Ground Moving Target Detection and Imaging Using a ... - IEEE Xplore

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 54, NO. 9, SEPTEMBER 2016

Ground Moving Target Detection and Imaging Using a Virtual Multichannel Scheme in HRWS Mode Li-Bao Wang, Dang-Wei Wang, Jing-Jing Li, Jia Xu, Senior Member, IEEE, Chao Xie, and Ling Wang

Abstract—Along-track multichannel synthetic aperture radar is usually used to achieve ground moving target detection and imaging. Nevertheless, there is a design dilemma between azimuth high resolution and wide swath (HRWS). To solve this problem in HRWS mode, we introduce a virtual multichannel (VMC) scheme. For each virtual channel, the low real pulse repetition frequency (PRF) improves the ability of resolving range ambiguity for wide-swath, and the high virtual PRF improves the capability of resolving Doppler ambiguity for azimuth high resolution. For multiple virtual channels, strong ground clutter is eliminated by the joint VMC processing. Furthermore, a detailed signal model of a moving target in the virtual channel is given, and the special false-peak effect in the azimuthal image is analyzed. Moreover, we propose a novel ground moving target processing method based on the VMC scheme and the clutter suppression interferometry (CSI) technique, which is called VMC-CSI. The integration of detection, location, velocity estimation, and imaging for ground moving targets can be achieved. Accounting for the unresolved main peak and false peak for a moving target, in the VMC-CSI method, we adopt a two-step scheme to estimate the radial velocity and along-track velocity, namely, rough estimation and precise estimation. Meanwhile, considering the same interferometric phases of the main peak and the false peak, we use false peaks first for the robustness of initial azimuth location estimation and remove false peaks afterward. Numerical simulations are provided for testing the effect of the false peak and the effectiveness of VMC-CSI. Index Terms—Ground moving target, high resolution and wide swath (HRWS), multichannel synthetic aperture radar (SAR), SAR, virtual channel.

I. I NTRODUCTION

S

YNTHETIC aperture radar (SAR) systems, as a type of all-time and all-weather microwave imaging radar, have undergone rapid development in the past decades and are widely used in disaster monitoring, topographic mapping, oceanographic research, military surveillance, and so on [1]–[3]. However, the traditional single-channel SAR system usually has limited performance due to the constraint of the radar system and limited degrees of freedom (DOFs). To

Manuscript received April 15, 2015; revised December 28, 2015; accepted February 3, 2016. Date of publication May 26, 2016; date of current version August 2, 2016. This work was supported by the National Natural Science Foundation of China under Grant 61201451 and Grant 61179015. L.-B. Wang, D.-W. Wang, J.-J. Li, and C. Xie are with Wuhan Radar Academy, Wuhan 430019, China (e-mail: [email protected]). J. Xu is with Beijing Institute of Technology, Beijing 100081, China (e-mail: [email protected]). L. Wang is with National University of Defense Technology, Changsha 430010, China. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2016.2544846

improve the performance of the traditional single-channel SAR, some innovative ideas have been proposed [4]–[7]. For example, the spotlight SAR can allow for an improved azimuthal resolution, but at the price of noncontiguous imaging and narrow swath [4], [5]. The scan-SAR can achieve wide swath, but it has to change the radar footprint and is at the cost of an impaired azimuthal resolution [6], [7]. Ground moving target detection and imaging is a main demand of the SAR system [8]–[14]. To detect a moving target, the strong ground clutter must be suppressed first. For a singlechannel SAR, dealing with a moving target, it lacks spatial domain (element) information, and the resource that can be exploited is only the temporal domain (pulse) information. Hence, a single-channel SAR mainly uses the Doppler centroid and the Doppler rate to differentiate between clutter and a moving target [15]–[18]. However, the movement of the platform results in clutter spectrum spreading, which usually makes the Doppler frequency of the slowly moving target submerge in the clutter spectrum, and hence, it is difficult to detect the target. In contrast, the multichannel SAR provides the spatial information, which can be used to achieve better performance [19]–[25]. For instance, the along-track multichannel SAR can exploit the united spatial element processing to suppress strong clutter [24], and hence, it enhances the signal-to-clutter ratio (SCR) for a moving target, particularly for the detection or imaging of a ground moving target. Meanwhile, the multichannel SAR can also be designed for the purpose of high-resolution and wideswath (HRWS) imaging for static scenes [25]. Although the along-track multichannel SAR provides superior performance in clutter suppression over the single-channel SAR, the former generally uses a single transmitting waveform. The sole manner to improve the system DOF is to increase the receiving elements. For the spaceborne or airborne systems, increasing the receiving elements is difficult due to limited physical space. To obtain high system DOFs, the multiple-input multiple-output (MIMO)-SAR concept has been proposed to improve SAR capability by exploiting waveform diversity [26]–[30], which integrates the advantage of both the SAR system and the MIMO radar system [31], [32]. In summary, the traditional multichannel SAR mainly focuses on either HRWS imaging for a static scene or detection and imaging for a moving target. More specifically, although the along-track multichannel SAR designed for ground moving target probing, e.g., the spaceborne RADARSAT-2 orbital system [33]–[35], can improve clutter suppression performance significantly, its demand on the radar pulse repetition frequency (PRF) in each channel is still no less than the single-channel SAR system. Hence, it is difficult to ensure

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WANG et al.: GROUND MOVING TARGET DETECTION AND IMAGING USING A VMC SCHEME IN HRWS MODE

