George W. Stimson introduction to Airborne Radar (Se)

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Number of PRFs for Deghosting. More PRFs may also be

required for deghosting. To deghost all possible combina-

tions of the observed ranges of more than two simultane-

ously detected targets, an additional PRF must be provided

for each additional target. Thus, if a single PRF suffices to

resolve range ambiguities, a radar employing N PRFs can

uniquely measure the ranges of (N – 1) simultaneously

detected targets.

The Trade-off. As with PRF jittering, one pays a price for

PRF switching. Each additional PRF not only reduces the

integration time—hence reduces detection range—but

increases the complexity of mechanization. The number of

PRFs actually used, therefore, is a compromise between

these costs and the cost of occasionally having to contend

with ambiguous ranges and unresolved ghosts (Fig. 32).

The optimum number of PRFs naturally varies with the

application. For most of the fighter applications in which

the required PRFs are low enough to make PRF switching

practical, one additional PRF generally suffices for resolving

ambiguities and another for deghosting—making a total of

three.

Single-Target Tracking

During single-target tracking, range measurement is sim-

plified in two respects.

First, only two adjacent range gates must be provided

(Fig. 33). The time delay between the transmission of a

pulse and the opening of these gates is automatically

adjusted to equalize the output of the two gates, thereby

centering them on the target. By measuring this delay, the

target’s apparent range may be precisely determined.

Second, once the ambiguities in the target’s range have

been resolved, no further resolution is necessary. Accurate

track can be kept of the true range simply by keeping con-

tinuous track of the changes in apparent range.

Summary

With pulse delay ranging, range is determined by mea-

suring the time between transmission of a pulse and recep-

tion of an echo. In rudimentary radars, the measurement is

made on the range trace of the display. In sophisticated ana-

log radars it is made by opening a succession of range gates.

Digital radars accomplish the equivalent by periodically

sampling the receiver output, converting the samples to

numbers, and storing them in a bank of range bins.

The range for which the round-trip transit time equals

the interpulse period is called the maximum unambiguous

range, R

. A target at greater range will appear to have a

CHAPTER 12 Pulse Delay Ranging

161

32. The number of PRFs actually used is always a compromise.

33. For single-target tracking, only two range gates are needed.

By positioning them to equalize their outputs, they are cen-

tered on a target.

PART III Radar Fundamentals

162

range equal to its true range minus some multiple of R

. As

long as there is a possibility of detecting any targets at

ranges greater than R

, all observed ranges are ambiguous.

What one does about range ambiguities depends upon

their severity and the penalty for ambiguous measurements.

If the PRF can be set low enough to make R

greater than

the maximum range of interest, ambiguities can be avoided

by discarding the return from those targets beyond R

These can be identified by jittering the PRF and looking for

a corresponding jitter in the apparent target ranges.

If higher PRFs are required, ambiguities must be

resolved. This can be done by switching between two or

more PRFs and measuring the changes, if any, in the appar-

ent ranges.

If two or more targets are detected simultaneously, each

target may appear to have two possible ranges, one of

which is a ghost. Ghosts can be eliminated by switching to

additional PRFs.

Besides increasing complexity, using more than one PRF

decreases detection range. The optimum number of PRFs is

a compromise between these costs and the cost of occasion-

ally having to contend with unresolved ambiguities and

ghosts.

Some Relationships To Keep In Mind

• Ranging time:

12.4

µs = 1 nmi of range

• Maximum unambiguous range:

(nmi) =

• When PRF switching is used to resolve

range ambiguities:

true

= nR

+ R

apparent

n =

PRF (kHz)

∆R

apparent

∆R

163

Pulse Compression

1. With chirp, transmitter frequency is increased linearly through-

out pulse. Echo is passed through filter that introduces time lag

inversely proportional to frequency.

deally, if we wanted both long detection range and

fine range resolution, we would transmit extremely

narrow pulses of exceptionally high peak power. But

there are practical limits on the level of peak power

one can use. To obtain long detection ranges at PRFs low

enough for pulse delay ranging, fairly wide pulses must be

transmitted.

