George W. Stimson introduction to Airborne Radar (Se)

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of the look angle, ε (Fig. 3). So the minimum acceptable

PRF is

PRF

min

≅

2 V

sin ε

where

= velocity of the radar

= null-to-null azimuth beamwidth of

real antenna in radians

ε = azimuth look angle

λ = wavelength, units consistent with V

In typical airborne applications, V

is between 800 and

1500 feet per second.

Grating Lobes. Some people find the limitation on min-

imum PRF easier to visualize in terms of antenna theory. In

those terms, what determines the minimum PRF is the dis-

tance, d

, between successive array elements. Now, d

equals the radar's speed times the interpulse period, 1/f

. If

is greater than half a wavelength, as it generally will be

in most SARs, so-called grating lobes will be produced.

These are replicas of the mainlobe, occurring at increasingly

large intervals on either side of the mainlobe

(Fig. 4).

CHAPTER 32 SAR Design Considerations

427

Geometric relationships

determining the spread

between doppler

frequencies of return

from leading and trail-

ing edges of the real

antenna’s mainlobe.

1. If we assume that

2λ/

l, where l is the length

of the real antenna, then

at an azimuth look angle

of 90˚, PRF

min

= 4V

/l.

4. Grating lobes are replications of an array’s mainlobe occurring

at increasingly large intervals on either side of the mainlobe.

Grating lobes are not unique to synthetic arrays. But

they are more of a problem in these arrays then in real

arrays. There are two reasons for this. First, because of the

restrictions on maximum PRF, the array elements generally

cannot be placed as close together in a synthetic array as in

a real array. Second, as we saw earlier, for a reflector at any

one angle off boresight, the difference in the phase shift of

the returns received by successive array elements is twice as

great in a synthetic array as in a real array.

2. They are called grating

lobes because they are the

kind of lobes produced

when monochromatic

light is passed through an

optical diffraction grating

(series of extremely nar-

row, closely spaced slits

in a flat plate).

Click for high-quality image

6. Minimum acceptable PRF places first grating lobe between

first and second sidelobes of real antenna.

PART VII High Resolution Ground Mapping & Imaging

428

How the lobes are produced can be explained as fol-

lows. If a reflector is gradually moved away from the bore-

sight line of the array, a phase difference develops between

the returns received by successive array elements (Fig. 5).

This difference is proportional to twice the spacing of the

elements times the sine of the azimuth angle (

) of the

reflector relative to the boresight line. The familiar pattern

of nulls and sidelobes is thus observed.

However, if the spacing of the array elements is much

greater than half a wavelength, as the azimuth of the reflec-

tor is increased, a point is soon reached where the phase

shift is 180˚. Beyond this point, the amplitudes of succes-

sive lobes start increasing (sin [180 +

] = – sin

). The

increase continues until the element-to-element phase shift

reaches 360˚. At this point, the returns received by all of the

elements add up, once again, exactly as they did when the

reflector was in the center of the mainlobe. This “replica” of

the mainlobe is the first grating lobe.

If the azimuth of the reflector is increased further, the

process repeats and successive grating lobes appear.

In a real antenna, the gains of grating lobes fall off grad-

ually from that of the mainlobe with increasing azimuth

angles; but in a synthetic array, the fall off is much greater.

The reason for

this is that the synthetic array is formed from

returns received through the real antenna. The strength of the

returns received from any one direction, of course, is propor-

tional to this antenna’s two-way gain in that direction. In gen-

eral, that gain decreases rapidly as the azimuth angle increas-

es. If the azimuth angle of the first grating lobe can be made

sufficiently large, the amount of energy received through the

grating lobes can be reduced to negligible proportions.

Generally, the restriction imposed on the PRF by the

requirement that range not be ambiguous is reasonably

loose. So the PRF can usually be set high enough to place

the first grating lobe well outside the mainlobe of the real

antenna. If it can’t be, it is placed in a null between side-

lobes (Fig. 6). But it must not be placed closer to the main-

lobe than the second null.

To maintain the desired spacing between array elements,

as well as to keep the number of pulses that must be

processed in a given array length constant, a common prac-

tice is to adjust the PRF to the speed of the radar.

Minimizing Sidelobes

Performance of a synthetic array radar may be degraded

by both range sidelobes due to pulse compression and the

sidelobes of the synthetic array. The sidelobes affect the

radar maps in two different ways. First, the peaks of the

stronger sidelobes may cause a string of progressively weak-

5. Conditions under which grating lobes are produced. If spac-

ing between array elements (d

) times sine of angle

off bore-

sight is a multiple of half a wavelength, returns received from

angle

by successive elements will be in phase.

