISTATIC SAR DATA 7 Fig.. Geometry of the bistati simulation example -D view). Fig. 2. How the target trajetories are hanged by SRC and RCMC. a) Range ompressed. b) Data after azimuth FT. ) Data after SRC. d) Data after RCMC. an inverse range FT is perrmed to obtain a 2-D signal in the range Doppler domain as S rd τ,f η )= ρ r τ ϕ rm,f η ) Waz f η f η )exp{ jφ az f η )} 2) where the range envelope ρ r τ,f η ) has a sin-like shape in range, and the range migration term ϕ rm is related to the phase φ rm f η ) by ϕ rm f η ) φ rm f τ,f η )= 2πf τ. ) The range inverse FT turns the linear phase omponent in f τ into the time delay ϕ rm / appearing in 2). The funtion W az f η f η ) is the target envelope in the Doppler frequeny domain, where the average Doppler frequeny the Doppler entroid) of the target is given by k f η =. 4) RCMC is perrmed by a range-varying interpolation operation at this stage. The RCMC operation straightens the trajetories so that they now run parallel to the azimuth frequeny axis. The final step is azimuth ompression, whih uses eah target to its mid-aperture range and mid-aperture time. The used point target signal is given by ŝτ,η)=ρ r τ k ) η ρ az η)exp{j2πf η η} 5) where ρ r ) and ρ az ) are the sin-like ompressed pulse envelopes. The exponential term in 5) is a linear phase ramp that ours when the beams are squinted. B. Compression Example The effet of these terms and their ompensation is illustrated in Fig. 2 using an example of a squinted bistati SAR. The same parameters are used as in the C-band simulation desribed in Setion IV exept that only a single point target is used in the present setion. The range-ompressed target trajetory has a large migration of several hundred range ells, as shown in Fig. 2a). When transrmed into the range Doppler domain, the range/azimuth oupling auses the trajetory to be dispersed in range by 00 range ells about 50 range resolution elements) see Panel b)]. SRC removes the range/azimuth oupling effet, as shown in Fig. 2) after the range inverse FT. We an view this proess as the reompression of data in range, hene the name SRC. After RCMC, the majority of the energy from the point target falls into one range ell, as shown in Fig. 2d). Without SRC, the energy would remain spread over many range ells, whih results in signifiant resolution degradation, as in the monostati ase. C. Appliation to the CSA The CSA 6] is an alternate way of implementing an RDAlike algorithm. It differs in that RCMC is perrmed in two parts i.e., a differential and a bulk part), and the interpolation operation is avoided. First, a phase multiply is applied to the rangeunompressed data in the range Doppler domain to equalize the target migration at different ranges. Then, a bulk RCMC is done in the 2-D FD to omplete the RCMC. Range ompression and SRC are also perrmed during the same phase multiply r effiieny. Beause of the 2-D FD operations of the CSA, it is straightrward to apply the bistati range ompression and SRC phase terms 7) and 0) to the CSA. For the RCMC operation, the bulk omponent is 9) with the range set to a mid-swath referene range and applied in the same 2-D FD. The differential omponent is omputed as the differene between 9) evaluated at the expliit range and that at the referene range. The differential omponent is inverse FTed and applied in the range Doppler domain, as in the monostati ase 6], 9]. IV. BISTATIC SIMULATION EXAMPLE To prove the validity of the rmulation and to show how a whole sene an be used, a simulation based on a flat earth model is presented in this setion. The radar geometry is illustrated in Fig..

