A SIMULATION ANALYSIS OF SPACE-BASEDAND AIRBORNE MOVING PLATFORMRADARS IN LOOK-DOWN CLUTTER

DTICP -,L. ipuk. ELECTE

~OCT 191983j

AffW W FMu AwRM -17UW mWWmE

WOMI Alt DEVELOPMENT CENTERAir ForceSyemCmedrVf .Air Force Se, NY 18441

83 10 18020

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RADC-TR-83-126 _______________

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A SIMULATION ANALYSIS OF SPACE-BASED AND In-House ReportAIRBORNE MOVING PLATFORM RADARS IN LOOKC- .PROMN01GRERTUBRDOWN CLUTTER S.PRORIG0/.APRTNME

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Rome Air Development Center (0CTM) 62702FGriffiss AnB NY 13441 4506176611. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

May 1983Rome Air Development Center (0CTM) 13, NUMBER OF PAGES

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RadarClutterSimulation

20. ABSTRACT (Coensew an ,evee sid. It noebo.ey ged Identify by block nirbe)

A stmulation technique has been developed to provide the radar engineerwith a tool for comparative examination of radar systems and target detec-tion in the presence of look-down clutter. Usin; a plotting interface

* such an the Dedicated User Interface System (DUIS), an engineer can* evaluate proposed radar designs against one another for target detection

performance in a precise graphical format.(Cont'd on reverse)

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UNCLASSIFIED3SCUP4TY CLASSIPICATION OP THIS PAGM(Vohi Datn Bom

The user is able to select an antenna function from either measured dataor derived data under the existing Parametric Antenna Analysis Software(PAAS). The antenna platform may be at any designated altitude andvelocity with respect to ground clutter scatterers. Entry of an exoatmos-pheric altitude automatically computes the proper circular satellite orbitvelocity and introduces Earth rotation. Target radar echoes at specifiedground locations are compared to clutter echoes in the sidelobes as wellas the radar mainbeam. Analysis of output data serves as a measure ofmoving target minimum detectable velocity (MDV) for the total radar system

Written for analysts with some technical doppler radar and clutter under-standing this report leads the engineer through the theory and equationswhich develop the simulation computer program. Example cases and analysesare given to show program utility and output results.

UN lSIFIEDSECURI?Y CLAWSSICATIOU Oe AO(WhI Date Bm..

2 -. -'

r

TABLE OF CONTENTS

TITLE PAGE

Introduction I

Range-Doppler Cells I

Geometric Analysis 4

Clutter Intensity Diagram 9

Directing the Antenna 12

Rotating Earth Model 13

The Clutter Simulation Program 15

Example Clutter Program Run 17

Antenna With Blockage 22

Minimum Detectable Velocity 24

Limitations 30

Future Development Efforts 31

Conclusion 31

DTIO TAB LSunannourecd

Du t i cab t i o n__ -------

i @°.

0aI

APPENDICES

I Listing of Program CLUTR

I1 Listing of Program RANGE

III Listing of Program SCAN

IV Glossary

L I ST OF FIGURES

NUMBER TITLE PAGE

la Equal Range Contours From a Moving Platform 2

lb Equal Doppler Contours From a Moving Platform 2

2a Equal Range and Equal Doppler Map on the 3

Earth's Surface

2b Sampled Resolution Limited Map 4

3 Geometry of a Moving Platform 5

4a Geometry at the Horizon 6

4b Geometry at Intermediate Ranges 6

5a Clutter Intensity Diagram 10

5b Relationship Between a Pencil Beam Antenna 10

Footprint and the Clutter Intensity Diagram

6 Clutter Intensity Diagram - Discrete Scatterer 11

7 Coordinate Transformation Axes 12

8 Rotating Earth Doppler Components 13

9 Program CLUTR Block Diagram 16

10 3-D Omnidirectional Antenna Clutter Intensity 17

11 40 dB Taylor Far Field Antenna Pattern 18

12 3-D Clutter Intensity Plot - 50 Grazing Angle 21

13 3-D Clutter Intensity Plot 300 Grazing Angle 21

14 40 dB Taylor Far Field Antenna Pattern 22

With 5% Central Blockage

15 3-D Clutter Intensity Plot With Blockage 2350 Grazing Angle

iii

NUMBER TITLE PAGE

16 3-D Clutter Intensity Plot With Blockage 23

300 Grazing Angle

17a Target to Clutter Ratio vs. Doppler Bin 24

300 Grazing Angle - Range Bin 55

17b Target to Clutter Ratio vs. Doppler Bin 25

300 Grazing Angle - Range Bin 55

18a Target to Clutter Ratio vs. Doppler Bin 26

50 Grazing Angle - Range Bin 115

18b Target to Clutter Ratio vs. Doppler Bin 27

50 Grazing Angle - Range Bin 115

19 3-D Clutter to Target Ratio 50 Grazing Angle 29

20 3-D Clutter to Target Ratio 300 Grazing Angle 29

iv

INTRODUCTION

Analysis of radar detection performance in moving platforms, either

in a satellite or aircraft, is a continuing area of interest. The need

to detect smaller targets in look-down geometries, plus the expected

difficulty of achieving deterministic low sidelobe patterns in space

deployable antennas and for conformal antennas on various airframes has

dictated a relook at the moving target detection design for such radar

systems.

