AZIMUTH NONLINEAR CHIRP SCALING INTEGRATED WITH RANGE CHIRP SCALING ALGORITHM FOR HIGHLY SQUINTED SAR IMAGING

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1 Progress In Eletromagnetis Researh, Vol. 143, , 2013 AZIMUTH NONLINEAR CHIRP SCALING INTEGRATED WITH RANGE CHIRP SCALING ALGORITHM FOR HIGHLY SQUINTED SAR IMAGING Qinglin Zhai *, Wei Wang, Jiemin Hu, and Jun Zhang College of Eletroni Siene and Engineering, National University of Defense Tehnology, Changsha , China Abstrat The diffiulty of fousing high-resolution highly squinted SAR data omes from the serious azimuth-range oupling, whih needs to be ompensated in the proedure of imaging. Generally, the linear range walk orretion LRWC) an redue the oupling effetively, however, it also indues the problem of azimuth-dependene of residual range ell migration RCM) and quadrati phase. A novel algorithm is proposed to solve this problem in this paper. In this algorithm, the azimuth nonlinear hirp saling ANCS) operation is used, whih an not only eliminate the azimuth spae variation of residual RCM and frequeny modulation FM) rate but also remove the azimuth misregistration. In addition, the range hirp saling operation is applied to orret the range-dependent RCM. After implementing the unified RCM orretion, range ompression and azimuth ompression sequentially, the foused SAR image is aquired finally. The eperimental results with simulated data demonstrate that the proposed algorithm outperforms the eisting algorithms. 1. INTRODUCTION SAR syntheti aperture radar) [1, 2] an provide high resolution images of remote region at all times and in all weather onditions, whih makes it widely applied in military fields suh as missile guidane and ivil fields suh as landform observation. In general, SAR works in broadside mode, i.e., the antenna beam is pointed perpendiularly to the flight path of the platform. However, missile-borne SAR should work in squint mode [3] to aquire target information in front of the platform, and squinting may also inrease the fleibility with whih Reeived 6 August 2013, Aepted 14 Otober 2013, Sheduled 29 Otober 2013 * Corresponding author: Qinglin Zhai qinglinzhai@139.om).

2 166 Zhai et al. a desired area on a surfae is imaged within a single pass of the platform [4]. However, the proessing of SAR eho in squint mode is more diffiult than that in the broadside mode and the diffiulty mainly omes from higher order range-azimuth oupling terms in the phase of the SAR transfer funtion [4 6]. Some algorithms for squint mode SAR involve modified range Doppler algorithm RDA) [7], hirp saling algorithm CSA) [8 10], range migration algorithm RMA) [11, 12], and azimuth nonlinear hirp saling ANCS) algorithm [13 17]. The standard RDA an only proess broadside and small squint SAR data, and its interpolation operation is not effiient. When seondary range ompression SRC) is applied, RDA an aommodate moderate squint mode. However, at higher squint the range dependene of SRC beomes signifiant, and the negleting of this dependene will make resolution broadened and sidelobe level inreased on the edge of the range swath. The CSA is more effiient beause the proedure only ontains fast Fourier transform and omple multipliation, but the performane of high squint angle is also onfined by negleting the range dependene of SRC. A nonlinear hirp saling algorithm is proposed in [4], where the range dependene of SRC is removed by inorporating a small nonlinear frequeny modulated FM) signal into the reeived range signal. In theory, the RMA is able to proess the SAR data olleted from any squint angle, but the Stolt interpolation operation in 2-D spetrum domain makes it impratial. In the algorithms mentioned above, SAR data is diretly proessed in range-doppler domain or 2-D spetrum domain, so high pulse repetition frequeny PRF) is required to avoid the ambiguity of Doppler frequeny. As a result, the high omputational burden of these algorithms redues the imaging effiieny. In [5], the LRWC is firstly applied to remove the linear omponent of the RCM and to redue the range-azimuth oupling, however, it auses the problem of azimuth fousing depth whih will restrit the imaging area. Two methods are available to aount for this problem, inluding the method of subaperture [5] and the method of ANCS. Generally, the method of ANCS is more effiient than the method of subaperture and several algorithms using ANCS are proposed. In [13] and [16], a ubi phase perturbation funtion is applied to equalize the FM rates of all targets at the same range gate. However, additional interpolation is required to eliminate the image misregistration. A modified ANCS operation is adopted in [15], and the image with better auray and little misregistration is obtained. However, it should divide the whole range swath into bloks satisfying that in eah blok the residual RCM is approimately range independent. As a result, the omputational ompleity inreases. In [14], the residual

