Bistatic Linear Antenna Array SAR for Moving Target ... - IEEE Xplore

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 45, NO. 3, MARCH 2007

Bistatic Linear Antenna Array SAR for Moving Target Detection, Location, and Imaging With Two Passive Airborne Radars Gang Li, Student Member, IEEE, Jia Xu, Member, IEEE, Ying-Ning Peng, Senior Member, IEEE, and Xiang-Gen Xia, Senior Member, IEEE

Abstract—In this paper, we propose a bistatic linear array synthetic aperture radar (BLA-SAR) system for moving target detection, location, and imaging. In the BLA-SAR system, a geostationary satellite is used as a transmitter, and two airborne linear array radars are used as passive receivers, where the transmitted waveforms from the geostationary satellite may have two different carrier frequencies, two linear array antennas on two different airplanes may be equipped with different spacings, or two airplanes may fly with two different velocities. It is shown that, using the BLA-SAR, not only the stationary clutter can be suppressed but also locations of both slow and fast moving targets can be accurately estimated. Furthermore, an effective BLA-SAR algorithm of moving target imaging is also proposed. Lastly, some numerical experiments are given to demonstrate the effectiveness of the BLA-SAR. Index Terms—Bistatic synthetic aperture radar (SAR), Chinese remainder theorem (CRT), moving target.

I. I NTRODUCTION

B

ISTATIC/MULTISTATIC radar has attracted much attention in recent years [1]–[10], [25], [26]. In bistatic radar systems, transmitter and receivers are usually separated and located on different flying platforms. The main advantage of this configuration is that the vulnerability of the system is reduced because the transmitter may be located beyond an attack range and the passive receivers are difficult to be detected. Moreover, the bistatic radar cross section differs from that of the monostatic case, which may increase the probability to find stealth targets. Furthermore, if multiple receivers are used, there are possibilities to look at the same scene from different angles with advantages for moving target detection and imaging. Two successful experiments on bistatic airborne synthetic aperture radar (SAR) had been carried out by ONERA/DLR in February 2003 [1] and by FGAN in October 2003 [2], respectively. Manuscript received February 1, 2006; revised July 26, 2006. This work was supported in part by the China National Science Foundation under Grant 60502012, in part by the China Ministry Research Foundation under Grant 9140A07020106JW0103, and in part by the Cultivation Fund of the Key Scientific and Technical Innovation Project under Grant 706004. G. Li and Y.-N. Peng are with the Department of Electronic Engineering, Tsinghua University, Beijing 100084, China (e-mail: ligang98@mails. tsinghua.edu.cn). J. Xu is with the Department of Electronic Engineering, Tsinghua University, Beijing 100084, China and also with the Radar Academy of Air Force, Wuhan 430010, China. X.-G. Xia is with the Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TGRS.2006.888145

In both experiments, the two airplanes (the transmitter and the receiver) were constrained to fly along parallel flight paths, and satisfying imaging results of the stationary scenes were obtained. These experiments have proved the feasibility of many important practical problems, such as the communication between two airplanes, the time, location, and phase synchronization of the two airplanes, the flight track aligning and the motion compensation, etc., which encourages us to study the issue on moving target detection and imaging by taking advantage of the similar configuration. Especially, an active topic in the research area of the bistatic radar is the integration of airborne and spaceborne radars, i.e., the bistatic radar system with airborne receiver and spaceborne transmitter. The distinct advantage of such configuration, compared with the airborne bistatic systems in [1] and [2], lies in the excellent capability of wide-area surveillance, and it is obviously helpful for moving target detection. Some useful suggestions on the practical design of such system had been proposed in [7] and [8]. In the existing literature, several methods of moving target detection and imaging based on monostatic multireceiver systems have been generalized to bistatic case. For example, it was demonstrated that the slowly moving targets immersed in strong ground clutter may be detected and located by applying space-time adaptive processing [5]–[9] and the displaced phase center antenna technique [9]–[10] to bistatic SAR. However, when targets move fast, the position and velocity parameters will not be estimated accurately due to the 2π modulo operation in the Fourier transform, and thus, the targets will still be mislocated accordingly. This problem is called azimuth location ambiguity [12]. In a monostatic system, it may be resolved by dual-speed single-channel SAR [13] and some extensions of linear array SAR (or VSAR) [11], e.g., multifrequency VSAR [12], nonuniform linear array SAR [14], and dual-speed VSAR [15]. Nevertheless, in the existing bistatic systems, these techniques have not been found and the azimuth location ambiguity has not been resolved. In this paper, we also focus on moving target detection, location, and imaging, but for bistatic systems. We propose a bistatic linear array SAR (BLA-SAR) system, where a geostationary satellite is used as the transmitter and two airborne linear array side-looking radars flying along parallel flight tracks are used as passive receivers. Then, we generalize the above techniques, i.e., multiple frequencies, multiple antenna spacings, and dual platform velocities to

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LI et al.: BISTATIC LINEAR ARRAY SAR FOR MOVING TARGET DETECTION, LOCATION, AND IMAGING

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BLA-SAR. Compared with the monostatic system proposed in [12]–[15], some of the above techniques, for example, multiple frequencies and dual platform velocities, are easier to cope with in BLA-SAR. The two airborne passive radars of BLASAR can receive echoes with different carrier frequencies, arrange the receiving antennas with different spacings, or fly with two different velocities, respectively, during the imaging time interval. Accordingly, BLA-SAR has three representative forms. 1) If the carrier frequencies of the transmitted waveforms from a geostationary satellite are different when everything else is the same in two airplanes, the system is called dual-frequency BLA-SAR (DFBLA-SAR). 2) If the antenna spacings are different when everything else is the same in two airplanes, the system is called dualspacing BLA-SAR (DSBLA-SAR). 3) If the platform velocities are different when everything else is the same in two airplanes, the system is called dualvelocity BLA-SAR (DVBLA-SAR). In each one of the two airborne linear array radars of BLA-SAR, multiple complex images are formed by multiple receiving antennas and are transformed into velocity images (V-images) (defined in [11]), where the moving target may be separated from strong stationary clutter in terms of its motion parameters, i.e., the clutter can be suppressed and the moving target can be detected. Moreover, the moving target will appear at different positions in the two V-image domains of the two airborne linear array SAR systems, due to the different carrier frequencies (for DFBLA-SAR), or different antenna spacings (for DSBLA-SAR), or different airplane velocities (for DVBLA-SAR). This information and the Chinese remainder theorem (CRT) [19], [20] are used to resolve the azimuth location ambiguity. Therefore, BLA-SAR has the ability not only to suppress clutter but also to accurately locate and image both slow and fast moving targets. This paper is organized as follows. In Section II, the BLA-SAR model is established. In Section III, the problem of detection, location, and imaging of the moving target is formulated by using a single linear antenna array. In Section IV, the principle of moving target accurate location using two linear antenna arrays is introduced, some practical problems are discussed, and an effective BLA-SAR algorithm of moving target imaging is proposed. In Section V, some numerical experiments are given to validate the BLA-SAR algorithm. In Section VI, some useful conclusions and comments are given. II. BLA-SAR M ODEL The BLA-SAR geometry is shown in Fig. 1. The X axis is the azimuth direction, the Y axis is the range direction, and the Z axis is the vertical direction. The X–Y plane represents the earth’s surface. A geostationary satellite is used as the transmitter, and two airplanes are used as passive receivers. Assume that the geostationary satellite transmits signal with dual-carrier wavelengths λ1 and λ2 and the two airplanes receive echoes with λ1 and λ2 , respectively. The two airplanes fly parallel along the azimuth direction (like the experiments

