George W. Stimson introduction to Airborne Radar (Se)

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12. If PRF is less than spread of maximum closing rates, radar has

no direct way of telling which repetition of carrier frequency it

is observing.

13. If PRF is 20 kilohertz and observed doppler frequency is 10

kilohertz, true doppler could have any of these values: –10,

10, 30, 50, and 70 kilohertz.

PART IV Pulse Doppler Radar

286

Thus, if the PRF is greater than the spread between the

maximum anticipated positive and negative doppler fre-

quencies, the only spectral line of the target echoes produc-

ing an output from the filter bank will be the central line—

the carrier. The difference between its frequency and the

transmitter’s carrier frequency is the target’s true doppler

frequency. Hence, no significant ambiguities will exist.

This would not be so, however, if the PRF were less than

the spread between the maximum positive and negative

doppler frequencies—as it often must be to satisfy other

operational requirements.

PRF Less Than Spread of Doppler Frequencies. Suppose

that in this same hypothetical situation—difference

between maximum anticipated positive and negative

doppler frequencies equals 98 kilohertz—we reduce the

PRF to only 20 kilohertz (Fig. 12). The separation between

a target echoes’ carrier frequency and first pair of side-

bands, as well as between successive sidebands above and

below them, is now only one-sixth of what is was before.

So that the return from any one target will appear at only

one point within the passband, we must make it somewhat

less than 20 kilohertz wide. But if the sidebands are only 20

kilohertz apart, no matter where we position the passband,

there is no direct way of telling whether the target return

that appears in the bank is the echoes’ carrier or a sideband,

or, which sideband it might be. To determine the target’s

true doppler frequency—hence its range rate—we must

resolve the ambiguity.

Resolving Doppler Ambiguities

To resolve doppler ambiguities, we must have some way

of telling what whole multiple of the PRF, if any, separates

the observed frequency of the target echoes from the carrier

frequency. If not too great, this multiple—n—may readily

be determined. There are two common ways: range differ-

entiation and PRF switching.

Range Differentiation. Generally, the simplest way to

determine the value of n is to make an approximate initial

measurement of the range rate by the differentiation

method. From this rate, we compute the approximate value

of the true doppler frequency. Subtracting the observed fre-

quency from the computed value of the true frequency and

dividing by the PRF yields the factor n.

Suppose, for example, that the PRF is 20 kilohertz and

the observed doppler frequency is 10 kilohertz (Fig. 13).

The true doppler frequency then could be –10 kilohertz

plus any whole multiple of 20 kilohertz up to 70 kilohertz.

The approximate value of the true doppler frequency com-

puted from the initial range rate measurement, let’s say,

Click for high-quality image

turns out to be 50 kilohertz. The difference between this

frequency and the observed doppler frequency is 50 – 10 =

40 kHz. Dividing the difference by the PRF, we get n = 40 ÷

20 = 2 (Fig. 14). The echoes’ carrier is separated from the

observed doppler frequency by two times the PRF.

Although in this simple example we assumed that the

initial range-rate measurement was fairly precise, it need

not be particularly accurate. As long as any error in the

doppler frequency computed from the initial rate measure-

ment is less than half the PRF, we can still tell in which PRF

interval the carrier lies and so tell what n is. The initially

computed “true” doppler frequency, for example, might

have been only 42 kilohertz, almost half way between the

two nearest possible exact values (30 and 50 kilohertz)

(Fig. 15).

Nevertheless, this rough initially computed value (42

kilohertz) would still be accurate enough to enable us to

find the correct value of n. The difference between the ini-

tially computed value of the doppler frequency and the

observed value is 42 – 10 = 32 kHz. Dividing the difference

by the PRF, we get 32 ÷ 20 = 1.6. Rounding off to the near-

est whole number, we still come up with n = 2.

After having determined the value of n just this once, we

can, by tracking the target continuously, determine the true

doppler frequency, hence compute R

⋅

with considerable pre-

cision, solely on the basis of the observed frequency.

PRF Switching. The value of n can also be determined

with a PRF switching technique similar to that used to

resolve range ambiguities (see Chap. 12). In essence, this

technique involves alternately switching the PRF between

two relatively closely spaced values and noting the change,

if any, in the target’s observed frequency.

