COMPARISON OF CHIRP SCALING AND WAVENUMBER DOMAIN ALGORITHMS FOR AIRBORNE LOW FREQUENCY SAR DATA PROCESSING

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1 COMPARISON OF CHIRP SCALING AND WAVENUMBER DOMAIN ALGORITHMS FOR AIRBORNE LOW FREQUENCY SAR DATA PROCESSING A. Potsis a, A. Reigbe b, E. Alivisatos a, A. Moeia c,and N. Uzunoglu a a National Technical Univesity Of Athens. Depatment Of Electical And Compute Engineeing 9, Ioon Polytexniou St.GR Zogafos, Athens, Geece, Tel/Fax (30) / b Technical Univesity of Belin, Photogammety & Catogaphy, Staße des 17. Juni 135, EB9 D-1063 Belin, Gemany, Tel.: , Fax.: c Geman Aeospace Cente (DLR) Institute fo Radio Fequency Technology. D-830 Obepfaffenhofen, Gemany. Tel/Fax (49) /81135 ABSTRACT In ecent yeas a new class of Synthetic Apetue Rada (SAR) systems, using low fequencies, have emeged. The combination of low fequencies with high bandwidths allows a vaiety of new applications. Seveal new fields aise in foesty, biomass estimation and in achaeological and geological exploation. The P-band SAR technology benefits fom technological advances in antenna design, low noise amplifies, band pass filtes, digital eceive technology, as well as new pocessing algoithms [1], []. Fo all the new applications of an aibone P-band SAR system, the high-esolution imaging is an impotant paamete, but it cannot be easily achieved with conventional pocessing techniques. In this pape, the pefomance and limitations of the Extended Chip Scaling (ECS) algoithm and wavenumbe domain Omega-K pocessing algoithm ae analysed and discussed. Additionally, modifications of both algoithms ae poposed, which optimise the espective algoithm fo pocessing low fequency, wide-beam and wide-band SAR data. Despite of the inheent limitations of the above mentioned pocessing algoithms, a deteministic phase eo, called digital phase eo, due to digital signal pocessing chaacteistics is fomulated and its effect to the pocessed SAR data is analytically descibed. The analysis is caied out, using simulated low fequency aibone SAR data. Keywods: Synthetic Apetue Rada -SAR, P-band SAR, Omega-K pocesso, Extended Chip Scaling pocessing algoithm. 1. INTRODUCTION An inceasing amount of inteest has evolved in VHF/UHF SAR applications. Fo most of the new applications high quality SAR data focussing is necessay. Although wavenumbe domain pocessos ae commonly used to pocess low fequency wide-beam and wide-band SAR data [1], they show cetain limitations in pefoming a high-pecision motion compensation of aibone SAR data. On the othe hand, the Extended Chip Scaling (ECS) algoithm [] is poven to be vey poweful in pocessing aibone data, but has limitations concening long apetue synthesis and heavily squinted geometies. The limits of the along-tack esolution of an aibone wide-band and wide-beam P-band SAR system ae investigated in this fist pat of the pape, though the compaison of the pefomance of the ECS and Omega-K * apotsis@esd.ece.ntua.g, National Technical Univesity Of Athens. Deptment Of Electical And Compute Engineeing 9, Ioon Polytexniou St.GR Zogafos, Athens, Geece, Tel/Fax (30) /773557

