George W. Stimson introduction to Airborne Radar (Se)

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151

Pulse Delay Ranging

1. Range is determined by measuring the time between

transmission of a pulse and reception of the target echo.

y far the most widely used method of range mea-

surement is pulse delay ranging. It is simple and

can be extremely accurate. But since there is no

direct way of telling for sure which transmitted

pulse a received echo belongs to, the measurements are, to

varying degrees, ambiguous.

In this chapter, we will look at pulse delay ranging more

closely—learn how target ranges are actually measured

and consider the nature of the ambiguities. We will see

how ambiguities may be avoided at low PRFs, and

resolved at higher PRFs. We will then consider ambiguities

of a secondary type, called “ghosts,” and see how these

may be eliminated. Finally, we will look briefly at how

range is measured during single-target tracking.

Basic Technique

When a radar’s transmission is pulsed, the range of a

target can be directly determined by measuring the time

between the transmission of each pulse and reception of

the echo from the target (Fig. 1). The round-trip time is

divided by two to obtain the time the pulse took to reach

the target. This time, multiplied by the speed of light, is

the target’s range. Expressed mathematically,

R =

where

R = range

c = speed of light

t = round-trip transit time

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PART III Radar Fundamentals

152

A useful rule of thumb is 12.4 microseconds of round-trip

transit time equals 1 nautical mile of range (Fig. 2). If you

wish to calculate ranges more accurately, the speed of light

in various units of distance is given in Chap. 4.

Just how the range is actually measured varies with the

type of radar.

Simple Analog Radars. In early radars, as well as many

radars of today, range is measured right on the operator’s

display. This method is most graphically illustrated by the

simple A display of World War II. For it, the electron beam

of a cathode ray tube is repeatedly swept across the face of

the tube (Fig. 3). It starts a new sweep each time the radar

transmits a pulse, moves at a constant rate throughout the

interpulse period, and “flies” back to the starting point

again at the end of the period. Each sweep is called a range

sweep; the line traced by the beam is called the range trace.

When a target echo is received, it deflects the beam, caus-

ing a pip to appear on the range trace. The distance from

the start of the trace to the pip corresponds to the time

between transmission and reception, thus indicating the

target’s range.

Sophisticated Analog Radars. In these, range is mea-

sured in an analogous manner by applying the receiver out-

put to a bank of switching circuits, called range gates

(Fig. 4). The gates are opened sequentially at times corre-

sponding to successive resolvable increments of range: first,

Gate No. 1, then Gate No. 2, and so on. A target’s range is

determined by noting which gate, or adjacent pair of gates,

its echoes pass through.

Enough range gates are provided to cover either the

entire interpulse period or the portion of it corresponding

to the range interval of interest.

Digital Radars. When digital signal processing is

employed, range is essentially measured in the same way as

in range-gated analog radars. The amplitude of the receiv-

er’s video output is periodically sampled by a range gate

(Fig. 5). The samples are taken almost instantaneously.

Each is held until the next sample is taken. During this

interval, the amplitude of the sample is converted to a

number. The numbers are temporarily stored in an elec-

tronic memory in positions called range bins. A separate

bin is provided for each range increment within the interval

of interest.

As noted in Chap. 2, to enable doppler filtering after the

received signals have been converted to video, the receiver

must provide both in-phase (I) and quadrature (Q) outputs

(see page 28). Consequently, in digital doppler radars two

2. Rules of thumb for approximating round-trip ranging times.

3. In simple analog radars, range is measured on the operator’s

display. Shown here is an A display of a World War II radar.

4. In sophisticated analog radars, range gates are sequentially

opened (switch closed). Range is determined by noting which

gate a target’s echoes go through.

5. In digital radars, receiver output is periodically sampled by a

range gate. Converted to a number, each sample is stored in

a separate range bin.

APPROXIMATE RANGING TIME

Unit of Distance µs

1 nautical mile 12.4

1 statute mile 10.7

1 kilometer 6.67

1.5 kilometer 10.0

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numbers are stored for each range increment. Together,

they correspond to the return passed by a single range gate

in an analog system.

The choice of the sampling interval is generally a com-

promise. The larger the interval—i.e., the longer the time

between samples—the less complex the system will be

(Fig. 6). Yet, if the interval is greater than the duration

(width) of the transmitted pulses, some of the signal will be

lost when a target’s echoes fall between sampling points.

Moreover, the ability to resolve targets in range will be

degraded.

