Joint Amplitude-Phase Compensation for Ionospheric ... - IEEE Xplore

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 55, NO. 6, JUNE 2017

Joint Amplitude-Phase Compensation for Ionospheric Scintillation in GEO SAR Imaging R. Wang, Cheng Hu, Senior Member, IEEE, Y. Li, S. E. Hobbs, W. Tian, X. Dong, and L. Chen

Abstract— The ionospheric scintillation induced by local ionospheric plasma anomalies could lead to significant degradation for geosynchronous earth orbit synthetic aperture radar (SAR) imaging. As radar signals pass through the ionosphere with locally variational plasma density, the signal amplitude and phase fluctuations are induced, which principally affect the azimuthal pulse response function. In this paper, the compensation of signal amplitude and phase fluctuations is studied. First, space-variance problem of scintillation is addressed by image segmentation. Then, SPECAN imaging algorithm is adopted for each image segment, because it is computationally efficient for small imaging scene. Furthermore, an iterative algorithm based on entropy minimum is derived to jointly compensate the signal amplitude and phase fluctuations. Finally, a real SAR scene simulation is used to validate our proposed method, where both the simulated scintillation using phase screen technique and the real GPS-derived scintillation data are adopted to degrade the imaging quality. Index Terms— Amplitude and phase fluctuations, autofocus, entropy minimum, geosynchronous earth orbit synthetic aperture radar (GEO SAR), ionosphere scintillation.

I. I NTRODUCTION EOSYNCHRONOUS earth orbit synthetic aperture radar (GEO SAR) could realize the observation on the region of interest with short-time revisit to satisfy the demands of disaster monitoring on finer temporal resolution [1], [2]. In recent years, many investigations on GEO SAR have been widely developed from imaging algorithms to system designs [3]–[11]. The ionospheric scintillation is induced by electron density irregularities, which can cause random variations in the amplitude and phase of a propagating wave [12]. The scintillation happens mainly at postsunset sector of the equatorial zone and

G

Manuscript received June 2, 2015; revised November 24, 2015, April 11, 2016, October 24, 2016, and December 20, 2016; accepted February 10, 2017. Date of publication March 13, 2017; date of current version May 19, 2017. This work was supported in part by the National Natural Science Foundation of China under Grant 61120106004, Grant 61225005, Grant 61427802, and Grant 61471038, and in part by the Beijing Natural Science Foundation under Grant 4162052. (Corresponding Author: Cheng Hu.) R. Wang is with the Department of Electronics Engineering, Tsinghua University, Beijing 100084, China (e-mail: [email protected]). C. Hu, Y. Li, W. Tian, X. Dong, and L. Chen are with the School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China (e-mail: [email protected]). S. E. Hobbs is with the Space Research Centre, Cranfield University, Bedford MK43 0AL, U.K. (e-mail: [email protected]). 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.2017.2672078

typically starts after 6 P. M. local time, increases in intensity until about 10 P. M ., and then slowly decays throughout the night until the early morning hours. Moreover, the frequency of the scintillation is related to the solar cycle and season of the year. The severity of scintillation is frequency-dependent [13]. At lower frequencies, especially at very high frequency, UHF, and L-band, the effects can be quite significant [14]–[17]. In recent paper [18], Advanced Land Observing Satellite Phased Array type L-band Synthetic Aperture Radar L-band images during October 2010 in equatorial zone over South America are analyzed statistically. It is shown that about 14% of the surveyed images are contaminated by visible stripes aligned to the local geomagnetic field, and these images are found during 23 of 31 days surveyed (74%). The stripes are only identified in nighttime data (ascending orbit direction), which are believed to be the results of ionospheric scintillations. Consequently, for L-band GEO SAR design [1], [10], [19], the effect of ionospheric scintillation cannot be neglected, and it could lead to significant degradation for GEO SAR imaging if the decorrelation distance is smaller than the SAR equivalent synthetic aperture length [20], [21]. As radar signals pass through the ionosphere with the locally variational plasma density, not only do signal delays become more indeterminate, but also the signal amplitude and phase vary unpredictably [22]. The former mainly influences the range direction while the latter degrades the azimuth focusing in SAR image formation. Therefore, it is essential to develop an effective method for scintillation compensation. In this paper, the compensation of signal amplitude and phase fluctuations is studied. Due to the unpredictability of signal disturbances, it is necessary to use the data-derived autofocus techniques. One of the most well-known techniques is phase gradient autofocus (PGA) [23], which estimates phase errors based on the isolated dominant scatterers. However, it is often difficult to pick up such dominant scatterers in severely blurred SAR images. In recent years, the autofocus methods based on sharpness optimization are developed widely, especially for the entropy minimum [24]–[26]. In [24], an adaptiveorder polynomial model is adopted to fit the phase error. However, the signal amplitude and phase fluctuations induced by scintillation are usually considered random [13], [21]. It means that a mass of polynomial coefficients are need to estimate, and the computational burden will be quite heavy. In [25] and [26], nonparameter model is adopted to estimate

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WANG et al.: JOINT AMPLITUDE-PHASE COMPENSATION FOR IONOSPHERIC SCINTILLATION

phase errors, and the good autofocus results are obtained. In addition, note that the existent autofocus methods are all only limited to the phase correction. The compensation of the amplitude fluctuation is still not studied in the public literatures. The SAR image autofocus methods are based on the assumption that all the scatterers should have the identical signal error at one azimuth sampling time. However, different scatters correspond the different ionospheric puncture points, and consequently, the signal fluctuations induced by scintillation are different for scatterers in the scene. As the basis of scintillation theory, the decorrelation distance is defined as the representation of the correlation of two puncture points [27], [28]. If the distance between two puncture points is smaller than the decorrelation distance, the signal fluctuations could be considered identical. The decorrelation distance is generally several kilometers for L-band, but the GEO SAR imaging scene is usually up to several hundreds of kilometers. Therefore, the image segmentation is needed, so as to make sure that the distance between puncture points for scatterers in the image segment is smaller than the decorrelation distance of scintillation. In this paper, the effect of ionospheric scintillation on GEO SAR imaging is discussed initially. First, space-variance problem of scintillation is addressed by image segmentation. Then, SPECAN imaging algorithm is adopted for each image segment, because it is computationally efficient for small imaging scene. The derivation of integral sidelobe ratio (ISLR) deterioration induced by scintillation is also analyzed. Furthermore, an iterative method based on entropy minimum is proposed to jointly compensate the signal amplitude and phase fluctuations induced by ionospheric scintillation. The principle of the proposed iteration is to construct a series of local quadratic fits to gradually approach the minimal entropy. This method has no any model assumption about signal amplitude and phase fluctuations. Finally, simulations and experiments are performed to validate the proposed method. Considering the similarities between GPS and GEO SAR satellites in the operating band and signal propagation through the complete ionosphere, GPS signal could be exploited to demonstrate the effects of scintillation on GEO SAR imaging. One occurrence of ionospheric scintillation was captured and recorded by a GPS receiver in the field experiment at Zhuhai in the southern China. The signal amplitude and phase fluctuations due to scintillation were extracted from the recorded GPS data. The echo data of a real SAR scene are simulated to test our proposed method, where the recorded amplitude and phase fluctuations are introduced. This paper is arranged as follows. Section II presents the effects of ionospheric scintillation on GEO SAR imaging. The space-variance problem of scintillation and the random fluctuations of signal amplitude and phase are analyzed in detail for the azimuth focusing. An iterative method based on entropy minimum is proposed to jointly compensate the signal amplitude and phase fluctuations in Section III. The simulation and experiment validations of the proposed method are shown in Sections IV and V. Finally, the conclusions are drawn in Section VI.

