sensors Article
A Real-Time Imaging Algorithm Based on Sub-Aperture CS-Dechirp for GF3-SAR Data Guang-Cai Sun 1, * 1 2 3
*
ID
, Yanbin Liu 1 , Mengdao Xing 1 , Shiyu Wang 2 , Liang Guo 2 and Jun Yang 3
National Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, China;
[email protected] (Y.L.);
[email protected] (M.X.) School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071, China;
[email protected] (S.W.);
[email protected] (L.G.) College of Geomatics, Xi’an University of Science and Technology, Xi’an 710000, China;
[email protected] Correspondence:
[email protected]; Tel.: +86-029-8820-1027
Received: 30 June 2018; Accepted: 2 August 2018; Published: 5 August 2018
Abstract: Conventional synthetic aperture radar (SAR) imaging algorithms usually require a period of time to process data that is longer than the time it takes to record one synthetic aperture or that corresponding to an adequate azimuth resolution. That is to say, the real-time processing system is idle during the long data recording time and the utilization of computational resources is low. To deal with this problem, a real-time imaging algorithm based on sub-aperture chirp scaling dechirp (CS-dechirp) is proposed in this paper. With CS-dechirp, the sub-aperture data could be processed to form an image with relatively low resolution. Subsequently, a few low-resolution images are generated as longer azimuth data are recorded. At the stage of full-resolution image generation, a coherent combination method for the low-resolution complex-value images is developed. As the low-resolution complex-value images are coherently combined one by one, the resolution is gradually improved and the full-resolution image is finally obtained. The results of a simulation and real data from the GF3-SAR validate the effectiveness of the proposed algorithm. Keywords: GF3-SAR; real-time; CS-dechirp; coherently combination; pipeline structure
1. Introduction Spaceborne synthetic aperture radar (SAR) can perform two-dimensional high-resolution imaging of ground targets at a long distance and in all-weather and all-day conditions [1–3], which makes it a key method for real-time information acquisition. SAR has been widely used in battlefield reconnaissance, target identification, resource exploration, disaster detection, and many other important areas [4,5]. Real-time imaging processing is a key technology of spaceborne SAR in earth observation. To achieve real-time imaging, the processing system is required to produce the final image at the same time as data recording ends or with a relatively short delay [6]. Therefore, how to improve the real-time processing capability of spaceborne SAR is a key issue. In ideal conditions, some classic algorithms such as the range Doppler algorithm (RDA) [7], chirp scaling algorithm (CSA) [8], range migration algorithm (RMA or omega-k algorithm) [9], and polar format algorithm (PFA) [10] can obtain well-focused images, which are usually used in SAR real-time processing. These algorithms usually process data in a time period longer than that required for one synthetic aperture or that corresponding to an adequate azimuth resolution [11,12]. That is to say, the real-time processing system is idle during the long data recording times and the utilization of computational resources is low. This problem is particularly obvious in spaceborne SAR systems due to their long radar range, high azimuth resolution, and thus long synthetic aperture length [13]. Sensors 2018, 18, 2562; doi:10.3390/s18082562
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In this case, if the imaging processing starts after recording the azimuth data of a full-aperture time, the required data storage and computational load increases substantially [14,15], which undoubtedly increases the requirements for the hardware processing system of a spaceborne SAR and hinders real-time imaging processing. To deal with this problem, a new sub-aperture approach for real-time SAR processing has been studied by Alberto Moreira [16]. This approach has shown good real-time performance and imaging results. The signal is divided into sub-apertures that are small enough, so the range cell migration in one sub-aperture datum can be ignored. However, the range cell migration is considered in sub-aperture signal stitching. The interpolation of samples is used for range cell migration correction in this approach. This correction is limited to migration within one sub-aperture, which is less than half of the range resolution. In addition, the overlap of the sub-apertures must be greater than 21% for sufficient attenuation of the grating lobes or paired echoes, which increases the computational load. As shown in the simulation, the grating lobes appear in the imaging results. In our opinion, this phenomenon occurs due to the overlapping sub-aperture data. On this basis, this paper proposes a real-time imaging algorithm based on sub-aperture chirp scaling dechirp (CS-dechirp), which can perform imaging processing while the data are recorded and thus without waiting for a full-aperture time. In the proposed method, the low-resolution complex-value image is formed by using sub-aperture data, which can be much shorter than a synthetic aperture length. Subsequently, a few low-resolution images are generated as the longer azimuth data is recorded. At the stage of full-resolution image generation, a coherent combination method for the low-resolution complex-value images is developed. As the low-resolution