Naturally, switching the PRF will have no effect on the

target echoes’ carrier frequency f

. It, of course, equals the

carrier frequency of the transmitted pulses plus the target’s

doppler frequency and is completely independent of the

PRF. But not the sideband frequencies above and below f

Because these frequencies are separated from f

by multiples

of the PRF, when we change the PRF, the sideband frequen-

cies correspondingly change (Fig. 16).

Which direction a particular sideband frequency

moves—up or down—depends upon two things: (1)

whether the sideband frequency is above or below f

and

(2) whether the PRF has been increased or decreased. An

upper sideband will move up if the PRF is increased and

down if it is decreased. A lower sideband, on the other

hand, will move down if the PRF is increased and up if it is

decreased.

CHAPTER 21 Measuring Range Rate

287

14. By making initial measurement of R

⋅

with differentiation

method, true doppler frequency, hence value of n, can be

immediately determined.

15. Initial measurement of true doppler frequency need not be par-

ticularly accurate. If error is less than half the PRF, value of n

can still be found.

16. If PRF is changed, each sideband frequency shifts by amount,

n∆, proportional to multiple of f

separating it from carrier.

Click for high-quality image

17. By noting the change in observed frequency when PRF is

switched, multiple (n) of f

contained in true frequency can be

determined.

18. True doppler frequency is computed by adding n times f

observed doppler frequencies. (Here n = 2.)

PART IV Pulse Doppler Radar

288

How much the observed doppler frequency moves also

depends upon two things: (1) how much the PRF has been

changed and (2) what multiple of the PRF separates the

observed frequency from f

. If the PRF is changed by 1 kilo-

hertz, the first set of sidebands on either side of f

will move

1 kilohertz; the second, 2 kilohertz; the third, 3 kilohertz,

and so on. If the PRF is changed by 2 kilohertz, each set of

sidebands will move twice as far, and so on.

By noting the change, if any, in the target’s observed

doppler frequency, we can immediately tell where f

is rela-

tive to the observed frequency (Fig. 17). If the observed fre-

quency does not change, we know that it is f

. If it does

change, we can tell from the direction of the change

whether f

is above or below the observed frequency. And

we can tell from the amount of the change by what multiple

of the PRF f

is removed from the observed frequency.

Thus, the factor n by which the PRF must be multiplied

to obtain the difference between the echoes’ carrier fre-

quency f

and the observed frequency is

n =

∆f

obs

∆f

where

∆f

obs

= change in target’s observed frequency

when PRF is switched

∆f

= amount PRF is changed

If, for example, an increase in PRF (∆f

) of 2 kilohertz

caused a target’s observed doppler frequency to increase by

4 kilohertz, the value of n would be 4 ÷ 2 = 2.

In order to avoid the possibility of “ghosts” when returns

are simultaneously received from more than one target, the

PRF must generally be switched from one to another of

three values, instead of two, just as when resolving range

ambiguities. As explained in Chap. 12, switching the PRF

has the disadvantage of reducing the maximum detection

range.

Calculating the Doppler Frequency. Having determined

the value of n by either of the methods just outlined, we

can compute the target’s true doppler frequency, f

, simply

by multiplying the PRF by n and adding the product to the

observed frequency (Fig. 18)

= n f

+ f

obs

where

= PRF before the switch

obs

= target’s observed doppler frequency

Click for high-quality image

Summary

A target’s range rate may be determined either by contin-

uously measuring its range and calculating the rate at

which the range changes—a process that approximates dif-

ferentiation—or by measuring the target’s doppler frequen-

cy. Because of inevitable random errors in the measured

range, the differentiation method tends to be less accurate

and provides poorer dynamic response.

The doppler method not only can be extremely precise,

but can be nearly instantaneous. The observed doppler fre-

quencies, however, are inherently ambiguous. Unless the

spread between the maximum anticipated positive and neg-

ative doppler frequencies is less than the PRF—and the

consequence of occasionally mistaking a very high-speed

target for a lower speed one is negligible—the ambiguities

must be resolved.

