Seybold J.S. Introduction to RF Propagation

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This is approximate because the actual resolution depends on the pulse shape

as well as the duration. Shorter pulses require larger receive bandwidths (more

noise) and provide less average power (less signal) but better range resolu-

tion. The matched ﬁlter has an impulse response that matches the transmitted

pulse. The range to the target is

(5.11)

where Dt is the elapsed time between transmission and reception of the pulse.

In a pulse or pulse-Doppler radar, the pulses are usually transmitted peri-

odically. This period is called the pulse-repetition interval (PRI) or the pulse-

repetition time (PRT). The term pulse repetition period has historically been

used as well, but it is not always appropriate since the pulses are not always

strictly periodic. The pulse repetition frequency is

The PRI deﬁnes the maximum unambiguous range of the system:

(5.12)

A large target beyond the unambiguous range may be interpreted as a

closer target. This occurs when the radar is listening for the return of the nth

pulse and actually receives a return from the (n - 1)th pulse. This is called a

multiple-time-around echo, and Figure 5.2 shows a diagram of how this can

occur.

For multiple-time-around returns to be an issue, the RCS of the distant

reﬂector must be sufﬁciently large so that the reﬂection can overcome the

additional path loss and still be detected. Ideally, R

unamb

should be well beyond

unamb

◊ PRI

PRF

PRI

∫

◊D

92 RADAR SYSTEMS

– R

unamb

Multiple time

around return

Nth pulse

Range

unam

Target return

(N – 1)th pulse

Figure 5.2 Depiction of radar range ambiguities for pulsed radar.

the maximum detection range of the radar so that even large targets will not

provide a large enough return to be detected (maximum detection range is

deﬁned for a given target RCS). In practice, this is not always practical, but

there are ways to mitigate the effect of range ambiguities. One technique is to

stagger the PRI’s. If the PRI is different from one pulse to the next, the true

target returns will remain stationary from one PRI to the next, while the

ambiguous returns will appear at a different range for each different PRI and

can thereby be eliminated from consideration.

5.3 RADAR MEASUREMENTS

Radar has progressed from a means of detection and ranging to a sensor

system that can provide complete position and velocity information on a target

as well as potentially imaging the target. The actual measurement can be

broken down into range measurement, angle measurement (azimuth and ele-

vation angle), and signature measurement (high-range and cross-range reso-

lution imaging of a target). The basic technology employed for each of these

types of measurements is discussed in the sections that follow.

5.3.1 Range Measurement

The most basic method of range measurement using a pulse radar is to simply

identify which range gate (receiver time sample) contains the majority of the

target energy. This provides a range measurement resolution on the order of

the pulse width:

To improve the range resolution without having to resort to extremely short

pulses (which increases the bandwidth required and raises the thermal noise

ﬂoor), pulse compression may be used. Pulse compression consists of further

modulating the radar signal within the transmit pulse. This can be done by

chirping the RF frequency or by applying a BPSK modulation with low auto-

correlation sidelobes. The result is a substantial increase of the range resolu-

tion of the radar without shortening the transmit pulse.

Another approach to enhanced range resolution is using a stepped fre-

quency sequence of pulses, which are then Fourier-transformed to provide a

high-range resolution proﬁle of the target [12]. This approach is often used in

millimeter-wave radar systems and is frequently used in conjunction with syn-

thetic aperture techniques to provide two-dimensional high-resolution target

images.

A less exotic means of improving range measurement resolution is to

simply interpolate between adjacent range gates that contain the target

energy. A similar approach for tracking radar is called the split gate tracker,

DRc=t2

RADAR MEASUREMENTS 93

where the radar positions a pair of range gates straddling the target [13]. Figure

5.3 shows a diagram of a split gate tracker that is straddling a target return

with some range error. By comparing the energy in each range gate and divid-

ing by the sum of the energy in each range gate, an error signal can be gen-

erated to determine how much to move the range gates to straddle the target.