3 Progress In Eletromagnetis Researh, Vol. 143, RCMC is firstly implemented, however, the azimuth-dependene of RCM is negleted, thus leading the lower auray of RCMC towards the azimuth edge. In this paper, the azimuth-dependene and range-dependene of RCM are both onsidered. After performing the LRWC operation, a third-order azimuth filter and a nonlinear perturbation funtion are both applied to eliminate the azimuth-dependene of RCM and to equalize the azimuth FM rates in eah range gate. Then, implementing the CS operation in range-doppler domain removes the range-dependene of RCM, thus failitating the overall RCMC. The proposed algorithm an not only avoid segment division in range or azimuth diretion, but also eliminate the image misregistration. This paper is organized as follows. Setion 2 analyzes the harateristi of signal oupling in 2-D spetrum domain after LRWC. A modified algorithm of ANCS integrated with CS ANCS-CS) is presented in Setion 3. Some simulation results of different methods are ompared in Setion 4 and we give onlusion in Setion 5 finally. 2. ANALYSIS OF SIGNAL COUPLING The general geometry relationship of the squint mode SAR is shown in Fig. 1. The platform travels along its ourse at an altitude of H with a onstant veloity V and the radar transmits and reeives pulses Platform flight diretion A H O θ 0 X R 0 R 0 R b R t P B R 0, ) Y O' Vt Figure 1. The geometry of the squint mode SAR.

4 168 Zhai et al. with a squint angle of θ 0. Point O is the position of the platform at slow time zero. Point O is the footprint of O, and the slant distane between them is R 0. The oordinate of target B is defined by its slant distane R 0 and the distane between B and O, i.e.,. As shown in Fig. 1, the losest distane of target B is R b. At slow time t, the platform loates at point A after traveling a distane of V t, and the enter of the imaging area is P. The instantaneous slant distane of the target B an be obtained by the triangle APB, and it is epressed as Rt; R 0 ) = R V t )2 2R 0 sin θ 0 V t ) 1) Assuming that the transmitted signal is LFM [18], with the arrier frequeny f, hirping rate K r, bandwidth B r, then the eho signal after demodulation is given by [ s r τ, t; R 0 ) = A 0 w r τ 2Rt) ep jπk r τ 2Rt) ] w a t) ep j4π ) 2 λ Rt) where τ is the fast time, λ the wavelength, the veloity of light, and w r ) and w a ) are the range window and azimuth window, respetively. After Taylor epansion, the instantaneous slant distane Rt; R 0 ) an be approimately as [19] Rt; R 0 ) R V 2 os 2 θ 0 t V sin θ 0 V ) 2 t ) + V 3 os 2 θ 0 sin θ 0 V 2R 2 0 2) t ) 3 3) V By substituting 3) into 2) and applying Fourier transform in range diretion, the result is sf r, t; R 0 ) = A 0 W r f r )w a t) ep j4πf + f r ) ep V t sin θ 0 ep j4πf + f r ) ep j4πf + f r ) j4πf + f r ) sin θ 0 ep R V 2 os 2 θ 0 t V V 3 os 2 θ 0 sin θ 0 2R 2 0 ) 2 t ) 3 V jπ f r 2 K r 4)