Fig. 1. BLA-SAR geometry.

in [1] and [2]) in the y = 0 plane with velocities ν1 and ν2 and altitudes H1 and H2 . The two airplanes are equipped with two M -element side-looking linear receiving arrays, where the element spacing at the first airplane is assumed d1 and the element spacing at the second airplane is assumed d2 , respectively. When t = 0, the first receiver antenna in the first airplane is assumed located at (0, 0, H1 ) and the first receiver antenna in the second airplane is assumed located at (0, 0, H2 ), and then the coordinates of other 2M − 2 receiver antennas are (d1 , 0, H1 ), (2d1 , 0, H1 ), . . . , ((M − 1)d1 , 0, H1 ), and (d2 , 0, H2 ), (2d2 , 0, H2 ), . . . , ((M − 1)d2 , 0, H2 ), correspondingly. At the same time, a moving target P with constant azimuth speed νx and range speed νy is assumed located at (x0 , y0 , 0) (in the area illuminated by the geostationary satellite beam). In the following, we first analyze the moving target imaging process using a single linear antenna array, address the azimuth location ambiguity problem similar to what is done in [11] and [12], and then propose BLA-SAR in details.

III. L OCATION AND I MAGING F ORMULATION U SING A S INGLE L INEAR A NTENNA A RRAY In this section, we first consider the clutter-free scenario and analyze the imaging process for P using the antenna array fixed in the first airplane similar to [11] and [12]. The problem about clutter suppression will be discussed in the next section. Suppose that the geostationary satellite transmits a linear frequency modulated (LFM) signal (or chirp signal)
 µ  s(τ ) = A exp j2π f1,c τ + τ 2 2

(1)

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 45, NO. 3, MARCH 2007

where A is the amplitude, f1,c is the carrier frequency, µ is the chirp rate, and τ is the fast time (or round-trip time, or range time). After the demodulation, the base band echo from P at the mth antenna of the first airplane is 



s1,m (t, τ ) = A1 exp jπµ τ −

R0 + R1,m (t) c

f (t) = fD,radar + fD,target + (fR,radar + fR,target )t

2 

fD,radar = (2)

where A1 is the echo’s complex amplitude, c is the light speed, the wavelength λ1 = c/f1c , and t is the slow time (or azimuth time); R0 is the distance from the geostationary satellite to P (it is reasonable to assume R0 constant in this paper, because the motion of the target in the limited time duration is normally much smaller than the distance between the geostationary satellite and the earth); R1,m (t) is the distance from the mth antenna of the first airplane to P at instantaneous slow time t; and  (x0 + νx t − ν1 t − md1 )2 + (y0 + νy t)2 + H12 (3)

for m = 0, 1, . . . , M − 1. After the range compression, (2) becomes approximately

2π (R0 + R1,m (t)) s1,m (t, τ ) = A1 exp −j λ1 

R0 + R1,m (t) ·δ τ − c

 (4)

Taking the Taylor series expansion of R1,m (t) in terms of t in (4), i.e., R1,m (t) ≈ R1 +

+

m2 d21 − 2md1 x0 2R1

(νx − ν1 )2 + νy2 2 (x0 − md1 )(νx − ν1 ) + y0 νy t+ t R1 2R1

we obtain

2π s1,m (t) = A1 exp −j λ1



m2 d21 − 2md1 x0 R0 + R1 + 2R1



  2π (x0 − md1 )(νx − ν1 ) + y0 νy · exp −j t λ1 R1 

2π · exp −j λ1



(νx − ν1 )2 + νy2 2 t 2R1

(6)

where



2π(R0 + R1,m (t)) · exp −j λ1

R1,m (t) =

 where R1 = x20 + y02 + H12 is the distance from the first antenna of the first airplane to P at t = 0. Then, the azimuth instantaneous Doppler frequency is

 (5)

(x0 − md1 )ν1 λ1 R1

fD,target = −

(x0 − md1 )νx + y0 νy λ1 R1

fR,radar = −

ν12 λ1 R1

fR,target = −

νx2 − 2νx ν1 + νy2 . λ1 R1

(7)

fD,radar , fD,target , fR,radar , and fR,target are the Doppler shifts and the Doppler rates due to the radar motion and the target motion, respectively. After the azimuth phase compensation according to the response function of the static target PS standing at (x0 , y0 , 0), fD,radar and fR,radar · t in (6) can be removed and PS is focused and located at its true azimuth position x0 . Here, the echo from the moving target P is also an LFM signal with Doppler shift fD,target and Doppler rate fR,target , i.e., the instantaneous Doppler frequency from P is f (t) = fD,target + fR,target t. The term of fR,target t can be compensated via estimating fR,target by using the method proposed in [16] and [17], and then the moving target P is focused but shifted away from its true azimuth position x0 . The amount of the shift is ∆1 =

λ1 R1 fD,target x0 νx + y0 νy md1 νx =− + ν1 ν1 ν1

(8)

where md1 νx /ν1 is the result of the receiver position difference and is normally smaller than one azimuth cell as explained in [18]. (To verify this conclusion, let us see an example. Take the parameters as what will be used in the later numerical experiments: azimuth resolution is ρx = 1 m, airplane speed is ν1 = 200 m/s, the antenna spacing is d1 = 1.5 m, and the element number of the antenna array is M = 10. We can calculate that if |νx | < 14.81 m/s then md1 νx /ν1 < ρx . Therefore, this conclusion holds for most of the normal moving targets, especially for the later numerical experiments of this paper.) Therefore, it can be neglected and (8) becomes ∆1 = −

x0 νx + y0 νy . ν1

(9)