3. Since the angle

between

this null and the boresight

line equals

, the PRF that

places the first grating lobe

here is the same as PRF

min

derived on page 427.

er false targets to appear on either side of a strong target

(Fig. 7).

Second, the combined power of all sidelobes—called

the integrated sidelobe return—together with receiver noise,

tends to fog or wash out the detail of the maps.

The effect of the integrated sidelobe return can be visu-

alized by imagining an area of ground the size of a resolu-

tion cell which produces no return—a smooth surfaced

pond, for example—in the middle of a region of uniform

backscattering—say a grassy field. The signal output when

the pond is being mapped is the sum of the simultaneously

received power of the range sidelobes and the azimuth side-

lobes (Fig. 8)—plus the receiver noise. To the extent that

this power is comparable to that received from the sur-

rounding terrain, the "hole" in the map corresponding to

the pond will be filled in. If nothing is done to reduce the

sidelobes, the integrated sidelobe return alone may contain

up to 10 percent as much power as the mainlobe return.

Consequently, the loss of contrast can be considerable.

Like the sidelobes of a real array, the sidelobes of a syn-

thetic array are produced by the elements at the ends of the

array. Consequently, just as the sidelobes of a real antenna

may be reduced through illumination tapering (see Chap.

8), the sidelobes of the synthetic array can be reduced by

weighting the returns received by the individual array ele-

ments (i.e., the returns from successive transmitted pulses)

so as to de-emphasize the returns received by the end ele-

ments relative to the returns received by the central ele-

ments. The cost of this reduction, of course, is a slight loss

of resolution. The weighting can be conveniently accom-

plished when the focusing corrections are applied to the

stored returns. The loss in resolution can be avoided by

increasing the array length (integration time), at the

expense of increased computational load.

Having reduced the range and azimuth sidelobes to

acceptable levels, the remaining loss in contrast due to

noise can be reduced by increasing the gain of the real

antenna or the average transmitted power.

Motion Compensation

In Chap. 31, it was assumed that the aircraft was flying

at constant speed in a perfectly straight line. But this is vir-

tually never the case. Since the whole SAR concept revolves

around the effect of very slight differences in the phases of

signals received over a comparatively long period of time,

typically 1 to 10 seconds, it is essential that any accelera-

tion of the aircraft during that period be compensated. The

acceleration may be measured either by accelerometers

mounted on the antenna or by a separate inertial navigation

CHAPTER 32 SAR Design Considerations

429

7. Close-up of a portion of a radar map showing effect of unsup-

pressed lower-order sidelobes when a strong point target is

mapped.

8. How integrated sidelobe return washes out detail. Cell in cen-

ter represents area from which no return is received.

Click for high-quality image

PART VII High Resolution Ground Mapping & Imaging

430

system, the outputs of which are referenced to the phase

center of the antenna.

On the basis of the measured acceleration, phase correc-

tions are computed. These may be applied to the received

signals at virtually any point in the radar system, from local

oscillator to final integration. Where presumming is

employed, the corrections may, for example, be applied on

a sample-by-sample basis after the presumming.

Limit on Uncompensated Phase Errors

The common sources of phase errors and their effects on

the radar’s performance are listed in the table.

The significance of these errors cannot be overstressed.

It can be shown mathematically that an uncorrected low-

frequency phase error of only 114˚ from the center to the

ends of an array will result in a 10 percent spreading of the

synthetic beam. At X-band wavelengths, 114˚ amounts to

only about 3/8 of an inch. As you might expect from look-

ing at Fig. 9 of the last chapter, though, the predominant

effect of uncompensated phase errors usually is increased

sidelobe levels. As a rule, to keep these within acceptable

bounds, the total random (high-frequency) phase error

must be held to within 2 to 6˚. Yet at X-band, 6˚ of phase is

equivalent to an antenna motion of only 0.01 inch!

Summary

If not duly considered, certain aspects of SAR design

may seriously degrade the radar maps. Among the more

important are choice of PRF, sidelobe reduction, motion

compensation, and uncompensated phase errors.

Two primary factors influence the choice of PRF. The

maximum value is limited by the requirement that no range

ambiguities occur within the span of ranges from which

mainlobe return is received. The minimum value is limited

by the requirement that there be no doppler ambiguities

within the band of frequencies spanning the central spectral

line of the mainlobe return. In terms of antenna theory, this

same minimum PRF places the first grating lobe between

the first and second sidelobes of the real antenna.

