Fast image-formation algorithm for ultrahigh-resolution airborne squint spotlight synthetic aperture radar based on adaptive sliding receivewindow

Transcription

1 Fast image-formation algorithm for ultrahigh-resolution airborne squint spotlight syntheti aperture radar based on adaptive sliding reeivewindow tehnique Wei Yang Hong-heng Zeng Jie Chen Peng-bo Wang

2 Fast image-formation algorithm for ultrahigh-resolution airborne squint spotlight syntheti aperture radar based on adaptive sliding reeive-window tehnique Wei Yang, Hong-heng Zeng, Jie Chen,* and Peng-bo Wang Beihang University, Shool of Eletronis and Information Engineering, Xueyuan Road 37, Beijing , China Abstrat. Adaptive sliding reeive-window (ASRW) tehnique was usually introdued in airborne squint syntheti aperture radar (SAR) systems. Airborne squint spotlight SAR varies its reeive-window starting time pulse-by-pulse as a funtion of range-walk, namely, the linear term of range ell migration (RCM). As a result, a huge data volume of the highly squint spotlight SAR eho signal an be signifiantly redued. Beause the ASRW tehnique hanges the ehoreeive starting time and Doppler history, the onventional image algorithm annot be employed to diretly fous airborne squint spotlight ASRW-SAR data. Therefore, a fast image-formation algorithm, based on the priniple of the wave number domain algorithm (WDA) and azimuth deramping proessing, was proposed for aurately and effiiently fousing the squint spotlight ASRW-SAR data. Azimuth deramping preproessing was implemented for eliminating azimuth spetrum aliasing. Moreover, bulk ompression and modified Stolt mapping were utilized for high-preision fousing. Additionally, geometri orretion was employed for ompensating the image distortion resulting from the ASRW tehnique. The proposed algorithm was verified by evaluating the image performane of point targets in different squint angles. In addition, a detailed analysis of omputation loads in the appendix indiates that the proessing effiieny an be greatly improved, e.g., the proessing effiieny ould be improved by 17 times in the 70- deg squint angle by applying the proposed image algorithm to the squint spotlight ASRW-SAR data. The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported Liense. Distribution or reprodution of this work in whole or in part requires full attribution of the original publiation, inluding its DOI. [DOI: /1.JRS ] Keywords: squint spotlight syntheti aperture radar; adaptive sliding reeive-window tehnique; modified Stolt mapping; azimuth deramping. Paper reeived Feb. 19, 2014; revised manusript reeived Apr. 30, 2014; aepted for publiation May 5, 2014; published online Jun. 4, 2014; orreted Jun. 6, Introdution Syntheti aperture radar (SAR) plays a signifiant role in remote sensing. 1 3 Reently, airborne squint spotlight SAR has beome one of the most important topis in mirowave remote sensing, as it has the advantages of illuminating a partiular area within a single pass of the platform by foreword/bakward-squinted antenna and providing higher azimuth resolution by operating at a spotlight mode. 4,5 Therefore, squint spotlight SAR urrently has signifiant appliations in intelligene surveillane, seurity monitoring, target detetion, et. 6,7 However, the state-of-the-art ultrahigh-resolution airborne squint spotlight SAR has to deal with an extremely huge volume of raw data due to the large range ell migration (RCM) that results from the highly squinted angle and high-signal sampling rate orresponding to a highrange resolution. As a result, it leads to higher omputation loads and lower effiieny in SAR image formation proessing. In this artile, the adaptive sliding reeive-window (ASRW) tehnique was introdued for effetively reduing RCM in a -squinted airborne spotlight SAR system. In this system, its reeive-window starting time varies pulse-by-pulse as a funtion of range-walk, namely, the linear term of RCM. Consequently, both data volume and *Address all orrespondene to: Jie Chen, henjie@buaa.edu.n Journal of Applied Remote Sensing Vol. 8, 2014