complex-value images are coherently combined one by one, the resolution is gradually improved and the full-resolution image is finally obtained. Compared with the study by Alberto Moreira [16], the method proposed in this paper does not require sub-aperture data to overlap, and the grating lobes did not appear in the simulation results. The range cell migration can be adequately corrected by the sub-aperture CSA without limitation. Since the processing system produces the image at the same time as recording the data, this pipeline structure is very suitable for the data stream in SAR real-time processing. This paper is organized as follows. In Section 2, the sub-aperture signal model for spaceborne SAR is established. In Section 3, the flow chart and equation derivation of the sub-aperture CS-dechirp imaging algorithm are detailed. In Section 4, the point targets simulation and the imaging results of the real data from the GF3-SAR are used to validate the effectiveness of the proposed algorithm. In Section 5, the content of this paper is summarized and analyzed. 2. Sub-Aperture Signal Model The geometry of the spaceborne SAR is depicted in Figure 1. The satellite moves along the trajectory from Pk to Pk+1 for the k-th sub-aperture data recording, where tk is the center of the k-th sub-aperture data and tsub is the slow time in the azimuth of the sub-aperture data. According to Figure 1, the instantaneous slant range between the point target Q( R B , X ) located in the scene and the ideal moving satellite can be written as: R(tsub ; R B ) =
q
R2B + (vtk + vtsub − X )2
(1)
where v is the equivalent speed of the spaceborne SAR, R B is the coordinate in the range, and X is the coordinate in the azimuth of the point target Q( R B , X ). Supposing that the transmitted signal is a linear frequency modulation (LFM) signal st (t) = ar (t) exp( jπγt2 ), where γ is the chirp rate of the LFM signal, t is the fast time in the range, and ar (t)
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is the window function of the LFM signal, which is a rectangular window [17], then the received sub-aperture signal of the point target Q( R B , X ) can be written in the t–tsub domain as: s(t, tsub ; R B )
2R(tsub ;R B ) ) aa (tk + tsub ) c 2R(tsub ;R B ) 2 ) ] exp[− j 4π × exp[ jπγ(t − c λ R ( tsub ; R B )]
= ar ( t −
(2)
where aa (·) is the beam window function in the azimuth, c is the speed of light, and λ is the wavelength of the signal. From Equations (1) and (2), the difference between the sub-aperture expression of the signal and the traditional full-aperture expression is only a sub-aperture center term, tk , which plays a very Sensors 2018, 18, x FOR PEER REVIEW 3 of 16 important role in image stitching, as detailed in Section 3.2.3. range satellite trajectory Pk
Pk
1
Q(RB , X )
azimuth o
tk
tsub
Figure 1. Geometry of the spaceborne synthetic aperture radar (SAR). Figure 1. Geometry of the spaceborne synthetic aperture radar (SAR).
3. Real-Time Imaging Algorithm Based on Sub-Aperture CS-Dechirp
Supposing that the transmitted signal is a linear frequency modulation (LFM) signal
st (t )
real-timet imaging algorithm based onrate sub-aperture CS-dechirp perform 2 ) , where is the chirp of the LFM signal, tcan is the fastimaging time inwhile the range, aThe r (t )exp( j
recording data. The data from each sub-aperture are processed by the CS-dechirp algorithm to obtain a low-resolution complex-value image; subsequently, a high-resolution complex-value image of all received sub-aperture of by thecombining point target be written in the t – tsub domain as: Q(sub-aperture RB , X ) can images received data can be signal obtained all the coherently.
and ar (t ) is the window function of the LFM signal, which is a rectangular window [17], then the
3.1. Description of Real-Time Imaging Algorithm 2R(tsub ; RB ) s(t, tsub ; RB ) ar (t )aa (tk tsub ) A sketch of the real-time imaging algorithm is shown in Figure 2. The GF3 satellite flies c (2) 2R(ntsub ; RB )of data recording. along the trajectory from P1 to Pn, experiencing times During data recording, 4 2 exp[ j (t ) ]exp[ j R(t ; RB )] the corresponding sub-aperture data are processedcto form a low-resolutionsubcomplex-value image, which is then coherently combined with the foregone images to form a new image with higher c is where window function in the azimuth, of light, and is the aa ( ) isAsthe resolution. thebeam sub-aperture images are coherently combined one bythe one,speed the resolution is gradually improved until full resolution is achieved. This forms the pipeline structure of the sub-aperture wavelength of the signal. data stream, in which imaging result between can be gradually generated as sub-aperture data are and From Equations (1) the andfinal (2), the difference the sub-aperture expression of the signal continuously recorded, which is suitable for the GF3-SAR real-time imaging processing. the traditional full-aperture expression is only a sub-aperture center term, tk , which plays a very The flow chart of the real-time imaging algorithm based on sub-aperture CS-dechirp is shown important role in image as detailed in Section in Figure 3. Data from stitching, each sub-aperture recorded by the3.2.3. GF3-SAR are processed by the CS-dechirp algorithm to obtain a low-resolution complex-value image; the high-resolution complex-value image 3. Real-Time Imaging Algorithm Based by onstitching Sub-Aperture of all received data can then be obtained togetherCS-Dechirp all the sub-aperture images.