One solution to this dilemma is pulse compression. That

is, transmit internally modulated pulses of sufficient width

to provide the necessary average power at a reasonable

level of peak power; then, “compress” the received echoes

by decoding their modulation.

This chapter explains the two most common methods of

coding—linear frequency modulation and binary phase

modulation. It also briefly describes a third method,

polyphase modulation.

Linear Frequency Modulation (Chirp)

Because of its parallel to the chirping of a bird, this

method of coding was called “chirp” by its inventors. Since

it was the first pulse compression technique, some people

still use the terms chirp and pulse compression synony-

mously.

Basic Concept. With chirp, the radio frequency of each

transmitted pulse is increased at a constant rate throughout

its length (Fig. 1). Every echo, naturally, has the same lin-

ear increase in frequency.

The received echoes are passed through a filter. It intro-

duces a time lag that decreases linearly with frequency at

exactly the same rate as the frequency of the echoes

increases. Being of progressively higher frequency, the trail-

ing portions of an echo take less time to pass through than

1. All methods of pulse com-

pression are essentially

matched filtering schemes in

which the transmitted pulses

are coded and the received

pulses are passed through a

filter whose time-frequency

characteristic is the conjugate

(opposite) of the coding.

PART III Radar Fundamentals

164

the leading portion. Successive portions thus tend to bunch

up. Consequently, when the pulse emerges from the filter

its amplitude is much greater and its width much less than

when it entered (Fig. 2). The pulse has been compressed.

Filtering may be done with an analog device—such as an

acoustical delay line—or digitally. Depending on the mech-

anization, the frequency can either be increasing, as

described here, or decreasing, in which case the delay

increases with frequency.

Incremental-Frequency Explanation. What actually hap-

pens when an echo passes through the filter can be visual-

ized most easily if we think of the echo as consisting of a

number of segments of equal length and progressively high-

er frequency (Fig. 3). In fact, in one form of pulse coding—

incremental frequency modulation—the transmitted wave

is modulated in exactly this way. The first segment, having

the lowest frequency, takes longest to get through the filter.

The second segment takes less time than the first; the third

less time than the second, etc.

The increments of frequency are such that the difference

in transit time for successive segments just equals their

width. If the segments are 0.1 microsecond wide, the first

segment takes 0.1 microsecond longer to go through than

the second; it, in turn, takes 0.1 microsecond longer to go

through than the third, etc. As a result, in passing through

the filter, the second segment catches up with the first; the

third segment catches up with the second, the fourth catch-

es up with the third, and so on. All segments thus combine

and emerge from the filter at one time. The output pulse is

only a fraction of the width of the received echo; yet, has

many times its peak power.

How Range Resolution Is Improved. Figure 4 shows

what happens when the echoes from two closely spaced

targets pass through the filter. Since the range separation is

small compared to the pulse length, the incoming echoes

are merged indistinguishably. In the filter output, however,

they appear separately—staggered by the target’s range sep-

aration.

It seems like magic, until you consider the coding.

Because of it, each segment of the echo from the near target

emerges from the filter at the same time as the first segment

of this echo. And each segment of the echo from the far tar-

get emerges at the same time as the first segment of that

echo. The difference between these times, of course, is the

length of time the leading edge of the transmitted pulse

took to travel from the first target to the second and back.

The range resolution is thus improved by the ratio of the

width of the individual segments to the total width of the

pulse.

2. Since trailing portions of echo take less time to pass through

filter, successive portions tend to bunch up: Amplitude of

pulse is increased and width is decreased.

3. Linear frequency modulated pulse can be thought of as being

made up of segments of progressively higher frequency. In

going through filter, second segment catches up with first;

third, with second; etc.

4. Echoes from closely spaced targets, A and B, are merged but,

because of coding, separate in output of filter.

Click for high-quality image

Range Sidelobes. If we look at an output pulse closely

(Fig. 5), we will see that it is preceded and followed by a

series of lesser pulses. These are called range sidelobes. They

are half the width of the compressed pulse, have the same

shape as antenna sidelobes, and are equally undesirable.