2 pocessing algoithms using simulated data. An efficient and obust coection algoithm, which compensates the eos intoduced to the data due to ECS appoximations, is addessed as well. A complete analysis of a deteministic phase eo (digital phase eo), intoduced to SAR data pocessed by both algoithms, is illustated at the end of the fist pat of the pape. The mathematical equation of the eo is deived and seveal simulated esults ae pesented as well. In addition, a detailed analysis of the motion compensation distotions elated to the wide beam azimuth pocessing using both ECS and Omega-K algoithms is pesented at the second pat of this pape, using mainly simulated data sets in diffeent motion eos scenaios.. ECS AND OMEGA-K ALONG TRACK RESOLUTION LIMITATIONS The ange esolution of a SAR system is detemined mainly by the tansmitted pulse duation and it can be easily adjusted. High along-tack esolution in high fequency (moe than 1 GHz) naow-beam SAR systems is elated mainly with the used pocessing algoithm. Fo wideband and wide azimuth beam SAR systems the along-tack esolution is stetched to its fundamental limits. Accoding to [3] in the ideal data collection scenaio, whee no motion eos ae intoduced to the data, the Omega-K algoithm povides the exact solution in the focusing pocedue, esulting in images with maximum possible along tack esolution and minimum esidual phase eos. At lowe cente fequencies, whee longe synthetic apetues and lage integation angle ae necessay to achieve high along tack esolution, the ECS pocessing algoithm, due to appoximations made in chip scaling pocessing, does not povide the exact solution in the focusing pocedue. As a esult of this, the intoduced phase eos ae limiting the maximum achievable along tack esolution. Accoding to [], thee ae two appoximations in chip scaling pocessing. Fist, thee is the Taylo appoximation in wavenumbe domain, which leads to SAR signal fomulation in ange-dopple domain. This appoximation is the basis fo the chip scaling pocesses. The second appoximation is elated with the lack of update of the Seconday Range Compession (SRC) with ange duing signal pocessing. The phase eo, aising fom the fist appoximation, is mainly cubic with ange fequency and causes an asymmetic ange impulse esponse function and, as a esult of this, an incease of the sidelobe level. In any case, the esidual phase eo, intoduced to the peak position, is small compaed to the coesponding phase eo intoduced by the second appoximation. Seveal methods fo phase eo compensation, caused by the appoximations in the chip scaling pocessing, can be found in the liteatue [4]. Fo the needs of ou analysis, we apply an efficient and obust coection algoithms as analytically descibed in [5]..1 Simulated data analysis A P-band aw data simulation has been pefomed to compae the pefomance of ECS and Omega-K algoithms in pocessing low fequency, high along-tack esolution, wide-band and wide-beam SAR data. The main simulation paametes fo both pocessing algoithms ae listed in Table 1. As mentioned above, no motion eos have been intoduced duing aw data simulation. The simulated aw data set consists of thee point tagets, placed in nea, middle, and fa ange (point tagets 1, and 3 espectively) of the pocessed scene. The phase esponse of the thee simulated tagets in fequency domain is shown in Figue 1. No weighting function has been applied to the data (alpha=1.0). Fom this figue it becomes clea, that in the case whee no motion eos ae intoduced to the data, the Omega-K algoithms esults to ideal point taget esponse whee almost no esidual phase eos ae pesent (solid line plots). Nevetheless, the standad ECS pocessing algoithm, due to the above-mentioned appoximations, intoduces phase eos. Fom Figue 1 it can be concluded, that fo 100Hz pocessed Dopple bandwidth (which coesponds to 1.0m azimuth esolution o altenatively 10 0 pocessed squint angle), the maximum

3 ( $ ' & & " esidual phase eo fo fa ange point taget is appoximately 55 0 (doted line plots). The esidual phase eo is quadatic with ange fequency, depends on the pocessed Dopple bandwidth and slant ange. Accoding to [5], the eo fom the appoximation 0 ef (whee ef scaling opeation in wavenumbe domain, can be expessed as: f ( 1) E( fa, f; 0 ; ef ) exp j ( 0 ) 3 ef 1 a( f ) c a 0 is the chip scaling efeence ange) afte chip (1) Whee fa ( fa ) 1 v 1, ( fa ) 1 ( f ) a, is the wavelength, a a f and f denote the azimuth and ange fequencies, espectively, c 0 is the velocity of light, v is the mean velocity of the ada platfom duing data collection and 0 is the distance to a point taget at closest appoach. The eo expessed by (1) can be coected vey efficiently by substituting the ange fequency f by the maximum pocessed bandwidth MPB multiplied with a eduction facto F [5]. The eduction facto is dependent on the phase eo at the end of the pocessed bandwidth and on the kind of weighting function [5]. The coection is only a function of azimuth fequency and slant ange, and as a esult of this it can be implemented in the azimuth compession stage of the chip scaling pocessing without any additional computation effot. The coection can be expessed as [5]: E co %! MPB ( 1) " F ( fa, 0 ; ef ; MPB ) exp j ( 0 ) 3 ef 1 a( f ) c a The simulated aw data set has been pocessed using the modified vesion of the ECS pocesso. The esults ae shown in Figue 1 (dash-dotted line). Fom this figue becomes evident that the modified vesion of ECS, which takes into account the appoximations made in the chip scaling pocessing, educes the maximum esidual phase eos fo all simulated point tagets to less than Figue depict the simulation esults of point taget 3 located in fa ange of the pocessed scene. The impovement achieved by the modified vesion of ECS is evident. 0 () Paamete Wavelength Range bandwidth Chip duation Sampling fequency PRF Velocity Azimuth esolution Hamming weighting Motion Eos Value m 100, 50 and 5 MHz 5 ) s 100 MHz 500 Hz m/s 1m a=1.0 Not simulated Table 1: Main paametes fo P-band aw data simulato.