3 omputation loads an be signifiantly redued. As a onsequene the squint SAR system makes real-time proessing feasible, espeially for the intelligene reonnaissane airborne SAR system. However, those lassial squint SAR data image algorithms, suh as the nonlinear hirp-saling algorithm, extended nonlinear hirp-saling algorithm, and wave number domain algorithm (WDA), 8 11 annot be employed to fous squint spotlight ASRW-SAR data diretly for not onsidering the sliding reeive-window effets. In this artile, a fast image-formation algorithm for ultrahigh-resolution airborne squint spotlight ASRW-SAR was proposed based on the priniple of WDA and the azimuth deramping tehnique. Azimuth deramping preproessing was implemented for eliminating azimuth spetrum aliasing. 12 Moreover, WDA is a good method for fousing squint spotlight SAR data beause of its high auray and effiieny. 1,13 In the WDA part, bulk ompression and modified Stolt mapping were utilized for implementing high-preision fousing. Geometri orretion was also employed for ompensating the geometri distortion that results from the ASRW tehnique. In this artile, Se. 2 analyzes the airborne squint spotlight SAR in detail using the ASRW tehnique. Subsequently, a fast image-formation algorithm for airborne squint spotlight ASRW- SAR was proposed in Se. 3. Then, the point targets simulation experiments were arried out in Se. 4 to prove the validity of the proposed algorithm, and it was verified to have a high-proessing auray and effiieny for squint spotlight ASRW-SAR data. Finally, onlusions are summarized in Se Airborne Squint Spotlight Syntheti Aperture Radar Using Adaptive Sliding Reeive-Window Tehnique Figure 1 shows the aquisition geometry of squint spotlight SAR. We define the retangular oordinate system OXYZ: the origin is the nadir at azimuth beginning time, the x-axis is parallel to the flight path and points along the azimuth diretion, the y-axis is perpendiular to the x-axis on the ground and points along the range diretion, and the z-axis provides a right-hand Cartesian oordinate system. As shown in Fig. 1, radar S is at (x, 0,H), moving at speed v. φ is the squint angle, r is the referene range, and x is the funtion of the azimuth time t whih indiates the position of the airplane along the azimuth diretion. C is the sene enter and A is a ertain target in the sene. Also, the azimuth distane between the sene enter C and target A is x A, where x A ¼ vt A. RðtÞ denotes the instantaneous slant-range distane from the antenna phase enter to a ertain target A. Combining all the geometry, the instantaneous slant-range distane RðtÞ an be written as 1,9 RðtÞ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 2 þ v 2 ðt t A Þ 2 2rvðt t A Þ sin φ ¼ r vðt t A Þ sin φ þ v2 ðt t A Þ 2 os 2 φ þ 2r λ 2 f λ dðt t A Þ fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} ¼ r þ range walk þ 4 f rðt t A Þ 2 fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} þ ; (1) range urve Fig. 1 Aquisition geometry of airborne squint spotlight syntheti aperture radar (SAR) mode. Journal of Applied Remote Sensing Vol. 8, 2014

4 range-walk range-urve RCM(km) squint angle(deg) Fig. 2 Range ell migration (RCM) variation as a funtion of squint angle. where λ is the signal wavelength and f d ¼ 2v sin φ λ and f r ¼ 2v 2 os 2 φ ðλrþ are referred to as the Doppler entroid and Doppler rate, respetively. 9 Figure 2 shows range-walk and rangeurve variations as a funtion of the squint angle using the SAR system parameters listed in Table 1 (in Se. 4). As range-walk is the prominent part of RCM in squint SAR, the removal of range-walk an be onsidered as the law of the ASRW tehnique. Also, the reeive-window starting time has been hanged as follows: ΔTðtÞ ¼2 λ 2 f dðt t A Þ ¼ 2vðt t AÞ sin φ ¼ 2ðx x AÞ sin φ ; (2) where is the veloity of light and x ¼ vt. Figure 3 shows the operation mehanism for airborne squint spotlight SAR using the ASRW tehnique. The geometry of the squint spotlight SAR operating mode is demonstrated in Fig. 3(a). Also, the eho from the target an be reeived by sliding the reeive window as the red lines show in Fig. 3(b). However, if the reeive window is fixed, as the green lines in Fig. 3() show, the RCM loses to the reeive window and the reeive window must be long enough to reeive all the RCM. As the RCM inreases with high resolution and squint angle, the RCM may be outside the reeive window. Figure 3(d) shows both of the two modes SAR ehoes in two-dimensional (2-D) signal proessor memory, and the red lines illustrate that the RCM is redued. As the range-walk is removed, the RCM is redued signifiantly. This implies that the ASRW tehnique redues the reeived eho data volume and saves the storage. Besides, most of the redued eho data are invalid for the RCM, whih would not affet the final imaging results. From the view of information entropy, the ASRW tehnique Table 1 Syntheti aperture radar (SAR) parameters. Parameter Value Parameter Value λ 1.0 m H 8000 m v 150 m s Pulse repetition frequeny (PRF) 600 Hz f s 1.7 GHz r 30.9 Km φ 40 deg 70 deg D 0.6 m τ 2 μs f 30.0 GHz Journal of Applied Remote Sensing Vol. 8, 2014