As with the compression process, the source of the range

sidelobes can be visualized most easily in terms of incre-

mental frequency modulation.

In Chap. 16, it will be demonstrated that the energy of a

single short pulse, such as an individual segment of an

incremental-frequency-modulated pulse, is not concentrat-

ed at a single frequency—as might be expected from the

uniform spacing of the wavefronts. Rather, it is spread over

a broad band, extending equally above and below that fre-

quency. The envelope of this spectrum (plot of amplitude

versus frequency) has a sin x/x shape.

As each segment of the uncompressed pulse passes

through the compression filter, the energy of the higher

frequency spectral sidelobes travels faster than the energy

of the main spectral lobe, and the energy of the lower fre-

quency spectral sidelobes travels slower. Consequently,

when the segments emerge in unison from the filter, their

combined amplitude—plotted against time—has the same

sin x/x shape as the spectra of the individual segments

(Fig. 6).

Like antenna sidelobes, range sidelobes can be reduced

to acceptable amplitudes. The reduction is accomplished by

designing the filter to do the equivalent of illumination

tapering in an antenna—i.e., taper the amplitude of the

uncompressed pulse at its leading and trailing ends. The

compressed pulse widens a bit, just as the antenna beam

does; but, again, this is a small price to pay for the reduc-

tion achieved in the sidelobes.

Stretch-Radar Decoding. For a narrow range swath, lin-

ear frequency modulation may be conveniently decoded by

a technique called stretch radar.

With this technique (described in detail in the panel on

the next page), pulse delay time (range) is converted to fre-

quency. As a result, the return from any one range has a

constant frequency, and the returns from different ranges

may be separated with a bank of narrowband filters, imple-

mented with the highly efficient fast Fourier transform (see

Chap. 20).

Incidentally, stretch radar is similar to the FM ranging

technique used by CW radars. The principal differences are

that instead of transmitting pulses the CW radar transmits

continuously, and the period over which the transmitter’s

frequency changes in any one direction is many times the

CHAPTER 13 Pulse Compression

165

5. Plot of filter output versus time has same shape as antenna

radiation pattern. Sidelobes can be reduced through weighting.

6. Energy of a single short pulse, such as a segment of an incre-

mental-frequency-modulated pulse, is spread over a band of

frequencies. Envelope has sin x /x shape.

PART III Radar Fundamentals

166

STRETCH RADAR DECODING OF CHIRP

For a narrow range swath, such as is mapped by a synthetic

array radar, linear ffrequency modulations is commonly decoded by

a technique called

stretch radar

As the return from the swath is received, its frequency is

subtracted from a reference frequency that increases at the same

rate as the transmitter frequency. The reference frequency,

however, increases continuously throughout the entire period in

which the return is received.

Consequently, the difference between the reference frequency

and the frequency of the return from any one point on the ground

is constant. Moreover, as can be seen from the above figure, if

we subtract the reference frequency’s initial offset, f

, from the

difference thus obtained, the result is proportional to the range

of the point from the near edge of the swath. Range is thus

converted to frequency.

To see how fine resolution is thereby achieved, consider the

returns from four closely spaced points after the subtraction has

been performed.

Although the returns were received almost simultaneously, the

slight stagger in their arrival times has resulted in clearly

discernible differences in frequency.

As indicated in the figure below, the continuously changing

reference frequency may be subtracted at one of three points in

the receiving system. One is the mixer, which converts the radar

returns to the receiver’s intermediate frequency (IF). A second

point is the synchronous detector, which converts the output of

the IF amplifier to video frequencies. A third point is in the signal

processor, after the video has been digitized.

To sort the difference frequencies, the video output of the

synchronous detector is applied to a bank of narrowband filters,

implemented with the highly efficient fast Fourier transform.

Click for high-quality image

For the pulses to be resolved, the frequency difference,

∆f, must at least equal one divided by the uncompressed

pulsewidth, τ.