4 Figue 1: Phase esponse in fequency domain of thee simulated point tagets located in nea (Pt1), middle (Pt) and fa ange (Pt3) of the pocessed scene. Afte the coection applied in the standad ECS pocessing algoithm, the esidual phase eo educe the minimum. Figue : Phase esponse of simulated fa ange point taget in fequency domain. The esidual phase eo educes fom 55 0 to less than 10 0 afte the coection implemented at the standad ECS pocessing algoithm. Recapitulating, when the standad ECS pocesso is used to pocess high-esolution low fequency SAR data, then the esidual phase eo, caused by appoximations made in the chip scaling pocessing, limits the maximum achievable along tack esolution. In this case, a coection function, which compensates the eo, is necessay. In the case whee no motion eos ae intoduced to the data, the coection function significantly educes the phase eo, esulting in a esponse compaable to the ideal esponse of the Omega-K pocessing algoithm..1.1 Digital mapping phase eo Despite the inheited phase eos of the two pocessing algoithms, as descibed above, the total esidual phase eo intoduced to pocessed SAR data includes a deteministic digital mapping phase eo. This digital phase eo depends on the ange distance between the taget (position of the taget s esponse maximum value, in a subpixel level) and the ange distance whee the digital mapping takes place as illustated in Figue 4. As expected, a taget that is positioned exactly in a ange bin of the image has a zeo digital mapping phase eo. In the case whee the taget s ange position diffes fom the image s ange bins, which means that the taget is located between two pixels in ange, the digital phase eo is non-zeo and it is intoduced to the analyzed data. In addition, the digital eo gows, negatively o positively, as the subpixel shift of the taget elative to the mapping ange (ange bin to be mapped) incease o decease espectively. The effect of the digital phase eo intoduced to SAR data pocessed by both algoithms (Omega-K and ECS) is analyzed in the next paagaph, using simulated data. Omega-K algoithm case In Figues 5 and 6 the digital mapping phase eo of a point taget esponse, which coincides with the esidual phase eo fo the Omega-K pocessing algoithm, is pesented fo diffeent positive o negative subpixel shifts of the maximum esponse of the simulated point tagets espectively. A positive shift of a point taget esponse coesponds to a backwads subpixel shift of the taget esponse and a negative shift to a fowad subpixel shift of the taget, elative to the mapping ange. The esidual digital phase eo, in the azimuth diection, of the Omega-K algoithm is given by the following equation [6]: digital eo ( f D ) f v D whee is the wavelength, v is the velocity of the senso, = map taget (Figue 4) is the distance between the ange of the taget and the ange bin being mapped and f D is the dopple fequency. It must be noticed that the phase eo has (3)

5 a paabolic behavio. Actually this is an appoximation of the phase eo fa fom the bandwidth edges. Thee is a moe exact expession at the bandwidth edges and equation 3 gets less capable to descibe the phase eo as the bandwidth pocessed in ange inceases. Using equation 3, the digital phase eo intoduced to simulated low fequency SAR data pocessed by Omega-K algoithm fo diffeent subpixel shifts has been analyzed. A maximum phase eo of 10 degees, when no MoCo eos ae intoduced to the data (ideal case) has been measued. Figue 4: The pocessed gid of the data (coss sections of the hoizontal with the vetical lines coespond to the pixels of the image). The ange distance between the taget (position of the taget s esponse maximum value, in a subpixel level) and the ange whee the mapping takes place can be distinguished. Figue 5: Phase esponse of a simulated point taget in fequency domain using paametes of Table 1, with diffeent subpixel shifts (16%, 3% and 48% of the ange sampling inteval) when the mapping ange is geate than the eal ange of the taget. The dashed line illustates the theoetical phase eo expessed by equation 3. Fom this figue becomes clea that the measued digital eo coincides with the eo calculated by equation 3. Figue 6: Phase esponse of a simulated point taget in fequency domain using paametes of Table 1, with diffeent subpixel shifts (16%, 3% and 48% of the ange sampling inteval) when the mapping ange is smalle than the eal ange of the taget. The dashed line illustates the theoetical phase eo expessed by equation 3. Fom this figue becomes clea that the measued digital eo coincides with the eo calculated by equation 3.