5 Range Azimuth Range Azimuth Reeive window Reeive window () Reeive time with fixed reeive window Flight Trajetory (b) Reeive time with sliding reeive window Nadia (d) SAR eho in 2D signal proessor memory Target (a) Geometry of squint spotlight SAR Fig. 3 Operation mehanism for airborne squint spotlight SAR using adaptive sliding reeive window (ASRW). atually performs a lossless ompression in the data aquisition stage. Therefore, the ASRW tehnique has no adverse effet on the final imaging. However, the reeive window should start at the speified range of the sampling time due to the radar hardware design priniple. This implies that the reeive-window starting time is disrete ΔTðtÞ ΔT dig ðtþ ¼ f 1 f s ; (3) s where b is an integral funtion. Also, a time-shift of the starting time results from ΔT dig ðtþ is given by ΔT shift ðtþ ¼ΔTðtÞ ΔT dig ðtþ: (4) So, the phase error, aused by ΔT shift ðtþ, an be ompensated for by Eq. (5) before the imaging fousing proess. Then, the ontinuous variable ΔTðtÞ will still be used in the subsequent mathematial derivation Ω 1 ðf τ ;tþ¼expfj2πf τ ΔT shift ðtþg; (5) where f τ is range frequeny. Journal of Applied Remote Sensing Vol. 8, 2014

6 3 Adaptive Sliding Reeive-Window Syntheti Aperture Radar Fast Image-Formation Algorithm Three omponents were proposed in this setion: First, the expression of 2-D mathed filtering funtion in the wave number domain was derived in detail. Then, based on the priniple of WDA, a new Stolt-mapping relationship was illustrated aording to the 2-D mathed filtering funtion. Finally, a presentation of the proess flow of the fast image-formation algorithm was given, whih was proven to fous the ultrahigh-resolution airborne squint spotlight ASRW-SAR data aurately and effiiently. 3.1 Two-Dimensional Mathed Filtering Funtion In the subsequent analysis, the antenna beam pattern, baksatter oeffiient, and other nonessential amplitude fators have been orreted. So, the point-target spetrum of the innovative mode an be given by Sðτ;xÞ¼p τ 2RðxÞ exp j 4πRðxÞ λ 2ðx x AÞ sin φ exp jπb τ 2RðxÞ 2ðx x AÞ sin φ 2 ; (6) where p½ Š is the signal envelope, b is the range hirp FM rate, and τ is the range time. Simply put, after range ompression, the 2-D mathed filtering funtion signal h r (τ;x) is given by adopting the impulse response funtion instead of the sin funtion as follows: h r ðτ;xþ¼δ τ 2ΔRðxÞ 2ðx x AÞ sin φ exp j 4πf ΔRðxÞ ; (7) where ΔRðxÞ ¼RðxÞ r and f denotes the arrier frequeny. Beause the position of the range-ompressed signal is hanged with ΔTðtÞ, the wave number distribution varied aordingly. By applying the priniple of stationary phase (POSP) to Eq. (7), h r (τ;x) is hanged from the range time domain to the range frequeny domain h r ðf τ ;xþ¼exp j4π f þf τ ðδrðxþþxsin φþ exp j4π f xsinφ expfjφ 1 ðf τ ;x A Þg; (8) where Φ 1 ðf τ ;x A Þ¼4πf τ x A sin φ. AsΦ 1 ðf τ ;x A Þ is independent of x, it an be ompensated for by a mathed filter in the range frequeny and azimuth time domain. Therefore, h r ðf τ ;xþ an be rewritten after ompensation as follows: h r ðf τ ;xþ¼exp j4π f þ f τ ðδrðxþþxsin φþ exp j4π f sin φ ; (9) where the azimuth wave number k x ¼ 2πf a v, k 0 ¼ 2πf d v, the range wave number k r ¼ 4πðf þ f τ Þ, and f a is the Doppler frequeny. Then, the signal h r (f τ ;x) is onverted to the range frequeny and azimuth wave number domain Z x H r ðf τ ;k x Þ¼ expf jk r ðδrðxþþxsin φþg exp j2πf d expf jk v x xgdx: (10) Substituting k 0 ¼ 2πf d v into Eq. (10), Z H r ðf τ ;k x þ k 0 Þ¼ expf jk r ðδrðxþþxsin φþg expf jðk x þ k 0 Þxgdx: (11) Journal of Applied Remote Sensing Vol. 8, 2014