This report describes a simulation analysis computer program which

examines the target detection performance of space based and airborne

surveillance radars in look-down clutter. The computer model samples

ground clutter with specified radar cross section and grazing angle

effect and analyzes clutter signal power intensity as an effective area

in range and range-rate (doppler) space. With included targets and

antenna parameter data, a computed target to clutter ratio plotted for

some range over all range-rates is shown as a means of measuring target

minimum detectable velocity. A 3-D plot of clutter intensity as program

output indicates how antenna systems may be compared with one another in

terms of target detectability. The program is capable of plotting in

3-D format the clutter intensity or clutter to target ratio over all

range and doppler which is visible to the antenna. The 3-D plots at a

glance indicate the relative merit of given radar antenna systems.

General program parameters are developed with geometric

consideration of both a non-rotating and a more complex rotating earth

model. Current program limitations are discussed as well as continuing

and future improvement efforts. Although this program is applicable to

any set of monostatic antenna and platform parameters, a specific

example is given as an illustrative example.

RANGE-DOPPLER CELLS

The problem of computing range-doppler sample data fram a moving

platform is outlined in figures la and lb. A range gated doppler radar

analyzes the returned signal in both time (range) and frequency

-1-

(doppler). The signal is processed by first dividing it into a number

of intervals in time (range gates) and then analyzed by passing it

through a set of doppler frequency filters. The locus of points of

equal range from a monostatic radar antenna which intersects the earth

is called an isorange and is a circle centered about the platfrm

subpoint. All such sampled ranges produce a series of concentric

circles on the earth (figure 2a).

TZ

EQUAL RANGE CONTOUS EQUAL DOPPLE CONTOURSFROM AN ZZVATE PLTFORM FROM AN ELEVATE MOVING PLAT.OR

Figure la. Figure lb.

Unfortunately, the locus of equal range-rates intersecting the

earth is not as easy to characterize. Relative to a moving platform the

locus of points in space of equal doppler shift is a cone whose vertex

is at the antenna, and whose axis coincides with the velocity vector of

the platform. Intersection with the spherical earth results in a

distorted conic section called an isodop. The maximum doppler component

of ground clutter is thus the platform velocity relative to the earth

multiplied by the cosine of the minimum cone angle which intersects the

e -th (fiq, e 1b). The zero doppler component will be at all range

poLor w. l -h lie orthogonal to the velocity vector (neglecting rotating

-2-

4. - - - a

earth effects).

The intersection of isoranges and isodops for a radar bystem with

contiguous range gates and doppler filters is sketched in figure 2a. To

limit the processing required, the radar clutter returns may be sampled

at a finite number of ranges equally spaced from the minimum to the

maximum expected range. The doppler data may also be sampled by a

finite number of doppler filters equally spaced between maximum and zero

doppler. The minimum width of the range gates may be taken down to the

range resolution limit of the radar system. Similarly, the doppler

filter bandwidth minimum limit depends on the radar system

characteristics. The intersection of N isoranges with M isodops and

their respective resolution widths define NxM range-doppler cells (see

figure 2b). It is from these cells that the simulation clutter data is

sampled and computed.

Range-dopplerCell

Ioorange

Figure 2a. Equal Range and EqualDoppler Map on Earth's Surface

i ~-3- '

Iop Range-dopplerI OP

Figure 2b. Sampled Resolution Limited Map

GEOMETRIC ANALYSIS

Figure 3 shows a moving platform radar antenna at a distance H

above the earth's surface in a right hand coordinate system. A

geometric analysis of figure 3 yields the equations necessary to

calculate the range-doppler cells and their effective clutter

contribution to the radar echo.

Any point in the far field of an antenna can be represented by a

pair of direction cosines T. and T, where the relationship with

spherical coordinate angles is:

T cos(Ax ) - sin(e)cos(4)

= cos(Ay) - sin(e)sin(O)

It is convenient to place the moving antenna platform at the center

of the coordinate system with the velocity vector V coinciding with the

-4-

. , . . . . .• ..-. .: , ,4

z

Antenna Dlatform Iwobserving a ground patch

A

x

patch'

7'izure lechmetrv of a Mcvnr~ 1tfzlrm

X -5-

Y axis and the Z axis pointing up. The reference to a point on the

ground may be given in term of a vertical elevation angle C and an

azimuthal scan angle S measured from V.The direction cosines are

simply related by:

Tx - sin(C)sin(S)

T y- sin(C)cos(S)

From figure 4a the elevation angle of the horizon, which is the

complement of the minimum horizon cone angle Ayin and the range to the

visible horizon Paxare:

sin(Cmax) - cos(Amin) -Re/(Re+-H)

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

-T angle

.amax C(I) Osi

horion 610G (I)

Re Re

Figure 4~a. Figure 4b.Geometry at the Horizon Geometry at Intermediate Ranges

-6-

Similarly, for any given range R(I) corresponding to some range bin I,

figure 4b and the law of cosines results in the elevation angle C(I):

R2(I) + (R +H)2 - R2

e eC(I) - arcco] 2R(I)(Re+H)

The grazing angle G(I) at a particular range R(I) is given by

figure 4b and the law of sines:

G(I) - arccos[--e sin(C(I))

Consider now the equally spaced sampled range and doppler bins of

figure 2b. The distance between the N range bins is determined by

dividing the total range difference by the number of range gates less

one:

Dr - (Rmar- H)/(N-1)

The range of the Ith (I-_ to N) bin is calculated from:

R(I) - (1-1)Dr + H

where the nadir is at R(1)-H and the horizon is at R(IiN)-Rmax.

To avoid the problems of clutter cell area on the horizon, for the

purposes of the simulation the range difference is divided by N instead

of N-1. This has the effect of decreasing Dr slightly and placing the

last range bin R(N) a small distance back from the horizon. If the

range resolution of the radar is Ar, from figure 4b the effective ground

range coverage for small Ar is Ar/cos(C(I)). Of course N must be chosen

so that D is significantly larger than this value to prevent rangeroverlapping in the range bins of interest.

The M equally spaced doppler bins are equivalently computed from

the radial velocity components, since the two way radar doppler shift is

proportional to the radial velocity seen at the antenna platform and the

wavelength of the radar operating frequency:

-7-

-- -- -'{-

F = 2V /Xd r

where the radial velocity component is related to the platform velocity

ifor a stationary earth):

V - V cos(A )r p y

Then the frequency difference between the M equally spaced doppler

filters, and the cone angles which yield the M isodops are:

D - 2V cos(A )/MAf p ymin

AJ) - arccos(JDf X/2Vp) J-1 to M

If the doppler filter width is Af, then the angles which yield the N

isodops of width Af are between A (J) and:

A yd(J) - arccos((JD f+Af)X/2V )

A critical factor arises at this point in the calculations. Since

a cosine function has its most rapid change at large angles, most of the

equally spaced doppler bins will be crowded at cone angles greater than

45 degrees away from the velocity vector. By the same reasoning, the

ground coverage due to these angles is larger for smaller cone angles

(i.e. close to the plane of motion near the horizon). In effect the

area of the range-doppler bins of figure 2b becomes larger as the plane

of motion is approached.

Now the clutter intensity in the radar echo will be a function of

the area of the range-doppler cells in figure 2b. From here on a

simplifying assumption must be made concerning the shape of the

range-doppler cells. As long as the resolution width of the range bins

and doppler bins is small compared to the distance between them, each

cell can be approximated as a rectangular area. The radial component is

a simple function dependent on the grazing angle and range resolution,

but the lateral component requires a somewhat more complicated geometric

-8-

analysis of the vectors which define the isodops and their equivalent

resolution widths at each range.

CLUTTER INTENSITY DIAGRAM

Consider the case of continuous scatterers uniformly distributed on

the earth's surface and a radar with infinitely fine resolution. If the

radar is unambiguous in both range and doppler, the clutter scatter

signal strength C(r,r) will be a function of at least four components.

First is the 1/R two way path loss attenuation factor from the radarrange equation. Second is the radar cross section ao , of the ground

scatterers. Several models are available which describe ground RCS as a

function of terrain type and grazing angle. The third component is the

two way relative antenna gain as a function of directional cosines Txand Ty. The directional cosines correspond to those angles which yield

r and i at the earth's surface. Finally, the area of the range-doppler

cells must be computed which will determine the number of discrete

scattering centers, providing the integrated clutter signal power.

Presuming for the moment an omnidirectional antenna with unity gain

and uniformly distributed range-doppler scatterers, the clutter

intensity diagram takes on the smoothly shaded appearance of figure 5a.

Range R is plotted along the ordinate axis and the direction cosine

angle Ay is plotted on the abscissa. Dark shading represents regions of

high clutter echo intensity (integrated radar return signal power).

The distinctive "U" shape of the expected clutter return of figure

5a is strictly a function of platform altitude and earth radius.

Outside this shaded area is a clutter free region where no combination

of range and cone angle intersect the earth's surface and in this region

a target would not compete with surface clutter. Directly beneath the

antenna platform corresponds to a zero degree elevation angle and 90

degree cone angle, with range equal to platform altitude (figure lb).