In this way, the moving target P is focused and detected at azimuth position (x0 + ∆1 ) in the complex image of the mth antenna at the first airplane, and has a complex amplitude [see (5)]  

2π m2 d21 − 2md1 x0 R0 + R1 + . A1 exp −j λ1 2R1

LI et al.: BISTATIC LINEAR ARRAY SAR FOR MOVING TARGET DETECTION, LOCATION, AND IMAGING

After the quantization by the SAR image azimuth resolution ρx , we have M images of P formed by the M receivers in the first airplane  

2π m2 d21 S1 (m) = A1 exp −j R0 + R1 + λ1 2R1   2πmd1 x0 · exp j · δ(n − n0 − ∆1,shift ) (10) λ1 R1 for m = 0, 1, . . . , M − 1, where m corresponds to the mth antenna and n is the discrete azimuth position; n0 and ∆1,shift are the quantization results by ρx , i.e., n0 = x0 /ρx and ∆1,shift =

∆1 x0 νx + y0 νy =− . ρx ρx ν1

(11)

Now, another important issue is how to relocate P to its true position n0 . To do so, ∆1,shift must be estimated accurately and subtracted from the detected position (n0 + ∆1,shift ), as described below. After removing the phase term caused by the receiver position difference, i.e., multiplying exp[jπm2 d21 /(λ1 R1 )], (10) can be rewritten as

2π S1 (m) = A1 exp −j (R0 + R1 ) λ1   2πmd1 ρx n0 · exp j · δ(n − n0 − ∆1,shift ) (12) λ1 R1 for m = 0, 1, . . . , M − 1. One can take the phase factor exp[−j2πmd1 ρx (n0 + ∆1,shift )/(λ1 R1 )] in terms of the detected position (n0 + ∆1,shift ) and multiply it to (12), we then obtain

2π S1 (m) = A1 exp −j (R0 + R1 ) λ1   2πmd1 ρx ∆1,shift · exp −j · δ(n − n0 − ∆1,shift ). (13) λ1 R1 Defining the normalized frequency f1 =

ρx d1 ∆1,shift d1 (x0 νx + y0 νy ) =− R1 λ1 R 1 λ 1 ν1

(14)

(13) becomes

2π S1 (m) = A1 exp −j (R0 + R1 ) λ1 · exp(−j2πf1 m) · δ(n − n0 − ∆1,shift ) (15) which shows clearly that via discrete Fourier transform (DFT) of S1 (m) with respect to variable m, f1 and therefore ∆1,shift can be estimated. The above analysis is similar to VSAR [11], but all the Doppler parameters of our BLA-SAR in (7) are different from the VSAR case followed by a scalar multiplier 2. This is because the satellite is geostationary, and therefore R0 , the distance between the satellite and the moving target P , is approximately constant and has no effect on the echo’s phase history.

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The DFT of S1 (m), which is called V-images like VSAR [11], gives f1 = mod(f1 , 1), which is folded residue of f1 due to 2π periodicity of the DFT. For a stationary target, f1 = 0, i.e., the stationary target stands in the zeroth V-image. For the moving target P , f1 = 0, i.e., P will stand in corresponding V-image in terms of its velocity. If P moves slowly such that ∆1,shift is small enough and corresponding f1 = f1 < 1, f1 can be estimated accurately via zero-padded DFT of S1 (m). Accordingly, ∆1,shift can be solved and the position n0 of P can be therefore solved by subtracting ∆1,shift from the detected position (n0 + ∆1,shift ). Otherwise, if P moves fast, ∆1,shift is large such that f1 = f1 + K1 for an unknown integer K1 , and thus, f1 will not be determined uniquely via the DFT of S1 (m). Accordingly, the estimation of ∆1,shift cannot be solved, i.e., the location ambiguity problem will occur. This argument shows that only one observation in the V-images is not enough to locate a fast moving target, and this is the reason why in VSAR systems walking people can be located, but moving vehicles may not be positioned accurately [11]–[15]. In monostatic linear array SAR, one way to resolve such a problem is to carry out multiple different observations for the V-images, such as multifrequency VSAR [12], nonuniform linear antenna array SAR [14], and dual-speed VSAR [15], where multiple carrier wavelengths λ [12] or multiple antenna spacings d [14] or multiple platform velocities v [15] are used in (14) to obtain the multiple folded residues of f [expressed as f1 in (14)]. Then, these multiple folded residues and the CRT are used to estimate the target’s azimuth migration accurately. We next consider these techniques, i.e., multiple carrier wavelengths, multiple antenna spacings, and multiple platform velocities, in BLA-SAR and introduce the BLA-SAR algorithm for moving target detection, location, and imaging. As we shall see later, some of the above techniques, for example, multiple carrier wavelengths and multiple platform velocities, may be easier to implement in bistatic systems than in monostatic systems.

IV. BLA-SAR A LGORITHM In this section, we first explain the principle of moving target accurate location using the two airborne passive linear antenna arrays. We then discuss some problems in practice. Finally, we give an integrated BLA-SAR algorithm for moving target imaging.

A. Principle of Moving Target Accurate Location Using Two Linear Antenna Arrays The analysis in previous section may be generalized directly to the echo processing at the second airplane. After range compression, the echo of P received by the mth antenna at the second airplane is

2π (R0 + R2,m (t)) s2,m (t, τ ) = A2 exp −j λ2   R0 + R2,m (t) ·δ τ − c

(16)

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where A2 is the complex amplitude and R2,m (t) is the distance from mth antenna of the second airplane to P at instantaneous slow time t, and  R2,m (t) = (x0 + νx t − ν2 t − md2 )2 + (y0 + νy t)2 + H22 . (17) After compensating the azimuth phase according to stationary scene and refocusing P , the M images of P formed by the M receivers at the second airplane are

2π S2 (m) = A2 exp −j (R0 + R2 ) λ2 · exp(−j2πf2 m) · δ(n − n0 − ∆2,shift )

(18)

where the azimuth shift ∆2,shift = −

x0 νx + y0 νy ρx ν2

(19)

and ρx d2 ∆2,shift d2 (x0 νx + y0 νy ) =− f2 = R2 λ2 R 2 λ 2 ν2  and R2 = x20 + y02 + H22 . In summary, we have

2π Si (m) = Ai exp −j (R0 + Ri ) λi

(20)

· exp(−j2πfi m) · δ(n − n0 − ∆i,shift ) (21) ∆i,shift = −

x0 νx + y0 νy ρx νi

(22)