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wide-swath observation at the same time. In contrast, although an along-track multiple-phase center (MPC)-SAR can be designed for HRWS imaging [36], [37], only a virtual channel is reconstructed by using multiple physical elements in essence. Thus, the performance of ground moving target detection is still limited by the single-channel SAR. To realize ground moving target detection and imaging and static-scene imaging simultaneously in HRWS mode, the existing multichannel SAR or advanced MIMO-SAR system can be used to reconstruct a virtual multichannel (VMC) scheme. For this purpose, we have proposed a simplified signal model of a moving target in MIMO-SAR [38]. Noticeably, special false peaks in the azimuthal image are observed, which are caused by the radial velocity of the moving target. However, the influence of along-track velocity and initial azimuth location of the moving target is not considered, and the detailed falsepeak trait and parameter estimation of the moving target is also not taken into account. In this paper, we give a signal model of virtual channels in more detail. It is shown that the falsepeak effect is not only caused by the radial velocity of the moving target but also influenced by the along-track velocity and initial azimuth location of the moving target. Furthermore, we propose a moving target processing method based on the VMC scheme and the clutter suppression interferometry (CSI) technique, which is referred to as VMC-CSI. The integration of detection, location, velocity estimation, and imaging for a ground moving target can be achieved in HRWS mode. The remainder of this paper is organized as follows. In Section II, we first introduce the concept of VMC and then give the signal model and the azimuthal image of a moving target. In Section III, we propose a moving target processing method of VMC-CSI. The integration solution of detection, location, velocity estimation, and imaging for the moving target is presented. In Section IV, several numerical examples are presented. Finally, conclusions are summarized in Section V. II. S IGNAL M ODEL AND A ZIMUTHAL I MAGE A. Concept of VMC Fig. 1(a) shows an along-track three-element SAR array, used for ground moving target indication (GMTI), where PRF denotes the real PRF of the SAR system. The middle element indicates a multiplexing element used for transmitting and receiving. In a T/R snapshot, three spatial samples are formed, in which the numbering of “11,” “12,” and “13” denote round-trip signification from the first transmitting element to the first receiving element, the second receiving element, and the third receiving element, respectively. Note that the location of the spatial sample can be approximately taken as an equivalent phase center that is positioned midway between the separate transmitting and receiving elements [27], [39], and it is defined as the location of the virtual element. Hence, we can obtain three data channels in multiple T/R snapshots. Fig. 1(b) shows an MPC-SAR array for the purpose of HRWS static-scene imaging. Similarly, in a T/R snapshot, it receives three spatial samples. However, they are jointly processed, and a virtual channel is reconstructed for the MPC-SAR system. To simultaneously achieve GMTI and static-scene imaging in

Fig. 1. Schematic of data channel reconstruction. (a) Multichannel SAR for GMTI. (b) MPC-SAR for HRWS static-scene imaging. (c) VMC scheme for GMTI and static-scene imaging in HRWS mode.

HRWS mode, VMC can be divided in a manner shown in Fig. 1(c). The numbering of “21,” “22,” and “23” denotes round-trip signification from the second transmitting element to the first receiving element, the second receiving element, and the third receiving element, respectively. The low real PRF ensures no range ambiguity in wide swath. Moreover, in each virtual channel, temporal sampling is replaced with spatial

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Suppose there are L assigned spatial samples in a virtual channel in a T/R snapshot, with L = 3 in Fig. 2(b). It follows that nm = ns − mod(ns , L), with mod(·) denoting the modulus operation. After range migration correction, the moving target locates in the same range bin of multiple T/R snapshots. Hence, the received signal in slow time in each virtual channel can be expressed as ns xi (ns ) = σm rect exp (−j4πRi (ns T )/λ) (1) Nm where i is the index of the virtual channel, σm is the backscattering coefficient of the moving target, rect(ns /Nm ) = 1 is the rectangular window with a width of Nm , Nm = Tm · PRFe is the number of spatial samples in the processed synthetic aperture time Tm , PRFe = L · PRF denotes virtual PRF, λ is the radar wavelength, Ri (ns T ) denotes the slant range from the virtual element to the moving target in the ns th slow time of the ith virtual channel, and the virtual pulse repetition interval is T = 1/PRFe . In the ns th slow time, the coordinate of three virtual elements is (va (ns + (i − 1)L)T, 0), i = 1, 2, 3, and the coordinate of the moving target in the azimuth-range plane is (x0 + vx nm T, Rc + vr nm T ). Moreover, the slant range Ri (ns T ) can be expressed as Fig. 2. Radar geometry in the azimuth-range plane. (a) Radar geometry for a physical channel. (b) Radar geometry for a virtual channel.

sampling, and this overcomes the contradiction between wide swath and high azimuthal resolution. In addition, the united processing among the VMCs can realize detection and imaging for the ground moving target in HRWS mode. It is noticed that although a MIMO-SAR array in Fig. 1(c) is used to illustrate the VMC concept, the VMC can also be reconstructed by the existing along-track multichannel SAR array at the price of more receiving elements. B. Signal Model of the Moving Target Fig. 2 shows the radar geometry in the azimuth-range plane for a single physical channel in a multichannel SAR system and a single virtual channel in the VMC scheme. vr and vx stand for the radial velocity and along-track velocity of the moving target, respectively. The initial location of the moving target is (x0 , Rc ), where x0 is the initial location of the moving target when ns = 0, and Rc is the vertical slant range between the moving target and the platform. ns and nm denote the indexes for the azimuthal spatial sample and slow time of the ground moving target, respectively. Remarkably, the locations of the spatial sample and the moving target change in different times in Fig. 2(a), where nm and ns are identical to each other. However, nm and ns are not identical in the virtual channel shown in Fig. 2(b). The reason is that the locations of the spatial samples in each T/R snapshot in the virtual channel are different, but the location of the moving target is not altered. The location of the moving target will change in different T/R snapshots.

Ri (ns T ) = (x0 +vx nm T −va (ns +(i−1)L) T )2 +(Rc +vr nm T )2. (2) Applying a second-order Taylor series expansion to (2), one can obtain (x0 −(i−1)Dc +(vx − va )ns T )2 Ri (ns T ) ≈ Rc + vr ns T + 2Rc x0 vx va vx ns T − vr + − mod(ns , L)T (3) Rc Rc where Dc = va LT , and it is also denoted by Dc = L · va /PRFe . Substituting (3) into (1), the slow-time signal xi (ns ) for the ith virtual channel is written as xi (ns ) = σm exp(jΦ)xc (ns )xe (ns )

(4)

where

4π Rc + (x0 − (i − 1)Dc )2 /(2Rc ) (5) λ ns (6) xc (ns ) = rect exp j2πfD ns T + jπkm T 2 n2s Nm 4π x0 vx va vx ns T xe (ns ) = exp j − ·mod(ns , L)·T . vr + λ Rc Rc (7) Φ= −

Note that the constant term σm exp(jΦ) in (4) has been ignored. Equation (6) is a chirp signal model for a moving target in a traditional single-channel SAR or one channel in a multichannel SAR, fD = −2vr /λ + 2(x0 − (i − 1)Dc (va − vx ))/(λRc ) is the Doppler centroid, where the first term of fD


is the Doppler caused by the radial velocity, and the second term of fD is the Doppler introduced by the virtual-element azimuth location and is usually small, and km = −2(va − vx )2 /(λRc ) is the Doppler rate of the moving target. In contrast, (7) is the periodic azimuthal modulated signal, which, for convenience, is referred to as the error signal, and it is affected by the radial velocity vr , along-track velocity vx , and the initial azimuth location x0 of the moving target. C. Azimuthal Image of the Moving Target Denote the slow time of the moving target in the ith virtual channel by xi (ns ) or, simply, x(ns ) for short. Denote the Fourier transformation (FT) of x(ns ), xc (ns ), and xe (ns ) by X(f ), Xc (f ), and Xe (f ), respectively. It is known from (7) that the phase factor mod(ns , L) · T has the periodicity property. Hence, xe (ns ) can be approximately expressed as xe (ns ) ≈ xe (ns ) ⊗ δ(ns − rL) (8) r∈Z

where ⊗ denotes the convolution operator, δ(·) is the delta function, Z denotes an integer, and xe (ns ) is the slow-time signal in a T/R snapshot, given by n 4π x0 vx s xe (ns ) = rect exp j ·l·T (9) vr + L λ Rc where l = mod(ns , L) = [0, 1, . . . , L − 1].