6 The digital mapping phase eo is shown in Figue 5 (Figue 6) fo positive (negative) subpixel shifts of 16%, 3% and 48% of the ange sampling inteval (the 0 subpixel shift coesponds to the case when the mapping ange coincides with the taget s ange). Simulated data analysis poved that the measued digital phase eo follows equation 3 with geat accuacy and it gets negative when the mapping ange is geate than the taget s ange and positive when the mapping ange is smalle than the taget s ange. The digital eo takes its maximum value when the subpixel shift appoaches the 50% of the ange sampling ate and as expected has the value of 10. ECS algoithm case The above-descibed digital mapping phase eo appeas, as expected, at SAR data pocessed by ECS algoithm, following equation 3. In this case it is caused by the diffeence of the azimuth focusing function at the taget s ange position with the actual mapping ange. In the ECS pocessing case the digital phase eo is intoduced to pocessed data additionally to the inheent algoithm phase eos due to appoximations in the chip scaling algoithm, as descibed in the pevious section of this pape. Figue 7 illustates the phase esponse of thee simulated point tagets in fequency domain located in nea (7a), middle (7b) and fa (7c) ange espectively following the same analysis as fo the Omega-K algoithm case of the pevious paagaph. A positive subpixel shift of 16%, 3% and 48% of the ange sampling inteval has been pefomed and the intoduced digital eo has been calculated. The illustated phase eo consists of the ECS pocessing algoithm limitation eo and the digital phase eo. Finally, the digital mapping eo that coesponds to cuent subpixel shift ( = k * (ange sampling inteval), whee k = 0.16, 0.3, 0.48), as calculated using equation 3, is subtacted fom the ECS esidual phase eo in the ideal case. The inheent phase eo of the ECS algoithm in the ideal case, afte the subtaction of the digital mapping eo is illustated in Figue 7. It is obvious that the diffeence is constant and sufficient to chaacteize the exta phase eo of the ECS against the Omega-K algoithm. With the dashed line, the ECS phase eo subtacted by the digital mapping eo is illustated, at the specific subpixel shift. It can be obseved that the diffeence between the two eos emains constant (50MHz pocessed bandwidth tin ange). (a) Pt1, (b) Pt, (c) Pt3. Additionally, the phase eo of the tagets located in the middle and the fa ange (Pt and Pt3 espectively) educes as the shift inceases. The eason fo this effect is that fo positive shifts the digital mapping phase eo is negative (see Figue 5). (a) (b)