The real-time imaging algorithm based on sub-aperture CS-dechirp can perform imaging while recording data. The data from each sub-aperture are processed by the CS-dechirp algorithm to obtain a low-resolution complex-value image; subsequently, a high-resolution complex-value image of all received data can be obtained by combining all the sub-aperture images coherently. 3.1. Description of Real-Time Imaging Algorithm A sketch of the real-time imaging algorithm is shown in Figure 2. The GF3 satellite flies along
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P2
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P3
P4
P5
Pn
Sensors 2018, 18, 2562 Sensors 2018, 18, x FOR PEER REVIEW first recording
second recording
third recording
P1 P2 subaperture data 1
first recording
second images recording stitching
4 of 15 4 of 16 fourth recording P3
third subaperture recording data 2
subaperture data 1 stitching images
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n-th recording P4
P5
fourth recording
low resolution
n-th recording low resolution
subaperture data 3 .. .
subaperture data 2 images stitching
images stitching
Pn
subaperture data n-1
subaperture data 3 images stitching .. . images stitching integrated SAR image
subaperture data n
subaperture data n-1
high resolution subaperture
images stitching
data n Figure 2. Sketch of the sub-aperture real-time imaging algorithm.
integrated SAR imagebased on sub-aperture CS-dechirp high resolution The flow chart of the real-time imaging algorithm is shown in Figure 3. Data from each sub-aperture recorded by the GF3-SAR are processed by the CS-dechirp algorithm to obtain aFigure low-resolution image; theimaging high-resolution Figure 2. Sketch Sketch of ofcomplex-value the sub-aperture sub-aperture real-time imaging algorithm.complex-value image 2. the real-time algorithm. of all received data can then be obtained by stitching together all the sub-aperture images. The flow chart of the real-time imaging algorithm based on sub-aperture CS-dechirp is shown subaperture subaperture subaperture by the GF3-SAR subaperture in Figure 3. Data from each sub-aperture recorded are processed by the CS-dechirp data 1 data 2 data 3 data 2 algorithm to obtain a low-resolution complex-value image; the high-resolution complex-value image of all received data can then be obtained by stitching together all the sub-aperture images.
subaperture
CSA
subaperture CSA
subaperture CSA
subaperture CSA
data 1
data 2
data 3
data 2
Dechirp processing CSA
Dechirp
Dechirp
Dechirp
CSA processing
CSA processing
CSA processing
subaperture stitching subaperture stitching subaperture Dechirp Dechirp Dechirp image 1 image 2 image 3 processing processing processing
stitching subaperture Dechirp stitching integrated image n SAR image processing
Figure Flow chart chart of of the the real-time real-time imaging Figure 3. 3. Flow imaging algorithm. algorithm. subaperture stitching subaperture stitching subaperture
3.2. Data Processing Based on image CS-Dechirp Algorithm image 1 2 image 3
stitching subaperture stitching integrated image n
SAR image
From slant range R(tsub changes with the slow time tsub , and the migration B ); R From Equation Equation(1), (1),thethe slant range R(;tR sub B ) changes with the slow time tsub , and the Figure 3. Flow chart of the real-time imaging algorithm. amount varies with R B , which shows the space-variance characteristic of the range cell migration. migration amount varies with RB , which shows the space-variance characteristic of the range cell Because the scaling processing in the CSA can adequately compensate the range cell migration with the 3.2. Data Processing Based on CS-Dechirp Algorithm migration. Because the scaling the CSA can adequately compensate cell space-variance characteristic andprocessing the CSA is in suitable for hardware implementation [18],the therange real-time migration with the space-variance characteristic and the CSA is suitable for hardware imaging algorithm takes algorithm the core to process sub-aperture data. From Equation (1), the theCS-dechirp slant range R(tsub ; Ras B ) changes with the slow time tsub , and the implementation [18], real-time imaging algorithm CS-dechirp algorithmgoasthrough the corethe to According to thethe flow chart shown in Figure 3, thetakes datathe from each sub-aperture R migration amount varies with , which shows the space-variance characteristic of the range cell process sub-aperture data. azimuth B dechirp module, and sub-aperture complex-value images stitching sub-aperture CSA module, migration. Because the scaling processing in the CSA can adequately compensate the range cell module to obtain a SAR image with higher resolution. migration with the space-variance characteristic and the CSA is suitable for hardware implementation [18], the real-time imaging algorithm takes the CS-dechirp algorithm as the core to process sub-aperture data.