To realize the full range-resolving potential of the pulses,

as well as to enable more accurate range measurement,

samples may be taken at considerably shorter intervals than

the pulse width (Fig. 7). Range is then determined by inter-

polating between the numbers in adjacent range bins. If, for

example, the numbers in two adjacent bins are equal, the

target is assumed to be halfway between the ranges repre-

sented by the two bin positions. Depending on the sam-

pling rate and the pulse width, the measurement can be

quite precise.

Using a comparatively high sampling rate also minimizes

the loss in signal-to-noise ratio that occurs when a target’s

echoes fall partly in one sampling interval and partly in the

next. This is called range-gate straddling loss.

Range Ambiguities

Pulse delay ranging works without a hitch as long as

the round-trip transit time for the most distant target the

radar may detect is shorter than the interpulse period. But

if the radar detects a target whose transit time exceeds the

interpulse period, the echo of one pulse will be received

after the next pulse has been transmitted, and the target

will appear, falsely, to be at a much shorter range than it

actually is.

Nature of the Ambiguities. To get a more precise feel for

the nature of the ambiguities, let us consider a specific

example. Suppose the length of the interpulse period, T,

corresponds to a range of 50 nautical miles, and echoes are

received from a target at 60 miles (Fig. 8). The transit time

for this target will be 20 percent greater than the interpulse

period (60/50 = 1.2). Consequently, the echo of Pulse No. 1

will not be received until 0.2T microsecond after Pulse

No. 2 is transmitted. The echo of Pulse No. 2 will not be

received until 0.2T microsecond after Pulse No. 3 is trans-

mitted, and so on.

If the difference between the time an echo is received

and the time the immediately preceding pulse was transmit-

ted is used as the measure of range, the target will appear to

CHAPTER 12 Pulse Delay Ranging

153

6. Video signal is generally sampled at intervals on the order of

a pulse width, τ.

7. To enable more accurate measurement and minimize loss of

signal-to-noise ratio, samples may be taken at intervals shorter

than a pulse width; range is then computed by interpolating

between samples.

8. If interpulse period corresponds to 50 nautical miles and tran-

sit time to 60 nautical miles, range will appear to be only 10

nautical miles.

1. If pulse compression is used,

the intervals must be shorter

than the compressed pulse

width.

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PART III Radar Fundamentals

154

be at a range of only 10 miles (0.2 x 50). In fact, there will

be no direct way of telling whether the target’s true range is

10 miles, or 60 miles, or for that matter, 110 or 160 miles

(Fig. 9). In short, the observed range will be ambiguous.

Not only that, but as long as there is a possibility of

detecting targets at ranges greater than 50 nautical miles,

the observed ranges of all targets detected by the radar will

be ambiguous—even though their true ranges may be less

than 50 miles. Put another way, if the range indicated by

any target blip on the radar display can be greater than 50

miles, the range indicated by every target blip is ambiguous.

There is no telling which of the blips represents a target at

the greater range (Fig. 10). Therefore, range is almost

always ambiguous. This point is often overlooked.

The extent of the range ambiguities in the return from a

single target are commonly gauged by the number of inter-

pulse periods spanned by the transit time. That is, by

whether the target’s echoes are received during the first,

second, third, fourth, etc., interpulse period following

transmission of the pulses that produced them. An echo

received during the first interpulse period is called a single-

time-around echo. Echoes received during subsequent peri-

ods are called multiple-time-around echoes, or MTAEs.

Maximum Unambiguous Range. For a given PRF, the

longest range from which single-time-around echoes can be

received—hence the longest range from which any return

may be received without the observed ranges being

ambiguous—is called the maximum unambiguous range

(or simply unambiguous range). It is commonly represent-

ed by R

. Since the round-trip transit time for this range

equals the interpulse period,

where

= maximum unambiguous range

c = speed of light

T = interpulse period

Since the interpulse period is equal to one divided by the

PRF (f

), an alternative expression is

A useful rule of thumb is R

in nautical miles equals 80 divid-

ed by the PRF in kilohertz (Fig. 11). For a PRF of 10 kilo-

hertz, for example, R

would be 80 ÷ 10 = 8 nautical miles.

In metric units, R

equals 150 kilometers divided by the

PRF in kilohertz.

9. There is no direct way of telling whether true range is really

10 nautical miles, or 60 nautical miles, or 110 nautical miles,

or . . . .

10. The true range of any target appearing on this radar display

may

be greater than 50 nautical miles. Ergo, all ranges are

ambiguous.

11. Longest range from which unambiguous return may be

received, R

, corresponds to interpulse period, T.