Progressing outward in range one reaches the radio horizon, which is the

range of the visible horizon from the elevated antenna platform.

Greater ranges would correspond to range-doppler cells which do not

intersect the earth. Range excursion along the central vertical of

figure 5a at a constant 90 degree cone angle is a vertical scan in

-9--- 9 -- -

elevation orthogonal to the plane of motion, while travel along the "U"

edge is a vertical scan in the plane of motion. A depiction of the

relationship between a pencil beam antenna footprint and the clutter

Intensity diagram is shown in figure 5b. Notice that near the edge,

close to the plane of motion, the intensity rises due to the increased

area size of the range-doppler cells. Since the cell area is larger,

effectively more point scatterers are covered per cell resulting in a

greater power intensity.

"tam

'.~1e sePt'or

-. -

am.. rai-.er

Figure 5a. Figure 5b.

Clutter Intensity Diagram C(r,) Relationship Between a Pencil Beam AntennnFootprint and the Clutter Intensity Diagram

-10-

Now consider a somewhat more realistic antenna with finite range

resolution Ar and finite doppler resolutionAr corresponding to discrete

noncontiguous range-doppler cell scatterers. The clutter scatter

function for each cell is depicted in figure 6. This discrete

characterization of the distributed returns C(Ar,&iA) for the Ph

specific range bin and the jth specific doppler bin is used in the

computer program simulation. The clutter scatter function of each cell

is an integral over the range and doppler cell widths.

ri+Ar/2 +Ai /2

C (A r,Ai) = C(r i i, )dr idi

--2i~j ii

rang bin

I Distance betvee n

Ar

Distanee be nI I doppler bins

Figure 6.Clutter Intensity Diagram

Discrete Scatterer Case C(Ar,b&)

For an unambiguous range gated pulse doppler radar with a known far

field antenna pattern weighting (including sidelobes) as a function of

directional cosines, one only needs to multiply the discrete clutter by

the weighting function ANT(TX ,Ty) to obtain the clutter intensity

function of the antenna.

- 11 -

DIRECTING TH ANTENNAThe question of directing the antenna main been toward some

specified point on the earth's surface must be Addressed. In a Phased

array this is accomplished by electronic beam steering, which simply

redefines the weighting function ANT(T T).Alternatively, the Antenna

platform may be mechanically steered in roll, pitch, and yaw as defined

in the right hand coordinate system of figure 7.

antenna inl

Pitchaxis -Y plant

Figure 7.

Coordinate Transformation Axes

Mechanical steering is accomplished by applying the Jacobian

matrix:

T1 cos(pit)cos(yaw) -cos(pit)sin(yaw) Tx x

sin(ro1)sin(pit)cos(yaw) -sin(rol)sin(Dit)sin(Yaw) Ty +cos(ro!)sin(yav) +cos(rol)cos(YaW) y

(From Mathematical Handbook for Scientists an Lngi&neers, Korn and Korn,

2n e,.,1cGraw Hill, 1968) -12-

where the primed coordinates are In the steered frame of reference.

These nw directional cosines are input to the modified weighting

function ANT(T x ' , T '). The antenna has been effectively steered toward

the specified patch of earth.

ROTATING EARTH MODEL

Up to this point the effects of the rotating earth have been

neglected. This assumption is valid for airborne antenna platforms

which are in a rotating earth frame of reference, but the motion of

space based radar platforms is independent of earth rotation and the

earth will provide a component of doppler velocity. Consider a platform

stationary in space with the earth rotating beneath as sketched in

figure 8.

U

4doppler -doppletr

component Lomponent

W8

Figure 8.

Rotating Earth Doppler Comnonents

Clearly for an orbiting platform, the earth's doppler velocity

component will be negative when looking in the eastern hemisphere,

positive in the western hemisphere, and zero along the central meridian.

Of course, to the earth component radial velocity must be added the

radial component due to the orbital velocity of the satellite. Note

that the line of zero total doppler velocity will no longer be precisely

orthogonal to the velocity vector (except in an equatorial orbit). In

-13-

general for a ioving platform in circular orbit, the radial doppler

velocity component depends on altitude, orbit inclination, and the

grazing angle of the ground clutter patch. In the simulation of a

range-doppler cell radar system the total radial velocity component from

each of the individual cells is given by:

Vr(I,J) - Vpcos(Ay) - Vecos(G)cos(lat)cos(scan)

scan - arccos(cos(AY)/sin(C)) - arccos(cos(inc)/cos(lat))

where A is a function of I and J; G and C are functions of I; "inc" isYorbital inclination; "lat" is instantaneous satellite sub-latitude; and

Ve is the equatorial rotational velocity of the earth. The term "scan"

is essentially the azimuthal scan angle measured from the satellite's

instantaneous velocity vector.