Performing the FT to the second term r∈Z δ(ns − rL) in (8) leads to PRFe PRFe Υ(f ) = δ f −k . (10) L L k∈Z

If we define fk = kPRFe /L and then perform the FT to (8), then we have Xe (f ) =

PRFe Xe (fk )δ(f − fk ) L

(11)

k∈Z

where Xe (fk ) = Xe (f )|f =fk denotes the discrete sampling of Xe (f ), which, in turn, is the FT of xe (ns ). It follows that Xe (fk )

2π x0 vx π = exp j T − k (L − 1) vr + λ Rc L x0 vx sin 2π v T L − πk + r λ Rc . (12) · x0 vx 2π π sin λ vr + Rc T − L k

According to the convolution theorem, X(f ) can be written as X(f ) = σm exp(jΦ)

PRFe Xe (fk )Xc (f − fk ). L

(13)

k∈Z

In fact, there exists a large time–bandwidth product for a SAR Doppler signal, i.e., D = Tm Bm 1, and thus, Xc (f )

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can be expressed as 1 Xc (f ) = √ rect km

f − fD Bm

(f − fD )2 exp jπ (14) km

where Bm = km Tm is the Doppler bandwidth in the processed synthetic aperture time Tm . Note that the constant term σm exp(jΦ)PRFe /L in (13) has been dropped for simplicity. Taking (14) into (13), (13) is further expressed as 1 f − fD − fk X(f ) = √ Xe (fk )rect Bm km k∈Z (f −fD )2 fk × exp jπ f · exp −j2π km km fk2 + 2fD fk × exp jπ . (15) km Assuming a normalized matched filter H(f ) is used to compare an azimuthal image with √ a conventional SAR image, i.e., H(f ) = αXc∗ (f ), where α = km is a normalized coefficient, and (·)∗ denotes a conjugate operator, then multiplying (15) by H(f ) leads to Y (f ) = H(f )X(f ) f − fD 1 = √ Xe (0)rect Bm km f − fD 1 √ + Xe (fk )rect Bm km k∈Z k=0 f − fD − fk × rect Bm fk · exp −j2π f km fk2 + 2fD fk × exp jπ . km

(16)

In (16), rect((f − fD )/Bm )rect((f − fD − fk )/Bm ) = rect((f −fD −fk /2)/(Bm −|fk |)) is fulfilled when |fk | ≤ Bm . Then, taking the inverse FT to (16) corresponding to azimuthal pulse compression results in √ y(ns ) = DXe (0)sinc(Bm ns T ) exp(−j2πfD ns T ) 1 +√ Xe (fk ) (Bm − |fk |) km k∈Z k=0 fk × sinc (Bm − |fk |) ns T − k m fk · exp −j2π fD + ns T 2 f 2 + 2fD fk × exp jπ k (17) km where sinc(ν) = sin(πν)/πν, and |ν| denotes the absolute of ν. Note that the first term in (17) occurs as a result of the main peak in the traditional azimuthal image for the moving target, whereas the latter term in (17) occurs as a result of false peaks.

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Fig. 3. Block diagram for the VMC-CSI method of a moving target.

From (17), three traits of the main peak and the false peak are as follows. 1) Peak interval: When the traditional matched filter for xc (ns ) is used, the main peak of the moving target occurs at tk = 0, k = 0, whereas the false peaks occur at tk = fk /km , where |k| ≤ floor(L/um ) and k ∈ Z ∩ k = 0, with the sign floor() as the floor integer rounding function. Hence, the interval of adjacent peaks is PRFe /(km L) = μm Tm /L, where μm is the oversampling factor of PRFe /Bm . 2) Peak number: In the total azimuthal pulse compression interval 2Tm , the peak number is floor(2L/um), including one main peak and floor(2L/um ) − 1 false peaks, since the peak interval is μm Tm /L. 3) Peak amplitude: The maximum amplitude of the main peak A0 and the of the kth false peak Ak √ maximum amplitude √ are A0 = D|Xc (0)| = D| sin((2π/λ)(vr + (x√ 0 vx /Rc )) T L)/sin((2π/λ)(vr + (x0 vx /Rc ))T )| and Ak = D|1 − | k|(μm /L)| · | sin((2π/λ)(vr + (x0 vx /Rc ))T L − πk)/ sin((2π/λ)(vr +(x0 vx /Rc ))T −(π/L)k)|, respectively. Hence, the amplitude ratio Ak /A0 in decibels (dB) is ηk = 20 log Ak /A0 , where |k| ≤ floor(L/um ) and k ∈ Z ∩ k = 0.

III. VMC-CSI M ETHOD FOR G ROUND M OVING TARGET A. Flowchart of Ground Moving Target Processing Fig. 3 gives the block diagram for ground moving target detection, parameter estimation, and imaging by the proposed VMC-CSI method. First, the three virtual channels are generated as shown in Fig. 1(c). Then, the strong ground clutter is suppressed by the displaced phase center antenna (DPCA) technique. Second, the interferometric phase information of the two cancelation channels after clutter suppression is extracted and used to estimate the initial location of the moving target. In theory, the real main peak and the false peaks have the same interferometric phase. Therefore, the mean of multiple interferometric phases can be used to improve the location precision. Third, Doppler centroids corresponding to the real main peak and false peaks are taken as candidates to be tested. Together with the initial location information, a set of radial velocity is obtained. Then, the phase error compensation function is constructed. The image entropy or image contrast is taken as the criterion, and the 2-D real velocity is united estimated. Finally, the multiple estimated parameters of the target are used to compensate for the error signal and construct the azimuthal matched filter of the moving target. Eventually, this accomplishes the focused image.