5 8 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 46, NO., JANUARY 2008 TABLE I SIMULATION PARAMETERS Fig. 5. Point targets used using the bistati RDA. Fig. 6. Measurement of point target us r point target A. Fig. 4. Geometry of the bistati simulation example top view). A. Simulation Parameters The simulation uses the airborne SAR parameters given in Table I. An appreiable amount of antenna squint is assumed to introdue severe range/azimuth oupling. The oversampling ratio is 2.0 in range and.5 in azimuth. The range resolution is 2.05 m 2.09 ells), and the azimuth resolution is.48 m, based on the definitions given in 22] and 2]. A Kaiser window with a smoothing oeffiient of 2.5 is used to suppress the sidelobes in both range and azimuth. Seven point targets are used in the simulation, as shown in Fig. 4. These point targets are illuminated at the same time by the omposite bistati beam. The separation between adjaent point targets is 200 m exaggerated in the figure). All the point targets lie along a vetor u g. This vetor orresponds to the projetion of the vetor gradient of the bistati range Rη) onto the ground plane. Geometrially, Rη) is a vetor passing through the angular bisetor of the bistati angle β; it is used to define the proessed resolution refer to 22] and 2]). The vetor gradient Rη) is given by Fig. 7. Measurement of point target us r point target D. TABLE II POINT TARGET QUALITY MEASUREMENTS Rη) = û t + û r ) 6) where û t is the unit vetor from the point target to the transmitter, and û r is the unit vetor from the point target to the reeiver. B. Simulation Results The simulated ompression results of the seven point targets are shown in Fig. 5. The SRC referene range is taken from the enter target, i.e., Target A. The impulse responses of Target A and the edge target D are shown in Figs. 6 and 7, respetively, where the measured impulse response width IRW) is annotated. The point target quality measurements r all the targets are given in Table II. It is seen that the referene target and its neighbors are well used, but the edge targets are notieably

6 NEO et al.: PROCESSING OF AZIMUTH-INVARIANT BISTATIC SAR DATA 9 Fig. 8. Simple illustration to show how an imaged retangular path beomes a parallelogram in the used map. degraded. This degradation is due to the appliation of a rangeinvariant SRC filter r the whole sene. If we restrit the quadrati phase error to be within ±π/2 at the ends of the range spetrum, the SRC filter an handle a range invariane region of 270 m r this example. Targets D and G are near the edges of the invariane region and have a phase error of 0.48π. The theoretial peak sidelobe ratio PSLR) and the integrated sidelobe ratio ISLR) in range are 20.9 and 8.5 db, respetively. In azimuth, the values are 8.4 and 5.8 db. They are governed by the weighting used and by the azimuth beam pattern. The measured values r the edge targets are within 2 db of the theoretial values. C. Implementation Issues To us the imaged sene, the range derivatives k,...,k 4 have to be determined as a funtion of range. Instead of alulating the derivatives r eah range gate, a urve-fitting approah an be utilized. This will improve the omputational effiieny of the algorithm. For instane, we alulate the range-varying derivatives r a representative set of targets equally spaed over a range invariane region. A urve is fitted r eah derivative to obtain a polynomial funtion in range a ubi polynomial was und to be suffiiently aurate r this.6-km range swath). Using these urves, we an then generate the required parameters r eah range ell. The image is used in the bistati range versus the azimuth time domain. The point targets are registered to their midaperture range and mid-aperture time. Fig. 8 illustrates how a retangular path beomes a parallelogram in the used map. The three targets, whih are denoted by white irles, lie along the same vetor u g and have the same beam enter rossing time. When used, they are registered at the same azimuth time. Thus, a retangular path on the ground plane appears as a parallelogram in the used image, unless u g is perpendiular to the flight path. Image registration maps the used image I τ,η) to a flat earth plane I 2 x, y), as shown in Fig. 8. The proess involves two steps. First, the positions of known grid points in I 2 x, y) are mapped onto I τ,η). These grid points are usually hosen to be parallel and perpendiular to the flight path. Then, an affine transrmation 24] is used to map the rest of the points. V. A PPROXIMATE BISTATIC RDA For oarser-resolution and lower-squint onfigurations, the range/azimuth oupling whih auses the widening of the energy observed in Fig. 2b)] is less dependent on the azimuth frequeny. In this ase, we an neglet the azimuth frequeny dependene when generating the SRC filter by using a oupling term that is fixed at the Doppler entroid frequeny f η.we an further simplify the derivation by negleting the thirdorder and higher order terms of f τ in the φ sr phase equation 0). Consequently, we an approximate the SRC phase by the quadrati funtion 9] φ sr f τ,f η ) πf2 τ 7) K sr where the onstant { K sr 2k 2 fη 2 + k ] k 4k2 fη fη + 9k2 4k 2 k 4 k 2 6k2 5 fη 2 + 6k 2 4 fη + 5 fη 4 ]}. 