The maximum total doppler velocity component will be at the horizon

in the plane of motion. (Actually, depending on the position of the

velocity vector, the rotating earth may change this maximum component

direction, but for circular orbits up to geosynchronous altitudes the

effect is small.)

Vra Vpcos(Aymin) - Vecos(inc)

The velocity differential between each of the M equally spaced doppler

bins is thus:

Vdiff" Vrmax/M

and the doppler velocity of the Jth doppler bin is:

JVrmax /M - V(IJ)

Solving for the cone angles A(IJ) which yield the desired equally

spaced doppler bins results in a considerably more complex function than

for the nonrotating earth model because of the combined I,J dependence.

- 14 -

coe(YMM DVl*DV2 : DV3.SQV-slfl(CCI))cos(3 .(IJ))DV2

2 + DV32

where:

DVl - (V cos(A ) -n V ecos(inc))/M

DV p -Vecos(iflc)/cos(Aymin

DV3 - (cos 2(lar) - Cos 2(inc))Ve /cos(Avrmin

SQV * [DV22 + DV3 2 - DVj2,/sin2(C(I))1]

If the doppler filter bandwidth is Lf, then the angles which yield

the N isodops of width Af are between A, (I,J) and:

Ayd ,J - AJ(I') lDV1DV! + f/

Care must be exercised when applying these equations to take into

account the direction of orbit and whether the antenna is pointed toward

the northern or southern hemisphere. For the nonrotating earth case

(V eO-), or for the satellite subpoint over a pole Cinc-90, 1at-90) the

equations reduce to the simpler form previously derived.

THE CLUTI' SI24ULATION PROGRAM

The program CLUTR is designed for either a space based radarantenna in circular orbit or for an airborne platform in level flight.The antenna far field weighting input data resides in a file which

either has been previously generated from PAAS (Parametric Antenna

Analysis Software) or from an actual antenna data tape.

The inputs f or a circular orbiting space based moving platformradar are:

(1) The altitude above the earth's surface.

(2) The range and doppler bin resolution size.

(3) The ra'qr operating frequency.(4) The orbit inclination and platform sub-latitude.

(5) The direction of orbit, est or west.

(6) The main beam pointing quadrant, north or south.

(7) The antenna roll, pitch, and yaw pointing angles.

(8) The target radar cross section.

(9) The far field antenna weighting values ANT(Tx,Ty).

Inputs for an airborne platform are the same except items (4), (5), and

(6) are omitted and an input ground speed is required. Figure 9 is a

block diagram of the basic components of the program.

:=_"1

Figure 9.

Program CLUTR Block Diagram

The data from two auxiliary programs are required for inputs to the

main program CLUTI. This is to insure that the radar main beam falls

within one of the sampled range-doppler cells. Program RANGE provides a

listing of range bin numbers with range R(I), elevation angle C(I), and

grazing angle G(I) for each range bin 1. Given a desired grazing angle,

for example, the range bin number yielding the nearest grazing angle is

selected. This grazing angle and corresponding elevation angle value

must be entered iL.o CLUTR and will center the main beam in range I.

Program SCAN provides a listing of azimuthal scan angle S(IJ) and cone

angle A (1,J) for each doppler bin J at the range I. The value S(IJ)

centers the main beam in doppler bin J.

-16-

EXAMPLE CLUTTER PROGRAM RUN

The utility of the simulation is best demonstrated with an example

case. Consider first an omnidirectional antenna (i.e. all T and Tx Yantenna weighting values are unity) with the antenna platform in a 4000

nautical mile high circular orbit. Samples of 128 range bins and 128

doppler bins are taken, resulting in 128 range-doppler cells. The 3-D

sampled clutter intensity diagram output is shown in figure 10. Notice

that figure 10 is just one half of figure 6, with the inter-cell spaces

compressed. The ragged edge is an artifact of the sampling process, as

no samples are taken exactly in the plane of motion, but the distinctive

"U" shape is clearly evident.

Figure

3-D Omnidirectional A enna ,- ue Intersiy

- 17-

Next consider PAAS generated far field weighting for the following

Diameter - 35m circular

Weighting - 40dB Taylor

Blockage - None

Wavelength - L Band

Range Resolution - 100m

Doppler Filter Bandwidth - 50Hz

Element Grid Spacing -. 5

The central portion of the far field antenna pattern is shown in figure

Figure 11.

4dB Taylor Far Field Antenna Pattern

-18-

Now place the antenna aboard an orbiting platform with the

following observation characteristics:

Altitude - 4000 nautical miles

Inclination - 60 degrees

Sub-latitude Point - 20 degrees

Main Beam Scan - True north (000 degrees true)

Desired Main Beam Grazing Angles - 5 degrees and 30 degrees

Target RCS - 20dBsm

From the auxiliary program output RANGE, the grazing angle closest

to 300 is 30.049P, corresponding to an elevation angle of 23.59P at

range bin number 55. Similarly from the same output listing, a grazing

angle of 4.84 is in range bin number 115 with an elevation of 27.4?.