Fig. 1.

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GEO SAR geometry.

II. E FFECTS OF I ONOSPHERIC S CINTILLATION ON GEO SAR I MAGING A. Space-Variance Problem Assume that the transmitted signal can be expressed as s(τ ) = w(τ ) exp{ j 2π f 0 τ − j π K r τ 2 }

(1)

where w (τ ) is the signal envelop, f 0 is the carrier frequency, K r is the range frequency modulation (FM) rate, and τ is the fast time. After the downconversion, the echo signal from Target A (Fig. 1) can be written as s R (t, τ ; A)

2|pS (t) − pA | w τ− = δ (t)e c 4π 2|pS (t) − pA | 2 |pS (t)−pA | −j × exp − j π K r τ − c λ A

j φ A (t )

(2) where t is the azimuth slow time and the beam center points at the imaging scene center while t is zero. |pS (t) − pA | is the slant range history of Target A, where pS (t) and pA are the position vectors of the satellite and Target A. In addition, δ A (t) and φ A (t) represent signal amplitude and phase fluctuations induced by scintillation, respectively. Then, after the range compression and range cell migration correction, the following relationship can be obtained as: 2R A A s R (t, τ ; A) = δ A (t)e j φ (t ) p τ − c 4π |pS (t) − pA | × exp − j (3) λ where p(·) is the pulse response function of range compression, and R A is the closest slant range from Target A to the satellite trajectory. With respect to Target A and Target B, because the ionospheric puncture points (a and b in Fig. 1) of radar wave are different, the signal amplitude and phase fluctuations are also not identical. The coherence of echo signal between Target A and Target B can be measured by the generalized ambiguity function [27]–[29]. The solution to the second moment of the generalize ambiguity function is the mutual correlation function, which can be expressed as (z, ρ, ζ ) = δ A e j φ · δ B e− j φ A

B

(4)

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Fig. 2.


Image segmentation.

where z and ζ represent the propagation path and propagation constant of radar wave, respectively. The denotation of · represents the operator of mutual correlation function, which is the function of the distance ρ between the ionospheric puncture points a and b. The decorrelation distance ρ0 is defined as [27]–[29] (z, ρ0 , ζ ) = e−1 . (z, ρ = 0, ζ )

(5)

In [27] and [28], the decorrelation distance of the intermediate scintillation could be several kilometers for L-band radar wave if the phase fluctuation is only considered. However, so far, there is no theoretical analysis about the decorrelation distance considering both amplitude and phase fluctuations. Moreover, for the phase fluctuation, the decorrelation distance of several kilometers is only a rough estimate even if the scintillation intensity index S4 and phase variance σφ2 are known. In order to satisfy the autofocus assumption that all the scatterers in the imaging scene have the approximately identical signal fluctuations at each azimuth sampling time (as shown in Fig. 2), the SAR image segmentation must be performed. Thoroughly considering decorrelation distance analysis mentioned earlier and computational burden, the choice of several kilometers is selected as an initial segmentation size in the SAR image correction. If the image quality after amplitude and phase compensations is not improved, the segmentation size will decrease further until the satisfied image is obtained. As thus, the target echo in the same image segment can be written as 4π 2R j φ(t ) ) exp − j |pS (t) − p| . p(τ − s R (t, τ ) = δ(t)e c λ (6) B. SPECAN Imaging The conventional SAR image formation methods including SPECAN, range-Doppler algorithm, chirp scaling algorithm, and ω–k or Range Migration Algorithm algorithm [31]. The latter four algorithms are suitable for the high-resolution and large-scene SAR imaging, where the accurate matching function is derived, and the space variance of rang migration and azimuth FM rate along the range direction is considered. For SPECAN, the matching function is structured based on a

reference point in the imaging scene, and the space variance is ignored. Thus, SPECAN is suitable for small SAR imaging scene. Meanwhile, because only one fast Fourier transform (FFT) for azimuth focusing is needed, SPECAN is computationally efficient [30]. For scintillation compensation, small image segmentation is performed to address the space-variance problem of scintillation. Therefore, considering the small image segmentation and computational efficiency, SPECAN is finally chosen. It is not necessary to adopt the high-accurate algorithm for small SAR scene imaging. In this paper, the SPECAN processing is adopted for azimuth focusing of each image segment, and the azimuth centers of each image segment are selected as the reference points. Then, utilizing quadratic Taylor approximation, the azimuth matched function of SPECAN processing can be expressed as yRef 2 |Ve |2 t− (7) sRef (t, τ ) = exp − j 2RRef |Ve | where yRef is the azimuth center of the image segment, and Ve is the equivalent velocity vector of the satellite. In addition, RRef is the closest slant range from the reference point to the satellite trajectory. Then, the SPECAN processing can be expressed as sSPECAN ( f, τ ) = F T [s R (t, τ ) · sRef (t, τ )∗ ] +∞ = δ(t)e j φ(t )s(t, τ )e− j 2π f t dt −∞

where F T [·] represents the Fourier transform and 2R s(t, τ ) = p τ − c ⎫ ⎧ 4π R 4π|Ve | y − yRef ⎪ ⎪ ⎪ +j t⎪ ⎬ ⎨−j λ λ R Ref . × exp 2 2 2π y − yRef ⎪ ⎪ ⎪ ⎪ ⎭ ⎩−j λ RRef

(8)

(9)

It can be found that if amplitude and phase fluctuations induced by scintillation are removed, the azimuth focusing can be achieved by FFT. C. Effects of Amplitude and Phase Fluctuations on Azimuth Focusing The signal amplitude and phase fluctuations induced by scintillation are usually considered as random variables. Assume that the probability density functions of signal amplitude and phase fluctuations are p(δ) and p(φ). While |φ (t)| < 0.5 rad, the quadratic approximation can be adopted 1 2 j φ(t ) δ(t)e = (1 + δ(t) − 1) 1 + j φ(t) − φ (t) 2 1 2 ≈ 1 + j φ(t) − φ (t) + d(t) (10) 2 where the cross terms of amplitude and square phase fluctuations are ignored and d(t) = δ(t) − 1.