A synthetic array’s stronger sidelobes may cause weak,

false targets to appear on either side of strong targets. And

the combined sidelobe return from all targets—integrated

sidelobe return—may wash out detail. The sidelobes may

be reduced through amplitude weighting.

Particularly important is motion compensation

—

measuring

the radar’s acceleration and introducing phase corrections

to compensate for deviations from a straight, constant-speed

course.

COMMON SOURCES

• Unmeasured velocity error

• Unmeasured acceleration along line

of sight during array time

• Non-linear motion of aircraft

• Equipment imperfection

• Processing approximations

• Atmospheric disturbances

EFFECTS

• Increased sidelobe levels

• Degraded resolution

• Reduced antenna peak gain

• Beam wander

PHASE ERRORS

431

SAR Operating Modes

perationally, SAR has several striking advan-

tages. First, with a small physical antenna oper-

ating at wavelengths suitable for long-range

mapping, SAR can provide azimuth resolutions

as fine as a foot or so. Second, by increasing the length of

the array in proportion to the range of the area to be map-

ped, the resolution can be made independent of range.

Third, since the array is formed in the signal processor, the

basic SAR technique can conveniently be adapted to a wide

variety of operational requirements.

Added to these advantages are those of all radar map-

ping. Maps can be made equally well day or night, through

smoke, haze, fog, or clouds. The maps are plan views and

can be made even at shallow grazing angles (Fig. 1, below).

While simple strip-mapping described in Chap. 31 is

quite useful, it has been improved upon and adapted to

special requirements in a variety of modes. Some of the

more important of these are squinted array, multilook map-

ping, spotlighting, doppler beam sharpening, moving-target

display, and inverse SAR (ISAR) imaging. Each is briefly

described in the following paragraphs.

1. Comparison of real-time SAR map with an aerial photo of the same region. Map was made from range many times as great as that from

which photo was taken. Radar not only sees through haze, but provides a plan view.

Click for high-quality image

PART VII High Resolution Ground Mapping & Imaging

432

Squinted Array

In real-time SAR mapping, if the radar’s azimuth look

angle is 90º, the leading edge of the map may lag behind

the radar by as much as two full array lengths. This limita-

tion can readily be eliminated. By training the beam of the

real antenna forward and making an appropriate focusing

correction and coordinate rotation, the synthetic array can

be squinted ahead by any desired amount within a fairly

wide zone to the side of the aircraft (Fig. 2). It can similarly

be squinted behind. The radar can thus be made to map

not only territory which it has long since passed, but terri-

tory which lies far ahead.

A price, of course, must be paid for this versatility. For,

as viewed from the patch being mapped, the effective

length, L

eff

, of the synthesized array is foreshortened in pro-

portion to the cosine of the squint angle, A (Fig. 3). The

azimuth (cross-range) resolution distance, d

, is corre-

spondingly reduced.

λR

2L cos A

But this reduction is generally a small price to pay for the

increased utility of the maps obtained.

Multilook Mapping

Sometimes the beam of the real antenna may be wide

enough to enable the same area to be mapped several times

without changing the antenna’s look angle. This is called

multilook mapping. When the maps are superimposed (i.e.,

when successive returns from each resolution cell are aver-

aged), the effects of scintillation are reduced.

Most of the maps used as illustrations in these chapters

were made with more than one look (Fig. 4).

Squint Angle

eff

= L cos A

To ground patch

being mapped

Synthesized

Array

Antenna

Broadside direction

2. If beam of real antenna is squinted forward and appropriate

focusing correction and coordinate rotation are made, region

ahead can be mapped.

3. Foreshortening of synthesized arrary that occurs when radar

beam is squinted forward (or backward) by an angle A for

SAR mapping.

4. All of SEASAT’s maps were made with four looks. In this one,

surface waves around Nantucket Island reflect the contours of

the ocean floor. (Courtesy Jet Propulsion Laboratory)

Click for high-quality image

Spotlight Mode

By gradually changing the look angle of the real antenna

as the radar advances and making appropriate phase correc-

tions, the radar can repeatedly map a given region of inter-

est. This mode, called spotlight, not only enables the opera-

tor to maintain surveillance over an area for an appreciable

period of time but can produce maps of superior quality.

Quality may be improved in three basic ways. First, since

the beam is continuously trained on the area being

mapped, the length of the synthetic array is not limited by

the beamwidth of the real antenna.

Second, the size of the real antenna can be increased

without reducing the array length. By using a larger anten-

na, the mainlobe gain can be increased and the signal-to-

noise ratio correspondingly improved (Fig. 5).

