Bistatic RCS Prediction with Graphical

V ol. 15　 N o . 3 　　　　　　　　　　　　 CHIN ES E J OU RN A L O F A ER O N A U T ICS　　　　　　　　　　　　　　 A ugust 2002

Bistatic RCS Prediction with Graphical Electromagnetic Computing ( GRECO) Method f or Moving Targets QIN De-hua, WANG Bao-fa ( Dep art ment of E lect ronic Engineering, Beij ing Univer si ty of A eronautics and A st ronautics, Beij i ng 100083, China ) Abstract: 　 G ra phical Elect ro magnetic Co mput ing ( G RECO ) is reco gnized as one o f the mo st v aluable m et hods of the RCS ( Ra dar Cr oss Sectio n) computatio n fo r the hig h-fr equency r eg ion. T he metho d o f G RECO and M o nostatic-bistatic Equivalence T heo rem w as used t o calculate the bistat ic RCS for mov ing tar g ets in the hig h-fr equency reg io n. Some computing ex amples ar e g iv en t o v erify the v alidity of the method. Excellent ag reement w ith the measured data indicates that the met ho d has practical eng ineering value. Key words : 　 electro magnetic wav e scat tering ; GRECO ; mo ving tar gets ; bistatic r ada r cr oss section; mo nostatic-bistatic equivalence theor em 动 目标双站 RCS 预估的图形电磁计算( GRECO) 方 法. 秦德华, 王宝发. 中国航 空学报( 英 文版) , 2002, 15( 3) : 161- 165. 摘 　要: 图形电磁计算( G RECO ) 技术是目前分析高频区复 杂目标雷达散射截面( RCS ) 最有效方法 之一。通过应用 G RECO 方法和单- 双站等效原理, 计算动目标高频区的双站 RCS, 给出了与实验 结 果符合良好的计算实例, 具有很好的工程应用价值。 关 键词: 电磁波散射; G RECO ; 动目标; 双站 RCS ; 单- 双站等效原理 文 章编号: 1000-9361( 2002) 03-0161-05　　 　中图分类号: V 243. 2　　　文献标识码: A

　　Since J. M . Rius brought out GRECO met ho d[ 1] , w hich is used for co mput ing t he radar

t o bist at ic RCS prediction , and gives t he bist at ic r esult s, w hich sat isfies t he measured r esult s w ell

cr oss sect ion of complex t arg et s fo r high f requency , it has been applied and st udied com prehensiv -

and has prov ed valid.

ely and is recog nized as one of t he mo st v al uable met ho ds to analy ze the RCS of larg e and com plex radar t arget s. T he met ho d no t only can model t he t arget s w it h accuracy, but also has adv ant ages of requir ing l ess mass-st orage memor y and avoiding t he “facet noise”. M oreover, the surf ace and line int egrals are ev aluat ed by g raphical processing of an image o f the t arget on t he com put er screen, t he elect romag net ic code is sm al l in size, and independent of t he tar get geom et ry . GRECO approach is mainly appl ied t o monostat ic RCS predict io n. T he bistat ic RCS ev al uat ion can be obt ained by using t he bist atic equivalence t heorem . T his paper applies t he GRECO m et hod

1　GRECO Wit h t he GRECO method t he hig h-frequency RCS o f a t arget can be at t ribut ed t o t he combinat ion of the f ollow ing analyt ic co mponent s. 1. 1　Scattering field caused by target surface By St rat t on -Chu equat ion in a source -f ree reg io n, t he scat t er ing field can be expressed in term s o f int egral over t he open surface S 1 and a line integ ral t erm about t he shado w -boundary . s 1 T E ( p) = [ j !( n × H )∀ 0 + 4 S 1 T T (n×E ) × ′ ∀ 0 + ( n -E ) ′ ∀ 0] ds +

∫

1 4 j #0

∮′∀ -H dlT

0

Received date: 2001-12-27; Revision recei ved dat e: 2002-03-01 Foundati on it em: Foundat ion of N at ional K ey Laborat ory of Elect romagneti c Environment al R es earch ( 00js 67. 1. 1. h k0101) A rt icl e U R L: ht t p: / / ww w . hk xb. net. cn/ cja/ 2002/ 03/ 0161/

( 1)

Q IN D e-hu a, WA N G Bao -f a

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s w here E is t he scat t er ing f ield; ∀ 0 is t he GREEN 's T T funct ion o f f ree space; -E and H are t he t ot al electr ic f ield and mag net ic f iel d respect ively .