8) We an then ombine the phase modulation of the range/ azimuth oupling and the range FM modulation together to rm a new FM rate K m 9] as =. 9) K m K r K sr In this ase, the SRC and range ompression an be implemented at the same azimuth time-domain step, whih results in a more effiient algorithm. The proessing steps r this approximate bistati RDA are illustrated in Fig. 9. The steps are similar to the onventional RDA refer to SRC Option in 9]). K sr and K m are weakly range dependent and an often be kept onstant r the imaged sene. If the range swath is too wide, the sene an be subdivided into ontiguous segments and proessed in range invariane regions. VI. SUMMARY The bistati SAR data an be proessed with the RDA in the same way as the monostati SAR data, but the RCMC,

7 20 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 46, NO., JANUARY 2008 Fig. 9. Funtional blok diagram of approximate RDA. SRC, and azimuth ompression funtions need to be modified aordingly. To ahieve this, a new analytial expression r the 2-D point target spetrum derived using series reversion is used r the RCMC, SRC, and azimuth ompression parameters. The arbitrary auray of the spetrum an be ahieved by retaining suffiient terms in the series reversion. The new spetrum applies to azimuth-invariant ases where the transmitter and reeiver are operating in parallel traks with the same veloity. A mild amount of azimuth variane an be aommodated using short azimuth blok sizes. The algorithm has been suessfully tested with targets plaed at different ranges. Although the RDA is used in the example, the approah to omputing the bistati spetrum an also be applied to the hirp saling and ω k algorithms. ACKNOWLEDGMENT The authors would like to thank DSO National Laboratories, Singapore, r providing sholarship funding r Mr. Neo and the National University of Singapore r enouraging Dr. Wong to study the interesting field of bistati SAR proessing. 0] I. Waltersheid, J. H. G. Ender, A. R. Brenner, and O. Loffeld, Bistati SAR proessing using an ω k type algorithm, in Pro. IGARSS, Seoul, Korea, Aug. 2005, pp ] V. Giroux, H. Cantalloube, and F. Daout, An Omega K algorithm r SAR bistati systems, in Pro. IGARSS, Seoul, Korea, Aug. 2005, pp ] R. Bamler and E. Boerner, On the use of numerially omputed transfer funtions r proessing of data from bistati SARs and high squint orbital SARs, in Pro. IGARSS, Seoul, Korea, Jul. 2005, vol. 2, pp ] D. Hale, Dip-moveout by Fourier transrm, Geophysis, vol. 49, no. 4, pp , Jun ] K. Natroshvili, O. Loffeld, and H. Nies, Fousing of arbitrary bistati SAR onfigurations, in Pro. EUSAR, Dresden, Germany, May ] O. Loffeld, K. Natroshvili, H. Nies, U. Gebhardt, S. Knedllik, A. Medrano-Ortiz, and A. Amankwah, 2D-saled inverse Fourier transrmation r bistati SAR, in Pro. EUSAR, Dresden, Germany, May ] M. Rodríguez-Cassolá, G. Krieger, and M. Wendler, Azimuth-invariant, bistati airborne SAR proessing strategies based on monostati algorithms, in Pro. IGARSS, Seoul, Korea, Aug. 2005, pp ] Y. Neo, F. Wong, and I. G. Cumming, A two-dimensional spetrum r bistati SAR proessing using series reversion, IEEE Geosi. Remote Sens. Lett., vol. 4, no., pp. 9 96, Jan ] M. Y. Jin and C. Wu, A SAR orrelation algorithm whih aommodates large-range migration, IEEE Trans. Geosi. Remote Sens., vol. GRS-22, no. 6, pp , Nov ] I. G. Cumming and F. H. Wong, Digital Proessing of Syntheti Aperture Radar Data: Algorithms and Implementation. Norwood, MA: Arteh House, ] K. Eldhuset, A new urth-order proessing algorithm r spaeborne SAR, IEEE Trans. Aerosp. Eletron. Syst., vol. 4, no., pp , Jul ] H. Zhong and X. Liu, A urth-order imaging algorithm r spaeborne bistati SAR, in Pro. IGARSS,Denver,CO,Aug.2006,pp ] G. P. Cardillo, On the use of the gradient to determine bistati SAR resolution, in Pro. Antennas Propag. So. Int. Symp., May 990, vol. 2, pp ] I. Waltersheid, A. R. Brenner, and J. H. G. Ender, Results