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3.2.1. Sub-Aperture CSA Supposing the sub-aperture Doppler frequency corresponding to tsub is f sub , the expression of the k-th sub-aperture echo signal shown in Equation (2) can be written in the t– f sub domain as:
= ar ( t −
sk (t, f sub ; R B )
2R( f sub ;R B ) ) aa ( c
q
R B λ f sub
)
1−( f sub / f aM )2 2π × exp[− j v R B f aM 2 − f sub 2 ] exp[− j2π f sub ( Xv 2R( f sub ;R B ) 2 ) ] × exp[ jπγe ( f sub ; R B )(t − c 2v2
p
− tk )]
(3)
2
sin θ = γ1 − R B 2λ , θ is the squint angle and f aM = 2v/λ. From Equation (3), c2 cos3 θ the difference between the sub-aperture expression of the signal and the traditional full-aperture expression is the second exponent term of tk , which shows the phase of the point target relative to tk in sub-aperture imaging. The chirp scaling quadratic phase function for the range cell migration correction is:
where
1 γe ( f sub ;R B )
H1 (t, f sub ; R0 ) = exp[ jπγe ( f sub ; R B ) a( f sub )(t −
2R( f sub ; R0 ) 2 ) ] c
(4)
q where a( f sub ) = 1/ 1 − ( f sub / f aM )2 − 1 is the CS factor, R( f sub ; R0 ) is the slant range with f sub as an argument, and R0 is the reference distance between the scene center and the radar trajectory. Since γe ( f sub ; R B ) changes less within the observed scene, R B in γe ( f sub ; R B ) can be replaced by R0 . In the following part, we use γe ( f sub ; R0 ) to substitute γe ( f sub ; R B ). After multiplying Equations (4) with (3) in the t– f sub domain, the signal is transformed to the f r – f sub domain as: sk ( f r , f sub ; R B )
= ar [− γe ( f
fr sub ;R0 )[1+ a ( f sub )]
] aa (
2v2
q
R B λ f sub 1−( f sub / f aM )2
)
f r2 ] exp[− j 4π c [ R B + R0 a ( f sub )] f r ] ;R )[ 0 1+ a ( f sub )] sub p 2π × exp[− j v R B f aM 2 − f sub 2 ] exp[− j2π f sub ( Xv − tk )]
× exp[− jπ γe ( f
(5)
where Θ∆ ( f sub ; R B ) = 4π γ ( f ; R0 ) a( f sub )[1 + a( f sub )]( R B − R0 )2 is the residual phase due to the c2 e sub operation of the chirp scaling quadratic phase function. The first exponent term in Equation (5) is the modulation phase function in the range frequency domain. R0 a( f sub ) in the second exponent term shows that the migration amount of all point targets in the observed scene becomes the same after the CS operation. Subsequently, the phase function for the range compressing, secondary range compressing, and range cell migration correction can be constructed as: H21 ( f r , f sub ; R0 ) = exp[ jπ
f r2 4πR0 a( f sub ) ] exp[ j fr ] γe ( f sub ; R0 )[1 + a( f sub )] c
(6)
After multiplying Equations (6) with (5), the signal is transformed to the t– f sub domain as follows: sk (t, f sub ; R B )
= sin car (t −
2R B c ) aa (
2v2
q
× exp[− j 2π f aM 2 − v RB X × exp[− j2π f sub ( v − tk )] p
R B λ f sub
)
1−( f sub / f aM )2 f sub 2 ] exp[ jΘ∆ ( f sub ; R B )]
(7)
Here, the CSA completes the range compressing and range cell migration correction. From Equation (7), the first exponent term is required to process matched filtering, and the second
2v 1 (fsub / faM ) (7) 22 RB faM22 fsub22 ]exp[ j (fsub ; RB )] exp[ j (7) exp[ j v RB faM fsub ]exp[ j (fsub ; RB )] v X exp[ j 2 sub (X exp[ j 2 ffsub ( v ttkk)])] v Sensors 2018, 18, 2562 6 of 15 Here, the CSA completes the range compressing and range cell migration correction. From Here, the CSA completes the range compressing and range cell migration correction. From Equation (7), the first exponent term is required to process matched filtering, and the second exponent Equation (7), the first exponent term is required to process matched filtering, and the second exponent term is the residual phase term that is required to compensate. Based on the above, the residual phase exponent term is phase the residual phase term that is requiredBased to compensate. on the phase above, term is the residual term that is required to compensate. on the above,Based the residual compensation function for Equation (7) can be written as: the residual phase compensation function for Equation (7) can be written as: compensation function for Equation (7) can be written as:
H22((tt,,ffsub;;R R0 ) exp[ jj ((ffsub;;R R )])] H H22 exp[− jΘ∆ (sub f sub ;BB R B )] 22 (t, fsub sub ; R00)) =exp[
(8) (8)(8)
However, the matched filtering used for the sub-aperture signal of Equation (7) will cause image However, However,the thematched matchedfiltering filteringused usedfor forthe thesub-aperture sub-aperturesignal signalofofEquation Equation(7) (7)will willcause causeimage image aliasing, which can be illustrated by the time-frequency distribution in Figure 4. To avoid this aliasing aliasing, which can be illustrated by the time-frequency distribution in Figure 4. To avoid this aliasing, which can be illustrated by the time-frequency distribution in Figure 4. To avoid thisaliasing aliasing caused by the matched filtering, zero padding in the azimuth must be used for the traditional CSA, caused causedbybythe thematched matchedfiltering, filtering,zero zeropadding paddingininthe theazimuth azimuthmust mustbebeused usedfor forthe thetraditional traditionalCSA, CSA, which undoubtedly increases the computation burden. Therefore, the azimuth dechirp can be used which undoubtedly increases the computation burden. Therefore, the azimuth dechirp can be used which undoubtedly increases the computation burden. Therefore, the azimuth dechirp can be used for azimuth compression. The azimuth dechirp can solve the problem of image aliasing without zero for forazimuth azimuthcompression. compression.The Theazimuth azimuthdechirp dechirpcan cansolve solvethe theproblem problemofofimage imagealiasing aliasingwithout withoutzero zero padding, which can be illustrated by the time-frequency distribution in Figure 5. padding, which can be illustrated by the time-frequency distribution in Figure 5. padding, which can be illustrated by the time-frequency distribution in Figure 5. fsub fsub
fsub fsub PRF PRF
aliasing aliasing
tsub tsub
Tsub Tsub
tsub tsub
aliasing aliasing
Tsub Tsub
(a) (a)
(b) (b)
Figure 4.4.Time-frequency distribution for matched filtering: (a) unprocessed sub-aperture signal; (b) Figure4. Time-frequency distribution matched filtering: (a) unprocessed sub-aperture signal; Figure Time-frequency distribution for for matched filtering: (a) unprocessed sub-aperture signal; (b) sub-aperture signal after matched filtering. (b) sub-aperture signal matched filtering. sub-aperture signal after after matched filtering. fsub fsub
fsub fsub PRF PRF
PRF PRF
tsub tsub
tsub tsub
Tsub Tsub
(a) (a)
(b) (b)
Figure 5. Time-frequency distribution for azimuth dechirp: (a) unprocessed sub-aperture signal; (b) sub-aperture signal after azimuth dechirp.