B. Clutter Suppression and Azimuthal FT The slow-time signal xi (ns ) in the range bin of interest is used for analysis. The slow-time signal in virtual channel 1, which is denoted as x1 (ns ), and the shifted slow-time signal in virtual channel 2, which is denoted as x2 (ns − L), are ns 4π x1 (ns ) = σm rect (18) exp −j R1 (ns T ) Nm λ ns − L 4π exp −j R2 (ns T −LT ) x2 (ns −L) = σm rect λ Nm ns 4π ≈ σm rect exp −j R1 (ns T ) λ Nm 4π × exp j vr LT (19) λ respectively. The signal after clutter cancelation by the DPCA becomes x12 (ns ) = x1 (ns ) − x2 (ns − L) ns 4π = σm rect exp −j R1 (ns T ) Nm λ 4π × 1 − exp j vr LT . (20) λ Similarly, the signal in virtual channels 2 and 3, after clutter cancelation, is x23 (ns ) = x2 (ns ) − x3 (ns − L) ns 4π exp −j R2 (ns T ) = σm rect Nm λ 4π × 1 − exp j vr LT . (21) λ It follows from (3) that R2 (ns T ) ≈ R1 (ns T ) +

Dc2 Dc (x0 + (vx − va )ns T ) − . 2Rc Rc (22)

Hence, x23 (ns ) can be recast as ns 4π x23 (ns ) = σm rect exp −j R1 (ns T ) Nm λ 4π × 1 − exp j vr LT λ 2 4π Dc Dc (x0 +(vx −va )ns T ) × exp −j − . λ 2Rc Rc (23) Then, multiplying x23 (ns ) with c1 (ns ) can eliminate the deviation of the Doppler shift, which is caused by the virtual channel interval. The reference function is 4π Dc va ns T · c1 (ns ) = exp j . (24) λ Rc For a slowly ground moving target, vx va , particularly in the spaceborne SAR. Thus, multiplying x23 (ns ) with c1 (ns )

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results in x23 (ns ) = c1 (ns ) · x23 (ns ) ns 4π = σm rect exp −j R1 (ns T ) Nm λ 2 4π Dc x0 Dc · exp −j − λ 2Rc Rc 4π × 1 − exp j vr LT . (25) λ Taking R1 (ns T ) into (20) and (25) yields ns 4π x12 (ns ) = σm rect xe (ns ) 1 − exp j vr LT Nm λ 2 4π x x0 va · exp −j ns T Rc + 0 + vr − λ 2Rc Rc 2 va − 2va vx 2 + (ns T ) 2Rc (26) ns 4π x23 (ns ) = σm rect xe (ns ) · 1 − exp j vr LT Nm λ 2 4π Dc x0 Dc × exp −j − λ 2Rc Rc 2 4π x0 x0 va ns T · exp −j + vr − Rc + λ 2Rc Rc 2 va − 2va vx + (ns T )2 . 2Rc (27) Consequently, multiplying x12 (ns ) and x23 (ns ) with the reference function, i.e., 2π (va ns T )2 · c2 (ns ) = exp j (28) λ Rc can cancel the linear frequency modulation (LFM) term, which is caused by the movement of the platform. Note that multiplying x12 (ns ) and x23 (ns ) with the reference function c2 (ns ) results in two signals, given by x ˆ12 (ns ) = c2 (ns ) · x12 (ns ) (29) x ˆ23 (ns ) = c2 (ns ) · x23 (ns ). Performing the FT to the signal in (29) leads to 4π x20 ˆ X12 (f ) = σm exp −j Rc + λ 2Rc 4π · 1− exp j vr LT · (Xe (f ) ⊗ I(f )) (30) λ 4π x20 Dc2 x0 Dc ˆ X23 (f ) = σm exp −j + − Rc + λ 2Rc 2Rc Rc 4π · 1− exp j vr LT · (Xe (f ) ⊗ I(f )) (31) λ

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⎧ 1 ⎪ 2 2 2 ⎪ √Tm (c(v ) + c(v )) + (s(v ) + s(v )) ⎪ 1 2 1 2 ⎨ 2D I(f ) = · exp −j π (f − f )2 + j arctan s(v1 )+s(v2 ) , |f − f | ≤ D D ⎪ c(v )+c(v ) km 1 2 ⎪ ⎪ ⎩0, |f − f D | >

where I(f ) is defined as in (32), shown at the top of the page, where D = Tm · Δf is the time–bandwidth product for the signal I(t) = rect(ns /Nm ) exp(j2πf D ns T +jπkm T 2 n2s ), Δf is the Doppler bandwidth of I(t), f D = −2vr /λ + 2x0 va /(λRc ), and k m =4va vx /(λRc ). v (32), c(v) = 0 cos((π/2)x2 )dx and s(v) = vIn 2 sin((π/2)x )dx are the Fresnel integrals [40], and v 1 and 0 v2 are given by D Δf 1 + 2(f − f D )/Δf 2 , |f − f D | ≤ 2 (33) v1 = 0, |f − f D | > Δf 2 D Δf 1 − 2(f − f D )/Δf 2 , |f − f D | ≤ 2 v2 = (34) 0, |f − f D | > Δf 2 respectively. When the time–bandwidth product D 1, (32) can be further rewritten as ⎧ ⎨ √1 exp j − π (f −f )2 + π , |f − f | ≤ Δf D D 4 2 km km I(f ) = Δf ⎩0, |f − f | > . D

2

(35) ˆ 12 (f ) and X ˆ 23 (f ) will appear In view of (11) and (35), X as a series of defocused regions in the amplitude image, the frequency interval is PRFe /L Hz, and the number of defocused regions is L. C. Moving Target Detection According to (30) and (31), we know that the scaling factor Xe (f ) ⊗ I(f ) corresponds to the defocused regions of L. In contrast, the scaling factor AΔ = 1 − exp(j4πvr LT /λ) is a key factor of magnitude for the fact that whether the moving target is successfully detected or not. Taking the module of the scaling factor AΔ leads to 2π Dc 4π |AΔ | = 1 − exp j vr LT = 2 sin · · vr . λ λ va (36)

(32)

