Int. J. Electron. Commun. (AEU) 64 (2010) 1182–1185

Contents lists available at ScienceDirect

Int. J. Electron. Commun. (AEU)

1434-84

doi:10.1

� Corr

E-m

gsliao@

journal homepage: www.elsevier.de/aeue

Clutter suppression method for heterogeneous environment

Jing Yu �, Guisheng Liao , Zhiwei Yang

National Laboratory of Radar Signal Processing, Xidian University, Taibai South Road 2, Xi’an 710071, PR China

a r t i c l e i n f o

Article history:

Received 23 September 2009

Accepted 27 November 2009

Keywords:

Synthetic aperture radar (SAR)

Ground moving target indication (GMTI)

Heterogeneous clutter

Subspace tracking

11/$ - see front matter & 2010 Elsevier Gmb

016/j.aeue.2010.01.014

esponding author.

ail addresses: yujing@mail.xidian.edu.cn, yujin

xidian.edu.cn (G. Liao), zwyang@mail.xidian.e

a b s t r a c t

Clutter suppression is a key process in ground moving target indication (GMTI). Adaptive filtering is an

effective method for clutter suppression but the performance degrades severely in heterogeneous

clutter environment. To solve this problem, a new clutter suppression method is proposed. The

approach uses subspace tracking technique to update clutter subspace of different clutter patches

which may mitigating the heterogeneous effects. Simulation results illustrate that the method performs

well when lacking of the independent and identically distributed (i.i.d.) samples.

& 2010 Elsevier GmbH. All rights reserved.

1. Introduction

Ground moving target indication (GMTI) combined withsynthetic aperture radar (SAR) can be used to detect ground orsea slowing moving targets from spaceborne and airborneplatforms. The most important issue in ground moving targetdetection is the suppression of ground clutters which competingwith and masking weak target returns. The well-known displacedphase center antenna (DPCA) [1] method compensates theplatform motion by a shift of the antenna’s aperture against theflight direction between two pulses. It has been generally appliedto suppress clutter for airborne radar. Along-track interferometry(ATI) [2] acts sensitive to slow moving targets and has beenwidely used to measure ocean surface currents. The space–timeadaptive processing (STAP) is a crucial and well-proven techniquefor airborne radar though not possible for long coherentintegration times [3,4].

In STAP, adaptive filtering is the main ideology for cluttersuppression which needs formation and inversion of the covariancematrix underlying the clutter and interference. But the unknowncovariance matrix is estimated from a set of independent andidentically distributed (i.i.d.) target-free training data that isrepresentative of the statistics in a cell under test. To meet thetechnical demand the number of training data must be sufficientdue to the RMB rule [5]. Unfortunately in heterogeneous environ-ment, the most serious drawback is the lack of i.i.d. samples whichleads to severely degraded detection. Currently, some approachesconsidering the effects of limited i.i.d. training data are proposedsuch as power select training (PST) [6], non-homogeneity detector(NHD) [7], generalized inner product (GIP) [8]. These methods all

H. All rights reserved.

gcathy@hotmail.com (J. Yu),

du.cn (Z. Yang).

wiped off the unsatisfied data which further reduced the number oftraining data.

In this paper, a novel clutter suppression approach usingsubspace tracking technique is proposed. The method utilizessubspace tracking approach to update the clutter subspace withfewer training data. Thus the projection of the data vector ontothe clutter subspace can disjoin the targets from clutter whichcould achieve the purpose of target detection. Simulation resultsillustrate that the approach has substantial performanceimprovement in heterogeneous environment.

2. Data model

Consider an along-track multi-channel radar system whichacquires images of a stationary scene at different time points.Assuming that the SAR images are accurately coregistered, thecomplex data of a pixel obtained by channel i can be denoted asfi(m,n) where (m,n) is the index in the image. The multi-channeldata vector can be modeled as

Xðm;nÞ ¼ ½f1ðm;nÞ; f2ðm;nÞ; . . . ; fNðm;nÞ�T ð1Þ

where N is the number of channel.According to the theory of adaptive filtering by sample

covariance matrix inversion (SMI) [1], the weight vector of cluttersuppression is formulated as follows

xopt ¼ mR�1s ð2Þ

where m is scalar quantity, s is the unknown steering vector of themoving target, R�1 is the inversion of the clutter-plus-noisecovariance matrix. In practice the unknown matrix R is replacedby estimated covariance matrix R .

