An Approach to Multistatic Spaceborne SAR/MTIProcessing and Performance Analysis

Delphine J. E. Cerutti-Maori, Joachim H. G. EnderFGAN-FHR, Neuenahrer Str. 20, 53343 Wachtberg, Germany

Tel: +49 228 9435-290, Fax: +49 228 9435-618, E-Mail: cerutti@fgan.de

Abstract—Multistatic spaceborne SAR offers in addition topowerful earth imaging and remote sensing the possibility todetect the presence of slowly moving objects due to the largebaselines. In contrary to monostatic multi-subaperture systemswith classical STAP processing the multi-satellite system over-comes the problem of blindness against certain directions oftarget motion. Moreover velocity and direction of target motioncan be estimated with considerably higher accuracy when takingadvantage of the geometry of the multistatic configuration.For this purpose non-classical algorithms have to be developed.

Furthermore, the application of optimum detection schemes andthe exact analysis of MTI performance are challenging tasks.Indeed the high system complexity and the huge amount of datato be analysed make the MTI processing exceedingly difficult.Therefore only sub-optimum methods can be implemented.In this paper we propose a sub-optimum approach for

multistatic spaceborne moving target detection. First of all wedefine a signal model for both moving targets and clutterproceeding from an arbitrary multistatic configuration. Secondly,we present the sub-optimum statistical processing based on theexploitation of the covariance matrix describing the commonstatistical properties of the random vector composed of a selectednumber of resolution cells in the range-Doppler-space for allsensor channels. Then we analyse the MTI performance ofrepresentative multistatic configurations. Finally this method isapplied to simulated data of multistatic satellite systems.

I. INTRODUCTION

The combination of SAR and MTI provides a powerfulsystem for a comprehensive surveillance of wide areas ofthe earth surface. Airborne systems achieve this capabilityby using an along-track multichannel antenna in combinationwith space-time adaptive processing (STAP) techniques. Someresults on bistatic airborne STAP are given in [11]. Neverthe-less, the observation range of these systems is limited andeach operation needs a special aircraft mission. It would betherefore desirable to obtain results with the same quality bya space based system.Investigations of spacebased STAP can be found in [1]

to [6]. Unfortunately, the MTI performance of a monostaticsystem in an earth near orbit suffers from the high speed of theradar platform leading to a wide spread of the clutter spectrum.This induces a high minimum detectable velocity (MDV) evenfor the STAP approach. Moreover, the accuracy of the azimuthposition estimate is low because of the long range.A good MTI performance can be accomplished by distribut-

ing the receive antenna over several separate satellites. Oneof the subapertures operates at transmission, whereas all the

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Fig. 1. Multistatic Geometry

subapertures are used for coherent multistatic reception of theechoes (see [9]).

II. GENERAL APPROACH

In this section we propose a suboptimum solution to theproblem of clutter suppression and moving target detection.We consider an arbitrary multistatic configuration consisting

of one transmitter and M receivers, where all the antennabeams are pointing to the same spot on the ground (”multi-spotlight situation”). The time of signal collection for pro-cessing is assumed to be short enough to apply a first orderapproximation of the flight paths and target motion, and toexclude secondary effects such as relative range walk andchange of Doppler.

A. Geometry and signals

The phase centre of the transmit antenna is moving alongRt(T ), that of the receive antennas along Rm(T ),m =1, · · · ,M . The target moves along r(T ), as illustrated in Fig. 1.All vectors are measured in an earth fixed coordinate system.Each receiver samples the data on a rectangular (k, T )-grid.Generally, the data can be written as

Zmnl = aSmnl + Cmnl +Nmnl (1)

where a is an unknown complex constant, Smnl are the echosamples of the target, Cmnl that of the clutter, which is mod-elled as a white stationary stochastic process. Nmnl represents

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the samples of the receiver noise, which are assumed to bei.i.d. Gaussian distributed. m = 1, · · · ,M is the number ofthe receiver, n = 1, · · · , N the index of the slow time, andl = 1, · · · , L the one of the wavenumber in the k-domain.If all the sample values are re-sampled to vectors with the

dimension P = MNL, the equation (1) can be written as

Z = aS + C + N. (2)

B. Optimum solution

The well known solution of detecting S in Z in (2) is tocompare the following statistic

Γ(Z) =∣∣SHR−1Z

∣∣2 (3)

with a threshold, where R is the clutter-plus-noise covariancematrix.