3) When the radial velocity of the target is vr = (m − 1/2) · λva /(2Dc ), with m being an integer, (36) reaches its maximum value, and the SCR attains the greatest improvement. 4) When (m − 1/2) ·λva /(2Dc ) < vr < m · λva /(2Dc ), the target signal will be partly canceled. 5) With a constraint on the same spatial sample spacing, there is Dc = va T in the conventional multichannel SAR; however, Dc is L times the length va T for the VMC in this paper. The increase of Dc is in favor of detection of a slowly moving target as another advantage, apart from wide-swath surveillance capability for the moving target. The cell-averaging constant false alarm rate (CA-CFAR) detector can be used to detect the target. After the CA-CFAR, the defocused domains with number L are assumed to survive for a moving target. D. Moving Target Location The initial azimuth location x0 for the target needs to be determined by phase interferometry. When the condition k m ≈ 0 is satisfied, the focused Doppler spectrum can be obtained, and then, the interferometric phase is usually computed by subtracting two phases corresponding to the maximum amplitudes of two channels. However, the condition k m ≈ 0 is not usually ensured because of the unknown along-track velocity, then there will exist spreading in the Doppler spectrum with frequency interval f ∈ [f1 , f2 ]. For this case, the phase difference Δφ(l) can be taken as the average mean of interferometric phases in the lth-target defocused domain. Let the phases of the cell, where the target exists within the cancelation channel, ˆ 23 (f ) be φ1 (f ), f ∈ [f1 , f2 ]. Similarly, the phases within X are denoted as φ2 (f ), f ∈ [f1 , f2 ]. Performing interferometry between φ1 (f ) and φ2 (f ) or, equivalently, subtracting φ2 (f ) from φ1 (f ) and performing the average mean result in 4π Dc2 x0 Dc Δφ(l) = − − . (37) λ 2Rc Rc Hence, the initial azimuth location of the target in the lth-target defocused domain can be obtained from (37), i.e.,

The following can be deduced from (36). (l)

1) For a stationary target, there is vr = 0. Hence, (36) is zero. In other words, the stationary target is effectively rejected. 2) When the radial velocity is vr = m · λva /(2Dc ), with m being a nonzero integer, (36) is also equal to zero. That is, the moving target will be canceled. In this case, the radial velocity is taken as the blind velocity, and the target cannot be detected.

Δf 2 Δf 2

x0 =

λRc Δφ(l) Dc + . 2 4πDc

(38)

Since there exist identical interferometry phases in the target defocused domains, the average mean of the estimators for all the initial locations is taken as the final result, i.e., 1 (l) x0 . L L

xˆ0 =

l=1

(39)


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Generally, the f D in the main peak contains the true radial velocity of the moving target. However, the false peaks appear, owing to the error signal, and the main peak may be lower than the false peak. Hence, it is difficult to determinate the area of the main peak by only using the maximum amplitude information. To overcome this problem, we use each Doppler centroid in the area containing a defocused domain as a sample to estimate the radial velocity. Thus, the set of radial velocity to be determined is va xˆ0 λ (1) (2) (L) T ˆr = v − fD , fD , . . . , fD (46) Rc 2 where (·)T denotes the transpose operator. Analogously, the set of along-track velocity to be estimated is T λRc (1) ˆx = Δf , Δf (2) , . . . , Δf (L) . (47) v 4va Tm

Fig. 4. Sketch map of a defocused domain.

E. Moving Target Velocity Measurement There are two steps for the estimation of the 2-D velocity, namely, radial velocity and along-track velocity, of a moving target, which are rough estimation and precise estimation, respectively. 1) Rough Estimation: The radial velocity and the alongtrack velocity can be estimated through Doppler centroid and Doppler bandwidth, respectively. When the LFM term, which is caused by the moving platform, in the echo is removed, the signal is also chirp, its Doppler centroid is determined by the initial location and radial velocity, and the Doppler rate is determined by the along-track velocity. The sketch map of a defocused domain for the Doppler centroid f D and Doppler bandwidth Δf is shown in Fig. 4. The Doppler shift due to the estimator of the initial location of the target is ˆ0 2va x f Dx = (40) λRc and the Doppler shift caused by the radial velocity of the target is 2vr . (41) f Dv = − λ Hence, the Doppler centroid of the moving target in the range bin of interest is f D = f Dx + f Dv . It follows that the radial velocity of the target is va xˆ0 λ vˆr = − fD. Rc 2

(42)

(43)

The estimator of the along-track velocity can be obtained through the Doppler bandwidth Δf , which is given by 4va vx Tm . Δf = |k m |Tm = (44) λRc It follows that vˆx =

λRc Δf . 4va Tm

(45)

The existence of the error signal in the virtual channel leads to the defocused main peak and false peaks for a moving target.

The Doppler bandwidths in the area of different defocused domains are approximately equal. Hence, the mean of (47) can be taken as the rough estimation of the along-track velocity. Note that the Doppler bandwidth does not reflect the sign of the along-track velocity. Therefore, the set of along-track velocity to be estimated is further expressed as T L L 1 λRc 1 λRc (l) (l) ˆx = Δf , − Δf . (48) v L 4va Tm L 4va Tm l=1

l=1

2) Precise Estimation: The precise estimation of the 2-D velocity can be achieved by unified search optimization. The detailed procedure is as follows. ˆx, ˆ r and v Step 1: According to the rough estimators of v ˆr + determine the search intervals Ωr = v ˆ x + Δvx (−Q/2 : Δvr (−Q/2 : Q/2 − 1) and Ωx = v Q/2 − 1), where Δvr and Δvx are the search steps for radial velocity and along-track velocity, respectively, and Q is the number of search steps. Step 2: Using the values in Ωr and Ωx , along with the initial location estimator x ˆ0 , to construct the error signal compensation function and compensate the data in the virtual channel after cancelation. Step 3: Constructing the azimuthal matched filter according to the values in Ωr and Ωx and accomplishing the matched filter between the reference function and the data after error signal compensation. Taking image contrast or image entropy as the evaluation index and the best one corresponding to the final estimator for the 2-D velocity. Step 4: The mean of the optimized search values in the two cancelation channels is taken as the final estimator. F. Moving Target Imaging Adopting an imaging method for a stationary target to a moving target, the location estimation of the moving target will depart from the actual one, and the image will become defocused [13]. Hence, to achieve a successful focused image for a moving target, the key step is using the estimated parameters, obtained according to the steps above, to construct an azimuthal