(11)


Thus, (8) can be rewritten as sSPECAN ( f, τ ) = so ( f, τ ) + sφ ( f, τ ) + sφ 2 ( f, τ ) + sd ( f, τ ) (12) where

sφ ( f, τ ) = j

+∞

(18) s (t, τ ) e

−∞ +∞ −∞

− j 2π f t

dt

Next, we assume ξ = t1 , η = t1 − t2 .

φ(t)s (t, τ ) e− j 2π f t dt

1 +∞ 2 sφ 2 ( f, τ ) = − φ (t)s (t, τ ) e− j 2π f t dt 2 −∞ +∞ sd ( f, τ ) = d(t)s (t, τ ) e− j 2π f t dt. −∞

(13)

E[|sSPECAN ( f, τ )|2 ] = E[|so ( f, τ )|2 ] + E[|sφ ( f, τ )|2 ] + E[|sφ 2 ( f, τ )|2 ] + E[|sd ( f, τ )| ] + 2Re{E[so ( f, τ )sφ ( f, τ )∗ ] + E[so ( f, τ )sφ 2 ( f, τ )∗ ] + E[so ( f, τ )sd ( f, τ )∗ ] + E[sφ ( f, τ )sφ 2 ( f, τ )∗ ]

(14)

Note that the cross terms related to sφ ( f, τ ) is pure imaginary, so (14) can be simplified as E[|sSPECAN ( f, τ )| ] = E[|so ( f, τ )|2 ] + E[|sφ ( f, τ )|2 ] + E[|sφ 2 ( f, τ )|2 ] 2

+ E[|sd ( f, τ )|2 ] + 2Re{E[so ( f, τ )sφ 2 ( f, τ )∗ ] + E[so ( f, τ )sd ( f, τ )∗ ] (15) + E[sφ 2 ( f, τ )sd ( f, τ )∗ ]}.

(16)

First, with respect to |sφ ( f, τ )|2 , the following relationship can be obtained as:

=

+∞

j φ(t1 )s(t1 , τ )e− j 2π f t1 dt1

+∞

−∞

∗

In general case, the profile of so ( f, τ ) is similar to the delta function, and the power is concentrated to the main lobe between −B/2 and B/2, where B is the width of main lobe. Thus, (21) can be simplified as +∞ |so ( f − ζ, τ )|2 dζ E[|sφ ( f, τ )|2 ] = Sφ ( f ) −∞

≈ Sφ ( f ) · PML

− j φ(t2 )s (t2 , τ )e ∗

Rφ (t1 − t2 )s(t1 , τ )s (t2 , τ )e

− j 2π f (t1 −t2 )

dt2 dφ

dt1 dt2 .

(17)

(22)

where PML is the energy of main lobe of so ( f, τ ). Thus, it can be obtained +∞ +∞ 2 2 E[|sφ ( f, τ )| ]d f < PML Sφ ( f )d f = σφ2 PML

B/2 B/2

−∞ B/2

E[|sφ ( f, τ )|2 ]d f = PML

−B/2

Sφ ( f )d f ≈ 0

(23)

where σφ2 is the variance of signal phase fluctuation φ (t). In like manner, for the cross term E[sφ 2 ( f, τ )sd ( f, τ )∗ ], we can obtain +∞ 2Re{E[sφ 2 ( f, τ )sd ( f, τ )∗ ]}d f 2 B/2

j 2π f t2

(20)

where ∗ represents the convolution operator. On the basis of Wiener–Khintchine theorem, the Fourier transform of correlation function Rφ (η) is the power spectral density Sφ ( f ) of the signal phase fluctuation φ (t). In addition, utilizing Fourier transform property of the convolution, (20) can be rewritten as +∞ Sφ (ζ )|so ( f − ζ, τ )|2 dζ. (21) E[|sφ ( f, τ )|2 ] =

< −PML

−∞

×

−∞

= F T [Rφ (η)] ∗ F T [ A(η)]

−B/2

Based on the definition of ISLR, it can be obtained +∞ 2 B/2 E[|sSPECAN ( f, τ )|2 ]d f ISLR = B/2 . 2 −B/2 E[|sSPECAN ( f, τ )| ]d f

−∞

E[|sφ ( f, τ )|2 ] +∞ +∞ ∗ = Rφ (η) s(ξ, τ )s (ξ − η, τ )dξ e− j 2π f η dη −∞ −∞ +∞ = Rφ (η)A(η)e− j 2π f η dη

−∞

2

+ E[sφ ( f, τ )sd ( f, τ )∗ ] + E[sφ 2 ( f, τ )sd ( f, τ )∗ ]}.

(19)

Then, (17) can be rewritten as

The first integral item is the ideal azimuth focusing, and the latter items are corresponding to the azimuth degradation induced by scintillation. Because the amplitude and phase fluctuations induced by scintillation can be considered as random errors, here, we use the mean square of SSPECAN ( f, τ ) to assess the effect of scintillation on azimuth focusing. Using (12), the following relationship can be obtained:

E[|sφ ( f, τ )|2 ] +∞ p(φ) =

Because the signal variation induced by scintillation can be considered as a stationary stochastic process [12], the autofocus function of Rφ (t1 − t2 ) in (17) can be expressed as +∞ Rφ (t1 − t2 ) = p(φ)φ(t1 )φ(t2 )dφ = E[φ(t1 )φ(t2 )]. −∞

so ( f, τ ) =

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+∞

−∞

Re{Sφ 2 d ( f )}d f

1 = − PML σφ22 +d − σφ22 − σd2 2 B/2

−B/2

E[|sφ ( f, τ )|2 ]d f

= −PML

B/2

−B/2

Re{Sφ 2 d ( f )}d f ≈ 0.