5 Progress In Eletromagnetis Researh, Vol. 143, where f r is the range frequeny and W r ) the range frequeny window. In 4), the seond eponential term is the range FM term, and the last three eponential terms are the LRW term, the quadrati RCM term and the ubi RCM term, respetively. The LRWC funtion is denoted as H 1 f r, t) = ep j4πf + f r ) V t sin θ 0 Multiplying 4) with 5) and applying Fourier transform in azimuth diretion, the signal in 2-D spetrum domain an be epressed as s 1 f r, f a ; R 0 ) = A 0 W r f r )W a f a ) ep j4πf + f r ) ep jπ f r 2 ep j4πr f ) 2 r λ ep K r jπr 0 f +f r )sin θ 0 λ 3 f 3 a 4V 3 os θ 0 sin θ 0 ep f [ 1+ f ) 2 r f 5) j2πf a V ) fa λ 2 2V ) ] fa λ 2 3/2 2V 6) where f a is the azimuth frequeny, W a ) the azimuth frequeny window, and V = V os θ 0. It is obvious that the range-azimuth oupling in 2-D spetrum domain eist in the fourth and fifth eponential term. Let Φf r, f a ; R 0 ) denote the summed phases of the last two terms, and it an be epanded into a power series of f r [15] as follows where Φf r, f a ; R 0 ) φ 0 f a ; R 0 ) + φ 1 f a ; R 0 )f r +φ 2 f a ; R 0 )f 2 r + φ 3 f a ; R 0 )f 3 r + Of 3 r ) 7) 1 D 3 f a) Df a ) + πr 0P 3 f a) 1 D 3 f a) 1 D 5 f a) D 3 f a 3πR 0P 3 f a ) 1 ) f D 5 f a ) φ 0 f a ; R 0 ) = 4πR 0 λ Df a) + πr 0P 3 f a) λ φ 1 f a ; R 0 ) = 4πR 0 1 3πR 0P 3 f a ) φ 2 f a ; R 0 ) = 2πR 0 f 1 D 2 f a ) + 3πR 0P 3 f a) 5 D 2 f a) 2f D 7 f a) φ 3 f a ; R 0 ) = 2πR 0 5πR 0P 3 f a) 2f 2 f 2 7 3D 2 f a) D 9 f a) 1 D 2 f a ) D 5 f a + 3πR 0P 3 f a ) ) 2f 2 5 D 2 f a ) D 7 f a ) 8a)

6 170 Zhai et al. Df a ) = 1 ) fa λ 2 2V 8b) P 3 f a ) = sin θ 0λ 3 f 3 a 4V 3 os θ 0 8) In 7), φ 0 f a ; R 0 ) is the azimuth modulation term, φ 1 f a ; R 0 )f r represents the residual RCM after LRWC, φ 2 f a ; R 0 )fr 2 is the term of SRC, and φ 3 f a ; R 0 )fr 3 denotes the third order range-azimuth oupling term. To quantifiationally analyze the amount of these terms, a simulation is implemented by substituting the maimum value of range frequeny and azimuth frequeny into them. Considering the fat that the theoretial range resolution is determined by the bandwidth B r and that the area of range frequeny is between B r /2 and B r /2 after signal demodulation if the over sampling rate in the fast time domain is 1. Then, the maimum value of range frequeny equals to /4ρ r ), where ρ r denotes the theoretial range resolution. Also, the theoretial azimuth resolution is determined by the Doppler bandwidth B a and that the area of Doppler frequeny is between B a /2 and B a /2 after linear range walk orretion if the over sampling rate in the slow time domain is 1. As a result, the maimum value of azimuth frequeny equals to V /2ρ a ), where ρ a is the theoretial azimuth resolution. In the simulation, ρ r and ρ a is 1 m, the losest distane of the target is 20 km, and the flight veloity of the platform is 1000 m/s. Fig. 2 shows the diagrams for the term SRC and the third order range-azimuth oupling term under various squint angles. From the quantitative simulation, it is obvious that both oupling terms beome more serious as the squint angle inrease under the same arrier frequeny. The third order oupling term is 3 orders of magnitude smaller than SRC, indiating that the ubi phase is negligible. However, the SRC term should be ompensated in highresolution highly squinted SAR imaging, and we an set the oeffiient of φ 2 f a ; R 0 ) at the referene slant range R ref beause the rangedependene of SRC is weak. On the basis of aforementioned analysis, the new type of 6) an be rewritten as s 1 f r, f a ; R 0 ) A 0 W r f r )W a f a ) ep j4πf + f r ) sin θ 0 ep j2πf a V