∆f =

If ∆f is the minimum resolvable frequency difference, the

compressed pulsewidth, τ

comp

, is the period of time in

which the frequency of the uncompressed pulse changes by

∆f (Fig. 9). If the frequency of the uncompressed pulse

changes at a rate of ∆f / τ

comp

hertz per second, then the

round-trip ranging time. Range is determined by measuring

the instantaneous difference between the frequencies of the

transmitted and received signals.

Pulse Compression Ratio. The extent to which the

received pulses are compressed—i.e., the ratio of the

uncompressed width, τ, to the compressed width, τ

comp

—is

called the pulse compression ratio. With incremental fre-

quency modulation this is the ratio of τ to the width of the

modulation increments (Fig. 7). But what is it when the

modulation is strictly linear? And what determines how

much the transmitter frequency must be increased over the

length of the transmitted pulse?

To answer these questions, it is necessary to consider an

important characteristic of the pulse compression filter

which until now we have ignored: frequency sensitivity. If

returns received simultaneously from two slightly different

ranges are to be separated on the basis of the difference in

their frequencies, besides providing a delay proportional to

frequency, a second requirement must also be satisfied. The

frequency difference must be large enough for the signals to

be resolved by the filter.

As will be made clear in Chap. 18, the frequency resolu-

tion of a filter increases with the duration of the signals

passing through it—in this case, the width of the uncom-

pressed pulses (Fig. 8).

CHAPTER 13 Pulse Compression

167

8. For a filter to resolve two simultaneously received returns, the

instantaneous difference in their frequencies (∆f) must at least equal

1 divided by their duration (τ).

9. If the minimum resolvable frequency difference is ∆f, the time

in which the frequency of the uncompressed pulse changes by

∆f will be the width of the compressed

pulse τ

comp

7. Relationship between uncompressed pulse width, chirp modu-

lation, and compressed pulse width.

Click for high-quality image

PART III Radar Fundamentals

168

total change in frequency, ∆F, over the duration of the

uncompressed pulse will be this rate times the uncom-

pressed pulsewidth, τ.

As is apparent from the geometry of Fig. 10, the pulse

compression ratio, τ / τ

comp

, equals the ratio of ∆F to ∆f.

Pulse compression ratio =

∆F

comp

∆f

Substituting 1/ τ for ∆f, we find that the pulse compres-

sion ratio equals the uncompressed pulsewidth times ∆F.

Pulse compression ratio = τ∆F

The quantity τ∆F is called the time-bandwidth product.

This simple relationship—pulse compression ratio

equals time-bandwidth product—tells us a lot. To begin

with, for a given uncompressed pulse width, τ, the com-

pression ratio increases directly as ∆F. Conversely, for a

given value of ∆F, the ratio increases directly as the uncom-

pressed width, τ.

If we set the time-bandwidth product equal to τ / τ

comp

τ cancels out,

τ∆F =

comp

and we find that

comp

∆F

The width of the compressed pulse is determined entirely

by the change in transmitter frequency over the duration of

the transmitted pulse—the greater the frequency change,

the narrower the compressed pulse.

Finally, when solved for ∆F, this last equation tells us

that the total change in transmitter frequency must be

∆F =

comp

To get a feel for the relative values involved, let us con-

sider a representative example of chirp. Assume that to pro-

vide adequate average power, the width of a radar’s trans-

mitted pulses must be 10 microseconds. To provide the

desired range resolution (5 feet) a compressed pulsewidth

of 0.01 microsecond is required. The pulse compression

ratio, therefore, must be

= 1000

comp

0.01

10. Ratio of uncompressed to compressed pulse widths equals

ratio of total change in frequency of compressed pulse (∆F) to

minimum resolvable frequency difference (∆f).

To achieve a compressed pulsewidth of 0.01 microsec-

ond (10

–8

s), the change in transmitter frequency (∆F) over

the

duration of each transmitted pulse must be 1/10

–8

= 10

hertz.

Since the duration of the uncompressed pulse is 10

microseconds (10

–5

s), the rate of change of the transmitter

frequency will be 10

/10

–

= 10

, or 10,000 gigahertz

(GHz)!