7 In squint mode, the enter of the azimuth wave number is k 0 x, and k x [ πðf PRF f d Þ v and πðf PRF f d Þ v ] in Eq. (11), where f PRF is equal to PRF. By using variable substitution, Eq. (11) an be written as follows: Z H r ðf τ ;k x Þ¼ expf jk r ðδrðxþþxsin φþg expf jk x xgdx; (12) where k x ( πf PRF v, πf PRF v). Then, by using POSP, the stationary phase point x 0 is given by x 0 ¼ r sin φ ðk r sin φ þ k x Þr os φ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x k 2 r ðk r sin φ þ k x Þ 2 A : (13) So, the expression of the 2-D mathed filtering funtion in the range frequeny domain and azimuth wave number domain is qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi H r ðf τ ;k x Þ¼expf jr½os φ k 2 r ðk r sin φ þ k x Þ 2 þ sin φðk r sin φ þ k x Þ k r Šg: (14) Then, taking FFT of Eq. (14) with respet to r, we an get the expression of the 2-D mathed filtering funtion in the wave number domain as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi H r ðk r ;k x Þ¼δðk r þ½os φ k 2 r ðk r sin φ þ k x Þ 2 þ sin φðk r sin φ þ k x Þ k r ŠÞ: (15) 3.2 New Stolt-Mapping Relationship Several modified Stolt-mapping relationships have been proposed in Refs. 14 and 15, whih rewrite the expression of RCM. But they do not essentially hange the mapping relationship between the frequeny domain and wave number domain. For the image-formation algorithm of the squint spotlight ASRW-SAR, a new mapping relationship should be found immediately due to the sliding reeive window. Assuming the range ompress signal is pðf τ ;k x Þ, an IFFT was implemented with respet to f τ after the mathed filtering operation Z Pðr; k x Þ¼ pðf τ ;k x ÞH rðf τ ;k x Þ exp j 4πf τ r df τ ; (16) where H rðf τ ;k x Þ is the omplex onjugate of H r ðf τ ;k x Þ. Then, by applying FFT with respet to r ZZ Pðk r ;k x Þ¼ pðf τ ;k x Þ H rðf τ ;k x Þ exp j 4πf τ r expð jk r rþdrdf τ Z ¼ pðf τ ;k x ÞH 4πfτ r k r;k x df τ : (17) Substituting Eq. (15) into Eq. (17), Z q Pðk r ;k x Þ¼ δ k r os φ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k 2 r ðk r sin φ þ k x Þ 2 þ sin φðk r sin φ þ k x Þ 4πf pðf τ ;k x Þdf τ : (18) So, a new mapping relationship is illustrated as follows qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k r ¼ os φ k 2 r ðk r sin φ þ k x Þ 2 þ sin φðk r sin φ þ k x Þ 4πf : (19) Aording to the new mapping relationship, it is easy to onvert pðf τ ;k x Þ from the range frequeny domain to the 2-D wave number domain pðk r ;k x Þ by interpolation. Finally, Journal of Applied Remote Sensing Vol. 8, 2014