If the incidence direction is - Z , t he monostat ic f ar field and t he RCS w er e easily obt ained as fo llow s i -Es ( p ) = - jkexp( jkR ) -E ( z 2 R S

∫

n) ex p( 2jkz ) dz

1

( 2) ∃ = lR→∞ im 4 R 2

-Es Ei

2

4 %2

=

cos&exp( 2jkz ) ds

S

∫e

ds′

SCREEN

　　In general w e assum e that o ne pixel is equiv alent to a rect ang ul ar aper ture wit h unifor m illum inat ion, t hen it s contr ibution to t he far field can be approx imat ed by a sinc f unct ion of t he ang le &, and t he P O surface int eg ral becomes, in the discret e do main, ∃ = 42 %

assumed as radiat ed by an equiv alent current locat ed on t he edge .

[ 2]

　 　 Discret e computat ion of t he surf ace int egr al Eq. ( 3) l eads t o 2jkz

in GRECO. 1. 2　 Scattering field for wedges Acco rding t o the hig h -f requency diff raction t heory , t he far -f iel d scat t ered fro m a w edg e can be

w edg e, r esult ing fro m the radiation of equivalent

1

( 3)

∃ = 42 %

t his st at io nary phase approx imat io n. Acco rding t o Eqs . ( 4) and ( 5) , t he f acet s scat t er ing f ield can be implement ed very ef ficient ly

T he monostat ic far -f iel d scat t er ing f rom t he

2

∫

CJA

∑ sinc( kl tan&) ex p( 2jkz ) ∋s

2

( 4)

current s , is Es = E 0

exp( - jkr ) [ - D ‖ sin(ei‖ 2 r EDGE

∫

D x cos(e i‖ - D ⊥ cos(e i⊥] ex p( 2jk z ) dl ′ ( 6) w here t he l ine int eg ral ext ends along t he edges ili i luminated by t he incident w ave , e‖ and e⊥ are respect ively t he unit vect ors parallel and perpendicular t o t he incidence plane, and ( is t he angl e bei t w een t he incident elect ric field and e⊥ . D ‖, D x , D ⊥ st and for the monostat ic incr em ent al diff ract ion coeff icient s ( IL DC) [ 3] .

2　M onost at ic-bist atic Equialence T heorem

observat ion, l is t he size of a square pix el in t he screen , and l/ cos&is t he size of t he ds projected on t his pixel. According to the hig h-frequency t heor y, t he co nt ribut ion to the monost at ic RCS fro m a curved surf ace com es f rom the specular ref lect ion point ,

In Fig . 1, t he angles &and ) define t he direct ion o f propag ation of t he incident f iel d, and t he angles &′and )′define t he direct ion o f pr opag ation o f t he scat t er ed f ield o f int er est . T he case w here &= &′and ) = )′is called m onost at ic scat t er ing or backscat t ering . T he special case of &′ = scat t er .

- &, )′ = )+

is called for w ar d

w here the norm al t o t he surface is cl osed to t he incidence direct ion. T he cont ribution f rom t he reg ion of fast phase v ar iat ion , close t o the boundary betw een illum inat ed and shadow ed regions, should be canceled o ut , but it is not , due t o t he err or in t he surface discret izatio n. As in t he shado w boundary , t his spurio us cont ribut ion can be remov ed f rom each pix el by a f act or cos n& 4 %2

[ 4]

P IXELS

w here & is t he angle bet w een t he normal direct ion of t he unit squar e surface ∋ s and t he direction of

∃=

lengt h

∑ cos &sinc n

P IXELS

kl sin& ex p( 2jkz ) ∋s cos&

2

( 5) w here n is a paramet er t hat cont rols t he ef fect of

F ig . 1　 Bista tic scat tering

Bist at ic R CS Pred ict ion wit h G rap hical Elect romagnetic Compu tin g ( G R ECO ) M et hod for ……

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Bistat ic radar cross sect ion is somet imes convenient to express as

[ 5]

∃( &, ); &′ , )′ ) =

%20

2

2

∃b is tatic = ∃m onostatic 1 + 2

( 10)

w here +is t he biangle in F ig. 2.

F( &, ); &′ , )′ ) =

4 2 F( &, ); &′ , )′ ) k0

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( 7)

w here F ( &, ); &′ , )′ ) is called t he scat tering amplitude f unct io n and k 0 is the fr ee space w av e num ber. T o the large and complex t arget , t he t ot al cro ss sect ion is obt ained by int egrat ing ∃ over al l solid ang les. T he t ot al r esul t ∃T is 1 ∃T = ∃( &′ , )′ ) d∗ 4

Based on t he GRECO m et hod , t he t ransmit -

∫

( 8)

　　Fo r a perfectly conduction or lo ssl ess dielect ric t arget , t he f orw ard scatt ering sect ion is ∃T =

4 2 I m F ( &, ); k0

- &, ) +

Fig . 2　 Biangle

)

( 9)

t ing direct io n i and scat t er ing direct ion s are set on t he x oz plane as show n in F ig . 3. In or der t o comput e t he bist at ic cr oss sectio n of a t arget , t he z direction has to be recog nized as an equiv al ence bist at ic direct ion.