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Strategy to Follow. What one does about range ambigui-

ties depends both upon their severity and on the penalty

that must be paid for mistaking a distant target for a target

at closer range. The severity, in turn, depends upon the

maximum range at which targets are apt to be detected and

on the PRF. Often, the PRF is determined by considerations

other than range measurement, such as providing adequate

doppler resolution for clutter rejection. The penalty for not

resolving an ambiguity, of course, depends upon the opera-

tional situation.

Obviously, the possibility of ambiguities could be elimi-

nated altogether by making the PRF low enough to place R

beyond the maximum range at which any target is apt to be

detected (Fig. 12). However, since targets of large radar

cross section may be detected at very great ranges, it may

well be impractical to set the PRF this low, even when a

comparatively low PRF is acceptable.

On the other hand, for the expected conditions of use,

the probability of detecting such large targets may be slight,

and the consequences of sometimes mistaking them for tar-

gets at closer range may be of no great importance.

Eliminating Ambiguous Return

If targets at greater ranges than R

are of no concern to

us, we can solve the problem of ambiguities simply by

rejecting all return from beyond R

(Fig. 13). This may

sound like a neat trick, but it can be accomplished quite

easily.

One technique is PRF jittering. It takes advantage of the

dependence of the apparent ranges of targets beyond R

the PRF.

Since the echoes received from these targets are not due

to the transmitted pulses that immediately precede them,

any change in PRF—hence in R

—will change the targets’

apparent ranges (Fig. 14). On the other hand, since the

echoes received from targets within R

are due to the pulses

that immediately precede them, changes in PRF will not

affect these targets’ apparent ranges.

Therefore, by transmitting at one and then the other of

two different PRFs on alternate integration periods, any tar-

gets at ranges greater than R

can be identified and rejected.

The ranges of all targets appearing on the display, then, will

be unambiguous.

Naturally, one pays a price for this improvement. As

explained in Chap. 10, the time-on-target is generally limit-

ed. Since it must be divided between the two PRFs, the

total potential integration time is cut in half (Fig. 15). This

reduces the maximum detection range.

CHAPTER 12 Pulse Delay Ranging

155

12. Ambiguities can be avoided completely only by making R

greater than the range at which

any

target may be detected.

13. If R

is greater than maximum range of interest, problem of

ambiguities can be solved by eliminating all return from

ranges greater than R

14. PRF jittering. If PRF is changed, apparent range of a target

beyond R

will change—identifying range as ambiguous.

15. The penalty for PRF jittering: potential integration time is cut in

half, reducing detection sensitivity.

18. A target appears in bin No. 24—apparent range, 6 nmi.

PART III Radar Fundamentals

156

Resolving Ambiguities

For reasons having nothing to do with ranging, the PRF

may have to be made so high that the maximum range of

interest is longer than R

—often many times so. The radar

must then be able to resolve range ambiguities.

Tagging Pulses. Superficially, it might seem that the easi-

est way to resolve the ambiguities would be to “tag” succes-

sive transmitted pulses (Fig. 16). That is, change (modu-

late) their amplitude, width, or frequency in some cyclical

pattern. By looking for corresponding changes in the target

echoes, one could then tell which transmitted pulse each

echo belongs to and thereby resolve the ambiguities.

But for one reason or another—problems of mechaniza-

tion, in the case of amplitude modulation; eclipsing

and

range gate straddling, in the case of pulse width modula-

tion—only one of these approaches has as yet proved prac-

tical: frequency modulation (see Chap. 8). For air-to-air

applications, even this approach has serious limitations.

PRF Switching. The resolution technique commonly

used is a simple extension of PRF jittering, called PRF

switching. It goes a step beyond jittering by taking account

of how much a target’s apparent range changes when the

PRF is changed. Knowing this and the amount the PRF has

changed, it is possible to determine the number of whole

times, n, that R

is contained in the target’s true range.

Determining n. How this is done is best illustrated by a

hypothetical example. We will assume that for other rea-

sons than ranging, a PRF of 8 kilohertz has been selected.

Consequently, the maximum unambiguous range, R

, is 80

÷ 8 = 10 nmi. However, the radar must detect targets out to

ranges of at least 48 miles—nearly 5 x R

—and undoubted-

ly it will detect some targets at ranges beyond that, as well.

The apparent ranges of all targets will, of course, lie

between 0 and 10 nautical miles (Fig. 17). To span this

10-mile interval, a bank of 40 range bins has been provid-

ed. Each bin position represents a range interval of

/4 mile

(10 miles ÷ 40 bins =

/4 mile per bin).