R ¼1

ð2Lþ1Þð2Kþ1Þ

XL

l ¼ �L

XK

k ¼ �K

Xðmþ l;nþkÞXHðmþ l;nþkÞ ð3Þ

J. Yu et al. / Int. J. Electron. Commun. (AEU) 64 (2010) 1182–1185 1183

where Xðmþ l;nþkÞ are assumed to be i.i.d. samples from theneighboring pixels. Due to the RMB rule, the number of i.i.d.samples which satisfy ð2Lþ1Þð2Kþ1ÞZ2N would make theestimation loss within 3 dB. To avoid the estimation of R, weanalyze the decomposition of the matrix below.

The eigen-decomposition of the covariance matrix can bedenoted as

R¼Xr

i ¼ 1

livivHi þs

2n

XN

i ¼ rþ1

vivHi ð4Þ

Since clutters are dominant in SAR images, so the dominanteigenvalues l1; . . . ; lr are termed the clutter eigenvalues and thecorresponding eigenvector v1; . . . ; vr are clutter eigenvectors.While vrþ1; . . . ; vN are referred to as the noise eigenvectors. Thecolumn spans of

UC ¼ ½v1; . . . ; vr � ð5Þ

UN ¼ ½vrþ1; . . . ; vN� ð6Þ

are defined as the clutter and noise subspace respectively. Theyare orthogonal to each other. Clutters belong to clutter subspacewhile targets and noise are not. If a set of orthonormal basis canbe found to form the clutter subspace, the difference between thedata vector and its projection onto the clutter subspace is causedby the targets and noise, thus the targets and clutter can bedistinguished. This property can be used to detect targets. Underheterogeneous environment, the terrain fluctuations are differentin each clutter patch. In our approach, clutter subspace iscalculated for each small clutter patch using its surrounding datasamples.

Clutter subspace of different clutter patches can be obtained bytypical subspace tracking techniques, which have been popularlyused in array signal processing [9–12]. The subspace can betracked using few samples with great accuracy.

Fig. 1. Eigenspectra of covariance matrix.

3. Clutter suppression approach

In SAR images, each pixel is assumed to be a sample. Inheterogeneous environment, owing to terrain fluctuation andother unexpected factors the neighboring samples normally donot satisfy i.i.d. condition. Using subspace tracking technique tosuppress clutters can alleviate the demand of i.i.d. samples.

The clutter suppression technique based on subspace trackingcan be generalized below where API [10] method is applied. Moredetailed information about API can be referred to [10].

(1) Initialization.For each data X(m,n), set an n� r orthonormal matrix W(0)

and an r� r positive definite matrix Z(0). For simplicity W(0) andZ(0) can be chosen as follows:

Wð0Þ ¼Ir

0ðn�rÞ�r

" #; Zð0Þ ¼ Ir ð7Þ

where Ir is r� r identity matrix.(2) For each surrounding sample which is denoted as X(t) for

simplicity:

YðtÞ ¼Wðt�1ÞHXðtÞ ð8Þ

HðtÞ ¼ Zðt�1ÞYðtÞ ð9Þ

GðtÞ ¼HðtÞ

bþYðtÞHHðtÞð10Þ

eðtÞ ¼XðtÞ�Wðt�1ÞYðtÞ ð11Þ

HðtÞ ¼ ðIrþJeðtÞJ2GðtÞGðtÞHÞ�1=2ð12Þ

ZðtÞ ¼1

bHðtÞHðIr�GðtÞYðtÞHÞZðt�1ÞHðtÞ�H

ð13Þ

WðtÞ ¼ ðWðt�1ÞþeðtÞGðtÞHÞHðtÞ ð14Þ

where b is referred to as the forget factor which 0rbr1.When all available samples are used to update the clutter

subspace:

Wðm;nÞ ¼WðtÞ ð15Þ

where W(m,n) is the clutter subspace of the small clutter patchwhich containing data X(m,n). Simulations in next section revealthat only several samples could make precise estimation ofW(m,n).

(3) Target detection.We can use the following expression to detect moving target.

Youtðm;nÞ ¼Xðm;nÞ�Wðm;nÞWHðm;nÞXðm;nÞ ð16Þ

where Wðm;nÞWHðm;nÞXðm;nÞ represents the projection of data

vector onto its clutter subspace.If the multi-channel data vector X(m,n) is target free, Youtðm;nÞ

will almost be zero. On the contrary, if the output is comparablelarge, the pixel may contain a suspected target. The similarideology has been described in [13].