　　Crispin, Goodr ich and Sieg el[ 4] have consider ed bist atic scat tering at angles less t han , and hav e dev elo ped t he “mo nost atic -bist at ic equiv alence t heorem”. T he t heor em st ates: “ Fo r perf ect ly co nduct ing bodies which are suff icient ly sm oot h , in t he limit of v anishing w av elengt h, the bist at ic cro ss sect ion is equal t o t he mo nost atic cr oss sect io n at the bisect or of t he bist at ic angle betw een t he directions t o t he t ransmit t er and receiv er . ” A corol lar y of t his t heo rem is t hat t he cro ss sect io n is unchanged if t he posit ions o f t he t ransm it t er and receiver are int erchanged. Crispin et al . show w it h t he physical opt ics approx imat io n t hat t he t heo rem is approx im ately t rue if the bist at ic angle is consider ably less t han radians. In GRECO m et hod each pix el is recog -

Fig . 3　 Bistatic radar co or dinat es

3　Bist atic GRECO for M oving T argets By using t he met hod discussed above, t he m oving dir ection and at tit ude of the targ et relat ed t o t he r adar sy st em have t o be t aken int o acco unt . It is assumed t hat a mo ving co mpl ex t arget in a r adar system is fly ing in a co nst ant velocit y v along a given rout e as show n in F ig . 4. One can t ake t he

nized as o ne scatt ering cent er. All t he am plit ude and phase cont ribut ion o f each cent er can be obtained fr om t he info rmat ion o f pix els o n t he screen, w hile the inf ormat ion is f orm ed by hardw ar e and does not occupy t he CP U time . In t he case of small biangle, t he cr oss sect ion is alm ost unchanged by changing t he fr equency. So , in order t o simplify t he co mput at io n in eng ineering application , t he ef f ect of frequency is gener all y neglected and the bist at ic cr oss sect ion ex pression is

F ig . 4　T ar get a nd ra dar system

Q IN D e-hu a, WA N G Bao -f a

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co ordinat e ( X , Y , Z) as a based r adar syst em , and t he ( x , y , z ) is t he t ar get sub -coor dinat e syst em . S 1 and S 2 ar e t he locations of bist at ic radars . ) is M oving ang le . R is t he distance bet w een based radar orig inal point O and t arget sub-coordinat e sy st em. H is the hig h alt it ude of the mov ing t ar get . P is the dist ance f rom t he point O of based radar co ordinat e ( 0, 0, H ) t o t he targ et air way . In o rder t o comput e bist atic RCS of a cert ain mov ing t arget at any tim e, t he biang le relat ed t o t he r adar sy st em and t he t arget has t o be obt ained,

CJA

4　Com puting Exam ples 4. 1　Bistatic RCS of a static aeropl ane model F ig. 5 is a st at ic aero plane mo del bistat ic RCS computing co nf iguratio n. T he biang le is +, and t he t ransm it t ing st ation and receiver stat ion are S 1 and S 2 respect iv ely , in o rder t o sat isfy t he bistat ic m easurement condit ions of a scat t ering laborat ory . T he com put ing result s are g iv en by defining t he t arg et and t he radars ( S 1 , S 2) lie in the same plane ( H = 0) .

and then put t he bisect or direct ion of biang le nor mal t o t he scr een of the co mput er , and f inally bist at ic RCS can be easily solv ed . T aking int o account t he ef fect of ear th radius R e , t he original point O of the t arg et sub-coordinat e is

F ig . 5　Bist atic RCS computing config ur ation

Fig . 6 ( a ) and ( b) are bist at ic com put ed and

R 2 - z 20 - P 2 cos)

x 0 = Psin) +

m easur ed result s r espect ively . T hey ar e in accor d R 2 - z 20 - P 2sin)

y 0 = - Pcos) +

2

z0=

2

(Re + H ) - R - R 2R e

2 e

( 11)

w it h each o ther and the m et hod is prov ed t o be reliable and accurat e.