7 Progress In Eletromagnetis Researh, Vol. 143, Quadrati phase rad) GHz 17GHz 35GHz 94GHz Squint angle deg) a) Cubi phase rad) GHz -6 17GHz 35GHz 94GHz Squint angle deg) Figure 2. a) Curves for the term SRC and b) the third order rangeazimuth oupling term under various squint angles. b) ep jπ f r 2 ep jφ 0 f a ; R 0 ) K r ep jφ 1 f a ; R 0 )f r ep jφ 2 f a ; R ref )fr 2 = A 0 W r f r )W a f a ) ep j4πf + f r ) sin θ 0 ep j2πf a V π ep jφ 0 f a ; R 0 ) ep jφ 1 f a ; R 0 )f r ep j K m f a ) f r 2 9) where K m f a ) is the integrated FM rate and it satisfies 1/K m f a ) = 1/K r φ 2 f a, R ref )/π. 3. ANCS INTEGRATED WITH CS ALGORITHM The LRWC an orret the linear migration of the target effetively. However, there is still some residual RCM whih should be ompensated in the afterward proedure. In addition, the LRWC also indues the problem of azimuth-dependene of RCM and azimuth quadrati phase. Therefore, the method of ANCS is applied to eliminate the azimuth variation omponent of residual RCM and azimuth FM rates in eah range gate. Then, the CS operation is performed in the range-doppler domain to remove the rangedependene of residual RCM. After implementing the unified residual RCMC, range ompression and azimuth ompression, the foused SAR image an be aquired finally. The details are presented as follows.

8 172 Zhai et al ANCS Operation Using the range inverse Fourier transform, the signal in 9) is turned to s 2 τ, f a ; R 0 ) A 0 w r τ)w a f a ) ep j4π λ sin θ 0 ep jπk m f a ) τ 2 sin θ 0 + φ ) 1f a, R 0 ) 2 2π ep j2πf a ep jφ 0 f a ; R 0 ) 10) V The last eponential term in 10) denotes azimuth modulation, whih an be epanded into a power series of f a, and the result is φ 0 f a ; R 0 ) 4πR 0 π fa 2 + ψ n fa n 11) λ K a where K a = 2V 2 os 2 / θ 0 λr0 is the azimuth FM rate at slant range R 0. From 10) it is observed that the slant range of a target with the oordinate R 0, ) will beome R 0 + sin θ 0, so the targets that have different initial slant ranges may lie in the same range ell. If the azimuth ompression is proessed with a filter with FM rate K a, the error of the FM rate will lead to azimuth defousing toward the azimuth edge. This is the problem of fousing depth aused by LRWC. Let R s denote R 0 +V t sin θ 0, where t = /V. Then the azimuth FM rate K a an be approimated to the linear form of t as n=3 K a 2V 2 os 2 θ 0 2V 3 os 2 θ 0 sin θ 0 λr s λr 2 s = K aref + K SAC t 12) In 10), the term φ 1 f a, R 0 )/2π ontains the original slant range and the residual RCM of the target, and it an be further represented as φ 1 f a, R 0 ) 2π = 2R 0 2R 0 3R 0P 3 f a ) 2 ) 1 Df a ) 1 + R 0P 3 f a ) 1 2 D 3 f a ) 1 D 5 f a ) = 2 R 0 2 αf a)r 0 13) where αf a ) = 1 Df 1 P 3f a ) a) 4D 3 f a ) + 3P 3f a ) 4D 5 f a denotes the oeffiient of the ) residual RCM whih is relevant to the azimuth frequeny. Substituting t