(24)

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With respect to E[so ( f, τ )sφ 2 ( f, τ )∗ ], the following relationship can be obtained as: E[so ( f, τ )sφ ( f, τ )∗ ] +∞ 1 E[φ 2 (t)]s ∗ (t, τ )e j 2π f t dt = − so ( f, τ ) 2 −∞ 1 = − μφ 2 |so ( f, τ )|2 2 where μφ 2 is the mean of the phase fluctuation φ 2 (t). Then, we can obtain +∞ 1 2 E[so ( f, τ )sφ ( f, τ )∗ ]d f = − μφ 2 PSL 2 B/2 B/2 1 E[so ( f, τ )sφ ( f, τ )∗ ]d f = − μφ 2 PML 2 −B/2

(25)

where αn and ψn are used to compensate the signal amplitude and phase fluctuations induced by scintillation. sc (k, m) represents the SAR image after amplitude and phase compensation while sap (n, m) is the contaminated echo data in the azimuth time domain after range compression and azimuth SPECAN processing [see (28)]. Note that there is no any parametric model assumption about αn and ψn . In this paper, image entropy is used to measure the SAR image quality. It is generally acknowledged that the better image quality is corresponding to the smaller image entropy. Consequently, the scintillation compensations can be considered to find a set of αn and ψn by minimizing the image entropy, which can be expressed as

(26)

E =−

k=0 m=0

where PSL is the energy of side lobes of so ( f, τ ). Similarly, the another terms in (15) can be derived, and the final ISLR can be simplified as ISLR < ISLROrignal +

3 2 2 σφ

+ 14 σφ22 + 32 σd2 − 12 σφ22 +d 1 − μφ 2 + 2μd

(27)

where σφ22 and σd2 represent the variances of the square item of signal phase and amplitude fluctuations, respectively. In addition, μd is the mean of amplitude fluctuation, and σφ22 +d is the variance of the φ 2 + d. Therefore, the ionospheric scintillation will lead to the increase in ISLR, and the weak scatterers should be submersed in the side lobes of strong scatterers. The final SAR image quality will be significantly degraded. For example, with respect to the ideal sinc function, ISLR is −10 dB or 0.1. If ISLRTotal is 0.1, the increase in ISLR will be 3 dB. Hence, it is essential to develop an effective method for scintillation compensation. In addition, note that the signal amplitude and phase fluctuations are usually considered as random variables. It implies that parametric model assumption is quite inadvisable for the signal amplitude and phase fluctuations. In Section III, an iterative method based on entropy minimum is proposed for scintillation compensation. III. I ONOSPHERIC S CINTILLATION C OMPENSATIONS BASED ON E NTROPY M INIMUM In the real processing, the data are discrete, and thus, s(t, τ ) is rewritten as s(n, m) in the next statement, where the indices n and m refer to the azimuth and range sample, respectively. Thus, (8) can be expressed as N−1 2π δn e j φn s(n, m) exp − kn s(k, m) = N n=0 N−1 2π = (28) sap (n, m) exp − kn . N n=0

Based on (28), the compensation model can be formulated as N−1 2π (29) sc (k, m) = αn e j ψn sap (n, m) exp − kn N n=0

N−1 M−1

|sc (k, m)|2 N−1 M−1 2 k=0 m=0 |sc (k, m)|

|sc (k, m)|2 × ln N−1 M−1 . 2 k=0 m=0 |sc (k, m)|

(30)

Note that it is rather difficult to derive the analytical solution of the minimum of image entropy in (30). Next, an iterative method is proposed to find the minimum of image entropy. First, (30) is expanded to the Taylor series i }, at α i = {α1i , α2i , . . . , α iN−1 } and ψ i = {ψ1i , ψ2i , . . . , ψ N−1 where the superscript refers to the i thiteration. The cubic and higher order items are ignored 1 2 E = E|α i ,ψ i + E α n α i ,ψ i αn −αni + E αn α i ,ψ i αn −αni 2 1 2 i E = E|α i ,ψ i + E ψn α i ,ψ i ψn −ψn + E ψn α i ,ψ i ψn −ψni . 2 (31) The detailed derivations are quite cumbersome, so the derivatives in (31) are directly given as follows: E α n

2Nαn M−1 |sap (n, m)|2 = N−1 m=0 M−1 2 2 k=0 m=0 |sc (k, m)|

×

N−1 M−1

|sc (k, m)|2 ln |sc (k, m)|2

k=0 m=0

−

2NRe

M−1

m=0 e

j ψns (n, m)IDFT[s (k, m) ln |s (k, m)|2 ]∗ ap c c k N−1 M−1 2 k=0 m=0 |sc (k, m)|

(32) where IDFT[·] represents the inverse discrete Fourier transform. Note that the computational burden can be significantly reduced by using FFT to replace discrete Fourier transform in (32) and (33)–(35), as shown at the bottom of the next page. Subsequently, the minimums of (31) can be derived E α n α i ,ψ i E ψ n α i ,ψ i i i , ψn = ψn − . (36) αn = αn − E E i i i i αn α ,ψ

ψn α ,ψ


The amplitude and phase corrections in the i + 1thiteration will be updated using (36), namely ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ α1i+1 α1i E α 1 E α1 ⎢ i+1 ⎥ ⎢ ⎢ ⎥ ⎢ α2 ⎥ ⎢ α2i ⎥ E α 2 E α2 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎢ ⎥ ⎥ ⎢ ⎥ . . . ⎢ ⎥ ⎥ ⎢ .. .. ⎢ ⎥ ⎢ .. ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎢ ⎥ ⎥ ⎢ i+1 ⎥ ⎢ i ⎢ E ⎥ ⎢ α N−1 ⎥ ⎢ α N−1 ⎥ E ⎢ ⎥ ⎥ α α N−1 N−1 ⎢ ⎥ . (37) ⎥−⎢ ⎥ i ⎢ ψ i+1 ⎥ = ⎢ E E ψ ⎢ ⎥ ⎥ ⎢ ψ1 ψ1 1 ⎢ 1 ⎥ ⎢ ⎥ ⎥ ⎢ i+1 ⎥ ⎢ ⎢ ⎥ E ψ 2 E ψ 2 ψ2i ⎥ ⎢ ψ2 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎢ ⎥ ⎥ ⎢ .. .. ⎢ ⎥ ⎢ .. ⎥ ⎢ ⎥ ⎢ ⎥ . . . ⎣ ⎦ ⎦ ⎣ ⎣ ⎦ i i+1 E E ψ N−1 ψ N−1 ψ N−1 ψ N−1 α i ,ψ i This iteration principle can be considered that a series of local quadratic curves are constructed to gradually approach the extremum of the objective function of (30). Note that the second derivative should be positive so as to make sure the iteration could converge toward the minimum. IV. S IMULATION VALIDATIONS A. Scintillation Effects on ISLR As analyzed in Section II, the signal amplitude and phase fluctuations due to scintillation can lead to the increase in ISLR. A point-target simulation is performed to test this conclusion. The signal amplitude and phase fluctuations are used to degrade the imaging quality. The amplitude and phase fluctuations due to scintillation are assumed to obey the Nakagami and Gaussian distributions, respectively. The normalized standard deviation of the intensity scintillation (S4) and the standard deviation of the phase scintillation (σφ ) are both set to be 0.4. The imaging results are shown in Fig. 3.