The error signal is

(5.13)

where

is the received energy in the early gate

is the received energy in the late gate

t is the length of each range gate

Dt is the additional time shift required to center the range gates over the

target

As mentioned earlier, the pulse width is one factor in determining how much

energy actually reaches the target to be reﬂected back to the radar.The actual

transmit energy is the peak power of the transmitter multiplied by the width

of the transmitted pulse.The peak envelope power (PEP) is referred to as peak

power in radar. It is still an average power in the sense that the output signal

is squared and averaged over an integer number of periods of the carrier, and

it does not mean the maximum instantaneous power within a period of the

carrier frequency. The average power as used in radar actually refers to the

peak power multiplied by the transmit duty cycle. That is, the peak power is

averaged over a transmit pulse, and the average power is averaged over the

entire pulse repetition interval. The normalized (R = 1 W) peak power of a

pulse radar is given by

where t is the pulse width and v(t) is the voltage at the radar output.The radar

average power is given by

Pvtdt

peak

()

94 RADAR SYSTEMS

Range

Early Gate Late Gate

Target Return

Figure 5.3 Split-gate tracking in range.

where T is the PRI, v(t) is the voltage at the radar output, and t is the pulse

width. When the power of a radar is speciﬁed, it usually refers to the peak

power and not the average power. This is because radar systems often employ

many different PRIs and pulse widths.

5.3.2 Doppler Measurement

Target velocity can be measured by estimating the Doppler shift on the return

signal. This is accomplished by collecting a series of returns and then applying

a discrete Fourier transform to them. For ground-based (stationary) radars,

the zero Doppler line is often removed to mitigate the effect of ground clutter.

By looking at the Doppler cell where the target appears, the direction and

magnitude of the target’s radial velocity can be determined. The Doppler res-

olution is determined by the number of pulse returns used for the Fourier

transform. More precisely, it is determined by the total time duration covered

by the radar samples. The Doppler extent is limited by the PRF or spacing

between pulses. If the target velocity exceeds the maximum of the transform,

the Doppler is aliased. This is called velocity or Doppler ambiguity and is

similar to the concept of range ambiguity. Some radar systems use an estimate

of target velocity based on successive range measurements rather than using

Doppler processing. This can be useful if sufﬁcient information for Doppler

processing is not available.

5.3.3 Angle Measurement

For angle measurements with precision greater than the antenna beamwidth,

various beam-splitting techniques must be used. Sequential lobing consists of

squinting the beam slightly above and below and then to the left and right of

the tracking point. The return from each position is then used to update the

estimated target position in azimuth and elevation. Conical scan uses a con-

tinuous circular scan about the track point to develop a tracking error signal.

Both of these techniques are subject to tracking error due to noise, target ﬂuc-

tuation, and electronic countermeasures. As a remedy, monopulse was devel-

oped. Monopulse uses the result of a single pulse to estimate both the azimuth

and elevation error in the antenna position relative to the target.This is accom-

plished by using a split aperture antenna that actually receives four distinct

beams simultaneously. Thus any pulse-to-pulse amplitude variations are elim-

inated as a source of angle measurement error.

There are different types of monopulse [14, 15], including amplitude and

phase monopulse. Standard angle tracking is usually accomplished with ampli-

tude monopulse. For simplicity, consider the amplitude monopulse case in one

Pvtdt

ave

peak

()

RADAR MEASUREMENTS 95

dimension. Two identical beams, squinted in angle, are generated from the

same aperture simultaneously by using a specialized feed or phased array. The

angle between the two beams is only a fraction of a beamwidth. This is

shown pictorially in Figure 5.4, for a single dimension. The signals from the

two beams are added and subtracted to produce a sum and a difference

pattern. The addition and subtraction can be done in the signal processor, or

it may be performed at RF using a hybrid junction such as Magic-Tee [16] or

similar device.

When a return signal is received, the samples from the sum and difference

patterns are represented by S and D, respectively. For that reason, the patterns

themselves are sometimes referred to as sum and delta patterns. Figure 5.5

shows a representative pair of individual beams and the corresponding sum

and difference patterns.The same curves, expressed in dB, are shown in Figure

5.6.This is the conventional way of expressing the sum and difference patterns.

The angle of the target from bore-sight is given by the ratio of delta to sum.

Both values are complex, so the denominator is rationalized.