9 Progress In Eletromagnetis Researh, Vol. 143, ) and 13) into 10) yields s 3 τ, f a ; R s ) = A 0 w r τ)w a f a ) ep j4πr s λ τ 2 R s 2 ) 2 αf a)r 0 ep ep jπk m f a ) j2πf a V ep jπ f a 2 ep j K a ψ n fa n 14) From 14), we an find that the targets in the same range gate have various urves of RCM if they have different original slant ranges. It will ause the error of RCMC toward the edge of azimuth if a unified RCMC is applied in eah range gate. Moreover, the third and higher order terms of f a an be ompensated by multiplying with their onjugate, so the ompensation funtion is H 2 f a ; R 0 ) = ep j ψ n fa n = ep j n=3 Multiplying 14) with 15) results s 4 τ, f a ; R s ) A 0 w r τ)w a f a ) ep 2 ) 2 αf a)r 0 n=3 [ φ 0 f a ; R 0 ) + 4πR 0 + π fa 2 λ K a j4π ep λ R s j2πf a V ] ep jπk m f a ) τ 2 R s ep jπ f a 2 K a 15) 16) Before employing the ANCS operation, an etra ubi azimuth filter is needed [14], whih an be epressed as H 3 f a ) = ep jπy 3 fa 3 17) Applying the range Fourier transform and azimuth inverse Fourier transform to the filtered signal yields s 5 f r, t; R s ) = A 0 W r f r )w a t)ep j4π λ R s ep jπ 4R s f r π ep j K m f a ) f r 2 ep jπ 4αf a)r 0 f r ep jπk a t t ) 2 ep jπy 3 Ka 3 t t ) 3 18)

10 174 Zhai et al. A hirp saling fator with ubi phase is introdued to eliminate the azimuth-dependene of the residual RCM and the azimuthdependene of the FM rate, and the fator an be presented as H 4 t) = ep jπq 2 t 2 + jπq 3 t 3 19) After multiplying 19) with 18) and applying the azimuth Fourier transformation, the signal in 2-D spetrum domain an be epressed as s 6 f r, f a ; R s ) ) fa t q 2 = A 0 W r f r )W a ep j4π K a + q 2 λ R s ep jπ 4R s f r ep jπ 4αf a)r 0 π f r ep j K m f a ) f r 2 ep j2π f a+k a t f a K a +q 2 π [ ep j K a + q 2 ) 2 K a f a q 2 t ) 2 + q 2 f a + K a t ) 2] π [ ep j K a + q 2 ) 3 Y 3 Ka 3 f a q 2 t ) 3 + q 3 f a + K a t ) 3] 20) Let Φf a ) denote the summation of the last three phases in 20). We an find that Φf a ) is relevant to the azimuth position and azimuth modulation of the target, then it an be epanded to a power series of t and f a as Φf a ) = Aq 2, q 3, Y 3, f a, f 2 a, f 3 a ) + Bq 2, q 3, Y 3 )t f a +Cq 2, q 3, Y 3 )t 2 f a + Dq 2, q 3, Y 3 )t f 2 a +φq 2, q 3, Y 3, t, t 2, t 3 ) 21) In 21), the first term is the azimuth-independent modulation, whih an be ompensated in azimuth ompression. The seond term denotes the azimuth position of the target. The third term represents the azimuth distortion, whih should be eliminated. The fourth term stands the azimuth dependene on the azimuth FM, and the last one refers to the summation of all of the other remained terms whih an be negleted in the following proessing. The oeffiients of these terms are showed as A q 2, q 3, Y 3, f a, fa 2, fa 3 ) f 2 = π a + π Y 3Karef 3 + q 3 K aref + q 2 K aref + q 2 ) 3 f a 3 22a) B q 2, q 3, Y 3 ) = 2πK aref K aref + q 2 22b)