One of the premises of subspace tracking approach is that thedimension of the subspace to be tracked is assumed to be known.Unfortunately, due to the unpredictable errors such as imagecoregistration error, channel mismatch et al, the dimension of theclutter subspace is diffused. That is to say, we cannot make surethe number of dominant eigenvalues which is referred to r inEq. (4). To help understand the subspace diffusion, in Fig. 1 weplot the eigenspectra of a covariance matrix formed by three-channel SAR data vector. In our simulation, only coregistrationerrors are considered, but other factors also have the similarimpact on the eigenspectra.

In Fig. 1, different coregistration errors are consideredrespectively: accurate coregistration, coregistration errors of(0.5,0.5) (which means the coregistration errors are 0.5 pixels inrange and 0.5 pixels in azimuth) and coregistration errors of (1,1).It can be seen from the figure that when the SAR images areaccurately coregistered, the number of dominant eigenvalues is 1which means the rank of the clutter subspace is 1. The increasedcoregistration errors also give rise to the number of dominanteigenvalues. When the errors are (1,1), the magnitude of threeeigenvalues are all relatively large and the number of dominanteigenvalues is not less than 2. It means we cannot decide the rank

J. Yu et al. / Int. J. Electron. Commun. (AEU) 64 (2010) 1182–11851184

of the clutter subspace. In the worst case the clutter subspace mayoccupy the whole dimension.

The problem is easy to solve, experimental results reveal thatthe dimension of the subspace can be overestimated and theperformance will not be affected. But if the dimension isunderestimated the results will be bad.

Fig. 3. Output SCNR against target radial velocity under heterogeneous environ-

ment.

4. Simulation results

In this section, we evaluate the performance of SMI andsubspace tracking method respectively. In our simulations analong-track SAR system with three satellites is considered. Theclutter is featured by power heterogeneous, which means thepower of the clutter fluctuates irregularly. The parameters ofsimulation are shown in Table 1.

The curves in Fig. 2 depicted the clutter rejection performanceof SMI and subspace tracking method under heterogeneousenvironment respectively. It can be seen from the figure thatthe output signal-to-clutter-plus-noise ratio (SCNR) of SMI existspeak near 3 samples but with the number of sample increasingthe output decrease dramatically. On the contrary theperformance of subspace tracking varies little with the numberof sample. Fig. 3 demonstrates the output SCNR vary with target’sradial velocity. It is obvious that the SMI method can hardlysuppress the clutter, while the output of the proposed method hasimprovement over SMI more than 10 dB.

Fig. 4 shows the comparison of output SCNR under different r.In Section 3, subspace diffusion has been discussed. To verify thesubspace can be over estimated, some modifications have beenmade in our simulation. The dimension of the simulatedcovariance matrix is 15 and the accurate dimension of cluttersubspace is 3. If r is overestimated (r=5), the performance has

Table 1Simulation parameters.

Parameter Value

Along track baseline (0,150 m,300 m)

Moving velocity 7000 m/s

Platform altitude 750 km

Central slanting range 1000 km

Wavelength of carrier 0.3 m

CNR 30 dB

SCR 0 dB

Fig. 2. Output SCNR against sample number under heterogeneous environment.

Fig. 4. Comparison of output SCNR under different r.

little change. On the contrary, if r is underestimated (r=2) theresult will decrease sharply.

5. Conclusion

A clutter suppression strategy for heterogeneous cluttercircumstance is proposed. In this method subspace trackingtechnique is used to update the clutter subspace of differentclutter patches. It overcomes the deficiency of i.i.d. samples inheterogeneous environments and demonstrates excellent perfor-mance compared to traditional SMI method.

Acknowledgments

The work described in this paper was supported by NationalScience Fund of China under Grant 60736009, 60901066 and60825104. It is also supported by the program for Cheung KongScholars and Innovative Research in University (IRT0645). Theauthors would like to thank the reviewers for their constructivecomments and suggestions that helped improve the manuscript.

J. Yu et al. / Int. J. Electron. Commun. (AEU) 64 (2010) 1182–1185 1185

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Jing Yu received her B.S. degree in Electronic Informa-tion Engineering from Xidian university, in 2004. Since2004 she has been working towards the Ph.D. degree inRadar Engineering, in National Laboratory of RadarSignal Processing, Xidian University, China. Her currentwork concerns signal processing of airborne/space-borne radar for GMTI and SAR.

Guisheng Liao (M’96) received his B.S. degree fromGuangxi University, Guangxi, China, and the M.S. andPh.D. degrees from Xidian University, Xi’an, in 1985,1990 and 1992, respectively. His research interests aremainly radar signal processing.

Zhiwei Yang received his M.S. and Ph.D. from XidianUniversity in 2005 and 2008, respectively, and thenbecame a teacher there. His main research interest isradar signal processing and ground moving targetindication.