The third way in which spotlighting improves the quality

of a map is by filling in gaps in the backscatter from points

on the ground. In Chap. 30, you may recall, it was pointed

out that when a radar illuminates an object on the ground

—such as a parked airplane—from a given angle, mappable

returns may be received from only a few main scattering

centers. The reason (explained on page 394) is that in terms

of fractions of wavelengths, hence radio frequency phase,

the distances from the radar to the various scatterers com-

prising the airplane may differ in such a way that much of

the scatter does not combine constructively in the radar’s

direction. The net result is that the airplane’s shape is not

necessarily as easily recognized as one would expect from

the ratio of the aircraft’s principal dimensions to the size of

th radar’s resolution cells.

In the case of distributed targets, such as fields, grass-

lands, paved areas, etc., this same effect makes the

backscatter spotty. The result in this case is a general graini-

ness of the images.

Since the wavelength is usually comparatively short, the

relative distances to the individual scatters (in fractions of

wavelengths) can change markedly when the same area is

viewed from slightly different angles. Consequently, the

graininess may be considerably reduced by repeatedly

mapping the same region from points progressively farther

along on the flight path and averaging successive returns

from each resolution cell.

The quality of the maps may be further enhanced by

periodically switching from one to another of several differ-

ent radio frequencies. These should be separated by at least

the bandwidth of the transmitted pulses, and the switching

should be done at points that are one or more array lengths

apart. By similarly changing the polarization of the antenna,

the quality may be improved even further.

CHAPTER 33 SAR Operating Modes

433

5. In spotlight mode, the beam of the real antenna is held on a

given region of interest so that it can be mapped repeatedly

from different angles and the array length can be increased,

without decreasing the size, hence the gain, of the real

antenna.

Click for high-quality image

PART VII High Resolution Ground Mapping & Imaging

434

Doppler Beam Sharpening (DBS)

This mode differs from other SAR modes in that the

length of the array is not increased in proportion to the

range of the area to be mapped but is the same for all

ranges. The maps, therefore, are the same as those pro-

duced by a real array having an extremely narrow beam—

hence the name doppler beam sharpening.

Typically, the antenna continuously scans the region of

interest on one side of the flight path or the other, or both.

Because the integration time is limited to the length of time

a ground patch is in the antenna beam—or, if you prefer,

the length of the array that can be synthesized is so limit-

ed—the resolution is coarser than can be achieved with a

nonscanning antenna. Moreover, since the integration time

is the same for the returns from all ranges, the azimuth res-

olution distance increases with range, rather than being

independent of it.

Nevertheless, except for the region directly ahead

(Fig. 6), where there is little or no spread in the doppler fre-

quencies within the mainlobe, the resolution is much finer

than could be achieved by the real antenna. Also, in con-

trast to the higher resolution modes, DBS can provide a

continuously updated map of a large expanse of ground.

Implementation is similar to that of the other SAR modes.

In one advanced design, the gap in the region ahead is filled

in by scanning it in a phase-comparison-monopulse detec-

tion mode providing substantially finer resolution than con-

ventional real-beam mapping (see APN-241, Part X).

Moving Target Display

Frequently, it is desired to show ground-moving targets on

the SAR map. Most of these are essentially point-source

reflectors: cars, trucks, etc. Because of their motion while the

radar is collecting the returns from which to synthesize the

array, they tend to wash out in the map. To detect them, a

ground-moving-target-indication (GMTI) mode is generally

interleaved with SAR mapping. Markers indicating the tar-

gets’ positions (Fig. 7)—and in some cases their range rates

as well—are then superimposed on the SAR map. In one

intriguing design, GMTI and SAR mapping are performed

simultaneously with the same antenna (see APG-76, Part X).

Bigger, larger-RCS targets, such as trains, are clearly visi-

ble on most SAR maps. If a train is moving and has a com-

ponent of velocity toward or away from the radar, however,

the resulting doppler shift will normally be interpreted by

the radar as indicative of a displacement in the cross-range

direction. As a result, the train will be displayed as though

it is traveling off its tracks. In more advanced SAR systems,

the error is sensed and the train is put back on its tracks.

6. With doppler beam sharpening, the antenna scans a wide

region—in this case on both sides of the flight path. Except

for the region directly ahead, resolution is comparable to

that achieved by a real antenna having an exceptionally

narrow beam.

