A methodology for modeling and simulating target echoes with ... - Wiley

RadioScience, Volume35, Number3, Pages773-782,May-June2000

A methodology for modeling and simulating target echoes with a moving polarimetric bistatic radar Olivier

Airiau

and Ali Khenchaf

LaboratorySyst•mesElectroniques et Informatiques,CentreNationalde la RechercheScientifique,IRESTE, Universityof Nantes, Nantes, France.

Abstract. We modelthe signalreceivedby a FM pulseradar,consideringthe generalcasewhere the transmitterandthe receiverare separatedand are moving.The electromagnetic wave polarization statechangegeneratedby the observedbodyis alsotakeninto accountin the modelproposed in thispaper.The expressionof the receivedsignalis writtenasthe voltagedetectedon the receivingantennaandis givenas a functionof time by takinginto accountthe antennaradiation (transmittingantennaandreceivingantenna),the polarimetricbehaviorof the target,andthe mobilesvelocityeffect.Numericalresultsare presentedconsideringa canonicaltargetor a slightly roughsurfaceusinga monostaticor a bistaticconfigurationto showthe accuracyof the theoretical resultsandto studythe velocityeffect of the mobiles.

1. Introduction

characteristics of the clutter would cost too much and

can be obtainedonly for limited configurations of radiolinks.The developmentof a versatilesimulationtool givescrucialhelp andsignificantlyreducesthe cost. Thispaperfocuseson themodelingof a movingpolarimetric radar working in a bistaticconfiguration.We proposewriting the receivedsignalas a functionof time for thegeneralcasewherethetransmitter, thetarget,and the receiverare moving.The radiolinkis completely modeled by introducingthe antennasradiation, the Dopplereffect. The polarimetricbehaviorof the target cation. Furthermore, this kind of radar tends to reduce is taken into accountusing its scatteringmatrix. The the efficiencyof furtivity andjammingtechniques.Polatransmittedsignal is a burst of pulses,linearly modurimetric bistaticradarsyield a great advantagefor delated in frequency,permittingboth a goodresolutionin tectionof targetsembeddedin a perturbedenvironment, range and velocity. Nevertheless,the improvementon as is the case in a natural media or in an electronic warresolutionin rangeintroducedby thiskind of signalled fare context. to a degradationof theresolutionin velocity. Having a realisticmodelfor the environmentin which Finally, we presentnumericalresultsobtainedwith a the radar operatesis crucial to developing a signaltargetfixed on the ground.We considertwo typicalconprocessingsystemleadingto good radar performances. figurations. On the one hand, a monostatic radar For a radiolink working in a complex environment, mountedon a helicopteris simulated.On the otherhand, contributions of clutter echoes reduce detection and we consider a bistatic configuration for which the identificationcapacitiesof the radar.Theseechoesvary transmitteris installedon a helicopter,whereasthe rewith time in a randomway and are relatedto the radar ceiveris fixed on the ground. parameters.An experimentalestimationof the statistical

Modem radars require sophisticated signalprocessing techniquesto obtainbetterresolutionandexcellent detectioncapabilities.That is dictatedby new missionsassignedto radar. In point of fact, they do not only carryout targetdetectionand localization,but they are also usedto identify the target [Skolnik,1985]. The useof a new kind of systemsuchas polarimetricradars developedin a bistaticconfigurationgivesadditionalinformationon the detectedtarget,improvingits identifi-

2. Antennas

Copyright 2000by theAmerican Geophysical Union.

Radiation

The performances of a radarsystemgreatlydepend on the radiationcharacteristics of the transmitting and receivingantennas. Consequently, it is necessary to use

Paper number 1999RS002158.

0048-6604/00/1999RS(302158511.00 773

774

AIRIAU AND KHENCHAF: MOVING POLARIMETRIC BISTATIC RADAR MODELING

The use of antennasfocusingthe radiatedenergyin the mainlobe,the energyradiatedin the sidelobesbeing low, permitsthe reductionof the contributionof echoes returnedfrom bodiesneighboringthe detectedtarget. The sidelobelevel decreasesis obtainedby weighting the electricfield acrossthe apertureby usinga suitable distribution law. In that case the reduction of the electric

field discontinuityon the boundaryof the aperturecontributes to sidelobe attenuation

as well as to the main

lobe expansion. Considera circularapertureplacedin the Oyz plane (seeFigure 1) and illuminatedwith the distributionlaw f definedby Figure 1. Circularaperturegeometry.