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Fig. 3. Effects of signal amplitude and phase fluctuations due to scintillation on point target. (a) Imaging result of point target. (b) Comparison of the azimuth PSF with and without signal amplitude and phase fluctuations. TABLE I S TATISTICAL VARIANCES OF S IGNAL A MPLITUDE AND P HASE F LUCTUATIONS

There is nearly no deterioration about the resolution or 3-dB width of point spread function (PSF). However, the side lobes rise evidently with the ISLR of −4.4 dB whereas the ideal value is −10 dB. Based on the statistical analysis, the variances of signal amplitude and phase fluctuations are listed in Table I. Using (27), ISLR is −3.9 dB slightly larger than −4.4 dB, and it is consistent with the analysis in Section II. B. Estimation Accuracy Analysis First, the simulation is used to illustrate the focusing performance under entropy minimum criterion. An ideal rectangular window without amplitude and phase fluctuations is adopted

E αn

E ψ n E ψ n

2 N−1 M−1 M−1 M−1 |sap (n, m)|2 8 Nαn m=0 |sap (n, m)|2 2N m=0 = N−1 M−1 |sc (k, m)|2 ln |sc (k, m)|2 2 − N−1 M−1 3 × 2 2 k=0 m=0 k=0 m=0 |sc (k, m)| k=0 m=0 |sc (k, m)| M−1 M−1 2 2 8N αn m=0 |sap (n, m)| j ψn 2 ∗ + N−1 M−1 e sap (n, m) · IDFT[sc (k, m) ln |sc (k, m)| ]k × Re 2 2 m=0 k=0 m=0 |sc (k, m)| N−1 M−1 M−1 2 2 |sap (n, m)|2 + 2 k=0 2 m=0 [2Nαn M−1 |sap (n, m)|2 ]2 m=0 |sap (n, m)| ln |sc (k, m)| − + N−1 m=0 2 N−1 M−1 M−1 2 2 k=0 m=0 |sc (k, m)| k=0 m=0 |sc (k, m)| N−1 M−1 j ψ ∗ n s (n, m)2 sc (k,m) exp{− j 4π kn 2Re ap k=0 m=0 e sc (k,m) N − N−1 M−1 2 |s (k, m)| k=0 m=0 c M−1 "∗ ! 2N j ψn 2 = N−1 M−1 Im αn e sap (n, m) · IDFT sc (k, m) ln |sc (k, m)| 2 k k=0 m=0 |sc (k, m)| m=0 M−1 2 j ψn 2 ∗ = N−1 M−1 αn sap (n, m)e · IDFT[sc (k, m) ln |sc (k, m)| ]k NRe 2 k=0 m=0 |sc (k, m)| m=0 M−1 N−1 s ∗ (k, m) 4π c + Re [αn sap (n, m)e j ψn ]2 · exp − j kn sc (k, m) N m=0 k=0 M−1 M−1 N−1 2 2 2 − |αn sap (n, m)| ln |sc (k, m)| − |αn sap (n, m)| m=0

k=0

m=0

(33) (34)

(35)

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Fig. 4. Compensation results for the ideal rectangular window using the proposed method (a) amplitude and (b) phase corrections. Fig. 6. Estimation accuracy versus the number of range cells and point scatterers in each range cell for (a) amplitude and (b) phase.

Fig. 5. Impulse response of the rectangular window and the weighed window under entropy minimum criterion. Fig. 7.

as the input of the proposed method. The amplitude and phase estimates are expected to the constant and zero, respectively. By applying our proposed autofocus method to the ideal rectangular window data, the amplitude and phase estimates are shown in Fig. 4. It can be seen that the phase estimate is zero, but the amplitude estimate does not keep constant. Namely, the optimal amplitude profile under entropy minimum criterion is some weighed window function Wn , rather than the rectangular window. Consequently, after compensation based on entropy minimum, the final amplitude profile will become this weighed window function Wn . If the amplitude error inducted by scintillation is denoted as δn and the amplitude compensation is denoted as αn , the final amplitude profile can be denoted as δn ·αn , which is equivalent to this optimal amplitude profile Wn under entropy minimum criterion. The impulse response of this weighed window is shown in Fig. 5. Compared with the sinc function, the side lobes are below −20 dB, but the width of main lobe is spread slightly. Next, the estimation accuracy of the proposed method will be analyzed. The echo data with different number of point scatterers and range cells are simulated. Without losing gener-

Removal of the weighed window function.

ality, the magnitudes of these point targets are of the Rayleigh distribution with the scale parameter of one while the phases are uniformly distributed between −π and π. The amplitude and phase fluctuations due to scintillation are assumed to obey the Nakagami and Gaussian distributions, respectively. The normalized standard deviation of the intensity scintillation (S4) and the standard deviation of the phase scintillation (σφ ) are both still set to be 0.4. The total sample time is 100 s with the sample rate of 100 Hz. The complex white Gaussian noise is added to adjust the signal noise ratio (SNR). Monte Carlo simulations are performed so as to reveal more accurate curves. Fig. 6 shows the rms estimate errors of amplitude and phase fluctuations. The weighed window is removed in the rms calculation of the amplitude estimate (as shown in Fig. 7), which is done by an eight-order polynomial fitting as follows: n = δn αn − polyfit{δn αn , 8}.