　　T he lo cat ion of t he t arget at any time t is x t = x 0 = vt cos) y t = y 0 - v tsin) zt =

2

2

2

( Re + H ) - x t - y t - Re

( 12)

　　Based o n the g eom et ric relat io n show n in F ig . 4, t he biang le +and t he equiv al ence m onost at ic direct ion , can be easily given S1 = ( x 1 - x t , y 1 - y t , z 1 - z t ) S2 = ( x 2 - x t , y 2 - y t , z 2 - z t ) += arccos ,=

S1 S1

S1 + S2 S1 + S2

S2 S2

Fig. 6　Computed result a nd measured result

( 13) ( 14)

( a ) Computed r esult ; ( b ) M easur ed result

4. 2　Bistatic RCS of a movi ng target

w here ( x 1, y 1, z 1 ) and ( x 2 , y 2 , z 2 ) are t he po sit ion

Assuming an ex ample of a moving t ar get w ith a co nst ant v elo cit y fly ing along a st raight line as

co ordinat es of S 1 st at ic and S 2 st at ic respect ivel y.

show n in Fig. 4, and the paramet ers are g iven as

t he relative po sit io ns o f t he radar and targ et . And

f ollo w P = 10km , R = 20km, H = 10km, )= 60° , t he

t hen o ne can obt ain t he equivalence mo nost at ic di-

posit ion of S 1 is ( 2km, 2km , 0) and S 2 is ( 1km , -

rect ion by t he mo nost atic-bistat ic equivalence t heo rem . T he RCS of t he mov ing t ar get can be ob-

2km , 0) , R e = 6380km , v= 50m/ s.

At any t ime, one can com put e t he biang le by

tained in real tim e by GRECO .

T aken int o acco unt t he ef fect of eart h r adius , it is no t diff icult t o obt ain t he biang le of t he bistat -

A ugus t 2002

Bist at ic R CS Pred ict ion wit h G rap hical Elect romagnetic Compu tin g ( G R ECO ) M et hod for ……

ic radar syst em and t he at tit ude of t he targ et at any t ime t. T hen t he plane's geomet ry mo del is displayed on t he screen according t o t he at t it ude o f t he t ar get , and t he RCS is solv ed w it h GRECO , w e can

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References [ 1] 　 R ius J M , Luis J. High -fr equency R CS of compl ex radar t argets in r eal t ime [ J ] . IEEE T ran s A nt ennas Propag at ion, 1993, 41( 9) : 1308- 1319. [ 2] 　 M icheal i A . Equivalen t edge current s for ar bit rary as pect s of obs ervat ion[ J] . IE EE T ran s A nt ennas Propag, 1984, A P-23

obt ain t he t arget RCS value at any t ime . Fig . 7 is t he computing bist at ic RCS cur ve

[ 3] 　 M itz ner K M .

w ith the flig ht t ime for an air craf t . ( com put ing t ime rang e is 0～10000s , f requency = 10GHz, VV po larizat io n)

[ 4] 　 Cr ispin J W, Jr, G oodrich R F, Sieg el K M . A t heoret ical

( 3) : 252- 258. Incr ement al lengt h d iff ract ion coef f icient s

[ R ] . T ech nical Report , N o. A FA L-T R-73-296, N ort hrop Corporat ion A ircraf t D ivis ion, 1974. m et hod f or th e cal cul at ion of radar cross sect ion of aircraf t and miss iles[ R ] . U n ivers ity of M ichigan, Report N o. 25911-M , 1959. [ 5] 　 G eorg eT R , Barrick D E, St uart W D , et al . R ad ar cros s s ection h andb ook [ M ] . N ew Y ork - Lodon: Plenum Pres s, 1970.

Biographies:

F ig . 7　Bista tic computed R CS cur ve

5　Conclusions By using t he most at ic -bist at ic equivalence t heorem and GRECO met ho d t o comput e t he RCS of mov ing targ ets in high frequency region, t his paper enlarg e the GRECO method applicat ion to co mput e bist at ic RCS f ield . It has been proved valid and accurat e by co mput ing stat ic Bist at ic RCS curv e, w hich agr ee w it h the m easur ed r esult w ell. M oreover it g ives t he co mput ing results of a pract ical fl ig ht t ar get f or a mult i-r adar m onit or syst em, w hich is import ant t o st ealth and ant i-st ealt h research and has pract ical eng ineer ing value .

Qin De-hua　Bo rn in 1975, he is a Ph. D . candidat e at the Dept. of Elect ro nic Engineering , Beijing U niver sity o f A er onautics and Astr onautics. His r esearch inter ests include Co mputa tio nal Electro mag netics and R adar T arg et Recog nitio n. Email: qdhweb@ sohu. co m. Wang Bao-fa　Bor n in A ug . 1938, he r eceiv ed B. S. deg r ee in 1961 fr om Beijing A er onautics and A str onautics Instit ut e. F ro m 1961 to 1983 he w as a lectur er w ith the BA A I. F ro m 1983 to 1985 he was a v isiting scholar o f the EM L ab. at the U niv ersity o f I llinois. He is cur rently a P ro fesso r o f the Beijing U niver sity of A ero naut ics and A str onautics. His resear ches include EM w av e pro pagat ion and scatter ing , micr ow av e and antenna application, electro mag netic co mpat ibility .