To resolve them, the number of times, n, that the PRF is

contained in the difference between the observed frequency

and the true frequency must be determined. If n is not too

large, it can readily be found either by measuring the range

rate initially with the differentiation method or by switch-

ing the PRF and observing the direction and amount that

the observed doppler frequency changes.

CHAPTER 21 Measuring Range Rate

289

293

Sources and Spectra

of Ground Return

round return falls into three categories: main-

lobe return, sidelobe return, and altitude

return, which is sidelobe return received from

directly beneath the radar. Mainlobe return is

signal for many applications—ground mapping, altimetry,

doppler navigation, etc. But both mainlobe and sidelobe

return are clutter for radars which must detect airborne

targets or moving targets on the ground (Fig. 1).

The principal means of discerning target echoes from

ground clutter is doppler resolution. In ground based

applications, separating targets from clutter is straightfor-

ward. Since the radar is stationary, all of the clutter has

essentially one doppler frequency—zero. In airborne

applications, however, this is far from true. Consequently,

the way in which the clutter is distributed over the band of

possible frequencies—its doppler spectrum—and the rela-

tionship of this spectrum to the doppler frequencies of

anticipated targets critically influence a radar’s design.

In this chapter, we’ll consider what determines the

amplitude of the ground return. We will then examine the

doppler spectrum of each of the three categories of ground

return, and the relationship of the composite spectrum to

the doppler frequencies of target aircraft in representative

situations. Finally, we’ll consider the problem of exception-

ally strong sidelobe return reflected by certain objects on

the ground.

For simplicity, we will assume that the radar is transmit-

ting at a sufficiently high PRF that doppler ambiguities are

avoided. Their effect—which can make ground clutter

much more difficult to deal with—will be covered in the

next chapter.

1. The three categories of ground clutter.

PART V Return from the Ground

294

What Determines the Amplitude of the Ground Return

In general, ground return is governed by the same basic

factors as return from an aircraft. For a given transmitter

frequency, the power of the return received from a small

patch of ground (Fig. 2) is

∝

avg

where

avg

= average transmitted power

G = gain of radar antenna in the direction of

the patch (G

= two-way gain)

= factor called the incremental backscattering

coefficient

= resolvable area of ground (ground patch)

R = range of ground patch

The backscattering coefficient,

, is the radar cross section

of a small increment of ground area, ∆A.

There are three reasons for using an incremental coeffi-

cient. First, the ground viewed by a radar is more or less

continuous. Second, the extent to which a given radar iso-

lates the return from any one portion of the total ground

area depends upon the radar’s design—antenna beamwidth,

etc. (In contrast, the radar cross section of a discrete target,

such as an aircraft, is independent of the radar’s design.)

Third, the backscattering coefficient may vary considerably

from one increment of ground to the next. As a rule,

though, statistical averages of the coefficient are used for

different types of terrain.

When the appropriate values of

is multiplied by the

area of a particular patch of ground—say the area at a spe-

cific azimuth and elevation that is delineated by a radar’s

range, angle, and doppler resolution—the product is the

radar cross section (

) of the patch (Fig. 3).

Like the radar cross section of a discrete target,

is the

product of three factors:

• Geometric area

• Reflectivity

• Directivity

2. Factors which determine the power of the return from a patch

of ground: two-way gain of the radar antenna, range to the

patch, area of the patch, and backscattering coefficient,

3. Radar cross section of a patch of ground equals backscattering

coefficient,

, times resolvable ground area, A

. Depending

on pulse width,

, at steep grazing angles (

), A

may be

determined solely by a radar’s doppler and angular resolution

and

. Generally, at shallow angles A

also is limited by

4. Factors of which the incremental backscattering coefficient,

is a product.

Reflectivity is the ratio of scattered energy to intercepted

energy. It varies widely with the conductivity and dielectric

constant of the ground, as well as with the nature of the

objects on it.

The directivity of an incremental ground area, like the

directivity of a discrete target, is the ratio of (a) the energy

scattered back toward the radar to (b) the energy that would

have been backscattered if the scattering had been isotropic.

This ratio depends in a complex way upon the angle of inci-

dence (

, in Fig. 5), the roughness of the surface relative to

the wavelength of the incident radio waves, the polarization

of the waves, the presence of man-made objects, etc.