7. Markers indicate locations of moving targets.

Click for high-quality image

Inverse SAR (ISAR) Imaging

The classic SAR is ill-suited for imaging targets such as

ships and aircraft which have rotational motion. For unless

the differential doppler shifts which such motions produce

are accurately predicted and compensated, they tend to

defocus the array and blur the image.

With slightly different algorithms, however, these shifts,

rather than those due to the radar’s forward motion can be

used to provide the angular resolution needed for imaging

a target (Fig 8). The technique then is called inverse SAR,

or ISAR.

ISAR is most easily explained by starting with the SAR

spotlight mode. As we have seen, in it the radar spotlights

the ground patch that is to be mapped and records the

returns received over a period of time. Returns simultane-

ously received from points at different azimuth angles are

then separated on the basis of differences in their doppler

(phase) histories due to the corresponding differences in

the points’ range rates.

With ISAR, the principle is the same. But the differences

in range rate are those due to rotation of the spotlighted

target about its yaw, pitch, and roll axes, as seen by the

radar. This difference is illustrated in Fig. 9.

CHAPTER 33 SAR Operating Modes

435

Since the target shown in Fig. 9 is turning away from the

radar (rotating clockwise) the range rate of point P

on the

tail is slightly lower than the range rate of point P

on the

nose. Consequently, the doppler frequency of the returns

from P

and all points on the target between it and P

differ

in proportion to their distances from P

9. With conventional SAR, the differences in doppler frequency

which enable fine angular resolution to be obtained are due

to the forward motion of the radar-bearing aircraft. With

ISAR, the differences are due to the angular rotation of the tar-

get as seen by the radar

8. An ISAR image of a fighter aircraft.

Click for high-quality image

PART VII High Resolution Ground Mapping & Imaging

436

To make an image of the target, phase corrections must

first be made to compensate for the displacement of the tar-

get relative to the radar while it collects the returns from

which the image will be produced. This is called motion

compensation. The returns from each resolvable range

increment are then applied to a separate bank of doppler

filters, and an image is produced from their outputs just as

in conventional SAR mapping.

As shown in the panel (left), the image’s cross-range reso-

lution, d

, is proportional to the ratio of the doppler filters’

3-dB bandwidth, BW

3dB

, to the target’s rate of rotation,

⋅

3db

⋅

The cross-range dimension, though, is not necessarily

horizontal, as with conventional SAR, but perpendicular to

the axis about which the target happens to be rotating. No

image is formed, of course, if that axis is colinear with the

radar’s line of sight, or if the target has no rotational motion

as viewed from the radar.

Besdies imaging targets having rotational motion, ISAR

has another important advantage over conventional SAR.

This advantage is illustrated in Fig. 10 (below).

With SAR, the cross-range resolution distance, d

, is

inversely proportional to the angle,

, through which the

radar flies during the doppler filters’ integration time, t

int

With ISAR, the cross-range resolution distance d

inversely proportional to the angle,

, through which the

target rotates during t

int

. The radar need not fly through any

angle to obtain an image of a target. In fact, the ISAR image

of a fighter aircraft shown in Fig. 8 on the preceeding page

was made by a stationary radar on the ground.

Assuming that

θ = Target’s rate of rotation.

= Desired cross-range

resolution

As is clear from the diagram,

∆R = incremental increase in

range rate of points on the

target separated by the

distance, d

, normal to the

line of sight from the radar

∆R= d

The resulting difference in the doppler

frequencies of the radar returns from

successive points on the target is

∆f

= =

The minimum difference in doppler frequency

the radar can resolve equals the 3-dB

bandwidth of its doppler filters. Accordingly,

= BW

3dB

making the cross-range resolution distance,

CROSS-RANGE RESOLUTION

OF ISAR IMAGES

2 ∆R

Line of sight

from radar

Target

∆R

2 d

3dB

2 d

eff

≈ θ R

Ground patch

mapped

eff

= R

2 L

eff

∴ d

≈ R ≈

θ R

2 θ

SAR

ISAR

Line of sight from radar

θ is the angle the target has

rotated through in the integra-

tion time, t

int

of the radar's

doppler filters.

Target

“Imaged”

= λ

3dB

int

3dB

≈

∴ d

≈ ≈

2 θ t

int

2 θ

θθ

θ is the angle the radar has flown

through in the integration time, t

int

of the radar’s doppler filters.

10. With conventional SAR, the cross-range resolution distance, d

, is inversely proportional to the angle,

, the radar flies through during the

doppler filters’ integration time, t

int

. With ISAR, the cross-range resolution distance, d

, is proportional to the angle,

, the target rotates

through in t

int