ρx di ∆i,shift di (x0 νx + y0 νy ) =− Ri λi R i λ i νi

(23)

and fi = fi + Ki =

where i(= 1, 2) denotes the airplane index, ∆i,shift are the azimuth migrations of P in SAR images, fi = mod(fi , 1) are folded residues after performing the DFT of Si (m) in terms of m(= 0, 1, 2, . . . , M − 1), and Ki are some unknown integers. The central idea of the following proposed methods is to produce “significantly” different fi for different index i in (23) such that the CRT can be used to resolve the ambiguity due to the folding. From (23), one can see that there are several ways to generate different fi for different index i. We next show that only geometric difference, i.e., the slant ranges Ri in (23) (or the heights Hi ), of two airplane receivers may not be enough to generate significantly different fi . When λ1 = λ2 = λ, d1 = d2 = d, and ν1 = ν2 = ν, (23) becomes fi = −

d(x0 νx + y0 νy ) d(x0 νx + y0 νy ) =−  2 . Ri λν λν x0 + y02 + Hi2

Thus, the difference between f1 and f2 is    d(x0 νx + y0 νy )H1   · |H1 − H2 |. δf = |f1 − f2 | ≈   λνR13

Fig. 2. Difference between f1 and f2 in terms of the difference between the heights H1 and H2 .

In practice, H1 and H2 are about several hundred or thousand meters while R1 and y0 are about a few tens of kilometers. Furthermore, νx and νy are normally much smaller than ν, so δf is smaller than 1/(2M ), which is called the resolution of the V-images and determined by the Rayleigh limit of DFT. To demonstrate it, we give the following example. Let x0 = 30 m, y0 = 20 km, νx = 2 m/s, νy = 3 m/s, M = 10, d = 1.5 m, λ = 0.03 m, ν = 200 m/s, H1 = 3 km, and H2 is variable in the range from 3.5 to 7 km. The difference between f1 and f2 in terms of the difference between H1 and H2 is shown in Fig. 2. It is obviously found that the difference between f1 and f2 is smaller than the V-image resolution 0.05. Hence, to provide two different observations in the V-images and locate both fast and slowly moving targets accurately, only two different Ri in (23) are not enough and different λi , di , or νi should be taken. This is the basic idea of the BLA-SAR. From (22), define Ω = ∆1,shift · ν1 = ∆2,shift · ν2 = −(x0 νx + y0 νy )/ρx (24) and from (23), one can see Ω = (fi + Ki )

R i νi λ i ρx di

(25)

for i = 1, 2. Let Γ be the smallest positive real number such that µi = ΓRi λi νi /(ρx di ) and µi · fi are integers for i = 1, 2. In addition, λi , di , and νi should be designed such that µ1 and µ2 are not integer multiples of each other. Notice that Γ and µi can be obtained since fi are estimated and Ri , λi , di , νi , and ρx are all known for i = 1, 2. Multiplying Γ to the two sides of (25), (25) becomes ΓΩ = (f1 + K1 )µ1 = (f2 + K2 )µ2

(26)

mod(ΓΩ, µi ) = µi fi

(27)

which means

for i = 1, 2. Therefore, using the two residues µi · fi and the CRT (see example in [19] and [20]), ΓΩ can be uniquely determined if it is less than the least common multiple of the

LI et al.: BISTATIC LINEAR ARRAY SAR FOR MOVING TARGET DETECTION, LOCATION, AND IMAGING

two integers µi [expressed as LCM(µ1 , µ2 ) for short], and then Ki can be estimated uniquely and Ω, therefore ∆i,shift , can be determined accordingly, for i = 1, 2, i.e., the location ambiguity is resolved by using BLA-SAR. We now calculate the maximal detectable target velocity without any ambiguity in BLA-SAR system. As mentioned above, we have Ω = −(x0 νx + y0 νy )/ρx and Γ · Ωmax = LCM(µ1 , µ2 ). In general, the term x0 νx can be neglected because x0 is much smaller than y0 , where y0 ≈ R1 ≈ R2 approximately. Thus, the determinable upper limit of ΓΩ can be represented as Γ · Ωmax ≈ −Γ

y 0 νy = LCM(µ1 , µ2 ) ρx

(28)

and then the maximal determinable target velocity is |νy,max | =

1 ρx · LCM(µ1 , µ2 ) · 2 Γy0

(29)

where 1/2 is multiplied because there are two possible directions of νy , toward and away from the radar, respectively. As pointed out in [11], using such a VSAR that has the parameter group (λi , di , νi ), the maximal determinable target velocity is |νy,max,VSAR | = λi νi /(2di ) = ρx µi /(2Γy0 ) for i = 1 or 2. In BLA-SAR, because µ1 and µ2 are designed not integer multiples of each other, LCM(µ1 , µ2 ) > µi for i = 1, 2. Thus, the determinable velocity range of a moving target is increased using the BLA-SAR compared with VSAR similar to the multifrequency VSAR in [12]. This is why the location ambiguity of fast moving targets can be resolved by the BLA-SAR system. Based on above principle, one can design the parameter group (λi , di , νi ) synthetically such that the velocity of a target of interest falls into the detectable range of the system. In particular, we change λi , di , and νi , respectively, and obtain three representative forms of BLA-SAR: DFBLA-SAR, DSBLA-SAR, and DVBLA-SAR. In other words, for DFBLA-SAR, λ1 = λ2 , d1 = d2 , and ν1 = ν2 ; for DSBLA-SAR, λ1 = λ2 , d1 = d2 , and ν1 = ν2 ; and for DVBLA-SAR, λ1 = λ2 , d1 = d2 , and ν1 = ν2 . These three forms can be seen as the generations of multifrequency VSAR [12], nonuniform linear array SAR [14], and dual-speed VSAR [15] from monostatic to bistatic systems, respectively. One can see that the separate implementations of different wavelengths, or different airplane velocities in two receive airplanes in a bistatic system are easier than the implementation in a single receive/transmit airplane in a monostatic system, respectively. B. Some Discussions About the above analysis, we have the following discussions. 1) Robustness of the BLA-SAR Location Algorithms for Moving Targets: What was studied above provides the basic idea of determining the azimuth migration by using the CRT in the V-images, which is based on two assumptions: 1) µi and µi · fi are integers and 2) the estimated residues fi in the V-image domain are accurate, for i = 1, 2. It was shown in the above section that the choice of Γ is a guarantee of the first