8 fine-fousing the image an be done using the azimuth IFFT, geometri orretion, and range IFFT operation. 3.3 Proessing Sheme of Fast Image-Formation Algorithm As Fig. 4 shows, the proessing steps of the fast image-formation algorithm are divided into six stages as follows: time-shift ompensation, azimuth deramping, data transform, bulk ompression, modified Stolt mapping, and geometri orretion. As analyzed in Se. 2, the time-shift ΔT shift (t) auses a phase error. So, the first step of the proposed algorithm is to ompensate for the phase error as in Eq. (5). The overlapped azimuth spetrum limits the diret appliation of the available stripmap imaging algorithm in the spotlight SAR mode. To resolve the problem, azimuth deramping is adopted to eliminate the azimuth spetrum aliasing. Azimuth deramping shares the same proessing flow as in Ref. 16. The data transform stage inludes four proessing steps, namely, range FFT, phase ompression, azimuth FFT, and residual phase ompensation. For ASRW-SAR, the reeive-window starting time is hanged pulse-by-pulse in the azimuth diretion. So, the Doppler history is variable in azimuth, whih means that the target loated only in the sene enter is preisely foused. As analyzed in Se. 3.1, in order to guarantee the fousing auray of all the targets loated in different azimuth positions, the third exponential phase term in Eq. (8) should be ompensated for, whih is given by Ω 2 ðf τ ;xþ¼exp j 4πf τx A sin φ : (20) Only the targets apart from the sene enter at the distane x A in azimuth diretion will be preisely foused. To ensure the imaging quality over the whole sene, a method based on blok Fig. 4 Flowhart of the proposed wave number domain algorithm (WDA). Journal of Applied Remote Sensing Vol. 8, 2014

9 Fig. 5 Flowhart of blok proessing. proessing was proposed in Fig. 5. Eho data an be divided into n bloks along the azimuth diretion, and eah blok an be ompensated for by using different x A values. Moreover, after performing the azimuth FFT, the residual phase aused by azimuth deramping proessing 16 should be ompensated for by Ω 3 ðf a Þ¼exp jπ f2 a : (21) f r In the bulk ompensation stage, the referene funtion is different from the traditional funtion in Ref. 1. Therefore, in a pratial proedure, the referene funtion in bulk ompensation is given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ω 4 ðf τ ;k x Þ¼expfjr os φ k 2 r ðk r sin φ þ k x Þ 2 þ sin φðk r sin φ þ k x Þg exp jπ f2 τ b exp j 4πf τr min ; (22) where r min is minimum slant range, r min ¼ r N r ð2f s Þ, and N r denotes the range resample point. In Eq. (22), the first exponential term ompensates for the phase at the referene slant range as the 2-D mathed filtering funtion H r (f τ ;k x ) shows in Eq. (14). The seond exponential term finishes the range ompression and the third exponential term allows for redundant phase ompensation, whih are all aused by digital proessing. After the bulk ompression, the target at the referene range is properly foused, but a residual phase still exists for the targets at other ranges. Different from the onventional Stolt mapping, the proposed Stolt mapping is modified as in Eq. (19) due to the hange in the data-mapping relationship aused by the ASRW tehnique. The modified Stolt mapping performs the differential RCMC, differential SRC, and differential azimuth ompression. After the modified Stolt mapping proessing, the whole sene is aurately foused. The last proessing part is the geometri orretion, whih ompensates for the hange in the reeive-window starting time aused by the ASRW tehnique. After the modified Stolt mapping, the azimuth IFFT is performed to transform the data into the azimuth time and range frequeny domain. After that, geometri distortion is orreted by sin φ Ω 5 ðf τ ;xþ¼exp j4πf τ x : (23) Finally, a range IFFT is applied to get the fine-fousing and a nondistorted SAR image. 4 Experimental Results In this setion, a Ka-band linear frequeny modulation transmission signal is adopted for simulation, and the azimuth resolution ρ a is 0.1 m. First, to prove the effetiveness of the ASRW tehnique, the experiments omparing the raw eho between the ASRW-SAR and onventional- SAR are arried out. Then, to verify the validity of the proposed image-formation algorithm, Journal of Applied Remote Sensing Vol. 8, 2014