C. Beamspace clutter cancellation

The above derivation is only theoretical, since the dimensionP of the vectors is tremendously high. To reduce the numericalimpact, the data can be transformed to a subspace with a muchlower dimension using a P ×K transformation matrix T withK << P

Z = THZ C = THC R = THRT

S = THS N = THN (4)

The optimum test statistics based on the transformed datais given by

Γ(Z) =∣∣∣SHR−1Z

∣∣∣2 (5)

To determine a suitable transformation matrix containing asmuch as possible information about target and interference,we apply a strategy well known in the field of interferencesuppression by a sensor array.If the sample vector Z is composed of a useful signal

S, white noise N, and a linear superposition of interferencemodel signals J1, · · · ,JL with a Gaussian random vectorB = (B1, · · · , BL)t

Z = aS +L∑

l=1

BlJl + N, (6)

the L + 1-dimensional signal-plus-interference subspace isgiven by

U = Lin (S,J1, · · · ,JL) (7)

According to [10], the application Z = THZ of any regulartransformation matrix T with columnspace(T) = U to thedata defines a statistic with no loss in efficiency for thedetection of S.An example of such a transformation matrix is given by the

set of beamformers T = (S,J1, · · · ,JL). The first columnforms a beam to the useful signal, while the remaining Lcolumns can be regarded as ’auxiliary beams’ focusing theinterference.Consequently, the strategy to solve our problem will be to

form ’beams’ to the useful source and the interfering sources.

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Fig. 2. Interfering clutter cells and auxiliary beams

A generalised ’beam’ means here a focusing in range andDoppler to the individual source. This principle has been usedfor space-time clutter rejection in airborne radar [11].

III. ANALYSIS

The analysis is performed as follows. Firstly we investi-gate the geometrical implications of Doppler ambiguities andanalyse the transformation matrix. Then the clutter covariancebased on Gaussian resolution cells is derived. Finally, the MTIperformance is presented.

A. Geometrical analysis of interference

As is generally known, the interference is concentratedon resolution cells of the earth surface, which present thesame range and Doppler as the moving target (see Fig. 2).These interference cells are delimited by the intersectionof the earth surface with two iso-ranges and two isodops,where the distance between the two iso-ranges and the twoisodops corresponds to the range and Doppler resolutionrespectively. The iso-range surfaces are ellipsoids whereasthe iso-Doppler surfaces look like deformed hyperboloids. Inboth cases, the focal points are the positions of a bistaticsatellite pair. For a given range-Doppler cell, the maximumnumber of corresponding interference cells is two. Generallyjust one interference cell has to be taken into account becauseof the antenna illumination characteristics. The position ofthese resolution cells can be determined from geometricalconsiderations. Due to the different positions and velocitiesof the receiving satellites, the cells are in general shifted witheach other.

B. Transformation matrix

To get a better picture, we separate the individual bistaticpairs considering the resulting M NL-dimensional vectors.Following the above sketched approach, beams have to begenerated both to the useful and interfering sources.

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�

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Fig. 3. Decorrelation of resolution cells (∆x = 0)

Let the ’beamformers’ of each bistatic pair to the usefulsource be denoted by b1, · · · ,bM . With no clutter interference,it would be sufficient to apply these beamformers and tocombine the results coherently.Let (ϑmi

, ϕmi), i = {1, 2} be the geographic coordinates

of clutter cells interfering with the useful signal of the m-th bistatic pair and amiµ with µ �= m be the ’beamformer’focusing the data of the µ-th bistatic pair to the i interferingclutter cells of the m-th bistatic pair.The application of all vectors b. and a. describes a trans-

formation which retains all of the target and most of theclutter information. The transformation is not perfect since theclutter is distributed and there will be a clutter interference alsothrough the sidelobes of the beamformer to the moving target.The transformation gives the values

Xm = bHmZm, m = 1, · · · ,M

Ymiµ = aHmiµZµ, m, µ = 1, · · · ,M, µ �= m, i = {1, 2}

(8)which can be collected in the transformed data vector Z.

C. Decorrelation for resolution cells

We regard one point of the earth surface on which twobistatic pairs are focused. Over the resolution cells, the surfacecan be regarded as flat, and the backscattering mechanismcan be modelled according to the far field approximation. Theamplitude functions am(x) of both cells where x denotes theposition on the earth’s surface, are assumed to be Gaussian,so the lines of equal amplitude form ellipses (see Fig. 3); thesigma contours are given by the half axes a1,b1 and a2,b2,respectively. The effective LOS vectors are denoted by u1 andu2, where an effective LOS vector means the vector sum ofthe unit vector to the transmitter and the unit vector to thereceiver.The clutter return for the mth bistatic pair is given by

Cm =∫

am(x) · exp{

−12xtMmx + jkut

mx}dx (9)

where the integral extends over the plane tangent to the earthsurface at the centre point. The cross covariance between thetwo clutter returns is calculated as follows

E [CmC∗n] = σ2

c · gmn(∆x)·∫

exp

{−1

2xt (Mm + Mn)x + jk (um − un)t x

}dx

(10)σ2

c denoting the clutter power and ∆x being the spacingvector between the two ellipse centers. The function gmn(∆x)represents a mismatch term due to the separation of the ellipsecenters. The matrix Mm is defined by

Mm =amat

m

(atmam)4

+bmbt

m

(btmbm)4

(11)

The half axes can be derived by the range and Dopplerresolution cells. After some calculations we get the result

E [CmC∗n] = σ2

c · 2π√det(Mm + Mn)

· hmn(∆x) · (12)

exp

{−k2

2(um − un)t (Mm + Mn)−1 (um − un)

}

where the function hmn(∆x) denotes the total phase andamplitude mismatch between the two resolution cells causedby the vector ∆x.