3.2.2. Azimuth Dechirp Since the high-order term in Equation (7) leads to the residual phase in the azimuth dechirp, the high-order term must be converted to a quadratic phase function. The conversion function can be written as: q 2π π H3 (t, f sub ; R B ) = exp[ j R B f aM 2 − f sub 2 − j f 2] (9) v k a0 sub
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where k a0 = −2v2 /λR0 is the time-domain chirp rate of the signal. After the compensation of Equation (8) and the conversion of Equation (9), the signal can be written as: 2R R λf sk (t, f sub ; R B ) = sin car (t − c B ) aa ( q B sub ) 2 2v 1−( f sub / f aM )2 (10) × exp[− j kπ f sub 2 − j2π ( Xv − tk ) f sub ] a0
The signal of Equation (10) is transformed to the t–tsub domain as: sk (t, tsub ; R B ) = sin car (t −
2R B X X 2 ) aa (tk + tsub − ) exp[ jπk a0 (tk + tsub − ) ] c v v
(11)
From Equation (11), there are only the first and quadratic terms in its phase. A quadratic phase function can be constructed to complete the azimuth dechirp as: H4 (t, tsub ) = exp(− jπk a0 (tk + tsub )2 )
(12)
After the dechirp processing in Equation (12), the signal of Equation (11) becomes: sk (t, tsub ; R B )
2R
= sin car (t − c B ) aa (tk + tsub − Xv ) × exp[− j2πk a0 Xv (tk + tsub ) + jπk a0 ( Xv )2 ]
(13)
3.2.3. Sub-Aperture Complex-Value Image Stitching The theoretical form of sub-aperture image stitching can be described as follows. For simplicity, Equation (13) can be rewritten as: sk (t, tsub ; R B )
2R
= sin car (t − c B ) aa (tk + tsub − Xv ) × exp[− j2π f d tsub − j2π f d tk + jπk a0 ( Xv )2 ]
(14)
where f d = k a0 X/v. According to Equation (14), the Fourier transformation (FT) must be performed on the azimuth signal to obtain the sub-aperture focusing results. However, the focusing position f d in the azimuth exceeds the range of (−PRF/2, PRF/2) (PRF, Pulse Repeating Frequency), resulting in azimuth-aliasing after the FT for the signal. Therefore, the FT cannot be directly performed. To deal with this problem, an azimuth compensation function for spectrum shifting is introduced: H5 (t, tsub ) = exp( j2π f M tsub )
(15)
where f M = k a0 tk . This function ensures that the focusing positions of point targets are within (−PRF/2, PRF/2). Multiplying Equations (15) with (14), the signal becomes: sk (t, tsub ; R B )
2R
= sin car (t − c B ) aa (tk + tsub − Xv ) i × exp[− j2π ( f d − f M )tsub − j2π f d tk + jπk a0 ( Xv )2
(16)
Then, the signal is transformed to the t– f sub domain as: sk (t, f sub ; R B )
2R
= sin car (t − c B )δa ( f sub + f d − f M ) × exp(− j2π f d tk ) exp( jπk a0 ( Xv )2 )
(17)
Because the focus position f M − f d is smaller than PRF, the single in Equation (17) is non-azimuth-aliasing.
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In addition, a coherent combination is required for sub-aperture images. Therefore, the phase coherence and simplicity of the combination also need to be considered when performing the above frequency compensation. Thus, a combination method based on the integer points of the azimuth frequency is proposed. According to Equation (17), one can note that exp(− j2π f d tk ) is a residual phase, which varies with tk or the azimuth sub-aperture index k. To combine the sub-aperture complex-value images coherently, this phase term should be compensated, and the phase compensation function can be written as: H6 (t, f sub ) = exp( j2π ( f M − f sub )tk ) (18) After the compensation of Equation (18), the SAR complex-value image of the k-th sub-aperture data can be obtained as: sk (t, f sub ; R B ) = sin car (t −
2R B X 2 )δa ( f sub + f d − f M ) exp( jπk a0 ( ) ) c v
(19)
4. Simulation and Real Data Results In order to illustrate the effectiveness of the proposed algorithm, the imaging results of a point targets simulation and the GF3-SAR real data, which are separately processed by the full-aperture standard CSA and the sub-aperture CS-dechirp algorithm, are used for comparative analysis. 4.1. Point Targets Simulation The simulation parameters of the spaceborne SAR are shown in Table 1 and the lattice in the scene is 3 (range) × 5 (azimuth). The distance between point targets is 1500 m in the range and 625 m in the azimuth. Table 1. Simulation parameters of the spaceborne SAR. Parameter
Value
Carrier frequency Bandwidth Sample frequency Velocity PRF Center line distance
9.63 GHz 50 MHz 60 MHz 7391 m/s 2738 Hz 617 km
The imaging results with the standard full-aperture CSA and the sub-aperture CS-dechirp algorithm are shown in Figure 6. To show the process of sub-aperture data imaging and coherent sub-aperture stitching, the focusing results and corresponding azimuth spectrums of the point target in the red rectangle of Figure 6b are shown in Figures 7 and 8. Figures 7 and 8 show the change in focusing results and azimuth spectrums as the sub-aperture images are combined. In this simulation, the length of the sub-aperture is one-fifth of the full-aperture length. The focusing results of 1–5 sub-apertures are presented in Figure 7a–e. From Figure 7, one can note that the resolution of the point target is gradually improved as the sub-aperture synthesis amount increases. Figure 8a–e, corresponding to Figure 7a–e, show the change in the azimuth frequency spectrum with sub-aperture combination. From Figure 8a–e, the bandwidths of the azimuth frequency spectrum are gradually increased as the sub-aperture synthesis amount increases. From Figures 7 and 8, it can be seen that the sub-aperture image combination in our method is equivalent to the coherent combination of the azimuth spectrum.