7 (c) Figue 7: Phase esponse in the dopple fequency domain of the ECS algoithm fo diffeent distances (diffeent subpixel shifts), between the ange of the taget (maximum of the taget s esponse) and the mapping ange. With the dashed line, the ECS phase eo, subtacted by the digital mapping eo at the specific subpixel shift, is illustated. It can be obseved that the diffeence between the two eos emains constant (50MHz pocessed bandwidth tin ange). (a) Pt1, (b) Pt, (c) Pt3. Fom this figue it can be concluded that the digital phase eo effects negatively o positively the esidual phase eo intoduced to SAR data due to ECS algoithm limitations and it must be always taken into account when analyzing SAR data pocessed by the standad ECS pocesso. 3. MOTION ERROR EFFECTS IN ECS AND OMEGA-K PROCESSORS A cucial poblem in most aibone SAR sensos is the compensation of motion eos, induced by atmospheic tubulence (i.e. the compensation of changes of the plat-fom fowad velocity vecto in oientation and/o in magnitude). Aibone sensos, in contay to spacebone sensos, always show deviations fom the ideal flight tack. SAR imaging fom such unstable platfoms equies an accuate measuement of the antenna position duing the flight and a modified pocessing scheme, which takes into account the non-linea movement of the senso []. The Chip Scaling (CS) algoithm [7] was developed mainly to avoid intepolations, which wee necessay when we had to deal with stong ange-cell migation data (i.e. when wide azimuth beam data have to be pocessed). A impoved vesion of the CS was the ECS algoithm, which was developed oiginally fo pocessing aibone data with stong motion eos (like the E-SAR Do-8 platfom [8]) and vaiable Dopple centoid in ange o/and in azimuth diection. Accoding to [], the ECS pocessing algoithm pefoms motion compensation in two steps. The fist ode motion compensation is defined as being the phase eo coection fo a efeence ange, and it is caied out diectly with uncompessed aw data. Afte the ange compession of the data has been pefomed, the motion compensation phase function is updated with ange. This called second ode motion compensation and it is pefomed ight befoe the azimuth compession. It has been demonstated that motion eos up to some tens of metes can be compensated, in the case of the E-SAR system, using the ECS pocesso. Additionally, the implementation of a sub-apetue algoithm in the ECS algoithm, when it is used to pocess low fequency wide beamwidth SAR data, as descibed in [9], suppesses the esidual motion compensation eo to minimum possible extend. The combination of the ECS coection function, as descibed in the fist pat of this pape, with the sub-apetue coection, esults to maximum possible along tack esolution with a esidual phase eo compaable to the eo illustated in the ideal pocessing case of Fig. 1 and. In most of the opeational examples, the emaining eos ae stongly elated with the accuacy of the navigation units (DGPS/INS/IMU) and not with the impoved ECS motion compensation coection algoithm itself. On the othe hand, due to pocessing achitectue of the Omega-K algoithm, a high pecision motion coection cannot be applied in it. Compaed with the ECS two-step motion compensation, in Omega-K only the fist ode motion eo

8 coection can be applied [3]. The fist-ode MoCo is the ange-independent pat of the eal MoCo, and is applied diectly afte ange compession. The ange-dependent pat can only be applied afte coection of the RCM, which is not possible in Omega-K. The P-band aw data simulato has been used to compae the pefomance of ECS and Omega-K algoithms in pocessing low fequency, high along-tack esolution and aibone SAR data with motion eos. The same simulation paametes of Table 1 have been used again, now adding one quate of typical motion eos typically occuing in case of the E-SAR. The phase esponse of one simulated point taget in fequency domain located in the cente of the pocessed scene is shown in Figue 8. Fom this figue it becomes clea that, even in the case of small motion eos, the Omega-K algoithm fails to emove completely the intoduced phase eos. The esidual phase eo is in the ode of On the othe hand the modified ECS pocesso compensates most of the motion eos accuately, esulting in maximum possible along tack esolution. It has to be noted that the fist ode MoCo coection of Omega-K has been optimized fo the ange distance of the taget; in the geneal case even wose esults can be expected. Figue 8: Phase esponse of one simulated point taget located in the cente of the pocessed scene, with motion eos in fequency domain. The Omega-K algoithm fails to compensate even small motion eos esulting to a maximum esidual phase eo of CONCLUSIONS AND FUTURE WORK The limits of the along tack esolution of an aibone wide-band and wide-beam P-band SAR system have been analyzed in this pape though the compaison of the pefomance of the ECS and Omega-K pocessing algoithms. Simulated data analysis poves that a coection function can be intoduced to the ECS, which esults in a focusing accuacy compaable with the ideal esponse of the Omega-K pocessing algoithm. Futhemoe, the digital mapping phase eo should be taken into consideation when an accuate estimation of the algoithm s esidual phase eo is desied. This deteministic phase eo has been fomulated and calculated using simulated low fequency SAR data in diffeent pocessing scenaios, esulting in a maximum phase eo of 10 0 fo 1m azimuth esolution and 50MHz pocessed bandwidth in ange. In the case whee stong motion eos ae intoduced to the data, the modified ECS pocesso compensates successfully most of the eos, even in the case of low fequency wide-band and -beam SAR data pocessing, esulting in maximum possible along-tack esolution with minimum esidual phase eo. On the othe hand, the Omega-K pocesso fails to compensate even small phase eos intoduced by motion of the ada platfom duing data acquisition. A modified vesion of the Omega-K pocesso, which combines its ideal point taget esponse accuacy with the ECS motion compensation coection pefomance, is unde development with quite pomising esults.

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