on bistati syntheti aperture radar, Eletron. Lett., vol. 40, no. 9, pp , Sep ] H. T. Croft, K. J. Faloner, and R. K. Guy, Unsolved Problems in Geometry. New York: Springer-Verlag, 99. REFERENCES ] P. Dubois-Fernandez, O. Ruault du Plessis, M. Wendler, R. Horn, G. Krieger, B. Vaizan, H. Cantalloube, D. Heuzé, and B. Gabler, The ONERA-DLR bistati experiment: Design of the experiment and preliminary results, in Pro. Adv. SARWorkshop, Jun , ] I. Waltersheid, A. Brenner, and J. Ender, Geometry and system aspets r a bistati airborne SAR-experiment, in Pro. EUSARConf., Ulm, Germany, May 2004, pp ] C. Wu, A digital system to produe imagery from SAR data, in Pro. AIAA Conf.: Syst. Des. Driven Sens., Ot ] J. R. Bennett and I. G. Cumming, A digital proessor r the prodution of SEASAT syntheti aperture radar imagery, in Pro. SURGE Workshop, ESA Pub. SP-54, Frasati, Italy, Jul. 6 8, ] C. Wu, K. Y. Liu, and M. J. Jin, Modeling and a orrelation algorithm r spaeborne SAR signals, IEEE Trans. Aerosp. Eletron. Syst., vol. AES-8, no. 5, pp , Sep ] R. K. Raney, H. Runge, R. Bamler, I. G. Cumming, and F. H. Wong, Preision SAR proessing using hirp saling, IEEE Trans. Geosi. Remote Sens., vol. 2, no. 4, pp , Jul ] D. D Aria, A. Monti Guarnieri, and F. Roa, Fousing bistati syntheti aperture radar using dip move out, IEEE Trans. Geosi. Remote Sens., vol. 42, no. 7, pp , Jul ] A. Monti Guarnieri and F. Roa, Redution to monostati using of bistati or motion unompensated SAR surveys, Pro. Inst. Eletr. Eng. Radar, Sonar Navig., vol. 5, no., pp , Jun ] O. Loffeld, H. Nies, V. Peters, and S. Knedlik, Models and useful relations r bistati SAR proessing, IEEE Trans. Geosi. Remote Sens., vol. 42, no. 0, pp , Ot Yew Lam Neo reeived the B.Eng. degree in eletrial engineering from the National University of Singapore, Singapore, in 994 and the Ph.D. degree from the University of British Columbia, Vanouver, BC, Canada, in From 994 to 200, he was an Engineer with DSO National Laboratories, Singapore, where he worked on SAR systems and software r real-time embedded systems. In 2006, he was a Visiting Sientist r three months with ZESS, University of Siegen, Siegen, Germany. He is urrently with the Sensor Division, Radar Tehniques Laboratory, DSO National Laboratories, where he is ontinuing his researh in bistati SAR signal proessing. Dr. Neo was awarded the Engineering Book Prize and was the winner of the Innovation Prize Award r his final year projet work on a VHF frequeny synthesizer.

8 NEO et al.: PROCESSING OF AZIMUTH-INVARIANT BISTATIC SAR DATA 2 FrankH.Wongreeived the B.Eng. degree in eletrial engineering from MGill University, Montreal, QC, Canada, the M.S. degree in eletrial engineering from Queen s University, Kingston, ON, Canada, and the Ph.D. degree in omputer siene from the University of British Columbia UBC), Vanouver, BC, Canada. Sine 977, he has been with MaDonald Dettwiler and Assoiates, Rihmond, BC, where he worked in the Landsat and SPOT imaging area r the first few years. Then, his interest swithed to SAR, and he has been working on airborne and satellite SAR proessing and Doppler estimation ever sine. He is affiliated with the Radar Remote Sensing Group, UBC, where he has also been a Sessional Leturer on image proessing r 8 years. He was a visitor to the National University of Singapore, Singapore, r a year in 999, where he did researh in bistati SAR proessing. Ian G. Cumming S 6 M 66 SM 05 LS 06) reeived the B.S. degree in engineering physis from the University of Toronto, Toronto, ON, Canada, in 96, and the Ph.D. degree in omputing and automation from Imperial College, University of London, London, U.K., in 968. In 977, he was with MaDonald Dettwiler and Assoiates, Rihmond, BC, Canada, where he developed SAR signal proessing algorithms, inluding Doppler estimation and autous routines. He has been involved in the algorithm design of digital SAR proessors r SEASAT, SIR-B, ERS-/2, J-ERS-, and RADARSAT, as well as several airborne radar systems. He was a Visiting Sientist with the German Aerospae Center, DLR, Oberpfaffenhofen, Germany, r one year in 999. Sine 99, he has been with the Department of Eletrial and Computer Engineering, University of British Columbia, Vanouver, BC, where he is the MaDonald Dettwiler/NSERC Industrial Researh Chair in radar remote sensing. The Radar Remote Sensing Laboratory has published papers in the fields of SAR proessing, SAR data enoding, satellite SAR two-pass interferometry, airborne along-trak interferometry, polarimetri radar image lassifiation, and SAR Doppler estimation.