in the red rectangle of Figure 6b are shown in Figures 7 and 8. Figures 7 and 8 show the change in in the red rectangle of Figure 6b are shown in Figures 7 and 8. Figures 7 and 8 show the change in focusing results and azimuth spectrums as the sub-aperture images are combined. In this simulation, focusing azimuth spectrums combined. this simulation, the lengthresults of theand sub-aperture is one-fifthasofthe thesub-aperture full-apertureimages length.are The focusing In results of 1–5 subthe length of the sub-aperture is one-fifth of the full-aperture length. The focusing results ofthe 1–5point subapertures are presented in Figure 7a–e. From Figure 7, one can note that the resolution of apertures are presented in Figure 7a–e. From Figure 7, one can note that the resolution of the point target is gradually improved as the sub-aperture synthesis amount increases. target is gradually improved as the sub-aperture synthesis amount increases.
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(a) (a)
(b) (b)
Figure 6. Imaging results of point targets: (a) standard full-aperture chirp scaling algorithm (CSA); Figure 6. Imaging results of point targets: (a) standard full-aperture chirp scaling algorithm (CSA);
chirpof scaling Figure(b) 6. sub-aperture Imaging results point(CS)-dechirp targets: (a)algorithm. standard full-aperture chirp scaling algorithm (CSA); (b) sub-aperture chirp scaling (CS)-dechirp algorithm. (b) sub-aperture chirp scaling (CS)-dechirp algorithm.
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(e) Figure 7. Imaging results after sub-aperture synthesis. (a) With one sub-aperture datum; (b) With two
Figure 7. Imaging results after sub-aperture synthesis. (a) With one sub-aperture datum; (b) With two sub-aperture data; (c) With three sub-aperture data; (d) With four sub-aperture data; (e) With five sub-aperture data; (c) With three sub-aperture data; (d) With four sub-aperture data; (e) With five sub-aperture data. sub-aperture data. Figure 8a–e, corresponding to Figure 7a–e, show the change in the azimuth frequency spectrum with sub-aperture combination. From Figure 8a–e, the bandwidths of the azimuth frequency spectrum are gradually increased as the sub-aperture synthesis amount increases. From Figures 7 and 8, it can be seen that the sub-aperture image combination in our method is equivalent to the coherent combination of the azimuth spectrum.
Figure 8a–e, corresponding to Figure 7a–e, show the change in the azimuth frequency spectrum with sub-aperture combination. From Figure 8a–e, the bandwidths of the azimuth frequency spectrum are gradually increased as the sub-aperture synthesis amount increases. From Figures 7 and 8, it can be seen that the sub-aperture image combination in our method is equivalent to the coherent combination of the azimuth spectrum. Sensors 2018, 18, 2562 10 of 15
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(e) Figure8.8. Frequency Frequency spectrum spectrum of synthesis. (a) (a) With oneone subFigure of the theazimuth azimuthsignal signalafter aftersub-aperture sub-aperture synthesis. With aperture datum; (b) With two sub-aperture data; (c) With three sub-aperture data; (d) With four subsub-aperture datum; (b) With two sub-aperture data; (c) With three sub-aperture data; (d) With four aperture data; (e) With five sub-aperture data. sub-aperture data; (e) With five sub-aperture data.
The contours and azimuth profiles of the point targets marked by the red box in Figure 6a,b is The contours and azimuth profiles of the point targets marked by the red box in Figure 6a,b is show show in Figure 9. From Figure 9, the focusing result processed by the sub-aperture CS-dechirp in Figure 9. From Figure 9, the focusing result processed by the sub-aperture CS-dechirp algorithm algorithm is consistent with the standard CSA, which proves that the proposed real-time imaging is consistent with the standard CSA, which proves that the proposed real-time imaging algorithm in algorithm in this paper is feasible. Figure 10 shows the phase of the point target processed by the subthis paper is feasible. Figure 10 shows the phase of the point target processed by the sub-aperture aperture CS-dechirp algorithm in the range and azimuth, indicating the good coherence of the subCS-dechirp algorithm in the range and azimuth, indicating the good coherence of the sub-aperture aperture signal. Since the high-order phase is compensated by the sub-aperture CS-dechirp method signal. Since the high-order phase is compensated by the sub-aperture CS-dechirp method and the and the sub-aperture overlapping is avoided, the grating lobes do not appear in our method. In other sub-aperture overlapping is avoided, the grating lobes do not appear in our method. In other words, words, our method has better performance in grating lobe suppression than that in Reference [16]. our method has better performance in grating lobe suppression than that in Reference [16].