The antenna is steered by providing the elevation angle as a roll or

pitch angle.

I NPlT TIE ALI TIIE IN NM=4000.

kLrItriJO 0.140A0000E 07 METERSiJMAX = O. 1221 17659E 00 METERSCEEIAX = 0.2 1540163E 02 DEGREES

IA;4GE(I) CFE(M) JRAZ(I)

:10 .03125E 01 21.3402605E 'JO 66.3459915E-OIIII ) .15413)IE 07 21.361 39t,8E 00 62.73399IIE-OI11 .1511816E 01 27.3812190E 10 59.1364515E-OII: .16164!2E 01 27.3999195E 100 55.5'j3Q829E-OI114 1.1,64021E 01 27.4113J50E )0 ,I.9-4 7126E-OI11,5 I.116916)3E 01 27.4335396E 10 48.43.12826E-01116 .* 1291 liE 07 27.4485452E )0 44.9)011 13E-0II7 ;.11667654E 07 27.4623659E 00 41.36355!54E-01II 1.1904329E 07 27.4750142E 10 37.8495091E-01

119 1.1941905E 01 21.4865022E ,10 34.3445"792E-01

120 1.1979440E 07 27.4968429E )0 30.8604159E-OI

Sample Output Program RANGE50 Grazing Angle Case

At this point in the orbit, the velocity vector heading relative

to true north is:

HDG - arcsin(cos(inc)/cos(lat))

- 32.15 degeees

- 19-

Thus to scan to a true heading of 000 degrees a steering yaw of 32.150

is required. From the auxiliary program output SCAN, the nearest scan

angle for the 55 t h range bin is 32.718 in the 103 r d doppler bin; for

the 115 t h range bin it is 32.2323 in the 1 19 th doppler bin.

I-RN SCAN

INPJUT PIE ALTIr.j0E IN N4=4000.

ALTITUDE 1 ). 40000)OOE 04 NMORBITAL VEL,)CITY : 0.5314546)E 04 M/SORBITAL vFLK'ITY * 0.10460711E T5 KNO S

INPIJT SAiELLIrE INCLINArkiN ANiLLEAND INAFoirNrE-111S LATITADE.0 . .20.IF FLYINc EAST ENTER EIF FLYING 'ESF ENTER 4' EIF L(R)KIl'; IN h)RTH OUADRANT -NrER NIF LOOKIN(; IN SMITH )JADRANT ENTER S=NENF R TA[ ?ANGE IIN NMIBERTo SEE &I L DOPPLER CIMPONENTS AT THAT RANGE

VE2, r ;r It ADING - 0.32146700E 02 DEGR FES

j .LPrtA(IJ) SCAN(I.J) VOoP KTS

114 ,.)241127E 0 31.3 180093E 00 3.90,6511E 03

15 ,4.2395192E Y) 36.4217615E 00 3.9409225E 031I' C".IA0 0 35.4333115E 00 3.9151914E 03117 ,57.65 1 73HE 00 34.409R479E 00 4.r094603E 03Il ,?i.36 ,3743qE r0) 33.3437486E 00 4.0437292E 03lI 'i.J 2045E 00 32.2323437E 00 4.077999OE 03I'20 , . 1.) 9 4 6 3E Myr 3 1-. 071 R 7E 10) "4.11 267"0E 03

'21 16.4445915E 00 29.840192RE 00 4.146535RE 03122 56.1251125E r" 2A.5393661E 0 4.1OR047E 03123 /5.7970142E 0' 27.14t)7679E 0 4.215073TE 03124 -S5.458296IRE 00 25. 6 3Q2066 F V0 4.2493425E 03

Sample Output Program SCAN

5; Grazing Angle Case

Figure 12 is a 3-D plot of the antenna pattern weighted clutter

intensity diagram for the 50 grazing angle case. The main beam clutter

region is clearly defined (centered at range bin number 115 and doppler

bin number 119), although it is smeared in range near the horizon. At

low grazing angles such as this, even if the main beam has relatively

narrow angular beamwidth, it will cover many range clutter cells due to

the curvature of the earth. Again the "U" shape similar to figures 5a

and 10 is apparent, with most of the clutter along the doppler edge.

Even though the main beam is pointed well out in range and the sidelobes

are very low, there is some close in clutter do to (1) the I/R factor

-20 -

.. .. . .. " " ,, ." j& ';-....

1as

Figure 12.

3-D Clutter Intensity Plot

50Grn. inr, Angle

Figure 1.3.

3-D Clutter Intensity Plot

300 Grazing Angle

-21-

which has much less effect for small R, and (2) the grazing angle effect

which increases the ground patch clutter RCS for near ranges.

A similar plot in figure 13 is for the 300 grazing angle case.