Since the purely geometrical relationship between angle

of incidence and

has nothing to do with the nature of the

ground, analysis may sometimes be simplified by math-

ematically cancelling it out. To do so, one merely divides

by cos

. The resulting coefficient, called the normalized

backscattering coefficient, is represented by the Greek letter,

gamma, γ.

γ =

cos

Any variation in the value of γ with the angle of incidence is

due solely to variations in reflectivity and directivity. Over

most angles of incidence, though, γ is more or less constant,

and that is why it is used.

Geometric area is the projection of the incremental area,

∆A, onto a plane perpendicular to the line of sight from the

radar (Fig. 5). This projection determines how much trans-

mitted energy will be intercepted by ∆A. (The power of the

intercepted radiation equals the power density of the inci-

dent waves times the projected area.) The depth (vertical

dimension) of the projected area is foreshortened in pro-

portion to the cosine of the angle of incidence,

. Con-

sequently,

decreases as the angle of incidence increases.

Put another way, as the grazing angle (Fig. 6) approaches

zero, so does the value of

CHAPTER 22 Sources and Spectra of Ground Return

295

5. The term for area included in the backscattering coefficient

, is the projection of the incremental area, ∆A, onto a plane

perpendicular to the line of sight to the radar.

6. As the angle of incidence,

, approaches 90° (the grazing

angle approaches 0

°), the projection of ∆A onto a plane

normal to the line of sight to radar goes to zero.

1. The normalized coefficient

is also represented by the

Greek letter eta (η).

Click for high-quality image

PART V Return from the Ground

296

Backscattering coefficients are normally expressed in dB.

The greater the fraction of the incident energy scattered

back in the direction of the radar is, the greater (less nega-

tive) the coefficient. Where the gain due to directivity is

high—as, for example, at small angles of incidence over

water—the decibel value of

becomes positive.

Table 1 lists the values of both

and γ for common

types of terrain at comparatively shallow grazing angles

(large angles of incidence). When operating over smooth

water, little or no energy is reflected back to the radar from

such angles. Over desert, the return is substantially greater.

Over wooded areas with a liberal sprinkling of man-made

structures, it is greater still. Over cities, it is even greater.

Mainlobe Return

Mainlobe return—or mainlobe clutter (MLC) as it is called

when it is not desired—is produced whenever the mainlobe

intercepts the ground, as when looking down or flying at

low altitudes and not looking up. It may be received from

long ranges, even when flying at high altitudes and looking

straight ahead.

Because the ground area intercepted by the mainlobe can

be extensive and the gain of the mainlobe is high, mainlobe

return is generally quite strong—far stronger than the

return from any aircraft.

Frequency Versus Angle. The spectral characteristics of

mainlobe return are best understood by visualizing the

ground area illuminated by the mainlobe as consisting of a

large number of small, individual patches (Fig. 7). The

doppler frequency of each patch is proportional to the

cosine of the angle, L, between the radar velocity and the

line of sight to the patch.

2 V

cos L

where

= velocity of radar

L = angle between V

and line of sight to

ground patch

λ = wavelength

The angle L is not the same for every patch. As a result, the

collective return occupies a band of frequencies.

When the antenna is looking straight ahead (Fig. 8), the

doppler frequency of the return from patches near the cen-

ter of the illuminated area (L ≈ 0) very nearly equals its

maximum possible value: f

max

= 2 V

/λ.

7. Area illuminated by mainlobe may be thought of consisting of

many small ground patches, each at a different look angle.

8. When looking straight ahead, closing rate for all look angles

within the beam is about the same, and f

≈ 2V

/λ.

TYPICAL BACKSCATTERING COEFFICIENTS

Coefficients (dB)*

Smooth Water – 53 – 45.4

Desert – 20 – 12.4

Wooded Area – 15 – 7.4

Cities – 7 0.6

*Values for a 10° grazing angle and 10 GHz frequency.

Terrain

The frequencies of those patches farther from the center

are somewhat lower. But, since the angles to these patches

are small and the cosine of a small angle is very nearly one,

the band of frequencies covered by the mainlobe return

when looking straight ahead is quite narrow.