10 Azimuth A B 125m C D Range 125m E Fig. 6 Simulation sene. the experiments with point targets imaging experiments are arried out. The speifi simulation parameters are listed in Table 1, and the simulation sene ( m 2, resulting in pixels in the SAR image) is illustrated by Fig. 6. In ASRW-SAR, the ASRW tehnique hanges the starting time of the reeive window in eah azimuth diretion by removing the range-walk. Also, the length of the range dimension is dependent on the RCM, whose main part is range-walk. Figure 7 shows the raw eho data of ASRW-SAR and onventional-sar systems at different squint angles (φ ¼ 40 deg 70 deg). Also, the range sample number in a onventional-sar and ASRW-SAR are N r and N 0 r, respetively. As shown in Fig. 7, the RCM is redued by ASRW, and the range sampling number dereases signifiantly. Further, the higher the squinted angle, the bigger the range sampling number saling and the more immediate the demand of ASRW. In the imaging experiments part, the imaging results of a onventional WDA and the proposed imaging algorithm are shown in Fig. 8. The omparison results of the proposed imaging algorithm with a onventional WDA shows that the proposed method is effetive. Also, Figs. 9 and 10 show the interpolated ontour plots of the orresponding fousing targets A, C, and E in different squint angles. The spatial resolution (azimuth resolution ρ a, range resolution ρ r ), peak side lobe ratio, and integrated side lobe ratio of the three Fig. 7 Comparing the eho data of ASRW-SAR and onventional SAR systems at different squint angles. (a) onventional SAR, φ ¼ 40 deg, Nr = 32768, (b) ASRW SAR, φ ¼ 40 deg, Nr =8192, () onventional SAR, φ ¼ 70 deg, Nr = , and (d) ASRW SAR, φ ¼ 70 deg, Nr = Journal of Applied Remote Sensing Vol. 8, 2014

11 Fig. 8 Comparing imaging results of onventional WDA and improved algorithm. (a) Conventional WDA. (b) Proposed imaging algorithm. Fig. 9 Imaging results of the improved algorithm in φ ¼ 40 deg. (a) Target A. (b) Target C. () Target E. Fig. 10 Imaging results of the improved algorithm in φ ¼ 70 deg. (a) Target A. (b) Target C. () Target E. point targets proessing results are listed in Table 2. Both the ontour plots and image evaluation results demonstrate that the fine-fousing performane of the proposed improved image-formation algorithm and all the evaluation results indiate that the image results are slightly affeted by the spatial variant slant range. Besides, the omparison of the omputation load of onventional-sar and ASRW-SAR is represented in the Appendix, and the omputation effiieny is γ ¼ in φ ¼ 40 deg 70 deg. The advantage of lessomputation load indiates its potential suitability in a real-time imaging system. ρ r denotes the slant range resolution. Journal of Applied Remote Sensing Vol. 8, 2014