(38)

From Fig. 6, the estimation accuracies of amplitude and phase fluctuations are directly proportional to the number of range cell and inversely proportional to target quantity in each


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range cell. It implies that the isolated dominant scatterer is helpful to improve the estimation accuracy. However, the same accuracy can also be achieved by increasing the number of range cells in the estimation. Therefore, our proposed method is still valid in case of no isolated dominant scatterer. In addition, note that the amplitude estimate is more sensitive to SNR. C. Space-Variance Compensation Validation Utilizing Phase Screen Technique The phase screen technique in [15], which can generate 2-D (azimuth and range) amplitude and phase fluctuations, is adopted to validate the effectiveness of image segmentation for ionosphere scintillation space-variant compensation. The parameters of phase screen are set to be consistent with that in [15]. The magnetic heading of satellite motion is set to −6.5°. The turbulence intensity (Ck L), phase spectral index ( p), and outer scale (L0 ) are 17.5 × 1033 , 9, and 5 km, respectively, in our simulation. A real SAR scene of 3.5 km (ground range) ×2.9 km (azimuth) is used to generate SAR echo data using our developed simulation software regarding L-band GEO SAR parameters. The semimajor axis of satellite ellipsoid orbit is 42 164 km with the eccentricity of 0.07 while the orbit inclination is 60°. The local time of the ascending node is about 20:35:10, and the geographic coordinate of simulated position is 3.8°S and 135.2°E. The transmitted signal band is 18 MHz, and the incidence angle is around 30°. For the central target in the scene, the FM rate is about 0.62 Hz/s, and the synthetic aperture time is 100 s in total. Consequently, the azimuth signal band is about 62 Hz while the pulse repetition frequency (PRF) is 100 Hz. Because the satellite’s equivalent velocity is 1.32 km/s, the azimuth resolution of the ideal SAR images is about 21 m. Because the irregularities are aligned to the local geomagnetic field, it is found that space variance in the range direction is severer and cannot be neglected. Consequently, the segmentation is further performed, and the segmentation length is 350 m along the range direction. The imaging results are shown in Fig. 8. It can be clearly seen from Fig. 8(d) that the autofocus result using our proposed method has significant improvement. The result using our proposed method without range segmentation is also shown in Fig. 8(c), and the increase in ISLR can be still observed. Therefore, the segmentation is necessary and effective to deal with the space-variance problem of ionospheric scintillation. In addition, to further show the maximal segmentation length for different phase and amplitude scintillations, different states of scintillations are also simulated. The turbulent intensity of Ck L represents the scintillation fluctuation in the range direction for phase screen method in [15]. Then, different states ofCk L are used to test the maximal segmentation length for our method, which are 1 × 1033, 5 × 1033, 10 × 1033, besides 17.5 ×1033 above. Through compensation simulations, the maximal segmentation lengths in range for these different scintillations are 3500, 1750, 700, 350 m, respectively.

Fig. 8. GEO SAR imaging results. (a) Ideal SAR image. (b) Degraded image by amplitude and phase fluctuations. (c) Autofocus image using our proposed method without range segmentation. (d) Autofocus image using our proposed method with range segmentation.

Fig. 9.

Experiment system for GPS data acquisition.

V. E XPERIMENTAL VALIDATIONS A. Scintillation Observation Experiment Using GPS Receiver GEO SAR is designed to operate at L-band in [1], [10], and [19], and meanwhile, considering the similarities between GPS and GEO SAR satellites in the operating band and signal propagation through the complete ionosphere, GPS signal could be exploited to demonstrate the effects of scintillation on GEO SAR imaging. From April 25 to May 6, 2014, the 24-h continuous GPS data acquisition experiment was carried out at Zhuhai in the southern China. The experiment system is shown in Fig. 9. The atomic clock was used to supply the stable frequency reference for the multichannel GPS signal receiver, and the data was finally recorded by a multichannel data collector. One occurrence of ionospheric scintillation was captured on April 30. The scintillation has been observed from GPS with the Pseudo Random Noise (PRN) of 1, 7, 8, and 20. The scintillation signal is extracted from GPS with PRN of 1. This scintillation was recorded between the universal time of 12:36 P. M .–12.50 P. M . on April 30, 2014 by our GPS receiver at Zhuhai. This scintillation is also observed by Guangzhou scintillation monitoring station of Space Environment Prediction Center (SEPC) in China. The public record is shown in Fig. 10. The signal amplitude and phase fluctuations due to scintillation were extracted from the recorded data (as shown in Fig. 11). Note that the spectra of signal amplitude and phase fluctuations have asymptotic power-law dependence,

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Fig. 12. (a) Nadir tracks of GPS and GEO SAR. (b) Similar ionospheric puncture points between GPS and GEO SAR.

Fig. 10. Guangzhou scintillation monitoring by SEPC in China on April 30, 2014.

Fig. 11. Real ionosphere scintillation measurement carried out in Zhuhai, Guangdong province, on April 30, 2014. (a) Amplitude fluctuation. (b) Phase fluctuation. (c) Amplitude spectrum. (d) Phase spectrum. TABLE II S TATISTICAL VARIANCES OF S IGNAL A MPLITUDE AND P HASE F LUCTUATIONS

which are consistent with the conclusion in [13]. The statistical variances of signal amplitude and phase fluctuations are shown in Table II. B. Experimental Validation Based on GPS-Derived Scintillation Signal While the extracted scintillation signal from GPS is introduced into the real SAR data, three potential problems are considered. 1) The operating altitude of GPS is about 22 000 km while GEO SAR almost 40 000 km. Although the complete ionosphere is propagated by the radar wave for both two

systems, the ionospheric puncture points and incident angles of radar wave are quite different. Consequently, from the view of illumination geometry, the amplitude and phase fluctuations induced by scintillation are different between these systems. The possible method is to find the most similar puncture points from 24 satellites in space, as shown in Fig. 12. In addition, from the view of statistics, the amplitude and phase fluctuations still satisfy the Nakagami and Gaussian distributions, and the difference could be scintillation intensity for these two systems. Based on the statistical similarity, to some extent, the extracted scintillation signal from GPS could be used to demonstrate the effects of ionospheric scintillation on GEO SAR. 2) The transmitted signal bandwidths are different between GPS and GEO SAR systems. GPS systems transmit two single wave frequencies while the signal with bandwidth is used for range resolution in GEO SAR. The extracted scintillation signal from GPS is based on L1-band with the carrier frequency of 1575.42 MHz. Because the impacts of scintillation principally affect the azimuthal impulse response function [32], and meanwhile, the signal bandwidth of GEO SAR is small with 18 MHz in the simulation, the dispersion of scintillation could be ignored, and the effects of scintillation on the range direction are negligible. Therefore, the extracted 1-D scintillation signal from GPS is introduced into the GEO SAR data along the azimuth direction. In addition, because the sample rate of GPS signal receiver is 1000 Hz while PRF of GEO SAR is 100 Hz, the extracted scintillation signal [Fig. 11(a) and (b)] is downsampled. 3) The GPS receiver can only acquire the one-way signal fluctuations while GEO SAR radar wave propagates through the ionosphere twice. Actually, the scintillation signal relationship between one- and two-way propagation is quite complex. They are identical only for the case of perfect correlation between the downward and upward paths [15], and under the Nakagami statistics assumption, the scintillation intensity index S4 for two-way propagation can be expressed as S42 = 4Sm2 + 2

Sm4 +1

Sm2

(39)


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Fig. 14.