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reference function, matched to the moving target. Particularly, accounting for the effect of the error signal for the moving target in the virtual channel, it needs to compensate for the error signal before the azimuthal matched filter. IV. N UMERICAL E XAMPLES Use of an airborne SAR system and a spaceborne SAR system is considered in this section, in which different assigned spatial samples in a T/R snapshot, i.e., L, are given for the purpose of validating the false-peak effect. The false peaks, the impact of the parameters on the azimuthal image, the effect of clutter suppression, the parameter estimation, and imaging for the moving target will be demonstrated in sequence in the following. The parameter setting for the airborne multichannel SAR system is given below. The velocity for the platform is va = 120 m/s, the slant range of the center of the swath is Rc = 15000 m, and the operation frequency is fc = 12.5 GHz. The number of the transmitting elements is M = 1, the number of the receiving elements is N = 6, the interelement space is q = 4 m, the number of the reconstructed virtual channels is Nc = 3, the number of the assigned spatial samples in a T/R snapshot is L = 2, the real PRF is PRF = 120 Hz, and the virtual PRF is PRFe = 240 Hz. For the spaceborne MIMO-SAR system, the velocity for the platform is va = 7200 m/s, the slant range of the center of the swath is Rc = 8 × 105 m, and the operation frequency is fc = 10 GHz. Three virtual channel data are constructed, and the array configuration with p = N · q in [41] is adopted, where the interelement spacing of the transmitting element is p = 12 m, the interelement spacing of the receiving element is q = 4 m, the number of the receiving elements is N = 3, the number of the transmitting elements is M = 3, the number of the assigned spatial samples in a T/R snapshot is L = 3, the real PRF is PRF = 1200 Hz, and the virtual PRF is PRFe = 3600 Hz. A simulating scene that includes a static scene and a moving target is designed, and the sketch map of the scene is given in Fig. 5. The triangle and rectangle stand for stationary targets, and the shaded part denotes the farmland, to be used for clutter with certain statistical property. The amplitude of the clutter in the farmland is subject to a Rayleigh distribution with variance σ 2 = 1, and the phase is ruled by a uniform distribution in [−π, π]. A road is also assumed in the static scene. The initial azimuth location of a moving target on the road is x0 . A. False Peaks’ Influence We first investigate the influence of the false peaks on the azimuthal image between the conventional signal model and the novel signal model of a moving target, applying the same matched filter of x∗c (−ns ). For the airborne SAR, the radial velocity of the moving target is set to be vr = 1 m/s, the alongtrack velocity is vx = 3 m/s, and the initial azimuth location is x0 = 13 m. Fig. 6 compares the azimuthal images of a moving target. For the spaceborne SAR, the radial velocity of the target is chosen as vr = 7 m/s, the along-track velocity is vx = 15 m/s, and the initial azimuth location is x0 = 60 m; the azimuthal images are shown in Fig. 7. It is shown in

Fig. 5. Sketch map of the simulating scene.

Fig. 6. Azimuthal image of a moving target in airborne SAR. (a) Azimuthal image for the conventional signal model. (b) Azimuthal image for the novel signal model.

Figs. 6 and 7 that there exist false peaks in the azimuthal images, due to the effect of error signal in the virtual channel. More specifically, three points can be deduced as follows. 1) The peak intervals in Figs. 6 and 7 are 1.505 and 0.279 s, respectively. This coincides with the theoretical results. In fact, according to the results given in Section II-C, the peak interval is μm Tm /L. For the airborne SAR, Tm = 2.4958 s, μm = 1.2, and L = 2, and thus, the peak


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Fig. 7. Azimuthal image of a moving target in spaceborne SAR. (a) Azimuthal image for the conventional signal model. (b) Azimuthal image for the novel signal model.

Fig. 8. MFPVR versus radial velocity. (a) Airborne SAR. (b) Spaceborne SAR.

interval is T1 ≈ 1.497 s. For the spaceborne SAR, Tm = 0.6939 s, μm = 1.2, and L = 3. Hence, the time interval is T2 ≈ 0.278 s. 2) The peak numbers in Figs. 6 and 7 are 3 and 5, respectively. This is the same as the theoretical analysis. According to the theoretical result floor(2L/um ), the peak numbers are floor(2 × 2/1.2) = 3 and floor(2 × 3/1.2) = 5, respectively. 3) The amplitude ratios of the two false peaks to the main peak are −2.8 and −2.9 dB in Fig. 6(b), and the theoretical computation values are η−1 ≈ −2.3 dB and η1 ≈ −2.3 dB. The amplitude ratios of the four false peaks to the main peak are −17.6, −12.3, −7.9, and −22.1 dB in Fig. 7(b), and the theoretical computation values are η−2 ≈ −17.5 dB, η−1 ≈ −12.4 B, η1 ≈ −8.0 dB, and η2 ≈ −22.0 dB. The theoretical and simulation results match well.

1. Influence of the Radial Velocity: To investigate the effect of the radial velocity, we set vx = 0 m/s, x0 = 0 m, vr ∈ [−20, 20]m/s for airborne SAR, and vr ∈ [−60, 60] m/s for spaceborne SAR. For the fixed radial velocity, the maximum value of the false peaks is used to compute the MFPVR. Fig. 8(a) and (b) shows the MFPVR versus the radial velocity. Three facts can be deduced from Fig. 8. First, the two curves of the MFPVR, corresponding to the theoretical result and the simulation result, match pretty well. Second, the MFPVR has the periodicity property. This is because when there only exists radial velocity, the error signal becomes xe (ns ) = exp(j4πvr mod(ns , L)T /λ), which has the periodicity property when vr = m · λ/(2T ), m ∈ Z, where Z is an integer. In particular, the theoretical results for the period of the radial velocity are vr = 2.88 m/s and vr = 54 m/s, respectively. This is in good agreement with the simulation results shown in Fig. 8(a) and (b). Third, when the radial velocity is moderately small, the effect of the false peak is not serious. However, with the increase in radial velocity, the effect of the false peak cannot be ignored. In particular, the value of the main peak does not remain the largest, and the maximum value of the false peaks can exceed the value of the main peak, e.g., MFPVR > 0 dB in Fig. 8. Hence, it is necessary to compensate for the error signal. In Fig. 8(b), we also see that there are two peaks of the MFPVR in a periodic zone of radial velocity vr ∈ [0, 54] m/s. It can be explained in Fig. 9, which is the result of choosing the maximum value of ηk for the fixed radial velocity.

B. Influence of Moving Target Parameters on the Azimuthal Image We calculate the maximum false-peak value ratio (MFPVR) of the maximum value of the false peaks to the value of the main peak as a measurement for the influence of the velocity parameters, including the radial and along-track velocities, and initial location parameter on the azimuthal image. The MFPVR is written as MFPVR = 20 log(max({Ak })/A0 ) = max(η), where η = {ηk } with {·} denoting the setting function.

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Fig. 9. Amplitude ratio ηk versus radial velocity.

Fig. 10. MFPVR versus along-track velocity and initial azimuth location. (a) Airborne SAR. (b) Spaceborne SAR.