12 Table 2 Targets A, B, and C evaluation results in different squint angles. ρ a (m) Azimuth Peak side lobe ratio (PSLR) (db) Range Integrated side lobe ratio (ISLR) (db) ρ r (m) PSLR (db) ISLR (db) A B φ ¼ 40 deg C D E A B φ ¼ 70 deg C D E Conlusion In this artile, an ASRW tehnique was introdued for effiiently aquiring the airborne highly squint spotlight SAR eho. The airborne squint spotlight ASRW-SAR varies its reeive-window starting time pulse-by-pulse as a funtion of range-walk, namely, the linear term of RCM. So, the RCM of ASRW-SAR is redued dramatially and the range sampling number is dereased, whih means the data volume and the omputation loads are redued. Therefore, the ASRW tehnique dereases the SAR system omplexity, and has great potential value in real-time imaging systems. In order to deal with the varying reeive-window starting times in airborne squint spotlight ASRW-SAR, a fast image-formation algorithm is presented for highly preise fousing of the ultrahigh-resolution (e.g., 0.1 m) airborne squint spotlight ASRW-SAR data. First, azimuth deramping preproessing is performed to eliminate the azimuth spetrum aliasing. Then, bulk ompression and modified Stolt mapping are utilized for preise fousing. At last, geometri orretion is implemented to remove the effet of the varying reeive-window starting time by the ASRW tehnique. The validity and auray of the proposed algorithm have been demonstrated by point targets simulation data. Also, the proessing results of point targets at different squint angles indiate that the proposed algorithm is suitable for high-resolution and high squint angle airborne spotlight SAR image formation. Further, the omputation load is redued, whih would be more markedly dereased in high squint angle, e.g., 17 times improvement of omputation effiieny at a 70-deg squint angle. Appendix: Comparison of Computation Load of Conventional-SAR and ASRW-SAR The number of multipliations is adopted as a omputation load indiator. Let the interpolation kernel length be M ken. Also, the azimuth sample numbers in onventional SAR and ASRW-SAR are N a and Na, 0 respetively. The partiular omputational load in eah imaging stage is listed in Table 3. C on denotes the entire omputational load for onventional-sar. C on ¼ð12 þ 2M ken ÞN a N r þ 6N a N r log 2 N a þ 4N a N r log 2 N r : (24) Journal of Applied Remote Sensing Vol. 8, 2014

13 Table 3 Computation load omparison. Conventional SAR ASRW-SAR Azimuth deramping 8N a N r þ 2N a N r log 2 N a 8N 0 an 0 r þ 2N 0 an 0 r log 2 N 0 a Range FFT 2N a N r log 2 N r 2NaN 0 r 0 log 2 Nr 0 Azimuth FFT 2N a N r log 2 N a 2N 0 an 0 r log 2 N 0 a Bulk ompression 4N a N r 4N 0 an 0 r Stolt mapping 2M ken N a N r 2M ken N 0 an 0 r Azimuth IFFT 2N a N r log 2 N a 2N 0 an 0 r log 2 N 0 a Geometri orretion 0 4N 0 an 0 r Range IFFT 2N a N r log 2 N r 2NaN 0 r 0 log 2 Nr 0 Also, the entire omputational load C ASRW for ASRW-SAR is expressed as C ASRW ¼ð16 þ 2M ken ÞN 0 an 0 r þ 6N 0 an 0 rlog 2 N 0 a þ 4N 0 an 0 rlog 2 N 0 r: (25) Assume that the omputational effiieny γ is defined as γ ¼ C on C ASRW : (26) With the ondition of the same parameters as listed in Table 1, N a and N 0 a are equivalent, N a ¼ N 0 a ¼½ðv PRFÞ ðρ a f r ÞŠ assuming an 8-point interpolation is adopted (M ken ¼ 8). And in different squint angle φ ¼ 40 deg 70 deg, N a (or N 0 a) is equal to 17,500/87,792. Also, the N r and N 0 r are listed in Fig. 6 in different squint angles. Therefore, the omputation effiieny γ is alulated by Eq. (26) in different squint angles, and the final value γ is listed in Table 2. Aknowledgments The authors would like to thank the anonymous reviewers for their valuable omments and useful suggestions. This work was supported in part by National Natural Siene Foundation of China (NSFC) under Grant No , and, in part, by National Natural Siene Foundation of China (NSFC) under Grant No Referenes 1. I. G. Cumming and F. H. Wong, Digital Proessing of Syntheti Aperture Radar Data: Algorithms and Implementation, Arteh House, Norwood, Massahusetts (2005). 2. S.-I. Hwang, H. Wang, and K. Ouhi, Comparision and evaluation of ship detetion and identifiation alogrithms using small boats and ALOS-PALSAR, IEICE Trans. Commun. E92-B(12), (2009). 3. H. Ang et al., Assessment of building damage in 2008 wenhuan earthquake from multitemporal SAR images using getis statisti, IEICE Trans. Commun. E94-B(11), (2011). 4. S. Cimmino et al., Effiient spotlight SAR raw signal simulation of extended senes, IEEE Trans. Geosi. Remote Sens. 41, (2003). 5. G.W. Davidson and I. Cumming, Signal properties of spaeborne squint-mode SAR, IEEE Trans. Geosi. Remote Sens. 35(3), (1997). 6. V. C. Koo et al., A new unmanned aerial vehile syntheti aperture radar for environmental monitoring, Prog. Eletromagn. Res. 125, (2012). Journal of Applied Remote Sensing Vol. 8, 2014