algorithm in this paper is feasible. Figure 10 shows the phase of the point target processed by the subaperture CS-dechirp algorithm in the range and azimuth, indicating the good coherence of the subaperture signal. Since the high-order phase is compensated by the sub-aperture CS-dechirp method and the sub-aperture overlapping is avoided, the grating lobes do not appear in our method. In other words, our2562 method has better performance in grating lobe suppression than that in Reference Sensors 2018, 18, 11 of[16]. 15
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Figure 9. Results of the standard full-aperture CSA and the proposed method: (a) standard CSA; (b) proposed (c) azimuth profiles based onCSA the standard CSA; (d) method: azimuth (a) profiles based on the Figure 9. method; Results standard full-aperture andthe theproposed proposed standard CSA; Figure 9. Results of of thethe standard full-aperture CSA and method: (a) standard CSA; (b) proposed method. proposed method; method; (c) (c) azimuth azimuth profiles based on (b) proposed profiles based on the the standard standard CSA; CSA; (d) (d) azimuth azimuth profiles profiles based based on on the proposed method. the proposed method.
Figure Phase of the point target processed proposed algorithm: phase in range; phase Figure 10.10. Phase of the point target processed by by thethe proposed algorithm: (a) (a) phase in range; (b)(b) phase in azimuth. Figure 10. Phase of the point target processed by the proposed algorithm: (a) phase in range; (b) phase in azimuth. in azimuth.
4.2. GF3-SAR Data Results 4.2. GF3-SAR Data Results 4.2. GF3-SAR Data Results The parameters of the GF3-SAR with stripmap mode are shown in Table 2. The imaging result The parameters of the GF3-SAR with stripmap mode are shown in Table 2. The imaging result based on the standardoffull-aperture CSA is stripmap shown inmode Figureare 11a and that based2.on theimaging sub-aperture the GF3-SAR shown Table The result based onThe theparameters standard full-aperture CSAwith is shown in Figure 11a and thatin based on the sub-aperture CS-dechirp algorithm isfull-aperture shown in Figure 11b. By enlarging the11a area marked by theon red box in Figures based on the standard CSA is shown in Figure and that based the sub-aperture CS-dechirp algorithm is shown in Figure 11b. By enlarging the area marked by the red box in Figures 11a and 12b,algorithm detailed images arein shown in11b. Figures 12–14. From onebox canin note that CS-dechirp is shown Figure By enlarging the the areadetailed markedimages, by the red Figures 11a and 12b, detailed images are shown in Figures 12–14. From the detailed images, one can note the result processed the sub-aperture algorithm is consistent with the standard 12b, detailedby images shown inCS-dechirp Figures 12–14. From the images, notefullthat that11a theand result processed by the are sub-aperture CS-dechirp algorithm isdetailed consistent withone thecan standard aperture the resultCSA. processed by the sub-aperture CS-dechirp algorithm is consistent with the standard fullfull-aperture CSA. aperture CSA. Table 2. Parameters of the GF3-SAR in stripmap mode. Table 2. Parameters of the GF3-SAR in stripmap mode. Parameter Value Parameter Value Bandwidth 100 MHz Sample frequency 133 Bandwidth 100 MHz MHz
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Table 2. Parameters of the GF3-SAR in stripmap mode. Parameter
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Bandwidth Sample frequency Wavelength Velocity PRF Center line distance Sensors 2018, 18, x FOR PEER REVIEW
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100 MHz 133 MHz 0.055 m 7132 m/s 2580 Hz 842 km
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(b)(b) Figure 11. Imaging results of the GF3-SAR stripmap data (from top to bottom range, is range, and from left Figure Figure 11. 11. Imaging Imaging results results of of the the GF3-SAR GF3-SAR stripmap stripmap data data (from (from top top to to bottom bottom is is range, and and from from left left to right is azimuth): (a) standard full-aperture CSA; (b) proposed algorithm. to proposed algorithm. to right right is is azimuth): azimuth): (a) (a) standard standard full-aperture full-aperture CSA; CSA; (b) (b) proposed algorithm.
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Figure Results of area (from bottom range, and from left right azimuth): 12. Results ofofarea A (from toptop totop bottom is range, and from left to right is to azimuth): (a) standard Figure 12.12. Results area AA (from to to bottom is is range, and from left to right is is azimuth): (a)(a) standard full-aperture CSA; (b) proposed algorithm. full-aperture CSA; (b) proposed algorithm.algorithm. standard full-aperture CSA; (b) proposed
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Figure 13. Results area B top to is and from left right (a) Figure 13. Results Resultsofof ofarea area B (from (from to bottom bottom is range, range, andleft from left to to right is is azimuth): azimuth): (a) Figure 13. B (from toptop to bottom is range, and from to right is azimuth): (a) standard standard full-aperture CSA; (b) proposed algorithm. standard full-aperture CSA; (b) proposed algorithm. full-aperture CSA; (b) proposed algorithm.