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assumption. Nevertheless, in practice, the second assumption may not hold. As a result of the inaccuracy of fi , the estimation of the azimuth shifts ∆i,shift may have large errors [27] and [28]. In this case, it is necessary to replace the conventional CRT by the robust CRT proposed in [27] and [28]. Based on the robust CRT, our BLA-SAR location algorithms for moving targets can deal with general case robustly. About the details of the robust CRT, we refer the reader to [27] and [28]. 2) Clutter Suppression: In practice, before locating a moving target P , clutter must be suppressed; otherwise, the detected position (n0 + ∆i,shift ) is difficult to be found for i = 1, 2, especially when the signal-to-clutter ratio is not too high. At each airplane, (22) and (23) show that the stationary clutter stands in the zeroth V-image while P with its motion parameters appears usually in one of other V-images. Occasionally, P may be imaged just in the zeroth V-image and also removed together with the clutter. But, it is impossible that P is imaged in both zeroth V-images at the two airplanes with respect to respective wavelengths λ1 and λ2 , or respective antenna spacings d1 and d2 or respective speeds ν1 and ν2 . Proof: If P is imaged in both zeroth V-images at the two airplanes with respective λ1 and λ2 (or d1 and d2 , or ν1 and ν2 ), we have ΓΩ = µ1 K1 = µ2 K2 . This means ΓΩ = K · LCM(µ1 , µ2 ) for one integer K. Based on the restriction of ΓΩ < LCM(µ1 , µ2 ) and Γ is positive, K = 0 and Ω = 0 accordingly. Moreover, x0  y0 and the values of νx and νy are comparable in (24); thus, Ω = 0 holds if and only if νx = νy = 0. This is inconsistent with the fact that P is moving. The proof is similar to the multifrequency VSAR in [12]. Therefore, the azimuth shifts also can be determined by the CRT, when one of its two residues is equal to zero. Accordingly, P also can be detected and located accurately in this case too. 3) SAR Image Registration Along the Range Direction: Due to the difference between R1 and R2 (see Fig. 1), the two SAR images of the same scene, obtained by the two airplanes, respectively, have a shift in range direction. As a result, the same moving target will appear at different range cells in two SAR images [see (4) and (16)]. If there are multiple targets in the scene, their images may be mismatched. Therefore, it is necessary to calibrate two SAR images in the two airplanes along the range direction. This calibration procedure is called image registration in interferometric SAR (InSAR), and it has been resolved by some effective methods [23], [24]. There are different requirements of the image registrations in InSAR, and in this paper, the image registration in InSAR is required to be accurate enough, e.g., the registration error is limited within 1/20 of range cell (or pixel) in [23], because InSAR is based on the accurate phase difference measurement among multiple complex signals; while the error of the image registration in this paper is only required to be smaller than one range cell (or pixel), because we only need to find the correct range cell numbers belonging to the same target in the two SAR images formed by the two airplanes. Thus, besides the algorithms presented in [23] and [24], a simpler method of image registration can be used here by the following three steps: 1) calculate range direction correlation of the two SAR images in the two airplanes; 2) find the position of the maximal peak in the correlation results; and 3) correct the range direction migration

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between the two SAR images at the two airplanes in terms of the peak’s position. This method, which is the basic principle of many algorithms of image registration, is simple but accurate enough here. In the integrated BLA-SAR algorithm, the image registration should be placed before the clutter suppression, because the presence of most covered parts of the two SAR images at the two airplanes, i.e., the strong stationary clutter, is helpful for the second step above. In addition, the accuracy of the image registration is also affected by the scene contrast. When the scene contrast is higher, for example in mountainous area or town, an obvious peak will occur in the correlation results and its position may be estimated accurately; therefore, the SAR image registration is accurate accordingly. Otherwise, when the scene contrast is lower, for example on a river surface or offshore plain, the maximal peak in the correlation results may not be found easily and the image registration may show relative poor performance. 4) Implementation of Two Carrier Frequencies in DFBLASAR System: In DFBLA-SAR, it is assumed that the interest area is illuminated by the signal on two different carrier frequencies λ1 and λ2 at any time. To do so, two different transmitting antennas need to be fixed in the geostationary satellite and the same waveform (chirp signal in this paper) needs to be modulated on λ1 and λ2 and transmitted by the two transmitters, respectively. Then, the different echoes on λ1 and λ2 are collected and demodulated by the two passive airborne linear antenna arrays, respectively. 5) Stable Geometry in DVBLA-SAR System: As mentioned above, to resolve the azimuth location ambiguity, the two airplanes are designed to fly with different speeds in DVBLASAR. Moreover, the azimuth-axis and range-axis coordinates of the two airplanes are assumed the same when t = 0 (see Fig. 1). On the other hand, this design may cause the aberration of the system geometry. The longer the observation time duration is, the larger the azimuth direction distance between the two airplanes is, i.e., the more serious the aberration of the system geometry is. As a result, the moving target may fall into the azimuth side-lobe beam of some receiving antennas, and accordingly, the location and imaging performance for the moving target will be degraded. To conquer this difficulty, we suggest that in DVBLA-SAR system, the speeds of the two airplanes alternate between ν1 and ν2 periodically. The principle of the speed alternation can be designed to enable the common illustrated area by both main-lobe beams of the antennas at the two airplanes to cover the whole observed scene. Therefore, at the moment when the azimuth main-lobe beam of the fast airplane exceeds that of the slow airplane, the speed alternation should be taken. If the azimuth mainlobe beamwidths of the antennas at the two airplanes are ϕ1 and ϕ2 (rad), respectively, then the azimuth widths illustrated by them are 2R1 tan(ϕ1 /2) and 2R2 tan(ϕ2 /2), respectively, so that the speed-alternating period Ta may be calculated as Ta = 2[R1 tan(ϕ1 /2) + R2 tan(ϕ2 /2)]/|ν1 − ν2 |. About how to switch the speed of each airplanes, we refer the readers to [13]. With the stable geometry configuration, DVBLA-SAR can satisfy the case of long observation time duration. There is no need for DFBLA-SAR and DSBLA-SAR to consider the aberration of the system geometry, because the velocities of the

two airplanes in DFBLA-SAR and DSBLA-SAR are assumed the same all the time. 6) Multiple Moving Target Registration: We have discussed the aforementioned BLA-SAR imaging of a single moving target. In general, there may be multiple moving targets in the scene. As we have seen in the previous section, if all the V-images only include a single target, the CRT (or robust CRT) can be used to estimate the correct position of the target. This implies that, if all the multiple moving targets can be coherently separated in V-images so that different individual moving targets are included in different sets of V-images, each moving target location can be estimated using the BLA-SAR similar to the processing for a single moving target. The target separation procedure is called multiple moving target registration [12] (note: the “multiple moving target registration” differs from the “SAR image registration along the range direction” mentioned above). We next explain how the multiple moving target registration is done by considering two moving targets and two V-images obtained from two airplanes. Assume that the true positions of the two targets are (x1 , y1 ) and (x2 , y2 ), and their azimuth shifts are ∆1 and ∆2 , respectively. There are two cases: 1) y1 = y2 or x1 + ∆1 = x2 + ∆2 , i.e., the two targets are focused in different range-azimuth cells; therefore, the multiple moving target registration can be done according to the range cell number or the azimuth cell number; and 2) y1 = y2 and x1 + ∆1 = x2 + ∆2 , i.e., the images of the two targets are superposed in the same range-azimuth cell, the multiple moving target registration should be done by generalized CRT [21], [22] that can match the sets of V-images with the corresponding targets. About the details of generalized CRT, we refer the readers to [21] and [22].