As the azimuth and depression angles of the antenna

increase, the cosine of L for patches at the center of the illu-

minated ground area decreases (Fig. 9). Consequently, the

frequency of these patches decreases. At the same time, the

spread between the values of cos L for patches at the two

edges of the area increases, causing the band of frequencies

covered by the mainlobe clutter to become wider.

To give you a quantitative feel for these relationships, the

cosine of the angle L off the center of the illuminated area is

plotted in Fig. 10 for values of L between ± 90°. The verti-

cal scale gives the corresponding doppler frequencies for a

radar velocity of 800 feet per second (approximately 480

knots) and a wavelength of 0.1 foot (3 centimeters).

Superimposed over the graph are two vertical bands.

Each brackets those angles encompassed by a mainlobe

having a beamwidth of 4°. The band in the center is for an

antenna azimuth angle of zero. The other band is for an

antenna azimuth angle of 60°. (In both cases, the antenna

depression angle is zero, and the aircraft is assumed to be at

very low altitude.)

When the azimuth is 0°, the central doppler frequency

of the return is 16 kilohertz. Yet, when the azimuth has

increased to 60°, this frequency is only 8 kilohertz—a

decrease of 50 percent (cos 60° = 0.5).

The width of the band of frequencies spanned by the

return, on the other hand, is vastly greater at the larger

antenna angle. When the azimuth is 0°, the doppler fre-

quency of a patch at the edge of the illuminated ground

area (f

max

cos 2°) is so close to that of a patch at the center

max

) that the difference cannot be read from the graph.

Actually, it is about 10 hertz. Yet (since the cosine changes

much more rapidly with angle at large angles), when the

azimuth is 60°, the return spans a band of frequencies near-

ly 1 kilohertz wide—f

max

(cos 58° – cos 62°) = 16 (0.53

– 0.47) = 0.96 kilohertz.

Influence of Beamwidth, Speed, and Wavelength. For

any one antenna azimuth (and/or depression) angle, the

wider the mainlobe, the wider the band of mainlobe fre-

quencies will be (Fig. 11). If the beamwidth were

increased from 4° to 8°, the width of the band for an

antenna angle of 60° would be 1.9 kilohertz—nearly

twice that for the 4° beam.

Both the center frequency and the width of the band

vary directly with the speed of the radar (f

max

∝ V

). If it

CHAPTER 22 Sources and Spectra of Ground Return

297

9. As angle L increases, value of cos L for patches at center of

beam decreases, and spread between values for patches at

edges of beam increases.

10. Variation in doppler frequency of mainlobe clutter with look

angle. Vertical bands represent width of lobe (λ = 0.1 foot).

11. The wider the mainlobe, the wider the band of mainlobe clutter

frequencies.

PART V Return from the Ground

298

decreases, they decrease; if it increases, they increase.

Suppose the center frequency is, say, 8 kilohertz. If the

speed were doubled, this frequency as well as the frequen-

cies at the edges of the band would double. Not only would

the entire band shift up by 8 kilohertz, but its width would

double (Fig. 12).

The width and center frequency vary inversely with

wavelength (f

max

∝ 1/λ). The longer the wavelength, the

narrower the band will be, and vice versa. Other conditions

being the same, at S-band wavelengths (10 centimeters),

the band is only three-tenths as wide as at X-band wave-

lengths (3 centimeters) (Fig. 13).

13. If the wavelength of the radar transmitter is decreased, both

the center frequency and the spectral width of the mainlobe

clutter will increase proportionately.

12. If the speed of the radar is doubled, both the center frequency

and the width of the spectrum will double.

Effect of Antenna Scan. During search, the antenna scans

back and forth through an azimuth angle which may be

±70 or more degrees. As it sweeps from one extreme to

straight ahead (Fig. 14, top of next page), the mainlobe

clutter band moves up in frequency and simultaneously

squeezes into a narrow line. As the sweep continues to the

other extreme, the clutter moves down in frequency and

spreads to its original width. Thus the band appears to

“breathe.”

Significance. Because of its strength, spectral width, and

variability, mainlobe return can be difficult to contend with

when searching for aircraft. On the other hand, the strength

and spectral width are advantageous when ground map-

ping. Then, the stronger the mainlobe return, the better;