Image entropy per iteration using our proposed method.

Fig. 15.

Estimate results. (a) Amplitude fluctuation. (b) Phase fluctuation.

Fig. 13. GEO SAR imaging results. (a) Ideal SAR image. (b) Degraded image by amplitude fluctuation. (c) Degraded image by phase fluctuation. (d) Degraded image by amplitude and phase fluctuations. (e) Autofocus image with phase compensation using the method in [25]. (f) Autofocus image with amplitude and phase compensations using our method.

where Sm is the scintillation intensity index for oneway propagation. In addition, assuming the scintillation phase satisfies the Gaussian distribution, the variance of scintillation phase becomes 4σφ2 , where σφ2 the variance of scintillation phase for one-way propagation. The purpose of this SAR image simulation is to validate the effectiveness of our proposed autofocus method. The proposed method is expected to be able to deal with strong ionospheric scintillation. In the simulation, the perfect correlation between the scintillation signals of downward and upward paths is assumed, because it corresponds to the severer scintillation than nonperfect correlation, which assumption is usually adopted in the effect analysis of ionosphere on SAR imaging [27], [28], [33]. Thus, the square of the complex scintillation signal from GPS is introduced into SAR echo simulation. Note that the GPS-derived scintillation signal is from a fixposition receiver, and hence, it cannot be used to validate the space-variance problem. Hence, the simulations using this real GPS-derived scintillation signal are used to show the autofocus performance of our proposed method based on the assumption that the scintillation amplitude and phase are space-invariant. Next, a real SAR scene of 3.5 km (ground range) × 2.9 km (azimuth) is first simulated, and the derived scintillation signal is introduced into SAR image along the azimuth direction. The SAR echo data are generated according to L-band GEO SAR parameters using our developed GEO SAR simulation software. The orbit geometry is the same as that in Section IV-C. The ideal SAR image is shown in Fig. 13(a)

with the image entropy of 11.22. The degraded SAR images by amplitude and phase fluctuations are shown in Fig. 13(b)–(d). It can be seen that either amplitude fluctuation or phase fluctuation could contribute to the increase in ISLR, but the effect of phase fluctuation is more severe relatively. The autofocus image with only phase compensation using the method in [25] is shown in Fig. 13(e), so as to illustrate the necessity of amplitude compensation. Its final image entropy is 11.46. In addition, PGA in [23] cannot be adopted, because it is quite difficult to pick up the isolated dominant scatterers in Fig. 13(d). The autofocus SAR image in Fig. 13(f) reveals the good performance of our proposed method, and the image quality has a significant improvement with the image entropy from 11.96 to 11.18 (Fig. 14). The proposed method takes about 18 min in total with 100 iterations for the 10 001 × 740 SAR complex data. The computer processor is Inter Xeon CPU E5-2620 at 2 GHz. To further evaluate the estimation accuracy of the proposed method, the estimates of signal amplitude and phase fluctuations are shown in Fig. 15. The rms estimate errors of residual amplitude and phase fluctuations are about 0.05 and 0.08, respectively. Therefore, the proposed method has the satisfactory performance on estimation accuracy. In addition, to show the effects of the number of range and azimuth cells on autofocus performance, the simulations are

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estimation accuracy indicate the proposed method has good performance on scintillation compensation. R EFERENCES

Fig. 16. RMS of residual phase estimation errors by applying our autofocus method on different segmentation sizes.

performed by applying different segmentations for SAR image scene. The original simulated scene size is 3.5 km × 2.9 km. The segmentation along the range direction is done as 100, 150, 350, 500, 700, 1750, and 3500 m, respectively, while it is done along the azimuth direction as 1000, 1450, and 2900 m. By applying our proposed autofocus method, the rms of residual phase estimation errors at different segmentation sizes is shown in Fig. 16. It can be clearly seen that the phase estimate accuracy is improved with the increase in segmentation size. This is consistent with the simulation analysis in Fig. 6 that the better estimation accuracy could be achieved by applying more sample cells. The smallest rms of phase estimation error is about 0.08 rad regarding to maximal image segmentation of 3.5 km × 2.9 km. Therefore, the image segmentation should be as large as possible to achieve better estimation under the constraint of space variance. VI. C ONCLUSION In this paper, the joint amplitude-phase compensation for ionospheric scintillation is studied in GEO SAR imaging. First, the space-variance problem of scintillation is addressed by image segmentation. The SPECAN imaging algorithm is adopted for each image segment, because it is computationally efficient for small imaging scene. Then, the effects of signal amplitude and phase fluctuations due to scintillation are analyzed in detail for the azimuth focusing. These sorts of random signal errors could lead to the increase in ISLR. Next, an iterative method based on entropy minimum is proposed to jointly estimate the signal amplitude and phase fluctuations. The principle of the proposed iteration is to construct a series of local quadratic fits to gradually approach the minimal entropy. Finally, several simulations are performed to validate the proposed method. It is found that the optimal amplitude profile under entropy minimum criterion is some weighed window function, rather than the rectangular window. The estimation accuracy is demonstrated by the theoretical simulations, and the proposed method is able to deal with the case of no isolated dominant scatterer. In addition, the echo data of a real SAR scene are generated to further test our proposed method using our developed GEO SAR simulation software, where both the simulated scintillation using phase screen technique and the real GPS-derived scintillation data are introduced, respectively. The final autofocus results and quantitative evaluations of