This, incidentally, explains why stretch decoding is

practical only for relatively narrow range intervals. The

ranging time for an interval of 50 nautical miles, for

instance, is 12.4 x 50 = 620 µs. If the receiver local-oscil-

lator frequency were shifted at a rate of 10,000 gigahertz

per second throughout that time (Fig. 11), the total shift

would be 10,000 x 620 x 10

-6

= 6.2 GHz! Even at Ku-

band frequencies (15 gigahertz), such a large shift is far

from practical.

Relative Merits of Chirp. Linear frequency modulation

has the advantage of enabling very large compression ratios

to be achieved. In addition, it is comparatively simple. No

matter when a pulse is received or what its exact frequency

is, it will pass through the filter equally well and with the

same amount of compression.

The principal disadvantage is a slight ambiguity between

range and doppler frequency. If the frequency of a pulse has

been, say, increased by a positive doppler shift, the pulse

will emerge from the chirp filter a little sooner than if there

were no such shift. The radar will have no way of telling

whether this difference is due to a doppler shift or to the

echo being reflected from a slightly greater range. However,

since the doppler shifts typically encountered are very

much less than the increment,

∆F, over which the frequency

of the individual transmitted pulses is swept, ambiguity is

generally not a problem.

Binary Phase Modulation

As the name implies, in this type of coding, the radio fre-

quency phase of the transmitted pulses is modulated, and

the modulation is done—as in incremental frequency mod-

ulation—in finite increments. Here, though, only two incre-

ments are used: 0˚ and 180˚.

Basic Concept. Each transmitted pulse is, in effect,

marked off into narrow segments of equal length. The radio

frequency phase of certain segments is shifted by 180˚,

according to a predetermined binary code. This is illustrat-

ed for a 3-segment code in Fig. 12. (So you can readily dis-

cern the phases, the wavelength has been arbitrarily

CHAPTER 13 Pulse Compression

169

11. If stretch processing were used over a 50 mile range interval

to decode a 10 microsecond pulse modulated for 1000 :1

compression ratio, receiver local oscillator would have to be

swept over an impractical 6.2 gigahertz.

12. Binary phase coding of a transmitted pulse. Pulse is marked

off into segments; phases of certain segments (here, No. 3)

are reversed.

PART III Radar Fundamentals

170

increased to the point where each segment contains only

one cycle.)

A common shorthand method of indicating the coding

on paper is to represent the segments with + and – signs.

An unshifted segment is represented by a +; a shifted seg-

ment, by a – sign. The signs making up the code are

referred to as digits.

The received echoes are passed through a delay line

(Fig. 13) which provides a time delay exactly equal to the

duration of the uncompressed pulses, τ. Thus, as the trail-

ing edge of an echo enters the line, the leading edge

emerges from the other end. The delay line may be imple-

mented either with an analog device or digitally.

Like the transmitted pulses, the delay line is divided into

segments. An output tap is provided for each segment. The

taps are all tied to a single output terminal. At any one

instant, the signal at this terminal corresponds to the sum

of whatever segments of a received pulse currently occupy

the individual segments of the line.

Now, in certain of the taps, 180˚ phase reversals are

inserted. Their positions correspond to the positions of the

phase-shifted segments in the transmitted pulse. Thus,

when a received echo has progressed to the point where it

completely fills the line, the outputs from all of the taps will

be in phase (Fig. 14).

13. Received pulses are passed through tapped delay line.

Separate tap is provided for each segment of pulse.

14. Phase reversal, R, is so placed that when a pulse completely fills

the delay line, outputs from all taps will be in phase.

Their sum will then equal the amplitude of the pulse

times the number of segments it contains.

To see step by step how the pulse is compressed, consid-

er a simple three-segment delay line and the three-digit

code, illustrated earlier.

Suppose an echo from a single point target is received.

Initially, the output from the delay line is zero. When

Segment No. 1 of the echo has entered the line, the signal at

the output terminal corresponds to the amplitude of this