14 7. D. Reale et al., Advaned tehniques and new high resolution SAR sensors for monitoring urban areas, in Geosiene and Remote Sensing Symposium (IGARSS), 2010 IEEE International, Honolulu, HI, pp (2011). 8. H. Cheng, T. Long, and Y. Tian, An improved nonlinear hirp saling algorithm based on urved trajetory in geosynhronous SAR, Prog. Eletromagn. Res. 135, (2013). 9. D. X. An et al., Extended nonlinear hirp saling algorithm for high-resolution highly squint SAR data fousing, IEEE Trans. Geosi. Remote Sens. 50(9), (2012). 10. Y. Wang, O. Loffeld, and S. Knedlik, Spotlight-mode SAR data fousing using a modified wavenumber domain algorithm, in Geosiene and Remote Sensing Symposium, IGARSS, pp (2007). 11. H.-S. Shin and J.-T. Lim, Omega-k algorithm for spaeborne spotlight SAR imaging, IEEE Geosi. Remote Sens. Lett. 9(3), (2012). 12. L. Riardo et al., Spotlight SAR data fousing based on a two-step proessing approah, IEEE Trans. Geosi. Remote Sens. 39(9), (2001). 13. R. Bamler, A omparision of range-doppler and wavenumber domain SAR fousing algorithm, IEEE Geosi. Remote Sens. 30(4), (1992). 14. M. Vandewal, R. Spek, and H. Sub, Effiient and preise proessing for squinted spotlight SAR through a modified stolt mapping, EURSAIP J. Adv. Signal Proess. 2007(1), (2007). 15. A. Reigber, E. Alivizatos, and A. Potsis, Extended wavenumber domain syntheti apeture radar fousing with integrated motion ompensation, IEEE Pro., Sonar Navig. 153(3), (2006). 16. D. Guo, H. Xu, and J. Li, Extended wavenumber domain algorithm for highly squinted sliding spotlight SAR data proessing, Prog. Eletromagn. Res. 114, (2011). Wei Yang reeived the MS and PhD degrees from Beihang University, China, in 2008 and 2011, respetively. He has been a leturer with the Shool of Eletronis and Information Engineering, Beihang University, sine His urrent researh interests inlude high-resolution spaeborne SAR image formation and modeling and simulation for spaeborne SAR systems. Hong-heng Zeng reeived the BS degrees in ollege of Information and Eletrial Engineering from China Agriulture University in He is urrently working towards his PhD at Beihang University. His researh interest is high-resolution spaeborne SAR image formation. Jie Chen reeived the BS and PhD degrees from Beihang University, China, in 1996 and 2002, respetively. He is a professor with the Shool of Eletronis and Information Engineering, Beihang University (BUAA) from His urrent researh interests inlude remote sensing information aquisition and signal proessing; topside ionosphere exploration based on spaeborne HF-SAR; high-resolution spaeborne SAR image formation; modeling and simulation for spaeborne SAR systems. Peng-bo Wang reeived the PhD degrees from Beihang University (BUAA), China, in He has been a leturer with the Shool of Eletronis and Information Engineering, Beihang University, sine His urrent researh interests inlude remote sensing information aquisition and signal proessing; high-resolution spaeborne SAR image formation; modeling and simulation for spaeborne SAR systems. Journal of Applied Remote Sensing Vol. 8, 2014