96 RADAR SYSTEMS

Figure 5.4 Squinted antenna beams for monopulse radar.

10 0 10

0.25

0.5

0.75

10 0

0.25

0.5

0.75

Figure 5.5 Overlapping beams and the corresponding sum and difference beams.

(5.14)

where k is a calibration constant that depends upon the actual beam shapes

and angular separation of the two beams. Of course the actual values must

be used in this expression, not the dB values. Figure 5.7 shows what the

monopulse ratio looks like for this theoretical antenna. For the plot, the value

e=k

RADAR MEASUREMENTS 97

–10 –5 0 5 10

–30

–15

Sum

Difference

Sum and Delta Patterns Superimposed

Angle

Amplitude in dB

Figure 5.6 Sum and difference patterns in dB.

6 5 4 3 210 1234 56

1.5

0.5

1.5

Monopulse Delta/Sum

Angle

Monopulse Ratio

Figure 5.7 Monopulse ratio for the theoretical antenna.

of k is unity. The actual value is chosen to make the slope of the linear part of

the curve unity so that angle error is read out directly. It is interesting to note

that if enough error is present, the monopulse ratio has other angles where

the error slope is positive. It is possible for a radar to see and actually track a

target in these regions if it is strong enough to be detected in the sidelobe. This

is called sidelobe lock or sidelobe tracking. Tactical systems use various tech-

niques such as a wide-angle spotting antenna to preclude sidelobe lock.

As stated earlier, monopulse angle measurements are very robust to signal

amplitude ﬂuctuations because all of the data comes from the same pulse. The

effect of noise on the monopulse ratio is not as well behaved, however. A the-

oretical analysis shows that the variance of the monopulse ratio is inﬁnite in

the presence of Gaussian noise [17–19]. This is due to the fact that there

is a ﬁnite probability of S being arbitrarily close to zero. This fact is not of

great practical concern because measurements that are that weak will be dis-

carded. It does, however, accurately suggest that monopulse is susceptible to

jamming by white noise. For that reason, regular monopulse cannot be used

to track a noise source. Instead, the two beams must be processed separately,

and the detected power in each must be used to determine the angle tracking

error.

5.3.4 Signature Measurement

Many modern radar systems employ radar signature measurement techniques

to permit the radar to identify targets. The most basic type of signature meas-

urement is the high-range resolution proﬁle. If multiple proﬁles are coherently

collected and stored with regular azimuthal spacing, it is possible to generate

a cross-range proﬁle for each cell and the range proﬁle [20]. This produces a

two-dimensional map of the target. The results can be used for target identi-

ﬁcation, system diagnostics, terrain mapping, and other remote sensing appli-

cations. The azimuthal spacing is ideally in angle, with the radar moving in an

arc whose focus is at the target, or a stationary radar viewing a target rotat-

ing at a constant angular velocity. In many applications, the motion is lateral

instead of angular, but it is possible to correct for the difference and still gen-

erate very high quality images.

The preceding technique is called synthetic aperture radar (SAR) if the

target is stationary or inverse synthetic aperture radar (ISAR) if the radar is

static and target rotation is used to produce the required changes in perspec-

tive. The images from SAR or ISAR processing are range/azimuth images. The

dimension of height can also be added by processing a set of coherent range-

azimuth maps taken at different elevation perspectives [21]. This method is

principally used for instrumentation purposes because the required setup, cal-

ibration, and data processing preclude most other applications. This is called

three-dimensional ISAR. Some radar systems also perform a monopulse

measurement on the contents of each resolution cell in a range-azimuth map

to provide limited information on the height of the scatter(s) in each cell. This

98 RADAR SYSTEMS

is also sometimes called three-dimensional ISAR, but that is a misnomer since

there is not actually any resolution in elevation, but rather a single composite

value.