C. BLA-SAR Imaging Algorithm for Moving Target We now present a BLA-SAR imaging algorithm for moving targets. All the following steps, except Step 2) and Step 7), are common operations for the two antenna array SARs at the two airplanes. To improve the estimation accuracy in the V-images, the sequence along the antenna array is zero padded to 1024 before DFT and inverse DFT are performed. Step 1) Like classical SAR imaging, the stationary scene image is formed via a 2-D matching filter with the impulse response function of the scene. Step 2) Calculate the range direction correlation of the two SAR images at the two airplanes, search the position of the maximal peak of the correlation values, and perform the SAR image calibration. Step 3) The DFT along the antenna array direction transforms SAR images into V-images. The zeroth V-image is removed to suppress the clutter. Step 4) The inverse DFT along the antenna array direction is taken to transform V-images back to SAR images. Step 5) Estimate the Doppler rate of target’s echo by applying the time–frequency analysis techniques (see for example [16] and [17]) and then focus the target by compensating the corresponding quadratic term, respectively.

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Step 6) The DFT along the antenna array direction is taken again to map SAR images into V-images. Step 7) In new V-images, get the residues fi and calculate µi fi (the residues of ΓΩ), determine ΓΩ uniquely via the CRT, and estimate ∆i,shift accurately, for i = 1, 2. Step 8) The inverse DFT along the antenna array direction is made again to map V-images back to SAR images. Step 9) Correct the azimuth migrations of the moving target and get the final image. V. N UMERICAL E XPERIMENTS To verify the BLA-SAR algorithm, some numerical experiments are designed in this section. For DFBLA-SAR, DSBLASAR, and DVBLA-SAR, the common parameters are: radar bandwidth B = 60 MHz, pulse duration T = 10 µs, pulse repetition frequency fPRF = 1 kHz, the range direction center of the observed area y0 ≈ 20 km, the altitudes of the two airplanes H1 = 3000 m and H2 = 4000 m; at each airplane, the element number of the antenna array M = 10, and the SAR azimuth direction resolution ρx ≈ 1 m. The simulated static scene (stationary clutter) is composed of several fields of plant and two roads with different reflectivities. The first and second roads have 45◦ and 135◦ angles with the radar moving direction, respectively. The mean clutter-noise ratio is set to 40 dB. A fast moving target moves away from the radar on the first road with speed 10.04 m/s, while another slow moving target moves toward the radar on the second road with speed 1.84 m/s. The corresponding velocity in the range direction is 7.10 and −1.30 m/s. At t = 0, their true azimuth position are 550 (azimuth cell) and 300 (azimuth cell), respectively. The signalnoise ratio is set to 10 dB. The parameters of the first airplane are assumed constant: the wavelength λ1 = 0.03 m, the spacing between all adjacent antennas d1 = 1.5 m, and the airplane velocity ν1 = 200 m/s. Therefore, the maximal determinable range direction velocity only using the first airplane is calculated as 2 m/s in terms of (29), where the LCM(x1 , x2 ) is reduced to x1 . The imaging results formed by the first airplane are shown in Fig. 3: after the stationary clutter suppression and the Doppler rate estimation, the refocused targets are shown in Fig. 3(a); after locating the targets on the scene, the image of targets and ground is shown in Fig. 3(b); the V-images of the targets are shown in Fig. 3(c). One can see that the targets shift out of the roads. In what follows, the parameters of the second airplane, i.e., the wavelength λ2 , the spacing between all adjacent antennas d2 and the airplane velocity ν2 , vary according to DFBLA-SAR, DSBLA-SAR, and DVBLA-SAR methods, respectively, and their imaging results are given below. A. Imaging Results Using DFBLA-SAR When ν2 = ν1 , d2 = d1 , and λ2 = 0.05 m = λ1 , the system becomes DFBLA-SAR. In this case, the maximal range direction velocity, such that there is no location ambiguity, using only the second airplane and the two airplanes are 3.33 and 10 m/s according to (29), respectively. Obviously, by using the DFBLA-SAR, the determinable range of target’s velocity is increased greatly. The image of targets, the image of the

Fig. 3. Imaging results formed by the first airplane. (a) Image of targets, (b) image of targets and ground, and (c) V-images of targets.

targets and ground, and the V-images of the targets are shown in Fig. 4(a)–(c), respectively. Compared with the case of the first airplane, the amounts of the targets’ shifts in azimuth direction

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Fig. 5. BLA-SAR imaging results. (a) Image of targets and (b) image of targets and ground.

∆i,shift [see (22) and (23)]. Furthermore, two SAR images formed by the two airplanes have a range direction migration about 34 range cells due to the difference of the slant ranges R1 and R2 . After the calibration of the two SAR images and accurate estimation of the location parameters, the imaging result of the targets and the final image after locating them on the scene by using DFBLA-SAR are illustrated in Fig. 5(a) and (b), respectively, where the targets are located accurately on the roads. B. Imaging Results Using DSBLA-SAR

Fig. 4. Imaging results formed by the second airplane with λ2 = 0.05 m. (a) Image of targets, (b) image of targets and ground, and (c) V-images of targets.

are the same, but the V-images are different observably. This is caused by the fact that the dual-carrier frequencies affect only the frequency of V-image fi but not the azimuth shift

When ν2 = ν1 , λ2 = λ1 , and d2 = 1.8 m = d1 , the system becomes DSBLA-SAR. In this case, the maximal range direction velocity, such that there is no location ambiguity, using only the second airplane and the two airplanes are 1.6 and 10 m/s according to (29), respectively. The determinable range of the target’s velocity is also increased greatly by using DSBLA-SAR. The image of targets and ground and the V-images of the targets are shown in Fig. 6(a)–(c), respectively.

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of the targets’ shifts in azimuth direction are the same but the V-images are different observably. The images also show a migration about 34 range cells in range direction caused by the difference of the slant ranges R1 and R2 . After the calibration of the two SAR images and accurate estimation of the location parameters, the imaging result of the targets and the final image after locating them on the scene by using DSBLA-SAR are also illustrated in Fig. 5(a) and (b), respectively, where the targets are located accurately on the roads.