11 Progress In Eletromagnetis Researh, Vol. 143, Cq 2, q 3, Y 3 ) = π K [ ) ] aref 3Karef q 2 2 Y 3 K aref +q 3 2KSAC q 2 K aref +q 2 )/K aref K aref + q 2 ) 3 22) Dq 2, q 3, Y 3 ) )] K aref [K SAC K aref + q 2 )/K aref 3 q 2 Y 3 Karef 2 q 3 = π K aref + q 2 ) 3 22d) To eliminate the azimuth distortion and azimuth dependene on azimuth FM, the oeffiients Cq 2, q 3, Y 3 ) and Dq 2, q 3, Y 3 ) should be set to zero. Moreover, we usually set Bq 2, q 3, Y 3 ) to 2π/β, where β 1 is a onstant. Therefore, three equations are presented as Bq 2, q 3, Y 3 ) = 2π/β Cq 2, q 3, Y 3 ) = 0 23) Dq 2, q 3, Y 3 ) = 0 The parameters in 17) and 19) an be aquired from 23), showing as q 2 = K aref β 1) q 3 = K SAC β 1)/3 Y 3 = K SAC2β 1) 3K 3 aref β 1) 24) By substituting 24) into 20), we an obtain the simplified signal as s 7 f r, f a ; R s ) ) fa t q 2 = A 0 W r f r )W a ep j4π K a + q 2 λ R s ep jπ 4R s f r ep jπ 4αf a)r s π f r ep j K m f a ) f r 2 ep j2π t β f a ep jπ f a 2 K SAC ep jπ 3Karef 3 ββ 1)f3 a 25) βk aref After range Fourier transformation, the signal in range-doppler domain is shown as ) fa t q 2 s 8 τ, f a ; R s ) = A 0 w r τ)w a ep j4π K a + q 2 λ R s ep jπk m f a ) τ 2 R s 2 ) 2 R sαf a )

12 176 Zhai et al. ep j2π t β f a ep jπ f 2 a βk aref K SAC ep jπ 3Karef 3 ββ 1)f3 a 26) Inspeting Equation 26), we an find that the azimuth FM rate has been regulated to a fied onstant, whih is independent of the azimuth position. Therefore, the operation of azimuth ompression an be easily implemented with a fied filter funtion. In addition, the azimuth distortion as well as the azimuth-dependene of the residual RCM has been eliminated. In order to failitate the orretion of the residual RCM, the range-dependene of the RCM should also be removed. And the details are presented in the net setion CS Operation in Range Diretion The priniple of CS is applied to deal with the range dependene of the residual RCM, and the hirp saling fator is employed by H s τ, f a ) = ep jπk m f a )αf a ) τ 2 R ref 2 ) 2 R ref αf a ) 27) After multiplying 26) with 27), the signal in range-doppler domain an be written as where s 9 τ, f a ; R s ) = s 8 τ, f a ) H s τ, f a ) ) fa t q 2 = A 0 w r τ)w a K a + q 2 ep jπ f a 2 ep ep βk aref jπ 1 + αf a )) K m f a ) ep j4π λ R s ep j2π t β f a jπ Y 3Karef 3 + q 3 K aref + q 2 ) 3 f a 3 [ τ 2 R s 2 R ref αf a ) ] 2 ep jθf a, R s ) 28) Θf a, R s ) = 4π 2 K mf a )αf a ) 1 + αf a )) R s R ref ) 2 29) After the range Fourier transformation, the signal an be

13 Progress In Eletromagnetis Researh, Vol. 143, epressed as s 10 f r, f a ; R s ) ) fa t q 2 = A 0 W r f r )W a K a + q 2 ep jπ f a 2 ep ep jπ ep βk aref f 2 r 1 + αf a )) K m f a ) j 4πf r R s + αf a )R ) ep j4π λ R s jπ Y 3Karef 3 + q 3 K aref + q 2 ) 3 f a 3 ep j2π t β f a ep jθf a, R s ) 30) Therefore, a filter that performs range ompression and RCMC is obtained H r,rm f r, f a ) fr 2 = ep jπ 1 + αf a )) K m f a ) ep j 4πf r αf a )R ref 31) Multiply 30) with 31) and perform range inverse Fourier transformation, the range-ompressed signal is epressed as follows s 11 τ, f a ; R s ) = IF F T [s 10 f r, f a ; R s ) H r,rm f r, f a )] ) sin fa t q 2 = A 0 W a K a + q 2 ep j4π λ R s ep ep jπ Y 3Karef 3 +q 3 K aref +q 2 ) 3 f a Azimuth Compression [B r τ 2R 0 + sin θ 0 ) j2π t β f a ep jπ f 2 a βk aref )] epjθf a, R s ) 32) On the basis of ANCS operation, range CS operation, and unified RCMC, the residual RCM has been ompletely removed. Also, the dependene of azimuth modulation is eliminated. Then the azimuth ompress funtion an be easily aquired as below. H a f a, R s ) = ep f 2 a K SAC jπ jπ βk aref 3Karef 3 ββ 1)f3 a 33) The last eponential term in 32) is the residual phase aused by CS operation, and the funtion for the phase ompensation is presented