Here the beamwidth on the ground is relatively narrow and the sidelobes

still contribute to the near range clutter, although performance is

better because there is not such a large difference between the range of

the main beam clutter and the nadir.

ANTENNA WITH BLOCKAGE

Consider the same PAAS generated antenna pattern, only this time

with a 5% central blockage. The far field pattern is shown in figure

14. Notice that the blockage has significantly degraded the sidelobe

structure so that this antenna would be expected to have degraded off

axis clutter suppression.

Figure 14.

40 dB Taylor Far Field Antenna PatternWith 5% Central Blockage

- 22 -

Figure 15 is a 3-D plot of the clutter intensity diagram for the 50

grazing angle case with the blockage antenna. The general form is, as

expected, the same as figure 12 but a considerable amount of sidelobe

clutter has been introduced. Figure 16 is similarly a dqraded version

of figure 13.

iF

MO dlD

mma.

7igure 15.

3-D Clutter Intensity Plot With Blockage50 Grazing Angle

VAX

________in nn4p

Figure L6.

300 Grazing Angle

- 23 -

MINIMUM DETECTABLE VELOCITY

The target to clutter ratio output of CLUTR for the 55th range bin

over all doppler bins is plotted in figure 17a and expanded in figure

17b. Output for the 115th range bin is plotted in figures 18a and 18b.

IJ.

Iwo I ............ .... ........... ........... ..... ... ..... ............ ...... ......

...... .. . . . . ..

F ITI. .. . .....

'U..."A........ .... ...................

+I ..... .........

+T ......* ~ . .. .

Fiur 17a

Tagtt lt e ai esu ope i30 Grzn Angl

Rag Bi 55i!

I 24

..- . . ........... ...... .. . ... ..... ....

c .. . ..i.. * .. ...

as s e. ~.. .... .. ..... 1

. .. I. . ... .

I 25

A Ar

'44~AkX

;..w~... ..... ~ *~~

...........

...... ..... .. ..

Figure 18a.