2. Influence of the Along-Track Velocity and Initial Azimuth Location: Apart from radial velocity vr , the term x0 vx /Rc also affects the azimuthal image. Fig. 10 shows the MFPVR versus the along-track velocity and the initial azimuth location. It is shown that the MFPVR is also affected by the along-track velocity and the initial location. Thus, when compensating for the error signal to achieve a highly qualified azimuthal image, the effect of vr , x0 , and vx should be taken into account. Moreover, the effect of the false peak on the spaceborne SAR is smaller than the effect of the false peak on the airborne SAR. This is due to the fact that the slant range Rc in spaceborne SAR is large, and hence, x0 vx /Rc becomes small. C. Clutter Suppression by VMC-CSI Let vr = 1 m/s, vx = 3 m/s, and x0 = 13 m. Suppose the scene is the same as in Fig. 5 and the parameters of airborne

Fig. 11. Virtual three-channel data after range compression. (a) Data in virtual channel 1. (b) Data in virtual channel 2. (c) Data in virtual channel 3.

SAR are unaltered. The virtual three-channel data after range compression are shown in Fig. 11, where SCR = −20 dB and CNR = 50 dB. It is indicated that the moving target cannot be discriminated due to strong clutter, and hence, clutter suppression is necessary. Fig. 12(a) shows the effect of clutter suppression for virtual channel 1 and virtual channel 2. The moving trajectory of the moving target is clearly shown. However, there exists range migration, which should be compensated. The result after range migration correction, conducted by least squares envelope fitting and interpolation, is given in Fig. 12(b). The azimuthal data for the moving target now locate in a common range bin. For brevity, the clutter suppression results for the spaceborne SAR are not shown.


Fig. 12. Cancelation channel 1 data after clutter suppression between virtual channel 1 and virtual channel 2. (a) Before range migration correction. (b) After range migration correction.

D. Parameter Estimation and Imaging in the VMC-CSI Method According to the procedure given in Fig. 3, after compensating the LMF term C2 due to the movement of the platform, we can perform the azimuthal FT to the two cancelation channels. Suppose the radial velocity is vr = 1 m/s, the along-track velocity is vx = 3 m/s, and the initial azimuth location is x0 = 13 m, the azimuthal FT result for the moving target in airborne SAR is displayed in Fig. 13(a). The azimuthal FT for the spaceborne SAR is shown in Fig. 14(a), where vr = 7 m/s, vx = 15 m/s, and x0 = 60 m. Note that for airborne SAR, L = 2, whereas for spaceborne SAR, L = 3. Hence, according to the theoretical analysis in Section III-B, there are two and three defocused regions in the Doppler interval [−PRFe /2, PRFe /2], respectively. This is consistent with the results shown in Figs. 13(a) and 14(a). Notice that Figs. 13(b) and 14(b) show the local enlarged results, which clearly show the defocused phenomenon, which is mainly caused by the along-track velocity of the moving target. For airborne SAR, the estimators of initial locations are 13.2974 and 13.4660 m for the two domains in Fig. 13(a) by using (38). The average mean x ˆ0 = 13.3817 m is taken as the final result, and the location error is 2.94%. Then, using (46) and (48), the rough estimators of radial velocity ˆ r = [−0.4388, 0.9976]T m/s and and along-track velocity are v T ˆ x = [2.8969, −2.8969] m/s, respectively. Moreover, taking v maximum image contrast as the evaluation factor, the pre-

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Fig. 13. Azimuthal FT for the airborne SAR. (a) Azimuthal FT. (b) Local enlarged result for domain 2.

cise estimators of the 2-D velocity are vˆr = 1.0226 m/s and vˆx = 2.9469 m/s, respectively. Similarly, the final results of initial location, radial velocity, and along-track velocity for the spaceborne SAR are x ˆ0 = 60.4685 m, vˆr = 7.0089 m/s, and vˆx = 14.4865 m/s, respectively. According to the estimated parameters, the accurate azimuthal reference function is formed, and the focused image of the moving target can be obtained. Take the airborne SAR as an example, the 2-D image of the moving target embedded in the static scene is shown in Fig. 15, where the origin of the coordinate stands for the position (0, Rc ). It is seen that the result well coincides with the designed scene given in Fig. 5. E. Influence of Residual Clutter on Parameter Estimation Suppose that both channels match perfectly and that the “DPCA condition” is satisfied, strong clutter can be effectively suppressed, and then, moving target parameters can be accurately estimated. However, a practical standpoint is the unavoidable effect of imperfect clutter cancelation due to imperfect channel match/nonuniform platform motion, particularly for the airborne platform case. To demonstrate the influence of residual clutter on the resulting parameter estimation, root mean square error (RMSE) is used to evaluate the performance. Fig. 16(a)–(c) shows the RMSE of initial azimuth location, radial velocity, and along-track velocity against SCR, respectively, where the SCR denotes the signal-to-residual-clutter

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Fig. 14. Azimuthal FT for the spaceborne SAR. (a) Azimuthal FT. (b) Local enlarged result for domain 1.

Fig. 16. Comparison of RMSEs against SCR. (a) RMSE of initial azimuth location against SCR. (b) RMSE of radial velocity against SCR. (c) RMSE of along-track velocity against SCR. Fig. 15. Two-dimensional image.

ratio for the cancelation channel in the temporal domain. It can be seen that with lower SCRs, there is a higher RMSE for lower SCR. In other words, lower SCR causes performance loss. The reason for poor performance is that when the clutter is not perfectly canceled, each of the real and false peaks in the Doppler domain will be contaminated by residual clutter, which may have dramatically different phases, ruining the initial location and velocity estimates. Without good initial estimates, the precise search may be stuck in a parameter region far from the truth, limiting the quality of the final estimates. However, when the SCR is greater than 3 dB, the performance loss is very small,

which benefits from the improved SCR in the Doppler domain using the azimuthal FT to achieve coherent accumulation. Moreover, compared with velocity estimation, the estimated initial azimuth location is usually more easier to deviate from the true value due to the contaminated interferometric phase in low SCR. F. Merits and Drawbacks of the VMC-CSI Method As we know, the higher the system PRF, the smaller the swath width becomes. The inequality Wg < c/(2 sin(θi )PRF) in [42] gives an upper bound on the swath that can be imaged


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However, the VMC-CSI method also has a few drawbacks, which are summarized as follows. First, a uniform sample distribution in each virtual channel is obtained only if the condition PRF = va /Dc is fulfilled, as with the MPC-SAR. Therefore, a nonoptimum PRF is associated with a nonuniform sample spacing in azimuth. To overcome this drawback, we can use the unambiguous SAR signal reconstruction algorithm [43] or azimuthal phase center adaptation on transmission, which allows for a pulse-to-pulse shift of the phase center to match them to the PRF [44]. Second, it is noticed that the problem of radial velocity ambiguity cannot also be avoided for the VMCCSI method when the Doppler shift exceeds half of the virtual PRF. Fortunately, several approaches, e.g., those in [45]–[47], can be employed to solve this problem. V. C ONCLUSION