C. Imaging Results Using DVBLA-SAR When d2 = d1 , λ2 = λ1 , and ν2 = 220 m/s = ν1 , the system becomes DVBLA-SAR. In this case, the maximal range direction velocity, so that there is no location ambiguity, using only the second airplane and the two airplanes are 2.2 and 22 m/s according to (29), respectively. Obviously, by using DVBLA-SAR, the determinable range of target’s velocity is increased greatly. The image of targets, the image of the targets and ground, and the V-images of the targets are shown in Fig. 7(a)–(c), respectively. Compared with the case of the first airplane, not only the V-images are different, but also the amounts of the azimuth shifts have the changes of 71 and 13 cells for the fast and the slow target, respectively. This is caused by the fact that the dual airplane velocities affect not only the frequency of V-image fi but also the azimuth shift ∆i,shift [see (22) and (23)]. Like the case of DFBLA-SAR and DSBLA-SAR, the range direction migration about 34 range cells due to the difference of the slant ranges R1 and R2 also must be corrected. After the calibration of the two SAR images and accurate estimation of the location parameters, the imaging result of the targets and the final image after locating them on the scene by using DVBLA-SAR are also illustrated in Fig. 5(a) and (b), respectively, where the targets are located accurately on the roads.

VI. C ONCLUSION

Fig. 6. Imaging results formed by the second airplane with d2 = 1.8 m. (a) Image of targets, (b) image of targets and ground, and (c) V-images of targets.

Compared with the case of the first airplane, because dual antenna spacings affect only the frequency of V-image fi but not the azimuth shift ∆i,shift [see (29) and (23)], the amounts

In this paper, a new system called BLA-SAR is introduced, and three algorithms for moving target detection, location, and imaging by using the three forms of the BLA-SAR are proposed, respectively. It is formulated that by using two airborne linear array SARs with two different carrier frequencies, two different antenna spacings, or two different airplane speeds, a moving target will show different information in the two V-images in the two airplanes. This information and the CRT are used to resolve the azimuth location ambiguity. Thus, BLASAR has the ability to locate fast moving targets as well as slowly moving targets accurately. Furthermore, some practical problems are studied. Lastly, some numerical experiments show the effectiveness of the BLA-SAR imaging algorithm for a moving target. As a remark, if a nongeostationary satellite or an airborne transmitter is used, the echo’s phase history would be affected by the transmitter. As a result, the Doppler information caused by the moving target is hard to be picked up from the echo’s phase history by the BLA-SAR method. This is the reason why

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As a final comment, besides the theory developed in this paper for BLA-SAR, some practical problems also need to be considered. For example, compared with the successful experimental systems with two single-channel airplanes in [1] and [2], the amount of the communications between the two airplanes, the memory, the computational complexity, and the economical cost will increase sharply in BLA-SAR. However, it is believed that these problems may be solved in the future with the fast development of electronic science and technology.

ACKNOWLEDGMENT The authors would like to thank the reviewers and the associate editor for their helpful comments that have helped to clarify the presentation of this paper. R EFERENCES

Fig. 7. Imaging results formed by the second airplane with ν2 = 220 m/s. (a) Image of targets, (b) image of targets and ground, and (c) V-images of targets.

we choose a geostationary satellite as the transmitter in this paper. Nevertheless, the nongeostationary satellite case will be under our future investigation.

[1] P. Dubois-Fernandez, H. Cantalloube, B. Vaizan, G. Krieger, R. Horn, M. Wendler, and V. Giroux, “ONERA-DLR bistatic SAR campaign: Planning, data acquisition, and first analysis of bistatic scattering behaviour of natural and urban targets,” Proc. Inst. Electr. Eng.—Radar, Sonar Navig., vol. 153, no. 3, pp. 214–223, Jun. 2006. [2] I. Walterscheid, J. H. G. Ender, A. R. Brenner, and O. Loffeld, “Bistatic SAR processing and experiments,” IEEE Trans. Geosci. Remote Sens., vol. 44, no. 10, pp. 2710–2717, Oct. 2006. [3] M. Weib, “Synchronisation of bistatic radar systems,” in Proc. IGARSS, 2004, vol. 3, pp. 1750–1753. [4] M. I. Pettersson, “Extraction of moving ground targets by a bistatic ultrawideband SAR,” Proc. Inst. Electr. Eng.—Radar, Sonar Navig., vol. 148, no. 1, pp. 35–40, Feb. 2001. [5] G. M. Herbert and P. G. Richardson, “Benefits of space-time adaptive processing (STAP) in bistatic airborne radar,” Proc. Inst. Electr. Eng.—Radar, Sonar Navig., vol. 150, no. 1, pp. 13–17, Feb. 2003. [6] R. Klemm, “Comparison between monostatic and bistatic antenna configurations for STAP,” IEEE Trans. Aerosp. Electron. Syst., vol. 36, no. 2, pp. 596–608, Apr. 2000. [7] M. P. Hartnett and M. E. Davis, “Operations of an airborne bistatic adjunct to space based radar,” in Proc. IEEE Radar Conf., May 2003, pp. 133–138. [8] ——, “Bistatic surveillance concept of operations,” in Proc. IEEE Radar Conf., May 2001, pp. 75–80. [9] R. L. Fante, “Ground and airborne target detection with bistatic adaptive space-based radar,” IEEE Aerosp. Electron. Syst. Mag., vol. 14, no. 10, pp. 39–44, Oct. 1999. [10] A. P. Whitewood, B. R. Muller, H. D. Griffiths, and C. J. Baker, “Bistatic synthetic aperture radar with application to moving target detection,” in Proc. Int. Radar Conf., Sep. 2003, pp. 529–534. [11] B. Friedlander and B. Porat, “VSAR: A high resolution radar system for detection of moving targets,” Proc. Inst. Electr. Eng.—Radar, Sonar Navig., vol. 144, no. 4, pp. 205–218, Aug. 1997. [12] G. Wang, X.-G. Xia, V. C. Chen, and R. L. Fiedler, “Detection, location, and imaging of fast moving targets using multifrequency antenna array SAR,” IEEE Trans. Aerosp. Electron. Syst., vol. 40, no. 1, pp. 345–355, Jan. 2004. [13] G. Wang, X.-G. Xia, and V. C. Chen, “Dual-speed SAR imaging of moving targets,” IEEE Trans. Aerosp. Electron. Syst., vol. 42, no. 1, pp. 368– 379, Jan. 2006. [14] G. Li, J. Xu, Y.-N. Peng, and X.-G. Xia, “Moving target location and imaging using dual-speed velocity SAR,” IET Radar, Sonar & Navigation, to be published. [15] ——, “Moving target location and imaging using dual-speed velocity SAR,” in Proc. IEEE AP-S Int. Symp., Jul. 2006, pp. 2701–2704. [16] J. C. Wood and T. D. Barry, “Linear signal synthesis using the Radon–Wigner transform,” IEEE Trans. Signal Process., vol. 42, no. 8, pp. 2105–2111, Aug. 1994. [17] V. C. Chen, “Time-frequency analysis of SAR image with ground moving targets,” Proc. SPIE, vol. 3391, pp. 295–302, Apr. 1998. [18] M. Soumekh, “Moving target detection in foliage using along track monopulse synthetic aperture radar imaging,” IEEE Trans. Image Process., vol. 6, no. 8, pp. 1148–1163, Aug. 1997.