5.4 CLUTTER

Clutter is deﬁned as any unwanted radar echo. For a weather radar system, an

aircraft might be considered clutter; similarly, for a terrain mapping radar, a

vehicle in the ﬁeld of view would be considered clutter. For the purposes of

this chapter, it is assumed that a vehicle or aircraft is the desired target and

that the natural reﬂectors in the scene represent clutter. Radar returns from

ground targets will include reﬂected energy from ground clutter—that is, the

surrounding terrain and vegetation. This type of clutter is called area clutter

since it is predominantly two-dimensional in nature. The amount of clutter

depends on the resolution of the radar in range and angle and the terrain char-

acteristics, as will be shown.

Airborne target returns seen by upward-looking radar may include volume

clutter from moisture or hydrometeors in the propagation path. Another

source of volume clutter is intentional clutter such as chaff (small metallic

strips) dispersed by an aircraft to overwhelm the radar receiver and conceal

the presence of aircraft. Chaff is an example of a radar countermeasure, but

it is treated as clutter since the effect is the same. Volume clutter as its name

implies is three-dimensional in nature. An upward looking radar may also

experience ground (area) clutter returns entering through the antenna side-

lobes. For moderately powered, ground-based radar, this can be a signiﬁcant

source of (stationary) clutter.

In addition to estimating the mean clutter return signal, the radar designer

must take into account the statistics of the clutter. Some clutter such as

uniform terrain or calm water may have very little variation, whereas rough

terrain may have considerable spatial variation and tall vegetation or bodies

of water in heavy wind will also show signiﬁcant temporal variation.

When designing a radar system for operation in a clutter environment, the

signal-to-clutter ratio (SCR) and the clutter-to-noise ratio (CNR) are of inter-

est. The SCR provides a measure of the expected target signal strength versus

the expected clutter return strength, which is used for detection analysis and

prediction. The CNR provides an indication of whether target detection is

limited by noise or limited by the external clutter.

5.4.1 Area Clutter

Area clutter, which is synonymous with ground clutter, is characterized by the

average clutter cross section per unit area, s

(sigma-zero). This parameter is

called the backscatter coefﬁcient, and the units are m

.The amount of clutter

received depends upon the backscatter coefﬁcient and how much of the

CLUTTER 99

ground area is illuminated. The backscatter coefﬁcient of clutter depends on

the grazing angle.

If the extent of the ground clutter is larger than the radar footprint, then

the width of the clutter patch is deﬁned by the antenna azimuth beamwidth

and the range or distance to the clutter patch. The (down-range) length of the

clutter patch is determined by either the range gate size for shallow grazing

angles, or by the elevation beamwidth for steeper grazing angles [22].

The width of the clutter cell is

(5.15)

where R is the range to the center of the clutter cell and q

is the two-way

antenna azimuth beamwidth in radians. The two-way beamwidth is used

because the same beam is illuminating and then receiving the reﬂection from

the clutter. Another deﬁnition of the two-way beamwidth is the -1.5-dB

beamwidth of the antenna pattern. The concept of the width of the ground

clutter cell is illustrated in Figure 5.8. The depth or length of the clutter cell is

determined by the smaller of the range gate projected onto the ground, or the

elevation beamwidth times the total range projected onto the ground.

Thus the length of the clutter cell can be expressed as

(5.16)

Figure 5.9 shows the geometry for the low grazing angle case where the range

gate size determines the down-range dimension of the clutter area. At higher

grazing angles, the antenna elevation pattern becomes the limiting factor as

illustrated in Figure 5.10. For the high grazing angle case, the two-way eleva-

tion beamwidth must be used rather than the one-way beamwidth, just as was

done in the range-gate-limited case with the azimuth beamwidth.

So at shallow grazing angles, where the clutter cell size is pulse-limited,

Figure 5.11 applies and

(5.17)

cAZ

()

sec

() ()

min sec csc

yq y

100 RADAR SYSTEMS

W ªR

Top Down View

Radar

Figure 5.8 Determination of total illuminated clutter area.

CLUTTER 101

y = grazing angle

2cos(

ct/2

sin(

◊

Radar

Figure 5.9 Range-gate-limited clutter area.

ct/2

)cos(2

y = grazing angle

)sin(

◊

Radar

Figure 5.10 Beam-limited clutter area.

Actual Clutter Area

Estimated Clutter Area

W = Rq

l =

sec(y )

Figure 5.11 Shape of range-gate-limited clutter cell.