Space-Time Adaptive Processing analysis for the moving target

on the sea surface indication purpose

Tomasz Gorski∗†‡, Jean-Marc Le Caillec†,

Laurent Lecornu†, Adam Kawalec∗,

Witold Czarnecki∗, Jerzy Pietrasinski∗,

Basel Solaiman†

Abstract: Space-Time Adaptive Processing (STAP) can improve target detectability in a presenceof a ground clutter for airborne radar. Ground clutter echo has a wide spectrum as a result of theradar platform (airplane or satellite) motion. To reject clutter echo and preserve target echo, STAPemploys antenna array. Simultaneous filtering in both spatial (angle) and frequency domain canimprove performance. In this paper we propose a new application of STAP. Assuming an antennaarray standing on a sea shore, the objective is to detect targets on the sea surface. Unfortunatelysea clutter has different statistical properties compared to airborne clutter. As a consequence, basicSTAP algorithm is not optimal in any sense. Future research will face the problem of evaluatingperformance of STAP applied to sea clutter. We hope to develop a new algorithm that can performbetter in the presence of sea clutter.

1 Overview of STAP

STAP is a modern signal processing technique, that can improve target detectability in a presence of astrong clutter. If we consider Moving Target Indication (MTI) for airborne radar, we face the problemthat echo coming from not-moving ground objects (ground clutter) possess non-zero Doppler bandwith[1].This is a result of relative velocity between antenna platform (aircraft) and ground area illuminated bythe radar system. As a consequence, target echo can fall within the clutter bandwith and may be hiddenunder the clutter. In this case clutter rejection will also reject target echo. However, employing antennaarray can improve detectability.

In Fig. 1 we can see radar system geometry. Axis Vp denotes flight direction. There are possible twobasic configurations: sidelooking and forwardlooking. For sidelooking configuration, receiving elementsare placed along the flight axis. For forwardlooking configuration, receiving elements are placed alongan axis perpendicular to the flight axis, but parallel to the ground plane. Sidelooking configuration issimpler to analyse, therefore we assume this configuration only. Also for simplicity reasons, we assumethat receiving elements are equally-spaced, with element spacing equal to λ/2 (λ denotes wavelength).Antenna array allows cone-angle (α in Fig. 1) filtering. Echo arriving from point P (Fig. 1) on theground is sampled in space by array elements. Wave-front coming from point P is arriving at antennareceiving elements at different moments in time. In other words: there is a phase difference among arraychannels. This phase difference is related to cone angle α.

If we consider moving radar system, it can be shown that Doppler shift of echo coming from not-moving environment depends on cone angle[2]. Cone is, therefore, surface of constant Doppler shift. Lineson the ground of constant Doppler shift are named isodops. Single isodop is an intersection of cone andground plane. Bunch of isodops is shown in Fig. 1.

For the specific range and the specific Doppler shift we receive echo from specific areas on the ground.This can be paraphrased: clutter from the specific range and of the specific Doppler shift is arriving fromspecific angles only. This relation is exploited in STAP.

In Fig. 2 we can see space-time clutter structure in Doppler frequency-cosinus of cone angle (α)

∗Institute of Radioelectronics, Military University of Technology, ul. Gen. Sylwestra Kaliskiego 2, 00-908 Warszawa 49,

Poland†Le departement Image et Traitement de l’Information, GET-Ecole Nationale Superieure des Telecommunications de

Bretagne, Technopole Brest-Iroise - CS 83818 - 29238 Brest Cedex 3, France‡tgorski@wat.edu.pl

Figure 1: Antenna configuration[2](left). Isodops[2](right).

Figure 2: Space-time structure of clutter[2].

Figure 3: Sea shore antenna(left). Sea clutter sinusoid(right).

coordinate system. Clutter occupy only part of the coordinate plane. Moreover for the simple case ofside-looking antenna configuration, clutter lays on a straight line. Separate Doppler or separate anglefiltering may filter-out target signal together with the clutter. Some of the targets will not be detected.Two-dimensional filtering allows to filter out clutter echo and preserve target echo.

To make profit of it, STAP utilises echoes from coherent pulse trains received by an antenna array.Pulse trains allow temporal (Doppler) filtering, whereas different channels of antenna array allow spatial(angle) filtering. For performance analysis of STAP, it is often assumed that clutter echo can be modeledby proper complex Gaussian process (multivariate complex Gaussian process with vanishing pseudo-covariance[3]). Under this assumptions STAP becomes linear filter. In this case, linear STAP is optimalunder meny different criteria: Maximum Likelihood estimation(ML), Signal to Noise(plus Interference)Ratio maximisation(SNR), Minimum Variance(MV) estimation and Least Mean Square Error(LMSE)estimation.

More exhaustive analysis of STAP can be found in Melvin tutorial[4] and Klemm book[2].