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[23] D. E. Wahl, P. H. Eichel, D. C. Ghiglia, and C. V. Jakowatz, “Phase gradient autofocus-a robust tool for high resolution SAR phase correction,” IEEE Trans. Aerosp. Electron. Syst., vol. 30, no. 3, pp. 827–835, Jul. 1994. [24] J. Wang and X. Liu, “SAR minimum-entropy autofocus using an adaptive order polynomial model,” IEEE Geosci. Remote Sens. Lett., vol. 3, no. 4, pp. 512–516, Oct. 2006. [25] K. J. Thomas and A. A. Kharbouch, “Monotonic iterative algorithm for minimum-entropy autofocus,” in Proc. Int. Conf. Image Process., Atlanta, GA, USA, Jun. 2006, pp. 645–648. [26] T. Zeng, R. Wang, and F. Li, “SAR image autofocus utilizing minimumentropy criterion,” IEEE Geosci. Remote Sens. Lett., vol. 10, no. 6, pp. 1552–1556, Nov. 2013. [27] Z. Xu, J. Wu, and Z. Wu, “Potential effects of the ionosphere on spacebased SAR imaging,” IEEE Trans. Antennas Propag., vol. 33, no. 10, pp. 1074–1084, Jul. 2008. [28] A. Ishimaru, Y. Kuga, J. Liu, Y. Kim, and T. Freeman, “Ionospheric effects on synthetic aperture radar at 100 MHz to 2 GHz,” Radio Sci., vol. 34, no. 1, pp. 257–268, Feb. 1999. [29] Z. W. Xu, J. Wu, Z. S. Wu, and Q. Li, “Solution for the fourth moment equation of waves in random continuum under strong fluctuations: General theory and plane wave solution,” IEEE Trans. Antennas Propag., vol. 55, no. 6, pp. 1613–1621, Jun. 2007. [30] M. Sack, M. R. Ito, and I. G. Cumming, “Application of efficient linear FM matched filtering algorithm to synthetic aperture radar processing,” IEE Proc., vol. 132, no. 1, pp. 45–57, Feb. 1985. [31] I. G. Cumming and F. H. Wong, Digital Processing of Synthetic Aperture Radar Data: Algorithm and Implementation. Norwood, MA, USA: Artech House, 2005. [32] N. C. Rogers, S. Quegan, J. S. Kim, and K. P. Papathanassiou, “Impacts of ionospheric scintillation on the BIOMASS P-band satellite SAR,” IEEE Trans. Geosci. Remote Sens., vol. 52, no. 3, pp. 1856–1868, Mar. 2014. [33] J. Liu, “Ionospheric effects on synthetic aperture radar imaging,” Ph.D. dissertation, Dept. Elect. Eng., Univ. Washington, Seattle, DC, USA, 2003.

R. Wang was born in Shanxi, China, in 1985. He received the B.S. degree in information engineering and the Ph.D. degree in information and communication engineering from the Beijing Institute of Technology, Beijing, China, in 2009 and 2015, respectively. From 2012 to 2013, he was a Visiting Scholar with the Mullard Space and Science Laboratory, University College London, London, U.K. Since 2015, he has been a Post-Doctoral Researcher with the Department of Electronics Engineering, Tsinghua University, Beijing. His research interests include bistatic synthetic aperture radar (SAR) imaging, stepped-frequency radar signal processing, ISAR imaging, and entomological radar signal processing to extract insect biological parameters. Dr. Wang was a recipient of the IEEE CIE International Radar Conference Excellent Paper Award in 2011.

Cheng Hu (M’11–SM’16) was born in Hunan, China. He received the B.S. degree in electronic engineering from the National University of Defense Technology, Changsha, China, in 2003, and the Ph.D. degree in target detection and recognition from the Beijing Institute of Technology, Beijing, China, in 2009. From 2006 to 2007, he was a Research Associate with the Microwave Integrate System Laboratory, University of Birmingham, Birmingham, U.K. Since 2012, he has been an Associate Professor with the School of Electronic Engineering, Beijing Institute of Technology. He has authored around 20 journal papers and over 40 conference papers, and holds over 20 patents. His research interests include the geosynchronous synthetic aperture radar (SAR) imaging processing, bistatic SAR imaging processing, and forward scatter radar signal processing.

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Y. Li was born in Liaoning, China, in 1990. He received the B.S. degree in information engineering from the Beijing Institute of Technology, Beijing, China, in 2012, where he is currently pursuing the Ph.D. degree with the School of Information and Electronics. His research interests include geosynchronous synthetic aperture radar (SAR) signal processing, SAR interferometry, and differential interferometry technique.

S. E. Hobbs received the B.S. degree in mathematics and physics from the Trinity College, Cambridge University, Cambridge, U.K., in 1980, and the Ph.D. degree in ecological physics from the Cranfield Institute of Technology, Bedford, U.K., with the focus on kite anemometry. He was with Cranfield University, Bedford, where he was involved in radar remote sensing and instrumentation with Cranfield’s Ecological Physics Research Group and the College of Aeronautics. In 2001, he joined Astrium U.K. Ltd., Hertfordshire, U.K., where he was involved in the European Space Agency’s GAIA mission and a small radar satellite. Since 1992, he has been involved with the School of Engineering’s space engineering research and teaching. Since 2004, he has been the Director with the Cranfield Space Research Centre, Cranfield University. His research interests include sustainability of space activities and measurement physics aspects of geosynchronous radar remote sensing. Dr. Hobbs is a member of the Royal Meteorological Society, the Institute of Physics, and the Remote Sensing and Photogrammetry Society, for which he is a Convenor of the Synthetic Aperture Radar Special Interest Group.

W. Tian received the B.S. and Ph.D. degrees from the Beijing Institute of Technology, Beijing, China, in 2005 and 2010, respectively. He is currently with the Beijing Key Laboratory of Embedded Real-Time Information Processing Technology, Beijing Institute of Technology. His research interests include synthetic aperture radar (SAR) system and signal processing, InSAR/DInSAR system, and bistatic radar synchronization.

X. Dong was born in Shandong, China. He received the B.S. degree in electrical engineering and the Ph.D. degree in target detection and recognition from the Beijing Institute of Technology (BIT), Beijing, China, in 2008 and 2014, respectively. From 2011 to 2013, he was a Research Assistant with the Centre for Terrestrial Carbon Dynamics, University of Sheffield, Sheffield, U.K. Since 2014, he has been a Post-Doctoral Researcher with the School of Information and Electronics, BIT. His research interests include geosynchronous synthetic aperture radar, microwave remote sensing, and weather radar. Dr. Dong was a recipient of the IEEE CIE International Radar Conference Excellent Paper Award in 2011 and the Chinese Institute of Electronics Youth Conference Poster Award in 2014.

L. Chen, photograph and biography not available at the time of publication.