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Figure 14. Results area C to is and from left right (a) C (from toptop to bottom is range, and from to right is azimuth): (a) standard Figure 14. 14. Results Resultsofof ofarea area C (from (from top to bottom bottom is range, range, andleft from left to to right is is azimuth): azimuth): (a) standard full-aperture CSA; (b) proposed algorithm. full-aperture CSA; (b) proposed algorithm.algorithm. standard full-aperture CSA; (b) proposed
4.3. 4.3. Computational Computational Load Load Analysis Analysis Assuming final image pixels, where range and N N a where Nr and the rangethe and azimuth a represent N×rr NaN Npixels, Assuming the the final finalimage imageisis isofof ofNrN where and represent the range and NrrNand Naa represent a pixels, azimuth points, respectively, the computational complexities of the standard full-aperture CSA and points, respectively, the computational complexities of the standard full-aperture CSA and the proposed azimuth points, respectively, the computational complexities of the standard full-aperture CSA and the proposed method are analyzed as follows. as method are analyzed operations canoperations be derivedcan as be 5Nderived Na log2 N rderived the proposed method as arefollows. analyzedThe as floating-point follows. The The floating-point floating-point operations can be asr for FFT in range and 5N N log N for FFT in azimuth. The complex multiplication needs 6N N r a r r a 55N N log N 5 N N log N 2 and Nrr Naa log22 Nrr for for FFT FFT in in range range and 5Nrr Naa log22 Nrr for for FFT FFT in in azimuth. azimuth. The The complex complex operations [19]. multiplication needs [19]. rr N 6N Nfull-aperture Naa operations For the standard CSA, the processing system processes all recorded data. multiplication needs 6 operations [19]. For the standard full-aperture CSA, the processing system recorded The The For standard full-aperture CSA contains four FFTs and threeprocesses complex all multiplications. the standard full-aperture CSA, the processing system processes all recorded data. data.Then, The standard full-aperture CSA contains four FFTs and three complex multiplications. Then, its computational complexity can be achieved by: standard full-aperture CSA contains four FFTs and three complex multiplications. Then, its its computational computational complexity complexity can can be be achieved achieved by: by: Scsa = 10Nr Na log2 Nr + 10Nr Na log2 Na + 18Nr Na (20) S 10 N N log N +10 N N log N 18 N N (20) r a r r a a r a 2 2 Scsa 10 N N log N +10 N N log N 18 N N (20) csa r a r a r a 2 r 2 a For the proposed method, the processing system processes data from one sub-aperture each time. For method, the processing system processes data one each For the the proposed proposed method,five theFFTs processing data from from one sub-aperture sub-aperture each The proposed method contains and five system complexprocesses multiplications. Assuming the sub-aperture time. The proposed method contains five FFTs and five complex multiplications. Assuming the subtime. Theinproposed method contains five FFTs and five points complex Assuming theThen, subnumber the azimuth is N, the number of azimuth of multiplications. sub-aperture data is Na /N. N aperture number in the azimuth is , the number of azimuth points of sub-aperture data is N / a N aperture number in the azimuth is , the number of azimuth points of sub-aperture data is N /N N a the computational complexity for one sub-aperture data can be achieved by: .. Then, the computational complexity for one sub-aperture data can be achieved by: Then, the computational complexity for one sub-aperture data can be achieved by:
Ssub
= 10Nr NNa log2 Nr + 15Nr NNa log2 Na /N + 30Nr NNa 15 30 15 = 10 N Nr Na log2 Nr + N Nr Na log2 Na + N Nr Na − N Nr Na log2 N
(21)
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Thus, the computational complexity of the proposed method is: S pro
= N ·Ssub = 10Nr Na log2 Nr + 15Nr Na log2 Na + 30Nr Na − 15Nr Na log2 N
(22)
The magnitudes of Scsa and S pro are similar, so the computational load of the proposed method is almost the same as that of the standard full-aperture CSA. However, the proposed method can perform imaging processing while recording data; therefore, the proposed method based on the pipeline structure has a relatively high computational efficiency. 5. Conclusions The GF3-SAR real-time imaging algorithm based on sub-aperture CS-dechirp can perform imaging processing while recording data, which reduces the amount of data storage and computational load for the GF3-SAR system and has good real-time performance. In order to illustrate the effectiveness of the algorithm proposed in this paper, the imaging results of point targets simulation and GF3-SAR real data, which are separately processed, are used for comparative analysis. The algorithm based on sub-aperture CS-dechirp is very suitable for the real-time imaging processing of the GF3-SAR. Author Contributions: All authors contributed extensively to the study presented in this manuscript. Conceptualization and formal analysis, G.-C.S.; Writing-Original Draft Preparation, Writing-Review & Editing, Y.L.; Investigation, J.Y.; Resources, L.G.; Supervision and validation, M.X. and S.W. Funding: This work was supported by the National Key R&D Program of China under grant 2017YFC1405600 and the Fundamental Research Funds for the Central Universities under grant JB180213. Conflicts of Interest: The authors declare no conflict of interest.
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