A target is detected in bin No. 24. The target’s apparent

range is 24 x

/4 = 6 miles (Fig. 18). On the basis of this

information alone, we know only that the target could be at

any one of the following ranges:

6 nmi

10 + 6 = 16 nmi

10 + 10 + 6 = 26 nmi

10 + 10 + 10 + 6 = 36 nmi

10 + 10 + 10 +10 + 6 = 46 nmi

10 + 10 + 10 + 10 + 10 + 6 = 56 nmi

16. By tagging transmitted pulses, we can tell which pulse each

echo belongs to. But except for frequency modulation, tagging

has proved impractical.

17. To span 10 nautical miles ranging interval, a bank of 40

range bins is provided. Each represents a range increment of

/4 nmi.

2. Echoes being received in part

or in whole when the radar is

transmitting and the receiver

is blanked.

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General Relationships. From the foregoing, we can draw

the following conclusions. The number of whole times, n,

that R

is contained in a target’s true range equals the

change in apparent range when the PRF is switched, divid-

ed by the change in R

for the two PRFs.

n =

∆R

apparent

∆R

The true range is n times R

plus the apparent range.

true

= nR

+ R

apparent

Eliminating Ghosts

When PRF switching is used, a secondary sort of ambi-

guity, called ghosting, is sometimes encountered. It may

occur when two targets are detected simultaneously—i.e., at

the same azimuth and elevation angles—and their range

rates are so nearly equal that their echoes cannot be separat-

ed on the basis of doppler frequency (Fig. 22). Under this

condition, when the PRF is switched and one or both tar-

gets move to different range bins, we may not be able to tell

To determine which of these is the true range, we switch

to a second PRF. To keep the explanation simple, we will

assume that this PRF is just enough lower than the first to

make R

/4 mile longer than it was before (Fig. 19).

What happens to the target’s apparent range when the

PRF is switched will depend upon what the target’s true

range is. If the true range is 6 miles, the switch will not affect

the apparent range. The target will remain in bin No. 24.

But if the true range is greater than R

, for every whole

time R

is contained in the target’s true range, the apparent

range will decrease by

/4 mile: the target will move one bin

position to the left in Fig. 20. For the PRFs used here, n

equals the number of bins the target shifts.

Computing the Range. We can find the true range, there-

fore, by (1) counting the number of bin positions the target

moves, (2) multiplying this number by R

, and (3) adding

the result to the apparent range.

Suppose the target moves from bin No. 24 (apparent

range, 6 miles) to bin No. 21, a jump of three bins (Fig. 21).

The target’s true range, then, is (3 x 10) + 6 = 36 miles.

CHAPTER 12 Pulse Delay Ranging

157

19. PRF is changed to increase R

/4 nmi.

20. For every whole time R

is contained in true range, apparent

range will decrease

/4 nmi when the PRF is switched.

21. If target jumps 3 bins, true range is (3 x 10) + 6 = 36 nmi.

22. If more than one target is detected at the same angle and the

targets are not resolvable in doppler frequency, a problem of

ghosts will occur.

3. A practical system would not

be mechanized with PRFs so

closely spaced. The principle,

though, is the same.

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PART III Radar Fundamentals

158

which target has moved to which bin. Each target will

appear to have two possible ranges. One is the true range;

the other, in radar jargon, is a ghost.

Example of Ghosts. Figure 23 shows two targets, A and

B, in the same bank of range bins as used in the preceding

example. When the radar is transmitting at the first PRF, the

targets are two bins apart: A is in bin No. 24 (apparent

range, 6 miles); B is in bin No. 26 (apparent range, 6

miles). When we switch to the second PRF, the targets

appear in bins No. 22 and No. 24. But we have no direct

way of telling whether A and B have both moved to the left

two bins, or, whether A has merely stayed put and B has

moved four bins to the left and is in bin No. 22.

Each target thus has two possible true ranges (Fig. 24). If

both A and B have moved two bin positions, the true

ranges are

Target A: (2 x 10) + 6 = 26 nmi

Target B: (2 x 10) + 6

/2 = 26

/2 nmi

On the other hand, if A stayed put and B moved four bin

positions, the true ranges are

Target A: (0 x 10) + 6 = 6 nmi

Target B: (4 x 10) + 6

/2 = 46

/2 nmi

One of the two pairs of ranges are ghosts.

Identifying Ghosts. The ghosts may be identified by

switching to a third PRF (Fig. 25). To simplify the explana-

tion, we’ll assume that PRF No. 3 is just enough higher

than PRF No. 1 to decrease R

/4 mile—i.e., shorten it

by one range bin (from 40 to 39 bins). Accordingly, when

PRF No. 3 is used, for every whole time R

is contained in

either target’s true range, the target will appear one position

to the right of the bin it occupied when PRF No. 1 was

used. This is the same number of positions it appeared to

the left of that bin when PRF No. 2 was used.