D. MTI performance

From the characteristics of the matched signal, the inter-ference cells are determined. Then the data are transformedaccording to (8) and the coefficients of the covariance matrixof dimension MP × MP , with M the number of receiveantennas and P the one of total considered interference cells,are calculated from (12). Afterwards, the transformed data arefiltered with regard to (5) as follows (σ2

n being the white noisepower)

Γ(Z) = σ2n · ||R−1S||2

SHR−1Z(13)

which represents the ratio between the SCNR (signal-to-clutter-plus-noise ratio) and the SNR (signal-to-noise ratio).

IV. NUMERICAL EXAMPLE

Fig. 4 presents the two-dimensional clutter cancellationperformance of a multistatic satellite configuration composedof 3 receiving satellites. The main feature of the method isto estimate both target velocity and direction of motion. Itis based on the fact that the relative target velocity vector isdifferent for each bistatic pair. The simulation parameters arelisted in Table I.As can be seen in this figure, the principle of beam

formation makes the detection of targets moving with verylow velocities possible. Indeed, targets presenting a dopplershift of more than the doppler resolution of the system(depending on the coherent integration time and not on themultistatic configuration) are able to be detected. Furthermorethe direction of target motion can be also determined with ahigh accuracy.An important effect has to be pointed out. Low parallel and

anti-parallel velocities of the target relative to the radar areparticularly critical to be detected. This is due to the fact that

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Vlong

(m/s)

Vla

t (m

/s)

−4 −3 −2 −1 0 1 2 3 4

−4

−3

−2

−1

0

1

2

3

4

SCNR/SNR (dB)

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

Fig. 4. Clutter cancellation performance

TABLE I

MAIN SIMULATION PARAMETERS

Wavelength 3.125cmPRF 1000HzPulse number 10000Range resolution 1cmTransmit satellite velocity 7500m/sOrbit inclination 45deg

The equispaced receiving satellites are positioned in anellipse formation around the transmitting satellite inthe same orbital plane (cartwheel configuration). The

baselines, which are varying between 100 and 200m, takethe values (100, 180, 180)m at the start of the simulation.

this configuration is equivalent to the one where the target ismotionless and the radar is moving with another velocity. Asa result, the algorithm interprets the target as interference. Asolution to this problem is to choose large baselines for themultistatic system. Because of the geometrical configuration,the resolution cells are shifted against each other and are nolonger overlapping the target together at the same time, whichallows its detection.

V. SUMMARY

In this paper, we have introduced a new approach tomultistatic spaceborne SAR/MTI. First of all, the suboptimummethod was presented. Then the processing analysis as wellas the MTI performance were investigated. To conclude, somesimulation results were shown.This method consists in forming beams to the useful source

and the interference cells in order to reduce the huge amountof data to be processed. The usual test statistic is then appliedto the transformed data.This method allows to detect targets moving at very low

velocities and estimate their direction of motion with high

accuracy. It is adapted to small baselines (≈ 100m) but failsto indicate the presence of slowly targets moving in a parallelway to the bistatic pair. This problem can be overcome bychoosing larger baselines.

REFERENCES

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[2] Bird, J. S., Bridgewater, A. W.: ”Performance of space-basedradar in the presence of earth clutter”, IEE Proc., Pt. F, Vol.131, No. 5, August 1984, pp. 491 - 500

[3] Fante, R.L.: ”Ground and Airborne Target Detection withBistatic Adaptive Space-Based Radar”, IEEE National RadarConference, 20-22 April 1999, Boston, USA, pp. 7 - 11

[4] Maher, J., Callahan, M., Lynch, D.: ”Effects of clutter modellingin evaluating STAP processing for space-based radars”, IEEERADAR2000, 8-12 May, 2000, Alexandria, VA, USA pp. 565 -570

[5] Sedwick, R.J., Hacker, T.L., Marais, K.: ”Performance anal-ysis for an interferometric space-based GMTI system”, IEEERADAR2000, 8-12 May, 2000, Alexandria, VA, USA, pp. 689- 694

[6] Wang, H. S. C. ”Mainlobe Clutter Cancellation by DPCA forSpace-Based Radars”, IEEE Aerosp Applications ConferenceDigest, Crested Butte, CO, USA, February 1991, pp. 1 - 28

[7] Ramongassie, S., Phalippou, L., Thouvenot, E., Massonnet,D.: ”Preliminary design of the payload for the interferometricCartwheel”, EUSAR’2000, Munich, May 2000, pp. 29 - 32

[8] Cerutti-Maori, D.: ”Space-Sim: Simulator for spaceborne mul-tichannel SAR/MTI with phased-array antenna”, EUSAR’02,Cologne, June 2002

[9] Ender, J. H. G.: ”Spacebased SAR/MTI using Multistatic Satel-lite Configurations”, EUSAR’02, Cologne, June 2002

[10] Scharf, L.L.: ”Statistical Signal Processing, Detection, Estima-tion, and Time Series Analysis”, Addison-Wesley Publishingcompany, July 1991

[11] Klemm, R.: ”Principles of Space-Time Adaptive Processing”,IEE, UK, 2002

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