Target to Clutter Ratio Versus Doppler Bin5 0Grazing AngleRange Bin 115

-26-

* ~~~ ..... . ....

4 .....

.. . . .. .. .. .. ... . . . .

......... ......... ......

I.A.

. . . . . . ...

. .I

................

... ... .. ......* . ............... ......... .... :.. ...... :4...

........ ....... ... .. .. . . J ~

b"N~~m It "O

Figure 18b.

Target to Clutt~r Ratio Versus Doppler Bin

5 Grazing AngleRange Bin 115

-27-

Notice that the minimum plot value falls in the 103rd doppler bin

for the 5 5 th range bin of figure 17b. This doppler bin corresponds to

the radar return of a target which is stationary with respect to the

earth. The rise to an infinite target to clutter ratio at doppler bin

112 corresponds to cone angle (target doppler) and elevation angle

combinations which do not intersect the earth and hence the target does

not compete with any clutter (clutter free region). Similarly, in

figure 18b the stationary target minimum value falls in doppler bin 119.

The fixed clutter echoes with which the desired target signal must

compete are those included within the same radar resolution cell as the

target, or those which enter the receiver via the antenna sidelobes. To

interpret the above plots in terms of minimum detectable velocity, note

that the minimum value of the target to clutter ratio corresponds to a

stationary target (relative to the earth) located in the same

range-doppler cell as the clutter patch that the main beam is pointed

to. This cell location is set to zero relative velocity between ground

and target. Thus, in order to detect a stationary target a hypothetical

receiver would require a detectability of better than -20dB at a 30 °

grazing angle and better than -12dB at a 50 grazing angle. However as

the target's radial velocity increases, detectability performance

Increases markedly. Each doppler bin number is equivalent to a radial

velocity difference of 34.3 knots (another output of SCAN), which is

constant over all range bins. At a 30 grazing angle, with a target

velocity of +64.6 knots (two doppler bins) the receiver detectability

requirement jumps to a more reasonable value of 25dB. Similarly at a 50

grazing angle, a target velocity of +64.6 knots increases the

requlirement to 32dB.

A composite of all 128 target to clutter ratio range bins produces

the 3-D clutter to target ratios of figures 19 and 20. As clutter is

the dominant factor and the target RCS is nonfluctuating, the 3-D

clutter to target ratio plots are near copies of their respective 3-D

clutter plots.

- 28 -

Figure 19.

3-D Clutter to Target Ratio

5 0 Grazing Angle

Figure 20.

3-D Clutter to Target Ratio300 Grazing Angle

-29-

LIMTTATIONS

The waveform characteristics are not included in the simulation

model. There are two consequences of this limitation. First, the total

energy transmitted in the radar range equation is unknown and as a

result there can be no absolute level set on probability of detection of

any given radar system; only the ratio of target to clutter return

signal. Second, the particular shape of the waveform determines the

resolution size (above that already determined by the physical antenna

parameters) and the ambiguity function. The true radar return signal

will be the convolution of the clutter intensity diagram and the

ambiguity function.

The minimum detectable velocity is computed radial to the antenna

platform, and as such the actual velocity of the target over the ground

may be much larger in specific cases. This is especially true for large

grazing angles where the target is illuminated from overhead. Dividing

by the cosine of the grazing angle will in some sense result in a

minimum ground speed in the radial plane.

The simulation presumes a "snapshot" radar image, and then only at

designated sampled range-doppler cell positions. The intersection of

the beam with the ground for a moving platform is a dynamic process

(even more so for a moving target) which in a real system must be

considered over an interval of time. Additionally, the target RCS is

assumed nonfluctuating and independent of aspect angle.

The simulation program orbit is presumed circular. Many

surveillance space radar applications, however, are in highly elliptical

orbits. A minor program modification will handle elliptical orbits if

the orbit's radial and tangential velocities are known.

To completely describe the far field antenna pattern of a radar

system requires an enormous amount of computer memory space. The

pattern can only be sampled at a finite number of discrete points in T

space. The quality of the program results depends to a large extent on

the fidelity of the far field pattern and the extent to which the

sidelobe structure is detailed.

- 30 -

FUTURE DEVELOPMENT EFFORTS

The program CLUTR is in a continuous state of change and

improvement. Current goals lead to inclusion of the radar waveform and

eventual convolution with the ambiguity function. This will result in a

true target to clutter ratio prediction for a given radar platform and

will allow quantitative analysis of the system. The present program is

only applicable to monostatic radars with no ambiguities, but the

increasing importance and development of bistatic radar systems will

dictate program expansion to bistatics capabilities as well. Ongoing

future developments seek to expand the utility of the simulation with

greater accuracy and a wider range of applications.

CONCLUSION

A major problem in designing a radar system with look-down

capability is determining target detectability in the presence of ground

clutter. The simulation analysis program is useful for the designer of

a range gated pulse doppler to determine the clutter levels with which a

target in a given cell must compete for detection. The results, while

only a model and subject to certain limitations, should be most useful

for comparing various candidate radar systems in the early concept

stages. Considerable engineering savings in time and cost may be

realized by the early elimination of inferior candidate antenna/platform

system designs. The procedure described in this report should lead to

more efficient radar system tradeoff analyses for the design engineer.

-31-

'-

APPENDIX - I

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A1-9

APPENDIX - II

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A2-2

APPENDIX - II

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A3+

APPENDIX - IV

Glossary

Mid

ri

ANT(T1 ,T) Antenna pattern weighting function.y

AX Polar angle from X axis.

AY Polar angle from Y axis.

Ayd1 Polar angle from Y axis with doppler increment Included.

Aymin Minimum Y axis angle which intersects the horizon.

C(I) Elevation angle as a function of range.

Cmax Maximum elevation angle which intersects the Earth.

C(r,r) Clutter intensity scatter function, dependent on range and doppler.

Of Frequency separation of consecutive doppler bins.

Dr Range separation of consecutive range bins.

Fd Two way doppler shift of radar echo.

G(I) Grazing angle as a function of range.

H Height of radar platform above the Earth's surface.

Inc Satellite orbit inclination angle.

Isodop Locus of equal doppler points on the Earth's surface.

Isorange Locus of equal range points on the Earth's surface.

lat Instantaneous satellite subpoint latitude.

R(I) Range as a function of range bin number.

Re Radius of the Earth.

Rm Range of the most distant range bin.

T Directional cosine from X axis.

T Directional cosine from Y axis.

Vdiff Velocity differential between successive doppler bins

Ve Equatorial velocity of the rotating Earth.

V r Radial velocity component of a target.

VMax Maximum relative radial velocity of the Earth's surface.

V P Radar platform air/orbital velocity.

Af Doppler filter bandwidth.

ar Range cell resolution width. A

A4-1

*1 1

* MISSION

Rome Air Development CenterRAVC ptana --id execwte6 'Ie~eaich, devetopuienit, teit andCoemtctio au..~n bAgwn Ic~ uppott o6 Command, Conto

Comwl~ca.Un6 and tC.gence (C31) ativitiea. Techn&,o..and enginevEitng 4u~ppc~.t wl-thZn a'ta oj techicat competenceei,6 p'Lovided to Ur1, Ptog~A" 6m 'e (POa6) and otiwt ESPetement6. The P'tincipat technicat miZaion eAea& ateICOMMwCitiOn, etecAomagnetic gidance and contoe, Au4-veZUance oj gtowid and aeao6pacze objeszt6, ntettigence dataeottection and handting, indo'unation 6tem technoeogg,i0n06pheAic puopagation, .6otid 6tate 6c.Zencea, mn'.cAowavephyaZcA and eectonic. tetiabit, minai&nabitity andcompatibitity.

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