:(/") • •zlq-(l--•zl) COS m

2aJ'

whereA representsthe electricfield attenuationon the radiationfeaturesoptimizedto the desiredapplication. boundaryof the aperture,a representsthe radiusof the The antennasusedin a radar systemare generallycho- circular aperture,and rn representsthe order of the sen to have a maximum radiation in the direction of the

targetanda verysmallradiationin the otherdirections in order to reduce the contribution of the undesirable

weightinglaw. The electric field distribution

is written as a vectorial

expressionby

echoes.

E•(r'): Eof(r') . (3) Most importantfeaturesof an antennaare its radiation pattern,its gain, and its polarization.The latter of the electricfield radiatedby the characteristic is definedas the polarizationof the wave Then the components antennain the far-field zone are given by the following

radiated in the direction of the maximum radiation.

relations:

Many antennas usedby radarsystems are reflectors thatcanbe considered as apertureantennas with various Er -0 geometry. In particular,thewell-knownparaboloidal ree-Jld• flectorcanbe modeledby a circularaperture. Eo=-jk 2rcR P,costp (4) The radiationpatternof an apertureantennais calcue-jkR latedin the far-fieldzoneby applyingtheHuygensprinE, = jk cosOsintp +PysinO) 2rcR(Pz ' cipleassociated withimagetheory.The electricfieldradiatedin any r direction(seeFigure1) is givenby the of thebidifollowing expression[Stutzmanand Thiele, 1981] wherePx, Py,andPz arethecomponents mensional Fourier transform of the electric field across

[Skolnik, 1980]:

E(r )=jke-• 2rcR (n^V)^r,

theaperture, expressed in the(x,y,z)antenna coordi-

(1) nate system.Vector P

is calculatedusing a bidimensionalfastFouriertransform(FFT) algorithm. where P= ae•k dS',isthebidimensional Fourier The antennapowergain in the directionof maximum radiationis givenby (5), assuming thatlossesare insigtransform of theelectricfield E a in theaperturesurface nificant.

Sa, n is theunitvectororthogonal to theaperture, and k is the wave number.We note, accordingto (1), that

the Er component of theelectricfieldin thedirection

f(r')r'dr'dO

Gm•4•: • a 2x •.-•

of thepropagation is null,meaningthattheelectromagneticfield radiatedby an apertureantennain the farfield zoneis a plane.

o

r'dr'dO' III f(r ')1 o

o

(5)

AIRIAU AND KHENCHAF: MOVING POLARIMETRIC BISTA TIC RADAR MODELING Elevation (0) -80

0

I

-60

0

3. Transmitted Electromagnetic Field The choice of the transmitted signal has a great influ­ ence on the detection capability of the radar and on its resolving power. The narrower the transmitted impulse,

-40

40

the better the radar resolution in range [Darricau, 1994]. However, minimum impulse duration is limited

-50

60 "r" ,

-80

-60

Figure 2.

-40

-20

=

,

20

0

40

Azimuth (0)

Ee

(a = 30 cm, A

·····;-Y:·.. ···

60

80

I

by constraints related to the transmitter component tech­ nology. In point of fact, in order to keep an acceptable

-60

detection power it is necessary to transmit a high peak power. This has led to the development of various pulse

component of the radiated electric field dB and A 3 cm).

-10

gvh

channel and in the cross-polarized channel, respectively,

-30

20

and

when the antenna is horizontally polarized.

-20

-20

ghh

characterizing the antenna radiation in the copolarized

-10

-40

80

We obtain in a similar way the coefficients

dB

775

=

compression techniques. These techniques allow the transmission of a low peak power, long-duration coded pulse in order to attain fine-range resolution and im­ proved detection performance of a short-duration, high

Ee

E�

peak power pulse system

[Mudukutore et al., 1998].

of the normalized radi­

This is accomplished by widening the bandwidth of the

ated electric field are drawn on Figures 2 and 3 for a

transmitted pulse by modulating it either in phase or fre­

The components

and

circular aperture vertically polarized, which is illumi­

quency, which yields a finer-range resolution than can

nated according to the cosine pedestal distribution law

be achieved with a conventional radar system using an

(2) with m 2 . Figures 2 and 3 show that the sidelobe level is -28 dB, whereas for uniformly illuminated circular aperture it is -17 dB [Stutzman and Thiele, 1981].

unmodulated pulse. Pulse compression can simply be

expressed by

=

""

""

In order to simplify the expression of the received signal, we express the radiation characteristics of the antenna polarized either horizontally or vertically, as a 2 x 2 matrix noted

g. The coefficients of this matrix are

written as a function of the maximum power gain and the components g=

Ee and E�:

[ghhv (e,