2 Sea Clutter

In this paper we propose a new application of STAP. Assuming an antenna array standing on a sea shore(Fig. 3) , the objective is to detect targets on the sea surface. In this application clutter consists ofreflection from sea waves. Waves are coming from some unknown a-priori direction. It can be seen thatDoppler shift of the sea waves clutter changes with the look angle of antenna (φ in Fig. 3). There is anangle with maximum Doppler shift and the other with zero Doppler shift. No surprise, both directionsdiffer by 90 degrees. Relation between look angle and Doppler shift is shifted-sinusoid (Fig. 3). Similarlyto airborne clutter, relation between angle and Doppler shift can be exploited in STAP. From that pointof view, STAP for sea shore antenna should be the same as for classical application for airborne radar.

Unfortunately sea clutter has different statistical properties[5]. In STAP we assume proper complexGaussian (bandpass) process as a model for ground clutter[2]. For the simple one-dimensional case sucha process can be represented as[6] [1]

ct = xt cos(ωct) − yt sin(ωct)

where xt, and yt, are independently, identically distributed from normal distribution of a zero mean valueand the same variance. In equivalent representation

ct = vt cos(ωct + θt),

phase θt is uniformly distributed, and voltage envelope vt is Rayleigh distributed. For the sea cluttersituation is different. Phase θt is also uniformly distributed but voltage envelope vt may be log-normal,Weibull, K or other distributed [5]. In such a situation we are talking about Spherically Invariant RandomProcess(SIRP) [7], which can be represented as[8]

Xt = ctIt

where Xt denotes Spherically Invariant Random Vector(SIRV), It is a multivariate Gaussian randomvector and ct is a positive random scalar with assumed probability density function(PDF). SIRP allow to

relax assumption of Gaussianity, while keeping many of its useful characteristics[8]. For SIRP, classicalSTAP is not optimal in any sense. STAP has a form of linear filter, which consists, inter alia, of inverse ofcovariance matrix. To improve performance, nonlinear filtering with utilisation of higher-order statisticsmay be necessary. This may be viewed as an example of the Edgeworth expansion. For great class ofdistributions their PDF can be expressed as[9]

f(x) = φ(x)

(

1 +

∞∑

k=3

Pk(x)

)

where φ(x) denotes normal distributed random variable, Pk is a polynominal depending only on momentsµ1, µ2, µ3, . . . , µk of the distribution in question.

Independent Component Analysis(ICA)[10] also may be helpful to improve performance. In thesituation where Non-Gaussian clutter is ”corrupted” by strong Gaussian noise, covariance matrix (usedin STAP) is not reliable in ”deducing” the nature of the clutter. ICA (and similarly Projection Pursuit)may better reveal structure of the clutter.

Yet another problem arises. With Non-Gaussian distributions, different optimisation criteria(ML,SNR,MV,LMSE) lead to different results. It is not so obvious which criterion is best.

Summarizing this part, there are two possible ways to deal with the problem. The first is to assumeGaussian process and hope that performance loss will be not so severe. The second is to develop amodification of STAP, fitting to the sea clutter problem.

3 Conclusions

In this paper we proposed a new application of a STAP concept. Sea clutter rejection for detection ofsurface targets may be imrpved using this technique. However, it is argued that basic STAP algorithm isnot optimal, because of Non-Gaussianity of the clutter. To approach optimal solution we have multiplechoices of mathematical tools that can be involved as well as assumed performance criteria. To face theseproblems, simulated data of sea clutter should be generated. On simulated data we plan to evaluateperformance of calssical STAP. We hope to propose new algorithm that can perform better in the presenceof Non-Gaussian clutter environment. For the new algorithm comparsion to classical STAP should bedone using simulated data. Finally, application of both thechniques to real data should be performed.

References

[1] D. C. Schleher, MTI and Pulsed Doppler Radar. Artech House, 1991.

[2] R. Klemm, Principles of space-time adaptive processing. IEE, 2002.

[3] F. Neeser and J. Massey, “Proper complex random processes with applications to information the-ory,” IEEE Transactions on Information Theory, vol. 39, pp. 1293–1302, July 1993.

[4] W. L. Melvin, “A stap overview,” IEEE A&E Systems Magazine, vol. 19, pp. 19–53, Jan. 2004. Part2 - Tutorials.

[5] W. Stehwien, “Statistics and correlation properties of high resolution x-band sea clutter,” pp. 46–51,1994. Record of the 1994 IEEE National Radar Conference, 9-31 March 1994.

[6] R. A. Monzigo and T. W. Miller, Introduction to Adaptive Arrays. John Wiley & Sons, Inc., 1980.

[7] K. J. Sangston and K. R. Gerlach, “Coherent detection of radar targets in a non-gaussian back-ground,” IEEE Transactions on Aerospace and Electronics Systems, vol. 30, pp. 330–340, Apr. 1994.

[8] A. Abdi, H. Barger, and M. Kaveh, “Signal modelling in wireless fading channels using spheri-cally invariant processes,” ICASSP ’00. Proceedings., vol. 5, pp. 2997–3000, June 2000. 2000 IEEEInternational Conference on Acoustics, Speech, and Signal Processing.

[9] W. Feller, An introduction to probability theory and its applications, vol. II. John Wiley & Sons,Inc., second ed., 1971.

[10] A. Hyvarinen, “Survey on independent component analysis,” Neural Computing Surveys, vol. 2,pp. 94–128, 1999.