Let’s say for example, that we switch to PRF No. 3 and

the targets appear in bins 26 and 28. Which of the two

pairs of ranges are ghosts?

As you can see from the figure (Fig. 26), bin 26 is two

positions to the right of the bin A originally occupied.

Likewise, bin 28 is two positions to the right of the bin B

originally occupied. Since, when we switched earlier to PRF

No. 2, one target appeared two positions to the left of the

bin A originally occupied and the other target appeared two

positions to the left of the bin B originally occupied, we con-

clude that n = 2 for both targets. Their true ranges are 26

miles and 26

/2 miles. The other pair of ranges are ghosts.

23. When PRF was switched, did A move to bin No. 22 and B to

bin No. 24, or, did A stay put?

24. Each target shown in Fig. 23 has two possible true ranges.

25. To identify the ghosts, a third PRF is added. In this case, it

creases R

by 1/4 nautical mile.

26. When radar is switched to PRF 3, targets jump to bins 26 and

28. The value of n for both targets must be 2.

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It may be instructive to consider where the targets would

have appeared when we switched to PRF No. 3 had the first

pair of ranges been ghosts and the second pair—6 miles

and 46

/2 miles—been the true ranges. In that case

(Fig. 27), since n = 0 for 6 miles, target A would have

stayed put. Since n = 4 for 40 miles, target B would have

moved 4 positions to the right—the same distance (for

these particular PRFs) that it must have moved to the left

when earlier we switched to PRF No. 2.

How Many PRFs?

From what has been said so far, it might appear that no

more than three PRFs would ever be required: one for mea-

suring ranges, another for resolving range ambiguities, a

third for deghosting simultaneously detected targets. This is

not so, however.

Number of PRFs for Resolving Ambiguities. Depending

on how great the detection ranges are and how high and

widely spaced the PRFs are, more than one PRF (besides

the first) may be required to resolve ambiguities. Figure 28

illustrates why.

CHAPTER 12 Pulse Delay Ranging

159

27. If A’s true range had been 6 miles, it would have stayed put

when the radar was switched to PRF 3, and B would have

jumped four positions to the right.

28. Range for which ambiguities can no longer be resolved by switch-

ing between two PRFs. Since 5R

= 6 R

, apparent range does

not change when PRF is switched. R

‘, is maximum unambiguous

range for this combination of PRFs.

29. If true range is increased beyond R

‘, apparent range will

change when PRF is switched, but (in this case) only by

amount corresponding to (n – 6).

The true range in that example includes six whole multi-

ples of the unambiguous range for PRF No. 1 (n = 6). This

is clear. But the difference in the unambiguous ranges for

the two PRFs (∆R

) is such that five times the unambiguous

range for PRF No. 2 exactly equals six times the unambigu-

ous range for PRF No. 1. Consequently, for the target range

assumed here (Fig. 29), when the PRF is switched the

apparent range remains the same, just as though n = 0.

If the true range were long enough to make n = 7 or

more, the apparent range would again change when the

PRF was switched, but the change then would only indicate

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PART III Radar Fundamentals

160

how much n exceeds 6. This particular combination of

PRFs extends the maximum unambiguous range to six

times the unambiguous range for PRF No. 1, but no farther

(Fig. 30).

In fact, a more general expression for the true range than

that given earlier might be

True range = n’R

’ + nR

+ R

apparent

where R

’ is the unambiguous range for the combination of

the two PRFs and n’ is the number of whole times R

’ is

contained in the true range. To find the value of n’ we must

switch to a third PRF.

With the aid of a diagram like Fig. 30, it can be shown

that for every additional PRF the unambiguous range for

the combination increases by the ratio of (a) R

for the

added PRF to (b) the difference between that value of R

and the value for the preceding PRF (Fig. 31). Thus, if the

unambiguous ranges for three PRFs taken individually are

3, 4, and 5 miles, the unambiguous range for the combina-

tion is

/1 x

/1 = 60 miles. How many PRFs are

required for resolving range ambiguities, then, depends

upon the desired maximum unambiguous range and the

values of R

for the individual PRFs.

30. Just as adding a second PRF increases the unambiguous range from R

to R

’, adding a third PRF increases it to R

”. For any one combina-

tion of R

, R

, and R

apparent

, there is only one possible value of the true range. It is uniquely indicated by the values of the three appar-

ent ranges, R

, R

, and R

31. For each additional PRF, the unambiguous range for the com-

bination is increased by the ratio of the unambiguous range,

, for the added PRF to the difference between R

for that PRF

and R

for the preceding PRF.

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