Fig. 17. Comparison of maximum imaged swath on ground versus virtual PRF and normalized amplitude versus radial velocity. (a) Maximum imaged swath on ground versus virtual PRF. (b) Normalized amplitude versus radial velocity.

for a given PRF, where Wg is the maximum imaged swath on ground, c is the speed of light, and θi is the incident angle. With the same interspacing of spatial samples between conventional multichannel SAR and VMC scheme in this paper, Fig. 17(a) compares the maximum imaged swath on ground versus virtual PRF, whereas Fig. 17(b) compares the normalized amplitude of (36) versus the radial velocity of the moving target, where the curve with L = 1 stands for the conventional multichannel SAR. Three merits can be concluded. First, the swath width in the VMC scheme is increased by L times, compared with the conventional multichannel SAR, since the real PRF in the VMC scheme has dropped L times. Second, although the number of bind velocities increases, the VMC scheme has a better performance to detect the ground moving target than the conventional multichannel SAR, particularly at lower target velocities. This is due to the fact that the virtual baseline length in the VMC scheme is L times the size of conventional multichannel SAR. Third, the VMC-CSI method can improve the performance of static-scene and ground moving target processing in HRWS mode simultaneously. The basic idea is that the contradiction between the wide swath and high azimuthal resolution for static-scene imaging is resolved by spatial sampling, instead of the temporal sampling in each virtual channel analogous to MPC-SAR. Meanwhile, the reconstructed VMC can be jointly used to detect the ground moving target similar to conventional multichannel SAR.

In this paper, we have introduced an approach to HRWS imaging and GMTI for SAR using a VMC scheme. First, a more detailed model of the ground moving target in the virtual channel and the azimuthal image has been derived. It is shown that the moving target signal in slow time consists of the product of a common azimuth chirp encountered in singlechannel or standard multichannel SAR with a moving target, as well as an “error” signal that originates from the VMC scheme. The periodic error signal causes a repetition of the desired signal in the frequency domain, which leads to false peaks (after azimuth compression) in the image domain. Furthermore, we develop a GMTI approach using the VMC scheme called VMC-CSI. Ground clutter suppression via the DPCA approach is applied to different pairs of virtual channels. The phase difference between the Doppler domain representation of the cluttercanceled virtual channels is used to estimate the location of a moving target, and a two-stage process is used for estimating the radial and along-track velocities of the moving target. It is shown that the moving target parameters can be accurately estimated by the VMC-CSI method by using false peaks first and removing them afterward for a moderate SCR. Moreover, with the same interspacing of spatial samples, a wider unambiguous swath is ensured for the VMC scheme, since the real PRF is lower than that of the conventional multichannel SAR. ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their comments, which are crucial in improving the quality of this paper. R EFERENCES [1] G. Franceschetti and R. Lanari, Synthetic Aperture Radar Processing. Boca Raton, FL, USA: CRC Press, 1999. [2] C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images. Raleigh, NC, USA: Sci Tech, 2004. [3] I. G. Cumming and F. H. Wong, Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation. Norwood, MA, USA: Artech House, 2005. [4] W. G. Carrara, R. S. Goodman, and R. M. Majewski, Spotlight Synthetic Aperture Radar: Signal Processing Algorithms. Norwood, MA, USA: Artech House, 1995. [5] C. V. Jakowatz, Jr., D. E. Wahl, P. H. Eichel, D. C. Ghiglia, and P. A. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach. Norwell, MA, USA: Kluwer, 1996.

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Li-Bao Wang was born in Hebei Province, China, in 1980. He received the B.S. and M.S. degrees from Wuhan Radar Academy, Wuhan, China, in 2003 and 2006, respectively, and the Ph.D. degree from the National University of Defense Technology, Changsha, China, in 2010. He is currently a Lecturer with the Wuhan Radar Academy. He has authored or coauthored more than 40 journal and conference papers. His research interests include synthetic aperture radar (SAR) moving target detection and imaging, multichannel radar system design, and multichannel radar signal processing, particularly multipleinput–multiple-output SAR.

Dang-Wei Wang received the B.S. and M.S. degrees from the Wuhan Radar Academy, Wuhan, China, in 2000 and 2003, respectively, and the Ph.D. degree from the National University of Defense Technology, Changsha, China, in 2006. He is currently an Associate Professor with the Wuhan Radar Academy. His research interests include multichannel radar target characteristics and advanced signal processing with application to radar target imaging and identification.


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Jing-Jing Li received the M.S. degree from the Wuhan Radar Academy, Wuhan, China, in 2003 and the Ph.D. degree from the National Defense Information Academy, Wuhan, in 2011. He is currently a Lecturer with the Wuhan Radar Academy. His main research interests include radar target detection and identification.

Chao Xie received the B.S., M.S., and Ph.D. degrees from the Wuhan Radar Academy, Wuhan, China, in 2004, 2007, and 2014, respectively. He is currently a Lecturer with Wuhan Radar Academy. His research interests include radar systems and multichannel radar target detection and imaging.

Jia Xu (SM’15) was born in Anhui Province, China, in 1974. He received the B.S. and M.S. degrees from the Wuhan Radar Academy, Wuhan, China, in 1995 and 1998, respectively, and the Ph.D. degree from the Navy Engineering University, Wuhan, in 2001. During 2002–2005, he was a Postdoctoral Researcher with Tsinghua University, Beijing, China. He was also an Associate Professor with the Wuhan Radar Academy during 2006–2009 and with Tsinghua University during 2009–2012. Since 2012, he has been a Full Professor with the School of Information and Electronics, Beijing Institute of Technology (BIT), Beijing. He has authored or coauthored more than 180 journal and conference papers. His current research interests include detection and estimation theory, synthetic aperture radar (SAR)/inverse SAR imaging, target recognition, array signal processing, and adaptive signal processing. Dr. Xu received the Outstanding Post-Doctor Honor of Tsinghua University in 2004 and the second-order National Invention Award in 2007. He was supported by the Outstanding Youth Teacher Training Plan of BIT in 2012 and by the New Century Excellent Talents Supporting Plan of the Ministry of Education of China in 2013. He is a Fellow of The Institution of Engineering and Technology and of the Chinese Institute of Electronics (CIE). He is also a member of the Academic Working Committee of CIE. He is an Associate Editor of nine radar-related international or Chinese domestic academic journals.

Ling Wang received the B.S., M.S., and Ph.D. degrees from the National University of Defense Technology, Changsha, China, in 1988, 1993, and 2006, respectively. She is currently a Full Professor with the School of Electronic Science and Engineering, National University of Defense Technology. Her research interests include modern radar signal processing, cooperative localization, information processing, and information systems.