14 178 Zhai et al. as H e f a, R s ) = ep jθf a, R s ) = ep j 4π 2 K mf a )αf a ) 1+αf a )) R s R ref ) 2 34) After azimuth ompression, residual phase ompensation and azimuth inverse Fourier transformation, the final foused SAR image an be obtained as s 12 τ, t; R 0 ) = A 0 sin [B r τ 2R )] 0 + sin θ 0 ) sin [B a t t )] ep j4π β λ R s 35) From 35), we an find that the foused position of the target is R 0 + sin θ 0, /β), whih is offset from the atual position R 0, ). The geometrial distortion omes from the LRWC and ANCS operation, and the method to orret this distortion is illuminated in [15]. Above all, the flow diagram of the proposed algorithm is shown in Fig. 3. Hft, ) 1 r LRWC Azimuth ompensation HfR ; ) 2 a 0 Eho signal Range FFT Range IFFT Azimuth FFT Hf ) 3 a Azimuth filter Range FFT Azimuth IFFT Azimuth FFT Range IFFT Range FFT Ht ) 4 ANCS fator Hs, τ fa ) CS fator Range IFFT Azimuth IFFT Geometrial orretion SAR image Hr, rm fr, fa) Range ompression RCMC H R, f ) ae, 0 Azimuth ompression Phase ompensation a Figure 3. Flow diagram of the proposed algorithm. 4. SIMULATION RESULTS In this setion, simulated results are provided to demonstrate the performane of the proposed algorithm. The simulation parameters

15 Progress In Eletromagnetis Researh, Vol. 143, are listed in Table 1 and the targets geometry is shown in Fig. 4. In this imaging plane, targets 1 5 are laid out along the diretion of beam enter with a distane interval of meter, and the eho signal of these targets have the same azimuth time. In addition, the slant distane of target 3 is seleted as the referene range, and targets 6 9 as well as target 3 loate in the perpendiularity diretion of slant range, and the distane interval is 250 meter. Then the eho signal of these five targets will have the same slant range after the operation of LRWC. Two simulations are arried out to prove the effetiveness of the proposed algorithm from two aspets and the hirp saling fator β is set to 1.1. In the first simulation, three algorithms, i.e., NLCS algorithm [13], ENLCS algorithm [15] and the proposed algorithm are applied respetively. Fig. 5 shows the subimages of targets 3 5 after 8-time interpolating. The upper images in Fig. 5 are obtained by traditional NLCS algorithm in the presene of negleting the quadrati range ell migration. It s obvious that all the images suffer serious distortion in azimuth diretion and the distortion of the farther target is more serious. The middle images are obtained by the ENLCS algorithm, whih orrets the quadrati RCM in referene range. As a result, there is residual RCM eept for target 3 and a slight urve still eists in the azimuth sidelobes of target 4 5. The imaging results aquired from the proposed algorithm are shown at the bottom. It is obvious that Azimuth Beam Center θ0 Range O Figure 4. Targets geometry of the simulation. Table 1. Parameters for simulation. Carrier Frequeny 10 GHz Veloity of Platform 1000 m/s Range Bandwidth 150 MHz Squint Angle 60 Pulse Repeat Frequeny Hz Referene Range 20 km Pulse Width 2.6 µs Theoretial Resolution 1 m 1 m