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[19] J. H. McClellan and C. M. Rader, Number Theory in Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1979. [20] C. Ding, D. Pei, and A. Salomaa, Chinese Remainder Theorem: Applications in Computing, Coding, Cryptography. Singapore: World Scientific, 1999. [21] X.-G. Xia, “On estimation of multiple frequencies in undersampled complex valued waveforms,” IEEE Trans. Signal Process., vol. 47, no. 12, pp. 3417–3419, Dec. 1999. [22] ——, “An efficient frequency-determination algorithm from multiple undersampled waveforms,” IEEE Signal Process. Lett., vol. 7, no. 2, pp. 34–37, Feb. 2000. [23] G. Fornaro and G. Franceschetti, “Image registration in interferometric SAR processing,” Proc. Inst. Electr. Eng.—Radar, Sonar Navig., vol. 142, no. 6, pp. 313–320, Dec. 1995. [24] M. Migliaccio and F. Bruno, “A new interpolation kernel for SAR interferometric registration,” IEEE Trans. Geosci. Remote Sens., vol. 41, no. 5, pp. 1105–1110, May 2003. [25] L. Otmar, N. Holger, P. Valerij, and K. Stefan, “Models and useful relations for bistatic SAR processing,” IEEE Trans. Geosci. Remote Sens., vol. 42, no. 10, pp. 2031–2038, Oct. 2004. [26] C. J. Bradley, P. J. Collins, J. Fortuny-Guasch, M. L. Hastriter, G. Nesti, A. J. Terzuoli, and K. S. Wilson, “An investigation of bistatic calibration techniques,” IEEE Trans. Geosci. Remote Sens., vol. 43, no. 10, pp. 2185–2191, Oct. 2005. [27] X.-G. Xia and G. Wang, “Phase unwrapping and a robust Chinese remainder theorem,” IEEE Signal Process. Lett., to be published. [Online]. Available: http://www.ee.udel.edu/~xxia/RobustCRT.pdf [28] G. Li, J. Xu, Y.-N. Peng, and X.-G. Xia, “An efficient implementation of a robust phase unwrapping algorithm,” IEEE Signal Process. Lett., to be published.

Gang Li (S’06) was born in Heilongjiang Province, China, in 1979. He received the B.S. degree from Tsinghua University, Beijing, China, in 2002, where he is currently working toward the Ph.D. degree. His current research interests are in the areas of array signal processing, parameter estimation, SAR imaging, and moving target detection.

Jia Xu (M’06) was born in Anhui Province, China, in 1974. He received the B.S. and M.S. degrees from the Radar Academy of Air Force, Wuhan, China, in 1995 and 1998, respectively, and the Ph.D. degree from the Navy Engineering University, Wuhan, in 2001. He performed postdoctoral research in 2005 with the Department of Electronics Engineering, Tsinghua University, Beijing, China. Currently, he is an Associate Professor with Tsinghua University and the Academy of Air Force and has published more than 40 papers. His current research interests include detection and estimation theory, SAR/ISAR imaging, target recognition, array signal processing, and adaptive signal processing.

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Ying-Ning Peng (M’93–SM’96) received the B.S. and M.S. degrees from Tsinghua University, Beijing, China, in 1962 and 1965, respectively. In 1993, he joined the Department of Electronic Engineering, Tsinghua University, Beijing, where he is currently a Professor. He has worked with real-time signal processing for many years and has published more than 200 papers and has received many awards for his contributions to research and education in China. Dr. Peng is a member of the Chinese Institute of Electronics.

Xiang-Gen Xia (M’97–SM’00) received the B.S. degree in mathematics from Nanjing Normal University, Nanjing, China, in 1983, the M.S. degree in mathematics from Nankai University, Tianjin, China, in 1986, and the Ph.D. degree in electrical engineering from the University of Southern California, Los Angeles, in 1992. He was a Research Scientist with the Air Force Institute of Technology, Wright-Patterson Air Force Base, OH, during 1993–1994 and a Senior/Research Staff Member with Hughes Research Laboratories, Malibu, CA, during 1995–1996. In September 1996, he joined the Department of Electrical and Computer Engineering, University of Delaware, Newark, where he is currently a Professor. He was a Visiting Professor with the Chinese University of Hong Kong, Shatin, Hong Kong, during 2002–2003, where he is currently an Adjunct Professor. He has published about 145 refereed journal articles and has authored the book Modulated Coding for Intersymbol Interference Channels (Marcel Dekker, 2000). He is the holder of seven U.S. patents. His current research interests include space-time coding and OFDM systems, as well as SAR and ISAR imaging of moving targets. Dr. Xia is currently an Associate Editor of the IEEE SIGNAL PROCESSING LETTERS, the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, and the Journal of Communications and Networks. He served as an Associate Editor of the IEEE TRANSACTIONS ON SIGNAL PROCESSING from 1997 to 2003, the IEEE TRANSACTIONS ON MOBILE COMPUTING from 2001 to 2004, and the EURASIP Journal on Applied Signal Processing from 2001 to 2004. He was a Guest Editor of the EURASIP Journal of Applied Signal Processing Special Issue on “Space-Time Coding and Its Applications” (March and May 2002). He is a member of the Sensor Array and Multichannel Technical Committees of the IEEE Signal Processing Society. He was the General Co-Chair of the 2005 International Conference on Acoustics, Speech and Signal Processing. He received the National Science Foundation Faculty Early Career Development (CAREER) Program Award in 1997, the Office of Naval Research Young Investigator Award in 1998, the Outstanding Overseas Young Investigator Award of the National Natural Science Foundation of China in 2001, and the Outstanding Junior Faculty Award of the Engineering School of the University of Delaware in 2001.