16 180 Zhai et al. all targets are well foused sine the RCM of all targets are ompletely orreted with range hirp saling. To further evaluate the performane of the proposed algorithm, the measured parameters inluding spatial resolution, peak sidelobe ratio PSLR), and integrated sidelobe ratio ISLR) are alulated, and the results are listed in Table 2. Observing Table 2, we an find that the measured parameters orresponding to the NLCS algorithm and the ENLCS algorithm beome worse when the target is far from the referene range. However, nearly theoretial parameters are obtained by the proposed algorithm and the parameters keep unhangeable along the range diretion. Azimuth samples) Azimuth samples) Azimuth samples) Range samples) Azimuth samples) Range samples) Range samples) a) Range samples) Range samples) Range samples) Range samples) Azimuth samples) Azimuth samples) b) Azimuth samples) Azimuth samples) Range samples) Range samples) Figure 5. Simulation results of different algorithms. a) NLCS algorithm. b) ENLCS algorithm. ) Proposed algorithm. The images from left to right orrespond to target 3, target 4 and target 5, respetively. ) Azimuth samples)

17 Progress In Eletromagnetis Researh, Vol. 143, In another simulation, the results obtained by the RD algorithm [7], the ANCS-based CS algorithm [14] and the proposed algorithm are ompared in Fig. 6. The upper images in Fig. 6 are obtained by traditional RDA. Sine the azimuth ompression is performed by a unified filter, only the target at the enter of the imaging sene i.e., target 3) is well foused. As the target s distane from the sene enter inreases, the fousing quality degrades quikly due to the mismathing of the azimuth FM rate. The middle images are obtained by the ANCS-based CS algorithm. We an find that the phenomenon of azimuth defousing is avoided by the operation of ANCS. However, the residual RCM is not ompletely orreted for Table 2. Measured parameters of imaged targets in Fig. 5. Algorithm NLCS algorithm ENLCS algorithm Proposed algorithm Algorithm NLCS algorithm ENLCS algorithm Proposed algorithm Range Target Resolution m) PSLR db) ISLR db) Target Target Target Target Target Target Target Target Target Azimuth Target Resolution PSLR ISLR m) db) db) Target Target Target Target Target Target Target Target Target

18 182 Zhai et al. that the azimuth dependene of the residual RCM is negleted. As a result, there is still a slight distortion in the images of target 8 and target 9. Observing the imaging results aquired from the proposed algorithm shown at the bottom, it s obvious that all the targets are well foused. It s onvined that the proposed algorithm improves the imaging result in both range and azimuth diretion by modified ANCS operation and more aurate RCMC. The measured parameters of the imaged targets are also Azimuth sample) Azimuth sample) Range samples) Range samples) Range samples) Azimuth sample) Azimuth sample) a) Range samples) Range samples) Range samples) b) Azimuth sample) Azimuth sample) Azimuth sample) Azimuth sample) Range samples) Range samples) Range samples) Figure 6. Simulation results of different algorithms. a) Traditional RDA. b) ANCS-based CS algorithm. ) Proposed algorithm. The images from left to right orrespond to target 3, target 8 and target 9, respetively. ) Azimuth sample)

19 Progress In Eletromagnetis Researh, Vol. 143, alulated, and the results are listed in Table 3. From Table 3, it is found that the range parameters orresponding to different algorithms are approimately similar, however, the azimuth parameters various largely. For the traditional RDA, the azimuth parameters beome worse as the relative distane of the target inreases. Although the performane of the ANCS-based CSA improves muh when ompared with the traditional RDA, there is still a bit worsening in the azimuth diretion. In ontrast, the proposed algorithm obtains the theoretial spatial resolution, PSLR, and ISLR. Table 3. Measured parameters of imaged targets in Fig. 6. Algorithm Traditional RDA ANCS-based CSA Proposed algorithm Algorithm Traditional RDA ANCS-based CSA Proposed algorithm Range Target Resolution m) PSLR db) ISLR db) Target Target Target Target Target Target Target Target Target Azimuth Target Resolution PSLR ISLR m) db) db) Target Target Target Target Target Target Target Target Target

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